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The Principles Underlying 
Radio Communication 


Radio Communication Pamphlet No. 40 
Prepared by the Bureau of Standards 

Revised to May 24, 1921 

Signal Corps, U. S. Army 

Washington : Government Printing Office : 1922 

AVar Department. 

Document Xo. 1069. 

Office of The Adjutant General, 

War Department, 

Washington.^ June 10^ 1921. 
The followinof publication entitled " The Principles 
Underlyinof Eadio Communication," is published for 
the information and guidance of all concerned. 

[062.11, A. G. O.] 

By order of the Secretary of War : 

Peyton C. March, 
Major General^ Chief of Staff. 

P. C. Harris, 

The Adjutant General. 








$1.00 PER COPY (Buckram) 

The Principles Underlying Radio Communication. 

Prepared by the Bureau of Standards under the direction of 
the Training Section of the Office of the Chief Signal Officer of 
tlie Army. 

Acknowledgment is made of the valuable service rendered 
the Signal Corps by the Bureau of Standards through the work 
of Dr. J. H. Bellinger, physicist, Bureau of Standards, and the 
following men engaged with him in the w'riting of this book : 

F. W. Grover, 

ConsuUing Physicist, Bureau of Standards ; Assistant Pro- 
fessor of Electrical Engineering, Union University. 
C. M. Smith. 

Associate Professor of Physics, Purdue University. 

G. F. Wittig. 

Assistant Professor of Electrical Engineering, Yale Uni- 
A. D. Cole, 

Professor of Physics, Ohio State University. 
L. P. Wheeler, 

AssistaJit Professor of Physics, Yale University. 
H. M. Royal, 

Professor of Mathematics, Clarkson College of Technology. 
In this book are presented briefly the basic. facts and princi- 
ples of electromagnetism and their application to radio com- 
munication. In the effort to present these topics in a simple 
manner for students with very little mathematical preparation, 
it has been necessary at times to use definitions, illustrations, 
and analogies which would not be used in a work prepared for 
more advanced students. Frequent references to standard books 
are given for further study, and students should be encouraged, 
as far as possible, to consult them. 

December 10, 1918. 


Digitized by tine Internet Arciiive 
in 2009 



The first edition of this book was prepared in the summer of 
1918 by the Bureau of Standards at the request and under the 
direction of tlie Training Section of tlie Office of the Chief Signal 
Officer of the Army for use as a textbook for the training of 
enlisted personnel of the Signal Corps for radio work. The book 
was prepared by the members of the staff of the Bureau of 
Standards mentioned in the preface to the first edition, some of 
wliom were members of the faculties of certain universities, 
and were temporarily added to the staff of the Bureau for this 

The book has been found useful not only for the purpose for 
which it was originally prepared — the training of Signal Corps 
personnel — but also as an elementary textbook of radio and gen- 
eral electricity for use in schools and colleges and elsewhere. 

A number of errors appearing in the first edition have been 
corrected, and some parts have been revised. The section on bat- 
teries has been rewritten. The material on apparatus for un- 
damped wave transmission and electron tubes has been replaced 
by new material. A brief discussion of ordinary wire telephony 
has been added. The section on transformers has been con- 
siderably amplified. Some new illustrations have been added, re- 
placing illustrations of apparatus now obsolete. New numbers 
have been assigned to all sections beyond Section 172, and new 
numbers have been assigned to all figures beyond Fig. 214. 
The first edition contained 355 pages, while the present edition 
contains 619 pages. 

Acknowledgment should be made of the assistance rendered 
by the many interested persons who have called attention to 
err(»rs appearing in the first edition. It is not possible to men- 
tion the names of all who have offered suggestions. Particular 
mention should be made of a very careful examination of the 
whole book made by Dr. H. S. Uhler, of Yale University. 

The work of revision and the preparation of a considerable 
part of the new material has been done by Mr, R. S. Ould. The 
revision has been under the general supervision of Dr. J. H. Del- 
linger. A number of other members of the staff of the Bureau 


of Standards have assisted in the work of revision by sugges- 
tions, and by preparing new material. The section on batteries 
has been rewritten by INIr. G. W. Vinal. Much of the revision 
of the chapter on electron tubes has been done by Mr. E. S. 
Purington and Mr. L, M. Hull. The authors who prepared the 
first edition have offered valuable suggestions for desirable 
changes. Mention is made of the work of Professor C. M. Smith 
on the index. 

Acknowledgment is made to the General Electric Co. for 
photographs of the Alexanderson alternator, to the Federal 
Telegraph Co. for photographs of the arc converter, to the 
Western Electric Co. for detailed drawings of a telephone trans- 
mitter and receiver, and to the Electric Storage Battery Co. 
for a photograph of a lead storage cell. 




1. What radio communication means 19 

2. Fundamental ideas of the electric circuit 21 

Chapter 1. Elementary Electricity. 

A. Electric Current. 

3. Effects of electric current 29 

4. Direction of current 30 

5. Measurement of electric current and quantity of elec- 

tricity 32 

6. Electrons 33 

B. Resistance and Resistivity. 

7. Resistance and conductance 34 

8. Resistivity and conductivity 35 

9. Temperature coefficient 37 

10. Current control 38 

11. Conducting materials 40 

12. Non-conducting or insulating materials 42 

C. Potential Difference, Emf., and Ohm's Law. 

13. The meaning of emf 44 

14. Ohm's law 48 

15. Sources of emf 51 

16. Internal voltage drop and line drop 56 

D. Electric Batteries. 

17. General description 59 

18. Simple primary cell 61 

19. Types of primary cells 63 

20. Storage cells 67 

21. Electrical characteristics of storage cells 70 

22. Charging and maintenance of storage cells 72 



E. Electric Circuits. 


23. Current flow requires a complete circuit 76 

24. Series and parallel connections — 77 

25. Divided circuits. The shunt law 82 

26. The potentiometer 84 

27. The Wheatstone bridge 86 

28. Heat and power losses 87 

F. Capacity. 

29. Dielectric current 89 

30. Condensers 90 

31. Dielectric properties 91 

32. Types of condensers 94 

33. Electric field intensity 97 

34. Energy storeil in a condenser 98 

35. Condensers in series and in parallel 99 

G. Magnetism. 

36. Natural magnets 100 

37. Bar magnets 100 

38. The magnetic field 101 

39. Magnetic flux and flux density 103 

40. The magnetic field about a current 103 

41. The solenoid and the electromagnet 104 

42. Magnetic induction and permeability 105 

43. The force on a conductor carrying current in a 

magnetic field 107 

H. Inductance. 

44. The linking of circuits with lines of magnetic flux 107 

45. Induced electromotive force 108 

46. Self-inductance 111 

47. Mutual inductance 112 

48. Energj' relations in inductive circuits 114 

I. Alternating Current. 

49. Reactance 115 

50. Nature of an alternating current 116 

51. Average and effective values of alternating cuirent — 118 



52. Circuit with resistance only 119 

53. Pliase and phase angle 120 

54. Alternating current in a circuit containing inductance 

only 121 

55. Circuit containing inductance and resistance in series- 123 

56. Charging of a condenser in an alternating current 

circuit 125 

57. Circuit containing capacity, inductance, and resist- 

ance in series 127 

58. The alternating-current transformer 128 

J. Measuring Instruments. 

59. Hot-wire instruments 136 

60. Magnetic instruments 138 

K. Wire Telegraphy and Telephony. 

60a. Wire telegraphy 144 

60b. Wire telephony 145 

Chapter 2. Dynamo-Electric Machinery. 

61. Generators and motors 152 

A. The Alternator. 

62. Production of enif. by revolving field 153 

63. Direction of emf 153 

64. Emf. curve 155 

65. Cycle, period, frequency 155 

66. Multipolar magnets 156 

67. Field and armature 156 

68. Coil- wound armature 157 

69. Concentrated and distributed windings 159 

70. Magnetic circuit 161 

71. Field excitation 162 

72. Stator and rotor 162 

73. Arrangement of parts 162 

74. Other forms of alternator 163 

75. Polyphase alternators 166 


B. Alternator Theory. Losses and Efficiency. 


76. Equations for frequency and emf 170 

77. Dependence of driving power on current 171 

78. Losses 172 

79. Rating; Name-plate data 174 

80. Efficiency 175 

81. Regulation 176 

82. Armature impedance and armature reaction 177 

83. Effect of power factor on regulation 177 

84. Effect of speed on regulation 178 

85. Voltage control 179 

C. Direct-Current Generators. 

86. Commutation 170 

87. Ring and drum winding 181 

88. Excitation : Separate, serie^^. shunt, compound 184 

89. Characteristics of terminal voltage 186 

90. Emf. equation 188 

9^1. Voltage control,, 189 

92. Effect of varying speed 189 

D. Special Alternators for Radio Uses. 

93. Audio frequency and radio frequency 191 

94. Audio-frequency generators 192 

95. Radio-frequency generators. Alexanderson High- 

Frequency Alternator 204 

E. Motors. 

96. Uses of d. c. and a. c. motors 210 

97. D. c. shunt motor 210 

98. D. c. series motor 218 

99. Other d. c. motors 219 

100. Combination a. c. and d. c. motors 219 

101. Alternating current motors. Induction motors 219 

F. Motor-Generators and Dynamotors. 

102. Motor-generators 223 

103. Rotary converters 224 



104. Dynamotors 226 

105. Double-current generators 227 

106. Common troubles 227 

Chapter 3. Radio Circuits 

A. Simple Radio Circuits. 

107. The simplicity of radio theory 231 

108. Tlie simple series circuit 232 

109. Series resonance 234 

110. Tuning the circuit to resonance 240 

111. Resonance curves 241 

112. The wavemeter 244 

113. Parallel resonance 246 

114. Capacity of inductance coils 250 

B. Damping. 

115. Free oscillations 251 

116. Frequency, damping, and decrement of free oscilla- 

tions 257 

C. Resistance. 

117. Resistance ratio of conductors 263 

118. Brush, spark, dielectric, and radiation resistance 266 

D. Coupled Circuits. 

119. Kinds of couplmg 267 

120. Double hump resonance curve 270 

121. Forced oscillations 272 

122. Free oscillations of coupled circuits with small 

damping 274 

123. Impulse excitation. Quenched gap 278 

Chapter 4. Electromagnetic Waves. 
A. Wave Motion. 

124. Three ways of transmitting energy 281 

125. Properties of wave motion 281 

126. Wave trains, continuous and discontinuous 285 


B. Propagation of Waves. 


127. Waves propagated by elastic properties of medium__ 286 

128. Properties of electromagnetic waves 287 

129. Modification of waves in free space near the earth- _ 288 

130. Difficulties in transmission 289 

C. Theory of Production and Reception of Electromag- 
netic Waves. 

131. Magnetic field produced by moving lines of electric 

displacement 294 

132. Mechanism of radiation from a simple oscillator 295 

133. Action in receiving 298 

D. Transmission Formulas. 

134. Statement of formulas 299 

135. Examples of use 301 

136. General deductions 302 

E. Device for Radiating and Receiving Waves, 

137. Description of the antenna 304 

138. Different types 306 

139. Current and voltage distribution in an antenna 308 

140. Action of the ground. Counterpoises 309 

F. Antenna Characteristics. 

141. Capacity 311 

142. Inductance 313 

143. Resistance 313 

144. Wave length and its measurement 316 

145. Harmonics of wave length 319 

146. Directional effect 319 

G. Antenna Construction. 

147. Towers and supports 322 

148. Insulators 322 

149. Antenna switch. Conductors ' 324 

150. Grounds and counterpoises 326 

150a. Ground antennas 327 


H. Coil Antennas. 


151. Coil antennas. Directional characteristics 330 

152. Direction finders 339 

Chapter 5. Apparatus for Transmission and Reception 
(Exclusive of Electron Tubes.) 

A. Apparatus for Damped Wave Transmission. 

153. Function of transmitting apparatus 353^ 

1.54. Simple spark discharge apparatus 354 

155. Transmitting condensers 356 

156. Spark gaps 356 

157. Simple induction coil set 365 

158. Operation of induction coils from power lines 366 

159. Portable transmitting sets 367 

160. Simple connections for the production of electric 

waves 367 

161. Inductively coupled transmitting set 370 

162. Direct coupled transmitting set 373 

163. Comparison of coupled and plain antenna sets 373 

164. Tuning and resonance 375 

165. Coupling 376 

166. Damping and decrement 378 

167. Additional appliances 379 

168. Adjustment of a typical set for sharp wave and 

radiation 381 

169. Efficiency of the set - .383 

170. Calculations required in design 384 

171. Simple field measurements 389 

B. Apparatus for Undamped Wave Transmission. 

172. Advantages of undamped oscillations 396 

173. High-frequency alternators 397 

174. Arc converters 400 

175. The characteristics of the direct-current electric arc_ 402 

176. Production of continuous oscillations by the arc 404 

177. Construction of arc converters 408 

178. Signaling methods 415 

53904° — 22 2 


C. Apparatus for Reception of Waves. 


179. General principles 419 

ISO. Typical circuits for reception of damped waves 422 

181. Typical circuits for reception of undamped waves 430 

182. Contact detectors 433 

183. Telephone receivers 440 

184. Receiving coils and condensers 443 

185. ^Measurement of received current 448 

Chapter 6. Electron Tubes in Radio Communication. 

186. The development of the electron tube 450 

A. The Electron Flow in Electron Tubes. 

187. The electron and the two-electrode tube 450 

188. Ionization in electron tubes 452 

189. Characteristics of two-electrode tubes 454 

190. The three-electrode electron tube 456 

J91, Characteristic curves 4.59 

192. Operating characteristics 464 

193. Practical forms of three-electrode tubes 469 

B. The Electron Tube as a Detector. 

194. Detector action 472 

195. Experimental data on detectors 477 

C. The Electron Tube as an Amplifier. 

196. General principle of amplification 479 

197. Elementary theory of amplification 482 

198. Audio-frequency amplification 484 

199. Regenerative amplification 487 

200. Electron tube amplifier with crystal detector 488 

D. The Electron Tube as a Generator. 

201. Conditions for oscillation 489 

202. Circuits used for generating oscillations 491 

203. Practical considerations in using electron tubes as 

generators 402 

204. Alternating-current plate supply 498 

205. Beat reception 501 


E. Radio Telephony. 


206. The wave forms used in radio telephony 507 

207. Methods of modulation 516 

208. IVIodulation of electron tube generators 519 

209. Operation of tube radio telephone transmitting sets 525 

210. Practical forms of apparatus 527 

211. Chopper modulation of tube transmitting sets for 

radio telegraphy 529 

212. Line radio communication 530 


Appendix 1. Suggested List of Laboratory Experiments- 537 

Appendix 2. Units 547 

Appendix 3. Symbols Used for Physical Quantities 552 

Appendix 4. Copper Wire Tables 554 

Appendix 5. Wave-length Table 557 

Appendix 6. Radio Laws and Regulations 561 

Appendix 7. International Code, Conventional Signals, 

and Abbreviations 565 

Appendix 8. Radio Publications 568 

Appendix 9. Safety Precautions 578 

Index 581 


1. What Radio Communication Means. — In military service all 
possible means of communication are used, including the most 
primitive. Some of the earliest methods were by means of 
beacon fires, and, much later, flags. However, the best and most 
rapid are the electrical methods. These include the ordinary 
wire telegraph and telephone and the wireless or radio ap- 
paratus. Without wire connecting lines, radio messages are 
sent from one point to another on the battle front, from ship to 
shore, across the oceans, to airplanes, and even to submerged 
submarines. Business and social life have been profoundly 
modified by the advent of electric communication, and recent 
developments in radio have done much to make communication 
easy between distant points. 

When a pebble is thrown into the smooth water of a pond it 
starts a series of circular ripples or waves, which spread out 
indefinitely with a speed of a few hundredths of a meter ^ per 
second (see the frontispiece). Similarly, an electric disturb- 
ance starts electric waves, which spread out in all directions, 
and travel with the velocity of light, which is 300,000.000 meters 
per second, or about 186,300 miles per second. It is by means of 
these electric waves that radio messages are sent. 

In order to make use of electric waves for the practical pur- 
pose of sending messages, it is necessary — 

(a) To produce regular electric disturbances in a circuit 
which start the waves. (These disturbances are electric cur- 
rents which reverse rapidly in direction.) 

(&) To get the waves out into surrounding space, through 
which they travel with great speed. (This is done by means of 
the transmitting antenna.) 

(c) By means of these waves, to set up electric currents in a 
receiving circuit at the distant station. (The device which 
these waves strike as they come in, and which turns them over 
to the receiving circuit, is called the receiving antenna.) 

1 The meter and other units are explained in Appendix 2, p. 547. 



(d) To change these currents so that they may be detected 
by electric instruments. (The operator usually receives the 
message through signals in a telephone receiver.) 

In communication by flags, messages are transmitted by a 
" code " in which each letter of the alphabet is represented by 
a position or combination of positions of flags. " In communi- 
cation by radio telegraphy, a code is used consisting of com- 
binations of very short signals, or " dots," and longer signals, or 
" dashes." In communication by radio telephony, the voice 
itself is transmitted, and no code is necessary. 

The student of radio communication needs a more thorough 
knowledge of electrical theory than that needed for some 
branches of electrical work. This fact needs emphasis for 
the beginner. Of course a man can learn to operate and care 
for apparatus without having a real imderstanding of its 
underlying principles. It only requires that he have a cer- 
tain type of memory, industry, and a little common sense. 
But a man with only this kind of knowledge of his subject 
is of limited usefulness and resourcefulness, and can not 
advance very far. The real radio man must have some train- 
ing in the whole subject of electricity and magnetism, as . 
well as a rather intimate familiarity with some restricted 
parts of it. An understanding of radio communication re- 
quires some knowledge of the following subjects : 

(a) Direct and alternating currents and dynamo ma- 

(&) High-frequency alternating currents, including the 
subject of condenser discharge. 

(c) Conduction of electric current in a vacuum as well as 
in wires. 

(d) Electric waves, which involve some acquaintance with 
modern ideas of electricity and the ether. 

(e) The apparatus used for the production and reception 
of electric waves.' 

" See " Visual Sig:naling," Signal Corps Training Pamphlet No. 4. 
Information regarding visual signaling is also contained in a book by 
J. A. White, " Military Signal Corps Manual." 

^ The roader who desires an introductory discussion of the funda- 
mentals of electrical phenomoua may consult Signal Corps Training 
Pamphlet No. 1, " Elementary Electricity." The reader who desires 
a briefer and more elementary discussion of the principles of radio 


2, Fundamental Ideas of the Electric Circuit. — It is common 
knowledge that a battery supplies what is known as a cur- 
rent of electricity. To obtain the current there must be a 
complete, closed, conducting path from the battery through 
the apparatus which is to be acted on by the current, and 
back again to the battery. 

For example, when connecting up an electric bell, a wire 
is carried from one binding post of the battery (Fig. 1) to 
one of the binding posts of the bell, and a second wire is 
brought from the other binding post of the bell back to the 
remaining binding post of the battery. Any break in the 
wire immediately causes the current to stop and the bell to 
be silent. This furnishes an easy method of controlling the 
ringing of the bell, since it is only necessary to break the 
circuit at one point to stop the current, or to connect across 
the gap \vith a piece of metal to start the current going 
again. Thus the battery supplies the power to operate the 
bell, and the button opens and closes the circuit and thus 
controls the delivery of that powder to the bell. Similar con- 
siderations apply when using the city lighting circuit. Wires 
from the generator at the central station are brought to 
the lamp, motor, or heating device to be supplied, and the 
flow of current to this device controlled by means of a switch. 
The switch consists of pieces of metal which may be brought 
into contact when desired. The operation of the switch 
makes or breaks the contact. One handle may control two 
switches, so that with one motion the circuit can be broken 
at two places. The switch may be located on the wall and be 
of any one of a number of different forms, such as the " snap 
switch," the " push-button switch," and the " knife switch." 
The switch may be located in the socket which holds the 
lamp ; such a socket is called a " key socket." It makes no 
difference at which part of the circuit the current is inter- 
rupted. The flow of current will stop whether the break is 
made at the lamp, or in one wire at some distance from the 
lamp, or by opening a switch at the switchboard at the central 

communication may consult Signal Corps Radio Communication Pam- 
phlet No. 1. Copies of either of these pamphlets may be procured from 
the Superintendent of Documents, Government Printing- Office, Wash- 
ington, D. C, for 15 cents for the former and 10 cents for the latter. 
See also pp. 569, 575. 



Station. Electricity must then be regarded as flowing in every 
part of the circuit, so that electricity is leaving the battery 
or dynamo at one side and going back to it at the other side. 

Current. — The current flowing in a circuit is "no stronger at 
one point of the circuit than at another. This can be proved 
by connecting a measuring instrument called an ammeter into 
the circuit at different points, a, b, or c, Fig. 2. It is found to 
register the same at whatever point this test is made. A useful 
illustration of the electric circuit is a closed circuit of pipe 
(Fig. 3) completely filled with water and provided with a pump, 
P, or some other device for causing the water to circulate. The 

riQ. 1 



Fig. 2 

I Dyn&r 


Switch Circuit 




■f^ Battery Circuit is \iKe a pipe 
circuit full of wa.ter 

amount of water which leaves a given point in each second is 
just the same as the amount which arrives in the same length of 
time. Now in the electric circuit we have no material fluid, but 
we suppose that there exists a substance, which we call elec- 
tricity. Electricity behaves in the electric circuit much like 
an incompressible fluid in a pipe line. We are very sure that 
electricity is not like any material substance which we know, 
but the conmion practice among students and shopmen of 
calling it " juice " shows that they think of it as like a fluid. 
We will, then, imagine the electric current to be a stream of 
electricity flowing anmnd the circuit. 

One way of measuring the rapidity with which water is flow- 
ing is to let it pass through a meter which registers the total 


number of quarts or gallons whicli pass through. By dividing 
the quantity by the time it has taken to pass we obtain the 
rapidity of flow. There are instruments by means of which it 
is possible to measure the total quantity of electricity which 
passes any point in the circuit during a certain time. If we 
divide this quantity by the time, we obtain the amount of elec- 
tricity which has passed in one second. This is a measure of 
the current strength. 

In practical work, however, the strength of the current is 
measured by instruments (ammeters) which show at each 
moment just how strong the current is, in somewhat the same 
manner as we may estimate the swiftness of a stream by watch- 
ing a chip on the surface. This kind of an instrument enables 
us to tell at a glance w^hat the current is without the necessity 
for a long experiment, and further we may detect changes in the 
strength of the current from moment to moment. In this con- 
nection it will be remembered that two measuring instruments 
are to be found on an automobile. The speedometer shows what 
the speed of the car is at each moment, so that the driver may 
know instantly whether he is exceeding the speed limit, and 
govern himself as he sees fit. The other instrument shows 
how many miles have been covered on the trip, and of course 
the average speed may be calculated from its indications, if the 
length of the trip has been timed. The instrument for measur- 
ing total quantity of electricity corresponds to the recorder of 
the total miles traversed; the ammeter corresponds to the 

Electromotive Force. — The water will not flow in the pipe line. 
Fig. 3, unless there is some force pushing it along — as, for ex- 
am.ple, a pump — and it can not be kept flowing without continu- 
ing the pressure. Electricity will not flow in a circuit unless 
there is a battery or other source of electricity in the circuit. 
The battery is for the purpose of providing an electric pressure. 
To this is given the name " electromotive force " — that is, a 
force which moves the electricity. This is usually abbreviated 
to " emf." The larger the number of cells which are joined in 
the circuit in such a way that their pressures will add, the 
greater the electric pressure in the circuit and the larger the 
current produced, just as the rapidity of flow of the water in 
the pipe line may be increased by increasing the pump pressure. 



Resistance. — There is always some friction in pipe, whatever 
its size or material, and this hinders the flow of the water to 
some extent. If it were not for the friction, the water would 
increase indefinitely in speed. Similarly, there is friction in the 
electric circuit. This is called the " resistance " of the circuit. 
The greater the resistance the smaller the current which can be 
produced in the circuit by a given battery, just as the greater 
the friction the less rapid the flow of water with a given pump 
acting. A resi.stance coil at any point in the circuit corre- 
sponds to a partially closed valve in the pipe at any point 
(Fig. 4.). 

FlQ A 

Fia 5 

FIG a. 

IIJL»Jtr<i"tion of resiitAnce by 
tJ&rtiAlly closed vaIvc 

Water Circuit 

Alternatinq Water Plow 
rifustrating Electric 
Displacement Current. 

rifastrating Action 
of Electric Condenser 

Steady and Variable Currents. — If a pipe is connected to a 
large reservoir of water maintained at the same level, the steady 
pressure of the constant head of water will cause a steady flow 
of water in the pipe. The quantity of water which will pass a 
given point in one second will be the same at all times. Certain 
sources of electricity, such as batteries and some kinds of dyna- 
mos, produce an electromotive force which is practically con- 
stant, and will cause a practically constant current to flow in 
circuits to which they are ccmnected. A steady electric current 
in one direction is called a " direct current." 

In the case of the ordinary force pump, the water is given a 
succession of pushes all in the same direction but separated 
by intervals when the water is not being pushed. The heart is 



such a pump which applies successive impulses to the blood 
and causes it to circulate. A pipe supplied by a force pump is 
usually discharging some water all the time, but successive 
spurts occur when an unusually large stream of water is dis- 
charged for a moment, the frequency of these spurts correspond- 
ing to the rate at which the pump is being run. Similarly, 
there are sources of electromotive force which act intermit- 
tently. When such an electromotive force is connected to a 
circuit, the current flows always in the same direction but 
varies in magnitude from instant to instant. A current of this 
kind, which pulsates regularly in magnitude, is called a " pul- 
sating current." 

A very important kind of current for radio work is that 
known as " alternating current." This is analogous to the 
kind of flow which would be produced if, instead of being acted 
on by a pump, the water were agitated by a paddle which 
moved back and forth rapidly over a short distance, without 
traveling beyond certain limits. Under this impetus the water 
no sooner gets up speed in one direction than it is compelled 
to slow up and then gather speed in the opposite direction, 
and so on over and over again. The water simply surges, first 
in one direction, and then in the other, so that a small object 
suspended in the water would not travel continuously around 
the pipe line, but would simply oscillate back and forth over 
a short distance. 

Effect of Condenser. — As a further case, let us suppose that 
an elastic partition E is arranged in the pipe (Fig. 5), so that 
no water can flow through or around it. If a pump P, or a 
piston, acts steadily, the water moves a short distance until 
the partition is stretched enough to exert a back pressure on 
the water equal to the pressure of the pump, and then the 
movement of the water as a whole ceases. If, on the contrary, 
a reciprocating motion is given to the water by P, the water 
moves back and forth, stretching the partition first in one 
direction and then in the other, and the water surges back and 
forth between short limits which are determined by the elas- 
ticity of the partition. We have in this case an alternating 
current of water in spite of the presence of the partition. 

An electric condenser acts just like an elastic partition in a 
circuit. No direct current can flow through it. but an alter- 


nating current, of an amount depending on the nature of the 
condenser, can flow when an alternating enif. acts on the circuit. 

As an extreme case, we may imagine the pipe line replaced by 
a long tube filled with water and the ends closed by elastic walls 
(Fig. 6). Suppose an alternating pressure to be given to the 
water in the tube, or even let the tube be tipped, first in one 
direction and then in the other. The water will oscillate back 
and forth a short distance in the tube, first stretching the wall 
at one end and then the wall at the other. A small alternating 
flow is thus set up, although there is not a complete circuit for 
the water to flow through. Analogous to this case is that of the 
electrical oscillation in an antenna. Such a flow of electricity 
without a complete conducting circuit is called a " displacement 
current." It is always necessary, in order to produce a dis- 
placement current, that the circuit shall have electrical elas- 
ticity somewhere ; that is, that an electric condenser shall be 

The importance of the electric current lies in the fact that it 
is an energ:^' current. A current of water transports energy ; so 
does a current of air. It is the motion that counts, and to 
utilize the energy of motion we must do something tending to 
stop the motion. In the case of water flowing in a channel we 
may do this by causing the water to flow under a water wheel 
whose resistance to turning causes it to absorb energy from the 
current of water. 

Any material substance, by virtue of its mass, can be made to 
act as a vehicle for transporting energy from one place to an- 
other provided only it is set into motion. In the case of the 
electric current, we do not need to inquire whether electricity 
has mass. We are concerned, in the use of electrical apparatus, 
with the transformation of the energy of the current into other 
familiar forms of energy — heat, light, and motion. The electric 
current is the vehicle by which we transmit energy from the 
central station to the consumer, and we are not, for practical 
purposes, concerned with the method of carrying the energy, 
any more than we need to inquire into the nature of the belt 
by which mechanical energy is carried from one wheel to an- 
other, or into the chemical nature of the water which is furnish- 
ing the power in a hydraulic plant. 


The electric current itself can not be seen, felt, smelt, heard, 
or tasted. Its presence can be detected only by its effects— 
that is, by what happens when it gives up some of its energy. 
Thus, an electric current may give up some of its energy, and 
cause a motor to turn. Electrical energj'^ has been given up, 
and mechanical energy takes its place. Similarly, electric 
energy may disappear and heat or light may appear in its place, 
or a chemical effect may arise. When a person feels an elec- 
tric shock, it is not the current itself he feels, but the muscular 
contractions and other physiological effects caused by the 
passage of the current. The electric lamp has an effect on the 
eye. We do not, however, see the electric current in the lamp, 
but the effect on the eye is due to the light waves sent off by 
the hot filament. The energj'^ of the current has been changed 
over into heat in the lamp. When we hear a sound in the tele- 
phone receiver it is not the electric current we hear, but merely 
the vibration of the thin diaphragm. The electric current has 
used some of its energy in causing the diaphragm to vibrate. 
The acid taste noticed when the tongue is placed across the 
poles of a dry battery is due to the chemical decomposition of 
the saliva into other compounds as a result of the passage of 
the current through it. 

In the next section, the electric current is studied through 
the effects it produces, and in later sections it is given a more 
exact and detailed treatment. 



A. Electric Current. 

3. Effects of Electric Current. — Most of the applications of 
electricity depend upon the movement of electricity ; that is, the 
electric current. The effects of stationary electricity (electric 
charge or quantity of electricity) are of importance in connec- 
tion with such subjects as electric condensers (see Sec. 30), and 
in the study of electrons, but it is moving electricity, or current 
flow, that is of greatest practical importance. 

A wire in which an electric current is flowing usually looks 
exactly like a wire without current. Our senses are not directly 
impressed by the phenomena of electricity, and hence it is neces- 
sary to depend upon certain effects which are associated with the 
flow of current through a conductor when it is desired to deter- 
mine whether or not a current exists. Some of these effects are 
as follows : 

(a) If a straight wire carrying an electric current is brought 
near a small magnet, such as a compass needle, which is so 
placed, that the axis about which it turns is parallel to the axis 
of the wire (Fig. 7), then the needle is deflected a certain 
amount and tends to become tangent to a circle about the wire. 
It then remains in the new position as long as the current does 
not vary. 

(&) A wire with a current passing through it will be at a 
higher temperature than the same wire before the current flows. 
If the wire is large or the current is small, this can be detected 
only by a sensitive thermometer, but under some conditions, as 
in an ordinary incandescent lamp, the rise of temperature is so 
great as to cause the wire to glow. 

(c) If the wire through which the current is flowing is cut 
and if the separated ends are immersed in a solution in \yater 
of any one of a wide variety of substances, there will be a chemi- 
cal change in the solution. This chemical change may become 
apparent by a change in the color of the solution, by a deposit 



on one of the wires, or otherwise, and gas may be evolved. 
Thus, if the solution is copper sulphate, copper will be de- 

The attention of the student should be fixed upon these effects 
of the current, rather than upon the current itself. It is in 
terms of these effects that electric currents are detected, meas- 
ured, and applied. Thus the majjnetic effect is the basis of 
dynamo-electric machinery and radio communication ; the heat- 
ing effect (&) makes possible electric cooking and electric light- 
ing; and the chemical effect (c) makes possible electroplating, 
electric batteries, and various chemical processes. All three 
effects are utilized in making electric measurements. 

It must be kept in mind that such expressions as " flow " and 
" current " and many other electrical terms are merely sur- 
vivors from an earlier day when electricity was supposed to be 
a fluid which actually flowed. Such terms are, however, help- 
ful in forming mental pictures of the real phenomena of elec- 
tricity. Attention must always be centered on the facts and 
effects which these terms represent and the words or phrases 
themselves must not be taken literally.^ 

4. Direction of Current. — By means of the magnetii: effect it 
is readily shown that electric current has direction. If the 
wire in Fig. 7 be withdrawn from the plate, O, and reinserted 
in the opposite direction, the compass needle will indicate a 
direction (Fig. 8) nearly opposite to that of its original posi- 
tion. The same result is secured if the wire is left unchanged 
and the connections to the terminals of the battery are re- 

The direction of flow of electric current is a ma.tter of 
arbitrary definition, and in practice the student will usually 
determine the direction by means of an instrument with its 
terminals marked + and — . It is assumed that current enters 
the instrument at the + terminal and leaves it at the — 

The magnetic effect may also be used in specifying the direc- 
tion of the current. See Section 40, page 103. Again referring 
to Fig. 7, it is seen that as the current flows down through the 
plane, the compass needle, at every point in the plane, tends to 
set itself tangent to one of the concentric circles al)Out the wire. 

1 Read Franklin and MacNutt, General rhysics, p. 238. 



As the observer looks along the conductor in the direction in 
which the current is flowing, the north-seeking or north-pointing 
pole of the needle will point in a clockwise direction around the 
conductor — that is, it will point in the direction it would assume 
if following the advancing hand of a clock having the conductor 
as a pinion. Other useful rules for remembering the same 
relative directions are as follows : 

(a) Grasp the wire with the right hand and with the thumb 
extended along the wire in the direction of the current. The 


Md^ctic fi'J id aboytA 
straight" Wire, j 
Current \-\o wirii, down 



RiAht hand 

Hood Screw 

field <ib<!>yf d strdit^t wire 
flawing ^\>- 

— m^ 

Rij^ht hdricL rule -^of xiirecticn oj c\)rr&ut d.nd 
lines of f<?rce 

curved finger tips will then indicate the direction of the mag- 
netic effect, Fig. 10. 

(6) Imagine an ordinary right-hand wood screw being ad- 
vanced into a block in the direction in which the current is 
flowing (Fig. 9), The direction in which the screw rotates then 
indicates the direction of the magnetic field around the wire or 
conductor as it would be indicated by a compass needle. 

The student should assure himself of complete familiarity 
with one of these rules by considerable practice with a small 
compass and a simple electric circuit. 

For the extension of this relation to determine the polarity 
of a helical coil carrying a current, see section 42, page 105. 
53904° — 22 3 


5. Measurement of Electric Current and Quantity of Elec- 
tricity. — All three of the simple ways by which electric current 
may l)e detected (see Sec. 3) provide meaas of current measure- 
ment. The ma^ietic effect of the current may be used by 
mouiitin.c: a wire and a magnet in such positions that when a 
current Hows in the wire either the magnet or the wire moves. 
The heating effect of the current is utilized in hot-wire instru- 
ments (Sec. 59), where the increase in length of the heated 
wire is utilized to move a pointer over a dial. These principles 
are used in a great variety of instruments for the measurement 
of current. The amount of current is read from the scale or 
dial of the instrument. The scale is usually graduated at the 
time when the instrument is standardized, in a unit^ called 
the " ampere." The instruments are called " ammeters." 

The ampere is a unit the magnitude of which has been 
defined by international agreement. In its definition the third 
effect of the electric current, described above, is made use of. 
The mass of a metal which is deposited out of a solution by an 
electric current depends on the product of the strength of the 
current by the time it is allowed to flow. Thus a certain current 
flowing for 100 seconds is found, experimentally, to be able to 
deposit as much of a metal as a current 100 times as great pass- 
ing for one second, etc. Remembering that the strength of the 
current is the rapidity of flow of electricity, it is evident that 
the product of strength of current by time of flow gives the total 
quantity of electricity which has passed. 

The mass of a metal deposited by the current is, then, propor- 
tional to the total quantity of electricity which has flowed 
through the solution. Equal quantities of electricity will deposit 
different masses of different metals, but the mass of any chosen 
metal is always the same for the same quantity of electricity. 

The ampere {properly called the international ampere) is that 
unvarying current ichich, nhen- passed through a neutral solu- 
tion of silver nitrate, icilt deposit silver at the rate of 0.001118 
gram per second. 

A convenient way of remembering this figure is that it is made 
up of one point, two naughts, three ones, and four twos — 8. 
While current could be regularly measured by the process used 
in establishing this unit this is not done in actual practice. 

2 See Appendix 2 on " Units," p. 547. 


The measuring instruments used in actual measurements are, 
however, standardized more or less directly in terms of the 
unit thus defined. 

Quantity of electricity is usually measured in a unit called 
the " coulomb." The coulomb is the quantity of electricity trans- 
ferred by a current of one ami>ere in one second. Another unit 
sometimes used for measuring quantity of electricity is the 
" amr>ere-liour,'' which is tlie quantity of electricity transferred 
by a current of one ampere in one hour, and is therefore equal 

to 3,600 coulombs. 

6. Electrons. — When electric current flows in a conductor 

there is a flow of extremely .small particles of electricity, called 
electrons. The study of these particles is important not only in 
connection with current flow, but also in light and heat and 
chemistry. The reason for this is that all matter contains them. 
Matter of all kinds is made up of atoms, which are extremely 
small portions of matter (a drop of water contains billions of 
them). The atoms contain electrons which consist of negative 
electricity. The electrons are all alike, and are in turn much 
smaller than the atoms. Besides containing electrons, each 
atom also contains a certain amount of positive electricity. 
Normally the positive and negative electricity are just equal. 
However, some of the electrons are not held so firmly to the 
atom but what they can escape when the atom is violently 
jarred. When an electron leaves an atom there is then less 
negative electricity than positive in the atom ; in this conditioa 
the atom is said to be positively charged. When, on the other 
hand, an atom takes on one or more extra electrons it is said 
to be negatively charged. 

The atoms in matter are constantly in motion, and when they 
strike against one another "an electron is sometimes removed 
from an atom. This electron then moves about freely between 
the atoms. Heat has an effect upon this process. The higher 
the temperature, the faster the atoms move and the more elec- 
trons given off. If a hot body is placed in a vacuum the elec- 
trons thus given off travel from the hot body out into the sur- 
rounding space. This sort of a motion of electrons is made use 
of in the electron tube, which is the subject of Chapter 6 of 
this book. The motion of the electrons inside a wire or other 
conductor is the basis of electric current flow. This is discussed, 


with the various important properties of electrons, in a book 
by R. A. Millikan, " The Electron," and. briefly, in " Radio In- 
struments and Measurements," Circular No. 74 of the Bureau of 
Standards, page 8. (This circular is sometimes referred to 
as C. 74.) 

B. Resistance and Resistivity. 

7. Resistance and Conductance. — The flow of current through 
a circuit is opposed by a property of the circuit called its 
" resistance" (symbol R). The resistance is determined by the 
kinds of materials of which the circuit is made up, and also 
by the form (length and cross section) of the various portions 
of the circuit. Provided that the temperature is constant, the 
resistance is constant, not varying with the current flowing 
through the circuit. This important relation is called Ohm's 
law and will be discussed further in Sec. 14. All substances 
may be grouped according to their ability to conduct electricity, 
and those through which current passes readily are called " con- 
ducting materials " or " conductors," while those through which 
current passes with difficulty are called " insulating materials " 
or " non-conductors." However, there is no known substance 
which admits current without any opposition whatever, nor is 
there any known substance through which some small current 
can not be made to pass. There is no sharp distinction between 
the groups, as they merge gradually one into the other. Never- 
theless, it should be kept in mind that conductors have a con- 
ducting power which is enormously greater than the conducting 
power of an insulator. The minute current which can be forced 
through an insulator under certain circumstances is aptly called 
a " leakage current." An ideal insulator would be one which 
would allow absolutely no current to flow. Examples of good 
conducting materials are the metals and that class of liquid 
conductors called electrolytes. Examples of insulating ma- 
terials are dry gases, glass, porcelain, hard rubber, and various 
waxes, resins, and oils. 

A circuit which offers but little resistance to a current is said 
to have good conductance. Representing this by g we may 

g=h or 7?=1 (1) 


For example, a circuit having a resistance of 10 ohms will 
have a conductance of 0.1 and one of 0.01 ohm will have a con- 
ductance of 100. The unit of resistance called the " ohm " is 
defined in terms of a standard consisting of pure mercury, of 
accurately specified length, mass, and temperature. 

Tlie international ohm is the resistance offered to the flow 
of an unvarying current hy a column of mercury 106.3 centi- 
meters high and tveighing 14.^521 grams at a temperature of 


For very small resistances the millionth part of an ohm is 

used as a unit and is called the " microhm." For high resist- 
ances a million ohms is used as a unit and is called the 

The opposition to flow of current referred to above is analo- 
gous to friction between moving water and the inner surface 
of the pipe through which it flows. It is always accompanied 
by the production of heat. If an unvarying current is main- 
tained through a conductor, this production of heat is at a 
constant rate. The total heat, produced in t seconds, is found 
to be proportional to the resistance of the circuit, to the square 
of the current, and to the time, thus 

W=RIH (2^ 

From this it follows that R, for a given portion of the circuit, 
might be measured by the heat generated in that portion. The 
heat will be measured in " joules " when the current is in am- 
peres, the resistance in ohms, and the time in seconds. To find 
the heat in calories, the relation W/J=H will be used, where 
W is in joules and -/ (1.18) is the number of joules in one 
calorie. The relation given in equation (2) is sometimes 
called Joule's law. 

8. Resistivity and Conductivity. — For a given piece of wire of 
uniform cross section, its resistance is found to be proportional 
directly to its length, and inversely to its cross sectional area ; 
and in addition the resistance depends upon the kind of mate- 
rial of which the wire is composed. These relations may be 
expressed by the following equation 

R=Pj (3) 


where R is the measured resistance of the sample, 7 is the 
length, s is its cross section and p is a constant, characteristic 
of the given material. Solving this equation for p we have 

P=r\ (4) 

If a piece of material is chosen having unit cross section and 
unit length, it is seen that p is equal to the resistance of the 
piece, measured between opposite faces. The factor p is called 
the " resistivity " or " specific resistance " of the substance, and 
is defined as the resistance between opposite faces of the unit 
cube. The ohm or the microhm is connuonly used as the unit 
of resistance and the centimeter as the unit of length. Instead 
of expressing resistivity in these units it may also be given in 
terms of ohms per foot of wire one mil (0.001 inch) in diameter, 
or in ohms per meter of wire one millimeter in diameter. 

Another group of resistivity units is based upon the mass of 
a sample instead of its volume, for example: (a) the resistance 
of a uniform piece of wire of one meter length and of one gram 
mass ; or ( 6 ) the resistance of a wire of one mile length and of 
one pound mass. Practically, for some purposes, the mass re- 
sistivity is preferable to the volume resistivity for the following 
reasons: (a) sufficiently accurate measurements of cross sec- 
tion of specimens are frequently difficult, or, for some shapes, 
impossible ; {h) material for conductors is usually sold by 
weight rather than volume, and hence the data of greatest value 
are most directly given. The mass units and volume units are 
readily interconverted, provided that the density of the material 
is known. If in equation (3) we substitute for s the value of 

y, where r is the volume, and for v its equivalent -j-, where 
L a 

■ m is the mass and d is the density, we have 

R=-P<1— (5) 

The quantity pd is called the mass resistivity of the material. 
The volume resistivity may then be transformed into mass re- 
sistivity, or vice versa, taking care that all the quantities are 
given in consistent units. As examples of resistance the follow- 
ing will be useful : 


1. One ohm is the resistance of about 157 feet of number 18 
copper wire (diameter about 1 mm., or 40 mils or 0.04 inch). 

2. One thousand feet of number 10 iron wire (diameter about 
2.5 mm., or 102 mils or 0.1 in.) has a resistance of about 6.5 ohms. 

Tables of resistivity for various materials are given in Table 
21, Circular 74 of the Bureau of Standards. 

Just as conductance is the reciprocal of resistance wiien con- 
sidering the properties of a circuit as a whole, so " conductivity " 
is the reciprocal of resistivity when considering the properties 
of a given material. Its unit is the "mho," or "reciprocal' 

9. Temperature Coefficient. — The electrical resistance of all 
substances is found to change more or less with any change in 
temperature. All pure metals and most of the metallic alloys 
show an increased resistance with rising temperature. Carbon 
and most liquid conductors like battery solutions show a de- 
crease in resistance as the temperature increases. Experiment 
shows that the resistance at a temperature t can be calculated, 
if the resistance at zero temperature (melting point of ice) has 
been measured. The formula is 

Rt=Ro-\-Roaot (6) 

where Ro is the resistance of the sample at zero, and ao is the 
change in 1 ohm when the temperature changes from zero to 
1° C. The factor ao is called the "temperature coefficient" of 
resistance for the material. Solving equation (6) for ao we have 




Equation (7) shows ao is the value of the change in the resistance 
per ohm per degree change in temperature, or it is the fractional 
change of the total resistance for 1 degree change in tempera- 
ture. If the resistance of the material decreases with a rise in 
temperature, then the temperature coefficient is negative. 

If a reference temperature ti is chosen, which is not zero, then 
the resistance R-, at some other temperature ^2, which is higher 
than ti, may be found from the resistance Ri at ti by the follow- 
ing equation, 

R2=^Ri[l+a^(t—U)] (8) 

where a, is the temperature coefficient for the reference tem- 
perature ti. 



Calculations of tliis sort are siiiiplilied by the use of a table of 
values of a for various initial reference temperatures. See 
Table 21, Circular 74. 

10. Current Control. — In electrical work the need is constantly 
arising for adjusting a current to a specified value. This is 
usually done by varying the resistance of the circuit. Changes 
in the resistance of a circuit can be made by means of re- 
sistors, which consist in general of single resistance units, or 
groups of such units, made of suitable material. These may be 
variable or tixed in value. Variable resistors are frequently 

Flui^ TCiiiUnce boK 


Connection in 5>ln5 

KtSiitarvce Wine 

ealU'd "resistance boxes" or "rheostats," dei>ending on their 
current-carrying capacity and range. 

A resistance box consists of a group of coils of wire assem- 
bled compactl.v in a frame or box. (Figs. 11, 12. and 13.) 
It is so arranged that single coils or any desired combination 
of such coils may be introduced into the circuit by manipulat- 
ing the switches or plugs. The extreme range of such a device 
may be from a hundredth or a tenth of an ohm up to 100,000 
ohms. Each of its component units is accurately standardized 
and marked with its resistance value. By this means it is 
possible to know precisely what resistance is introduced into 
the circuit by the resistance box. The coils are wound with 



relatively fine wire, and in such a way that they do not have 
any appreciable magnetic fields about them. They are in- 
tended solely for carrying feeble currents, usually no more 
than a fraction of an ampere. 

Resistors of single fixed values are convenient for many 
purposes. If they are carefully made and precisely meas- 
ured, they are called standard resistance coils. Such stand- 
ards may be secured in range from 0.00001 ohm to 100,000 
ohms and of any desired current-carrying capacity and degree 
of precision. Resistance boxes and precision resistors are de- 
signed primarily for use in the laboratory. 

The name " rheostat " is, in general, applied to a variable 
resistor having a fairly large current-carrying capacity. A 

Tube Rheoatit 

r\Q. 14 

Field Rheostdt 
r\Q. 15 

simple form of rheostat consists of a layer of German silver 
or nickel-steel wire wound on an insulating tube with a sliding 
contact traveling along the tube so that the current may be 
made to pass through any desired length of the wire. (Fig. 
14.) Such rheostats are not usually made to handle large 
amounts of power. Larger rheostats are made of resistance 
units connected between the points of a switch, as shown in 
Fig. 1.5. The units are made of resistance wire embedded in 
vitreous enamel on a metal plate or wound on a porcelain tube 
and then enameled. For very large units the resistors are 
made in the form of grids of cast iron, nickel steel, or similar 
metal, which are exposed to the air for cooling. The grid 
type of resistor is by far the most common in commercial use, 
especially for railway and electric-crane control. For ex- 
tremely^ large currents a convenient compact rheostat is made 
by immersing metal plates to a variable depth in a conducting- 


liquid ; such a liquid rheostat can be easily cooled by using a 
metal container, or by changing the liquid as it becomes 

Banks of incandescent electric lamps in various arrangements 
are often used as resistors. The resistance of such lamps is 
subject to large variations in value with changes in teirrpera- 
ture. However, when operating under steady conditions, either 
hot or cold, they are satisfactory for many purposes. Such a 
rheostat offers the advantage of being readily adjustable by 
turning lamps off or on. It is compact and there is no danger 
of overheating. 

Another type of rheostat for handling large currents consists 
of a pile of carbon blocks or plates which are compressed by a 
screw or lever to reduce their electrical resistance. 

11. Conducting Materials. — Conducting materials, usually 
metals or metallic alloys, are utilized in electric circuits with 
two different jiurposes in view. In one case a high degree of 
conductivity is required, while in the other case relatively high 
resistivity is desired. These cases will be discussed in turn. 

(a) If the conductor is transmitting energy to a distant point 
by means of the electric current it is seen from equation (2) 
that some energy will be wasted in the conductor in the form of 
heat. This loss should be kept as small as possible, and to this 
end great care is taken in choosing the size and material of the 
conductor. For reasons of economy the cross section must not 
be too great, hence a desirable nvaterial for conducting lines 
must have low resistivity and must be abundant and relatively 
cheap to produce. Such a material is copper. Where lightness 
is important and where increased dimensions are not a disad- 
vantage, aluminum is much; used. Steel is used where great 
strength is desired and where the current is small, as in tele- 
graph lines. For lines which must stand great strain and at 
the same time be good conductors, such as radio antennas, a 
stranded phosphor bronze wire is often used. 

(6) A material to be used for resistor coils, on the other 
hand, should have the following properties: 

1. The resistivity should be fairly high so that a large resist- 
ance may be obtained without too great a bulk. 

2. The material should remain strong mechanically when 


3. The cost of material should not be excessive. 

For precision rheostats for careful laboratory measurements 
the following qualities, which are of comparatively small im- 
portance for ordinary electrical engineering work, should also 
be considered : 

4. The temperature coefficient must be small, so that heating 
does not change the resistance appreciably. 

5. The resistivity must not change with time, even when the 
unit is heated for long periods. 

6. The thermoelectric force (Sec. 15) between the chosen 
material and copper or brass must be small, so that the con- 
tacts between the different parts of the circuit will not cause 
troublesome thermoelectric currents. 

Iron is by far the most common material used ^in rheostats, 
since it is cheap, strong, and has a fairly high resistance. It is 
used in the form of grids for street car, locomotive, train, 
elevator, and crane control and in the form of wire coils for 
handling smaller powers. German silver and the various nickel 
steels rank next in frequency of use and, with iron, make up 
the great bulk of commercial rheostats. Special alloys, such as 
those called " manganin " and " invar," are used for laboratory 
units where the last three requirements mentioned above must 
be met. Table 21, of Circular 74 of the Bureau of Standards, 
gives the properties of some pure metals and the composition 
and electrical properties of certain of the more common alloys. 

Wire Gauges. — Sizes of wires are specified in two general 
ways, either by giving the actual diameter in millimeters or in 
mils (1 mil=0.001 inch), or by assigning to the wire its place in 
an arbitrary series of numbers called a wire gauge. Only two 
of these arbitrary wire gauges are of importance in American 
practice, the American Wire Gauge and the Steel Wire Gauge. 
To avoid confusion the name of the gauge must always be 
given with the gauge number. Most steel wire is specified in 
terms of the steel wire gauge. Wire used in electrical work, 
such as copper, aluminum, and the copper-nickel alloys, is 
specified in terms of the American Wire Gauge. This is the 
only gauge in which the successive sizes have a definite mathe- 
matical relation. See Appendix 4, page 5.54. 

It is convenient to remember that any change of three sizes 
of this gauge doubles (or halves) the resistance of a wire; a 


change of six sizes doubles (or halves) the diameter, and there- 
fore quadruples (or divides by four) the resistance of the 

12. Non-conducting or Insulating Materials. — The importance 
of good conductors, in practical applications of electricity, has 
been dwelt on in the preceding? section. It is, however, equally 
important to have non-conducting materials in order that elec- 
tric current may be confined to definite and limited paths. Such 
materials are commonly called insulators or dielectrics. It is 
a familiar fact that electric wires are covered with layers of 
cotton, silk, rubber, and other non-conducting compoimds, and 
are supported t»n porcelain knobs or in clay tubes. This is done 
to prevent the current from escaping along a chance side path 
before the desired terminal point is reached. 

Strictly, there is no such thing as a perfect non-conductor. 
The matei'ials commonly used for this purpose have volume 
resistivities ranging from 10.000 ohms to 10" ohms between 
opposite faces of the unit cube. This means that 1 volt im- 
pressed across such a unit cube by means of proper metal 

terminals, would cause a current of from jqqqq "^^ iqvt ampere 
to flow. (See Sections 13 and 14.) 

Most insulating substances show a decrease in volume re- 
sistivity with increase in temperature. These changes are 
irregular and sometimes rapid. They are not directly propor- 
tional to the changes in temperature. Humidity is of great 
influence, and tends to lower the volume resistivity in such 
materials as slate, marble, hard fiber, and materials of the 
phenolic type such as the material called " bakelite." Very fre- 
quently surface leakage is of greater importance than volume 
conduction, and this surface leakage is largely dependent upon 
the conductivity of the moisture film upon the surface. In any 
event, care must be taken to ensure that the effects of surface 
leakage are either minimized or allowed for. 

In work involving high potential differences the property of 
dielectric strength is of greater importance than volume re- 
sistivity. If the potential difference applied between opposite 
sides of a sheet of dielectric material exceeds a certain critical 
value, the dielectric will break down, as though under a me- 
chanical stress, and a spark will pass between the terminals. 


In case the dielectric is a liquid or a gas, its continuity is im- 
mediately restored after the spark has passed. However, in a 
solid dielectric the path of the spark discharge is a permanent 
defect, and if enough energy is being supplied from the source, 
a continuous current will persist, which flows along the arc 
or bridge of vapor formed by the first spark. " Dielectric 
strength " is a property of the material which resists this 
tendency to break down. It is measured in terms of volts or 
kilovolts required to pierce a given thickness of the material 
and is sometimes called the " puncture voltage." Values of 
dielectric strength of air are given in Section 171, page 389. It 
is a quantity that can not be specified or measured very pre- 
cisely, because the results vary with (a) the character of the 
voltage, whether direct or alternating, (&) the distance be- 
tween the terminals, (c) the time for which the voltage is 
applied, and (d) the shape of the terminals. The presence of 
moisture lowers the dielectric strength. Dry air is one of the 
best of the insulating substances, but its dielectric strength is 
lower than that of many liquids and solids. The dielectric 
strength of different specimens of the same insulating material 
is not directly proportional to the thickness of the specimen. 
The properties of most electrical insulating materials are 
very different when subjected to radio-frequency voltage than 
when subjected to the low-frequency voltage such as is used on 
house-lighting mains, or when subjected to direct current. As 
an example, a piece of insulating material of the phenolic type 
may withstand 100,000 volts at a frequency of 60 cycles per 
second, but may deteriorate and become conductive very rap- 
idly when subjected to a voltage of the order of 20.000 volts or 
less at radio frequencies (say 120,000 cycles per second). In 
other words, some materials which are suitable for ordinary 
electrical work, may be entirely unsuitable as radio insulators. 
Thus slate is extensively used in ordinary electrical work with 
60-cycle alternating currents, but is entirely unsuitable for use 
as an insulating material in radio-frequency circuits, A 
certain amount of power is lost in every insuhiting ma- 
terial subjected to an alternating voltage, but the amount 
of power lost must ordinarily be small if an insulating material 
is to be satisfactory for most radio uses. Radio-frequency 


power loss." therefore, becomes of particular importance in 
selecting insulating material for certain locations about a radio 

In addition to the constant currents which flow through or 
over insulating substances, due to the " body leakage " and 
" surface leakage " we find two other currents, which are tem- 
porary when a direct voltage is applied, but which it is im- 
portant not to overlook. 

1. The " displacement current " which is discussed later in 
Section 29. This current appears and becomes negligible in a 
very short time, not more than a few thousandths of a second. 

2. The " absorption current " which persists longer and is ob- 
served when an emf. is applied to a plate of a dielectric by 
means of electrodes as in the case of a condenser. (See Sec. 

At first there is a considerable rush of current but the 
strength of the current falls off with the time, at first rapidly, 
then more slowly. It may not become negligible for several 
hours. It is due to some rearrangement of the molecules of the 
substance under the stress of the applied emf. 

C. Potential Difference, Emf., and Ohm's Law. 

13. The Meaning of Emf. — In Section 2 it was stated that one 
of the important electrical quantities is the electromotive force, 
which is the cause of the electric current. In order to fix in 
mind the ideas underlying the electric circuit it will be helpful 
to consider some illustrations drawn from experiences familiar 
to everyone. Assume that a body of 1 pound weight is raised 
from the floor to a table, through a height of 3 feet (Fig. 16). 
Work is done upon the body, and the amount of work done is 
given by 1X3=3 ft.-lb. The body has acquired "potential 
energy " by this change in its position. That is, it is capable of 
falling back to the floor by itself, •and in falling back it will, 
when brought to rest, do an amount of work exactly equal to 
that which was done in lifting it. 

" For furthor information regarding dielectric power loss and proper- 
ties of insulating materials, see Bureau of Standards Circular 74. The 
Bureau of Standards will issue during 1922 publications giving detailed 
information regarding the properties of electrical insulating materials 
of the laminated, phenol-methylene type. 



The difference in level between floor and table may be ex- 
pressed in either of two ways — first, in the ordinary way, by 
stating directly the vertical distance through which the body 
was raised ; and second, by stating the amount of work re- 
quired to carry 1 pound of matter from the lower to the higher 
level. This difference in level, then, defines a very definite 
difference in condition between the two positions. The higher 
position, considered as a point in space, has a characteristic 
which distinguishes it from the lower position, and that is the 





Fi& 16 Fig I?. 

S'mple Illustration of Potential enerqu due. to dilierence 

>tential Lnerqu. of head of two "bodies of water 



t TfACK, 

Hg 18. Electrical Fotential Difference Exists betweeri Wire and Track 

amount of potential energy possessed by a body when placed 
there. In other words, a body placed at this point is able, by 
virtue of its position, to do a certain amount of work. If we 
assume that the body has unit mass, this characteristic is called 
the gravitational potential of the point. The higher position is 
said to have a higher potential than the lower position, and the 
difference in potential, measured in terms of work, is a measure 
of the difference in height. 

Following this illustration a little further, we may consider 
the case of a simple pump, which raises water from a level Si to 
some higher level St (Fig. 17). The water raised by the pump 


to the level /S^j possesses potential energy or enerjiy of position. 
That is, it is able to fall back by itself to the lower level, and 
in falling back it will do an amount of work exactly equal to 
that which was done in lifting it. Instead of measuring the 
difference in level by the height h as before it may be meas- 
ured in terms of the work done in lifting 1 pound of water from 
Si to Sz. This difference in level may be called the difference 
in potential between ^S^i and S2. 

The purpose of the pump is to transform the energy supplied 
by some steam engine or other prime mover into potential 
energj', with the corresponding difference in level or pressure 
head. This establishes what might be called a watermotive 
force, which causes or tends to cause a flow of water through a 
return connecting pipe. 

Energy may exist in many different forms. The position 
energy- or potential energj^ of a body has been just described. A 
moving body has energy of motion or " kinetic '* energj'. Sound, 
heat, light, and electricity are all forms of energy ; these par- 
ticular forms of energy are due to "wave motion." (See Sec. 
125.) Chemical reactions involve transformations of energy. 
Every action of everyday life involves a transformation of 
energy from one form into another. In the case of every trans- 
formatiofn of energy from one form into others, it is found that 
the energy which disappears as one form can be entirely ac- 
counted for by the energy which appears in other forms. If 
the transformation is confined to one body or system of bodies, 
the total amount of energy possessed by that body or system 
of bodies is the same before and after the transformation; that 
is, energy can neither be created nor destroyed. This principle 
is usually referred to as the " conservation of energy." It 
should be noted, however, that some forms of energy are far 
more available for use than others. Thus the potential energy 
possessed by the water in a reservoir can be easily used, but 
the energy changed into heat by the friction of water with the 
sides of a pipe through which it is flowing is usually con- 
sidered as being "lost," because it is not practically available 
for use. 

Coming now to the electrical case, let us consider that electric 
current is supplied to the motors of an electric car by means of 
a generator G, Fig. 18, and two conductors, the trolley wire and 


the track. Mechanical energy is being supplied to the generator 
by some source of power, such as a steam engine, and is being 
transformed into electrical energy. This transformation results 
in a flow of current as indicated by the arrows, when a com- 
plete circuit is made through the car motors. This condition 
is described by saying that there is a difference of electric 
potential between the terminals of the generator, or between the 
trolley wire and the track. It is the purpose of any electric gen- 
erator to set up this difference of potential between its terminals, 
which corresponds to the difference in level of the water in the 
earlier illustrations. Difference of electric potential is then a 
difference in electric condition which determines the direction 
of flow of electricity from one point to another. 

Just as height of water column or difference in level may be 
regarded as establishing a pressure or watermotive force, which 
in turn causes a flow of water when the valves in the pipe are 
open, so the electric potential difference may be regarded as 
establishing an electromotive force which causes a flow of elec- 
tricity when a conducting path is provided. Electromotive force 
may be defined as that which causes or tends to cause an electric 

The unit of electromotive force is the volt. It is that emf. 
which u-iU cause a current of 1 ampere to flow through a re- 
sistance of 1 ohm. 

The relation between electromotive force, current, and resist- 
ance is called Ohm's law. This law is discussed further in the 
next section. 

The potential difference between two points may be measured 
in terms of the work done in conveying a unit quantity of elec- 
tricity from one point to the other. In general 

where E is in volts, W is in joules, and Q is in coulombs. (See 
Appendix 2, Units.) In practice, however, it is measured by 
direct application of an instrument called a "voltmeter." (See 
Sec. 60.) 

The unit of work or energy is the joule. It is the energy ex- 
pended when a current of one ampere flows through a resistance 
of one ohm for one second. 

53904° — 22 4 



Power is the rate at which worlv is done. The unit of power 
is the watt, wiiich is the power expended by a current of one 
ampere flowing tlirough a resistance of one olim. 

Power is sometimes measured in units of horsepower. 1 horse- 
power equals 746 watts. 

14. Ohm's Law. — If the pressure upon a pipe line is increased, 
the flow of water through it in gallons per minute is increased. 
Ohm found that an increase in the emf. applied to a given con- 
ductor caused a strictly proportional increase in the current. 
Doubling the emf, causes exactly twice as great a current as be- 
fore, trebling the emf., three times as great a current, etc. This 
means tliat for a given conductor the ratio of emf. to current is 
a constant, and this constant has been called the resistance of 
the conductor. This important relation is known as Ohm's law, 
and may be written : 



or. in the alternative forms, 







Ohm's law derives its great importance from the fact that it 
applies to each separate portion of an electric ciruit and also 
to the circuit as a whole. 

Case I. Ohm's Law for a Portion of a Circuit, — Assume some 
part of a complete circuit, R, Fig. 19, which is held at a con- 
stant temperature, and has no battery or other source of emf. 
between the points A and B. If current from an outside source 
is then caused to flow through R, and correct instruments are 
used for measuring current and voltage, respectively, the fol- 
lowing data may be taken, showing that R has a value of 2 
ohms, and that R being constant the current is directly pro- 
portional to the voltage. 



























Suppose two straight lines OY and OX are drawn at right 
angles to each other, Fig, 20. Divide each line into units and 
set down the proper numbers at regular intervals along these 
two lines.^ The numbers on the OY axis may be used to repre- 
sent values of E, and the numbers on the OX axis to represent 
values of /. 

At a point 1 on the E axis draw a light line parallel to the 
OX axis, and from the point ^ on the OX axis draw a light line 
parallel to the OY axis. Where these two lines intersect make 
a dot. Proceed in this way for all the corresponding values of 
E and / in the table above, and then connect the dots by a line. 
It is seen that the ratio of E to I is the same for every point 
that may be taken on the line OP. This means that E and / 
are connected by a constant factor and / is said to be directly 
proportional to E. This process is called plotting the relation 
between the two quantities E and /. Proportionality is indi- 
cated by the straightness of the plotted line. 

Again, assume that a constant voltage E' is applied across the 
terminals of R, Fig 19. By some suitable means, change the 
values of R through a considerable range. The following are 
some values which careful observation might yield : 

























Plot the values of R and / on cross-section paper. Fig. 21. and 
the curve Axi is obtained. 

Also we may plot reciprocals of R (values of — 

on the 

axis of abscissas against values of I on the axis of ordinates, 
Fig. 22. It is now seen that / is proportional directly to the 
reciprocal of R or, in other words, / is inversely proportional to 

3 These lines are called axes. F is called the axis of ordinates and OX is called 
the axis of abscissas. A distance measured along l^is called an ordinate. A dis- 
tance measured along OX is called an abscissa. 



R. The student should make some experiments of this sort 
with a resistance box, battery, ammeter, and voltmeter. He 
should also make a careful record of the readings taken, and 
then should plot them ori cross-section paper, as suggested above. 
From such a study it will be found that : 

(a) For a constant resistance, the current flowing is directly- 
proportional to the voltage. 

(&) For a constant voltage the current is inversely propor- 
tional to the resistance. 



ft - 





T— * 







^ E , , 












Fig 19 Simple Circuit for • 
Study of Ohm'i Low ^' J 













t « t » !• •» 

I - Current -Amperes 
Pic. 20. Current -Voltaic Relation 
Simple Circuit 





















, i 













A ^ 


7 t: 



t 4 A b le IT 

t- Current -Amperes 

IG. S.I. Curreni-Pes\stonc 

ations in Sirnple Circ 

J, I Re 

Xr % % % % % Vfi 

Ig 22 Current -resistooce 
otions in Oirnp/e Circuit 

It is customary to speak of the current flowing "in" a 
circuit ; of the resistance " of " a circuit and of the emf. •' be- 
tween the terminals " of, or " across " any portion of a circuit. 

The relation expressed in equation (10) applied to a part of 
a circuit is used so much practically that the value of E' be- 
tween A and B (Fig. 19) has been given various names. It is 
called (o) the RI drop, (&) the potential drop, or (c) the fall 
of potential in the portion of the circuit between A and B. If 
a branch circuit which contains a current-indicating instrument, 

ohm's law. 51 

such as a voltmeter, (Fig. 19), is connected between these two 
points, a flow of current is shown to be taking place. The point 
A is at a higher electric potential than B, and hence current 
will flow along the path A — V — B. 

Case II. OJun's Laic fot^ a Complete Circuit. — In extending^ 
this idea to the entire circuit, the total resistance of the circuit 
must be used. This must include the internal resistance of the 
generator or battery, or the sum of the resistances of all the 
generators, if there is more than one. Likewise the voltage 
must be the resultant or algebraic sum of all the emfs. in the 
circuit. Ohm's law for the complete circuit may then be written 
in the form : 

T___ ±Ei±E2±Es± _E ,^. 

^- R,-\-R,+R,-{- -R ^'^^' 

In this equation R must be the sum of all the resistances in the 
circuit, including the resistances of all the batteries or genera- 
tors. In the same way E must be the sum of all the emfs., 
each with its proper sign. For example, there might be a num- 
ber of cells or batteries in series (see Sec. 24), and one or more 
of these might be connected into the circuit with the poles re- 
versed. These emfs. would have to be subtracted, hence the 
negative sign for the terms in the numerator. 

Another way of stating this general law when all parts of the 
circuit are in series is to equate the total emf. impressed on 
the circuit to the sum of the RI drops in every separate portion 
of the circuit, 

E=RI=RJ+RJ-^Ra-\- (13) 

Ohm's law is to be regarded as an experimental truth, which 
has been established by countless tests for all metals and con- 
ducting liquids. For gases at low pressures it does not hold, 
nor does it apply to certain non-conductors, such as insulating 
oils, rubber, and paraflSn. 

15. Sources of Emf. — There are a number of ways in which 
electric energy can be derived from other forms of energj-. 
Each one of these energy transformations sets up a <'ondition 
which causes current to flow, that is, it produces an emf. The 
principal sources of emf. will be discussed briefly in the follow- 
ing sections. 


Static or Frictional Electricity. — ^When a piece of hard rubber 
is brought into close contact with a piece of cat's fur and then 
separated from it, two things may be noticed : 

1. The bodies have both acquired new properties, and are said 
to be electrified. 

2. A force is required to separate the bodies and work is done 
if they are moved apart. 

Both bodies now have the power of attracting light bits of 
chaff or tissue paper. The rubber is said to have a negative 
charge and the fur a positive charge. These charges exist in 
equal amounts and taken together they neutralize each other. 
An uncharged body is said to be neutral. When these charges 
are at rest upon conductors they are called electrostatic charges. 
Electric charges may bo communicated to small light bodies, like 
pith balls, and if these are suspended from silk threads the 
effects and properties of the charges may be studied in terms of 
the motions and behavior of the pith balls. Two pith balls 
charged oppositely are found to attract each other, and two 
with like charges to repel each other. The force between them 
in either case is proportional to the product of the charges and 
inversely proportional to the square of the distance between 
them. The force is also inversely proportional to the value of 
the dielectric constant of the material between the charges, if 
the charges and the distance between them remain constant. 
(See Sec. 31.) 

Electrostatic forces are ordinarily very small. There are many 
substances other than the two mentioned which become charged 
by friction with other materials. As glass is such a substance, 
the glass face of an instrument should never be wiped with a 
cloth just previous to use, as it thus may accidentally become 
charged to such an extent as to affect the light needle below it 
and cause a considerable error in its reading. In case this has 
happened, breathing upon the glass or wiping it with a moist 
.cloth will remove the charge. 

If two conducting bodies carrying opposite charges are con- 
nected by a conductor, a momentary flow of current takes 
place and the two bodies come to the same electrical condition. 
If the original charges were equal, both bodies are discharged. 
The flow of current continues for only a moment because 
there is no source of electricity, such as a battery, maintaining 
a constant difference of potential between the bodies. 


Electrostatic experiments can be best performed on a cold 
day when the air is dry.* 

Batteries. — When two plates of different substances, such as 
two metals, or a metal and carbon, are placed in a water solu- 
tion of certain salts or acids, there is found to be a difference 
of potential between them. If the exposed parts of the plates, 
called the electrodes, are connected by a conductor, current 
will flow. The following list contains the names of some of 
the substances which are used as battery electrodes. The order 
of the arrangement is such that when any two are taken, cur- 
rent will flow through the wire to the one appearing higher in 
the list from the one farther down. In selecting materials to act 
as electrodes in batteries, the farther apart the metals are in 
this list the greater is the electromotive force of the cell. The 
order shown is not absolutely invariable, but in some cases 
may depend on the electrolyte used. 











The salt and acid solutions used are conductors of electricity, 
but their conductivity is not so high as that of the metals. 
They are called " electrolytes."^ Some examples are solutions 

■* For further study of electrostatic phenomena the student is referred 
to Crew, General Physics, Chap. IX ; Franklin and ^MacNutt, General 
Physics, Chap. XV ; Starling, Electricity and Magnetism, Chap. V ; 
S. P. Thompson. Elomentary Lessons in Electricity and Magnetism, 
Index ; W. H. Timbie, Elements of Electricity, Chap. XI ; Watson, A 
Textbook of Physics, pp. 633-680. 

^ Not only do electrolytes conduct electricity but when a current is 
passed through them the molecules of the acid or of the salt are do- 
composed or broken up. The metallic part of the molecule, or its 
hydrogen, always travels toward the terminal from which the current 
leaves the solution, and is deposited there. This is the basis of 
electroplating processes, and it is in terms of such a process that the 
ampere was defined. (See Sec. 5.) 



of sulphuric acid, copper sulphate, potassium chloride, and 
sodium chloride or common salt. Ordinary water from the 
service pipes contains enough dissolved substance so that it 
conducts electricity to a slight extent. With any two materials 
of the table dipped in one of the solutions mentioned, there 
will be produced an emf. and a res^ulting flow of current. The 
farther apart the selected materials stand in the list the greater 
will be the effect produced. 

This arrangement for producing a current is called a " voltaic 
cell." Several types of this cell will be described in sections 17 
to 19. 

Thrrmoclectricitif. — A.ssume pieces of two different metals CJ 
and C'J, Fig. 23, soldered together at the point J. The other 

ends are connected by a 

copper wire through the 
galvanometer fi. If the 
point of contact, or junc- 
tion J, is heated to a 
temperature above that 
of C and C\ there will be 
a flow of current through 
the galvanometer. This 
is commonly explained by 
saying that at the junc- 
tUm J, heat energy is 
transformed into electri- 
cal energy, and this 
junction is regarded as the seat of an emf. In case the tem- 
I)erature of J is lower than that of CC\ the direction of the 
current will be reversed. In the following table some common 
metals are so arranged that when any two of them are chosen 
for the circuit, current flows across the heated junction from 
any one to one standing lower in the list. 
The presence at the junction of an intermediate metal or 
alloy like solder, will not affect the value of the emf. developed. 


because whatever effect is developed at one point of contact 
with the solder, is annulled at the other. Of the pure metals, 
a thermocouple made of bismuth and antimony g:ives the 
greatest thermoelectromotive force for a given difference in 
temperature. However, certain alloys are frequently used for 
one or both of the materials. The purity and physical state of 
these materials is an important factor in securing uniformity 
of results. A thermoelement or thermocouple may be cali- 
brated with a given galvanometer ; that is, a curve may be 
plotted coordinating microvolts and temperatures. It then 
becomes a valuable device for measuring temperatures, espe- 
cially where other forms of thermometer can not be used. For 
the range from liquid air temperatures, — 190° C, to 200' or 
300° C, copper-advance^ or iron-advance thermocouples are 
often used. For high temperatures, upward of 1,700° C, a 
thermocouple of platinum and a platinum-rhodium alloy is 

Thermocouples find application in radio measurements in 
hot-wire ammeters. See Section 59. page 136. 

Induced Emf. — Electromotive force may be set up in a cir- 
cuit by the expenditure of mechanical work in pushing wire 
conductors across magnetic lines of force. See Section 45, 
page 108. Also when electric current in any circuit is caused 
to vary, an emf. which is the result of this variation arises in 
any nearby circuit. The principles which apply to these cases 
are fully stated in Sections 45 and 47, pages 108, 112. The de- 
velopment of machinery based upon these principles is the sub- 
ject of Chapter 2. 

The RT Drop. — When for some purpose a voltage is desired 
which is less than that of the available battery or generator, 
or one which can be readily adjusted to any desired value, it 
is often convenient to take advantage of the RI drop across a 
given resistance, as described in Section 14, and to arrange a 
circuit as in Fig. 24. The current from the battery which flows 
through the resistance ab can be adjusted to any desired value 
by properly choosing the value of ab. 

^ Advance is a trade name for an alloy of copper and nickel. This 
material is widelj' used for resistance coils and rheostats. Its re- 
sistivity is high and its temperature coefficient is practically negli- 
gible. It has, however, a large thermoelectromotive force against 
copper or brass. 


Since the voltage drop along aJ) is directly proportional to 

the resistance r, any desired fraction, i-^' may be obtained bv 

setting the contact c at such a point that the resistance ac is 

^ual to — r. This follows from equation (10) where it is seen 
that the emf. across any resistance is directly proportional to 
that resistance so long as the current remains constant. This 
is nearly enough true for practical purposes if it be assumed 
that the resistance of crb is relatively large as compared to the 
internal resistance of the battery. The resistance ab may be 
in the form of a resistance box with a travelling contact at c, 
or it may be a uniform homogeneous wire, with an adjustable 
contact point at c. Such a device for subdividing a voltage is 
called a " voltage divider," and has often been erroneously 
called a potentiometer. 

Staiidard of Electromotive Force. — The emfs. due to the ordi- 
nary battery cells are usually between 1 and 2 volts. A certain 
type of cell has been selected by international agreement as a 
standard of emf. The type now most used is called the Weston 
standard cell, because it was first suggested by Weston. It is 
also called the " cadmium cell," because cadmium is used as 
the negative electrode. This cell is made from carefully selected 
chemicals of great purity, and when used under controlled tem- 
perature conditions its voltage can be depended upon to remain 
constant within a few parts in 100,000. At 20" C. (68° F.) its 
emf. is 1.0183. The value of the volt is maintained by reference 
to similar cells kept in the national standardizing laboratories. 
16. Internal Voltage Drop and Line Drop. — Reference to equa- 
tion (13), page 51, will show that the voltage or emf. of the 
generator, whether battery or dynamo, must always be thought 
of as being expended in three parts, as follows : 

1. That part which sends current through the generator itself, 
called the " internal drop." 

2. That part which sends current through the line, called the 
" line drop." , 

3. That part which sends current through the terminal appa- 
ratus, such as lamps, motors, or heating coils. This is the use- 
ful part of the emf., the first two being wasted so far as useful 
work is concerned. 



This division of the generated emf. is illustrated in Fig. 25. 
Since part 3 is the part which is applied in the external cir- 
cuit, it is clear that the generator must always supply a higher 
voltage than is needed at the terminals in order to take care of 
parts 1 and 2. The above facts may be again stated in the form 
Total emf.=drop in generator +drop in line+useful drop in load. 

Voltage Drop in Battery or Generator. — ^Assume a circuit as 
shown in Fig. 26. As long as the key K is open, the cell is not 
sending current through the circuit R. A high resistance volt- 


L 1 

XL J J^'6 24 Vo/taje T>\\i\der 



FjG. 25. Voltage Distribution in Circuit. 

„ ^K Internal \^/ta^e 
W\AAAA'V\ fl<3'2& Drop m deW. 

meter Y gives a reading E, which is the full open circuit voltage 
of the cell. The voltmeter current is so small that the cell may 
be regarded as supplying no current through it. If, without 
removing the voltmeter, the key K is closed, a current / flows 
through the external circuit R, and the voltmeter reading is 
seen to drop back to some value E' which is less than E. As R 
is made smaller the value of E' continues to decrease, until when 
12=0, that is, wlien the poles of the cell are short-circuited, the 
voltmeter shows no deflection whatever. The rate of change of 
the current, /, is less than the rate of change of the external 
resistance, R. The voltmeter indicates at any instant tlxe 


tJien existing value of the voUaoe at the eell terminals and 
this may vary from the op^i^ circuit voltage or emf, E, to zero. 
dei>ending upon the external circuit condition. For any value 
of R the current flowing is given by the equation 

where r is the internal resistance of the cell, or 

E=RI-\-rI (15) 

Thus the emf. E is equal to the sum of the potential drop in 
the cell and the RI drop in the external circuit. Denoting RI by 
E', we may wiite equation (15) in the form 

E'=E~rI (16) 

The quantity E' is called the " terminal potential difference," 
or the " terminal voltage " of the cell, and it is always less than 
the full emf. by the RI drop in the cell itself. It may be de- 
fined as the useful part of the emf., or that part which is avail- 
able for sending current through the external circuit. 

The emf. E is detern.ined once for all by the choice of ma- 
terials used in the cell, and it can not be in any way altered 
after the cell is once chosen. The terminal voltage, however, 
can be varied through all possible values from E to zero. Any- 
thing that may be done to lessen the internal resistance of the 
battery, such as putting several cells in parallel (see Sec. 24), 
will lower the RI drop and correspondingly increase the ter- 
minal voltage E'. After the RI drop has been subtracted from 
the emf. E the balance is the terminal voltage, or that part of 
the emf. which is available for wM)rk in the external circuit. 
The current drawn from the battery must be regarded as flow- 
ing through the entire circuit. As this value of I increases, the 
internal voltage drop in the battery increases, and a corre- 
spondingly smaller fraction of the total emf. is available for 
the external circuit. 

What has been said here of a cell is equally true of any other 
form of genenitor. 

Voltage Drop in the Line. — Suppose that a d. c. generator, 
capable of supplying 118 volts at the outgoing wires of a power 
house, is furnishing current to a distant building for lighting 


lamps which require 110 volts. Suppose that the line resistance 
is 0,16 ohm and that the lamps require 50 amperes of current. 
There is then a line drop of 8 volts, and the available voltage 
at the generator is just right to operate the lamps at their 
rated voltage. Suppose, however, that other apparatus near 
the lamps, say, the motor of an electric elevator, is put in 
operation, and that this requires 70 amperes of current. The line 
drop is then increased by 11.2 volts, or 19.2 volts in all, and the 
voltage available at the distant end of the line has fallen to 
98.8 volts. This is not enough to maintain the lamps at full 
brightness and they are dimmed perceptibly every time the ele- 
vator is operated. To correct this difficulty, a new line of lower 
resistance must replace the old one ; that is, the line drop must 
be decreased, so that for the maximum current demand the 
lamps will not fall below 110 volts.'' 

Another example of the line drop is seen in the dimming of 
the lights of a trolley car when the car is starting. The re- 
sistance of the trolley wire is kept low by using a large cross 
section of copper, and the track resistance is kept as low as 
possible by careful bonding at the rail joints. However, a few 
defective joints raise the track resistance and increase the line 
drop to such a degree that the necessary lamp voltage can not 
be maintained when the car starts. 

D. Electric Batteries. 

17. General Description. — An electric battery consists of two 
or more connected cells which convert chemical energy into 
electrical energJ^ The cell is the unit part of the battery, but 
the term " battery " is sometimes incorrectly used to mean one 
cell. The essential parts of any cell are two dissimilar elec- 
trodes, such as zinc and carbon, immersed in an electrolyte in 
a suitable jar or container. The electrolyte is a solution of 
certain acids, hydroxides, or salts in water, according to the 
type of cell. 

'' Prohlem. — Assuming that the distance from power house to lamps is 
one-eighth mile, calculate the resistance of the line which is necessary 
to maintain the lamp voltage at 110 volts while the elevator is oper- 
ating. Find also the size of copper wire which should be used for 
this line. 


There are a iuiml>er of different kinds of cells in common 
use. These are classitied as primary or secondary cells. The 
most familiar primary cell is the dry cell. Secondary cells are 
storag:e cells or acciinmlators. The distinction between primary 
and secondary cells is based on the character of the chemical 
reactions which occur in them. Primary cells can not be 
charged by an electric current. When they are exhausted 
they are discarded or provided with new electrodes and new 
electrolyte when this is possible. Storage cells, on the other 
hand, convert chemical energy into electric energy by reactions 
which are essentially reversible ; that is, they may be charged 
by an electric current passing through them in the opposite 
direction to that of their discharge. During this process electric 
energy is transformed into chemical energy which may be made 
use of at a later time as electric energy. The electricity is not 
stored as electricity by these cells. 

The capacity of a battery may be specified as the quantity 
of electricity which it will deliver under given operating condi- 
tions. It depends, among other things, on the temperature, 
current delivered, lowest voltage permissible at end of service, 
and the nature of the service required. Thus the capacity of a 
storage battery is usually given in ampere-hours (see sec. 5) 
under specified operating conditions. 

Cells may l)e connected together to form batteries by con- 
necting them in "series" or in "parallel." (See Sec. 24.) 
When cells are connected in series, the positive terminal of one 
cell is connected to the negative terminal of the next cell and 
so on to the end of the group. The voltage of such a group is 
the sum of the voltages of the individual cells. The ampere- 
hour capacity of such a battery is no more than the ampere-hour 
capacity of a single cell. Cells are connected in parallel when 
all the positive terminals are connected and all the negative 
terminals connected together. The voltage- of such a group is 
no more than that of a single cell, but the ampere-hour capacity 
of such a battery is the sum of the capacities of all the cells. 
Sometimes groups of cells are connected in series and the groups 
are connected in parallel making a series-parallel arrangement, 
but the most familiar grouping is the simple series connection. 
Cells to be connected in parallel should be of the same type and 



18. Simple Primary Cell. — The simplest form of primary cell 
is made of a strip of copper and a strip of zinc immersed in 
water acidulated with sulphuric acid. Such a cell is illustrated 
in Fig. 27. If the zinc is sufficiently pure to be free from local 
action (see below), no visible action will take place until the 
zinc and copper are connected by a wire. The strips are, how- 
ever, at different potentials with respect to each other and when 
they are connected by a wire a current of electricity will flow 
in the wire. As this action progresses, the strip of zinc will 
pass into solution and bubbles of gas will appear on the copper 
strip. The electric current flows from copper strip through the 
wire to the zinc strip and from the zinc strip through the liquid 
to the copper. The current is transported through the liquid, 
which is called the " electrolyte," by particles of molecular size 
that carry electric charges. These particles are called " ions." 







- - 

^1 r 




5imt>le. Voltaic Cell 

storage Eatfery ^Kar^in^ 

The external circuit is connected to the cell at its terminals or 
" poles." The copper terminal is usually called the positive 
terminal and may be indicated by a + sign. Similarly the zinc 
is the negative terminal. When a voltmeter is used to measure 
the voltage of a cell or to determine its polarity, the voltmeter 
terminal which is marked + is always to be connected to the + 
terminal of the cell. To avoid an ambiguity that sometimes 
arises in the designation of the positive and negative electrodes 
of the cell, the exact terms " cathode " and " anode " may be 
used. The cathode is the electrode toward which the ions with 
positive charges move while the ions with negative charges 
move to the anode. The cathode terminal is the one which we 
have defined above as the positive terminal. The anode terminal 


similarly is the negative terminal. This is the generally accepted 
convention as to positive and negative terminals. When a cell or 
battery is represented in the diagram of a circuit, it is customary 
to represent each positive terminal of the cell by a long thin 
line and each negative terminal by a short thick line. 

The simple cell which has been described above is subject to 
limitations in actual use, and it is therefore desirable to employ 
other primary cells that are better adapted for the service 
required of them. These will be described in the next section. 
It is convenient, however, to describe here the difficulties which 
arise in using the simple zinc-copper cell to illustrate the mean- 
ing of the terms "local action," "polarization," and "internal 
resistance," which are frequently used. 

Local action is the wasting of the zinc when the cell is 
not in use. If zinc of absolute purity could be used, it would 
pass into solution only when the cell was furnishing current to 
the outside circuit. Zinc generally contains impurities, and 
each little particle of foreign matter acts with adjoining zinc 
particles to make a tiny cell on the surface of the zinc. The 
result is that the zinc is continually passing into solution at 
many places with the evolution of bubbles of a gas, which is 
hydrogen. Each of these little parasitic cells gives rise to a 
current of electricity, useless for practical purposes, in the 
inmiediate vicinity of the foreign particle. Hence the wastage 
of the zinc is commonly called local action. It was discovered 
many years ago that if the surface of the zinc is amalgamated 
with mercury that the local action is greatly decreased. A 
simple method of amalgamating the zinc is to dip the zinc in 
dilute sulphuric acid and rub some mercury on the zinc with 
a brush. 

Polarization is caused by the film of gas bubbles deposited 
on the copper strip when the cell is in operation. This gas 
is hydrogen, and the amount of it that is produced is propor- 
tional to the current that flows and to the time. This layer 
of hydrogen bubbles produces a voltage that opposes the voltage 
of the cell and it diminishes the surfaces of contact between 
the copper and the electrolyte. This increases the resistance. 
For two reasons, therefore, this layer of gas bubbles diminishes 
the useful output of the cell. The practical result is that the 
voltage and the current which the cell can furnish are con- 


siderably reduced within a short time after the circuit is 
closed. Polarization may be prevented or in a hir^e measure 
reduced by " depolarizers." A variety of chemical substances 
are used as depolarizers. Some of them are solids, some liquids, 
and some gases. In addition, mechanical means, such as shak- 
ing the cell, may also accomplish depolarization. The forma- 
tion of hydrogen bubbles on the cathode is the most familiar 
form of polarization, but there are also other causes for 
polarization that will not be discussed here. 

Tiie internal resistance of any cell is dependent on the kind 
and condition of the cell. The resistance of the cell or battery 
is properly to be considered as part of the resistance of the 
entire circuit — that is, tlie resistance of any circuit containing 
a battery is the sum of the resistance of the external circuit and 
the resistance of the battery. For practical purposes the in- 
ternal resistance of a primary battery may be measured by 
determining tlie change in voltage at the terminals of the 
battery when a known change is made in the current which it 
discharges. If the voltage at the terminals of the battery is Ei 
when the current h is flowing and E2 when current T2 is flow- 
ing, then by Ohm's law the resistance R \vill be 

P_E^^, (17) 

R is not strictly a constant quantity, however. The internal 
resistance of a storage battery is very small and can not con- 
veniently be measured by the above method. Lead storage bat- 
teries in particular have very low internal resistance and for 
this reason can deliver very large currents. It is dangerous to 
short-circuit a storage battery, since excessively large currents 
will be produced, which may cause fusing of the terminals and 
other damage. Since lead storage cells have particularly low 
internal resistance, it is especially dangerous to short-circuit a 
lead battery because a very large current may flow. 

19. Types of Primary Cells. — Although a potential difference 
may be observed whenever two dissimilar conductors are im- 
mersed in any electrolyte, certain combinations give more volt- 
age, more output, or possess other desirable features, so that 
they have become the practical primary cells in use at the 
53904°— 22 5 


present time. The desirable qualities of a primary cell are 
large voltage and large current capacity, low internal resistance, 
freedom from local action and noxious fumes. Dry cells possess 
these characteristics and in addition are readily portable, but 
they are subject to some polarization. Primary batteries are a 
convenient source of electrical energy. In isolated localities 
they may be indispensable, but they are expensive to operate if 
any considerable amount of energy is required, as for lighting 
or running a motor. 

The emf. of a cell depends upon the materials chosen for 
the electrodes and to some extent on the electrolyte, but not 
on the size or arrangement of the electrodes. 

The dry cell is the commonest form of primary eel at the 
present time. Several hundred million are made annually. 
Small dry cells are used in flashlight batteries. The piate cir- 
cuit of an electron tube used for receiving radio signals is 
usually supplied with voltages from 20 to 60 volts, but it is 
necessary to supply only a small current. Small dry cells are 
sometimes used for this purpose and are usually manufactured 
in units of 15 cells in a single container, each cell being f by 1| 
inches. The most familiar dry ceil is 2^ inches in diameter and 
(5 inches high and weighs about 2 pounds. This is frequently 
called the No. 6 size. A larger size, the No. 8, which is 3^ by 
8 inches, is less commonly made and weighs 5^ pounds. There 
are other sizes also, which are described in Circular 79 of tlie 
Bureau of Standards, entitled " Electrical Characteristics and 
Testing of Dry Cells." 

Dry cells are so called because the electrolyte is held in an 
absorbent material which permits the use of the cell in any 
position. The cell is, however, not dry. Ordinarily the zinc 
serves as the container for the cell and as one electrode. The 
electrolyte consists of a water solution of ammonium chloride 
(sal ammoniac) and zinc chloride. This electrolyte is held 
partly by an absorbent material that lines the zinc container 
and partly by the black mixture of ground carbon and man- 
ganese dioxide which is the other electrode. This mixture is 
bulky and occupies most of the interior of the cell. The electri- 
cal connection from the mixture of carbon and manganese to 
the positive terminal of the cell is made by means of a carbon 
rod embedded in the center. The manganese dioxide is the 


depolarizer. During the discharge of the cell this is reduced to 
a lower state of oxidation. 

The most familiar method of construction for the larger sizes 
made in this country is the paper-lined method. Before the cell 
is filled with the depolarizing mixture a lining of pulpboard is 
placed in the cell. This serves a double purpose. It is an ab- 
sorbent for the electrolyte and it separates the manganese-diox- 
ide mixture from the zinc. If the manganese dioxide were in di- 
rect contact with the zinc, an internal short circuit would result. 
Bag-type cells on the other hand are so called from the fact 
that the depolarizing mixture is contained in a cloth bag which 
is surrounded by the electrolyte in the form of a paste or jelly. 
This latter method of construction is generally used in the 
smaller cells for flashlight batteries and is commonly used in 
the European cells of all sizes. 

The open-circuit voltage of the dry cell is about 1.5 volts. Its 
maximum or short-circuit current depends on the size and kind 
of cell. No. 6 cells of American manufacture for ignition pur- 
poses will ordinarily give 25 to 35 amperes on short circuit, 
telephone cells and bag-type cells from 15 to 25 amperes. A test 
of the short-circuit current is of value only in showing the uni- 
formity of cells. In no case should dry cells be used where such 
excessive currents are required. Dry cells are intended pri- 
marily for intermittent use, but may be used continuously for 
small currents. The current which can be supplied economi- 
cally by the No. 6 size cell depends upon the duration of its use. 
For one-half of one hour per day, 1 ampere is not excessive, 
four to eight hours per day, one-fourth of an ampere, and for 
continuous service 0.1 ampere are reasonable currents. 

Dry cells deteriorate even when not in use. In general, the 
smaller sizes deteriorate faster than the larger sizes. This de- 
terioration can be considerably retarded by keeping the cells 
and batteries in a cool, dry place. Dry cells should not be al- 
lowed to freeze. 

Another form of dry cell is the silver-chloride cell, which is 
made in small sizes and used in apparatus in which a cell is 
required for intermittent service over long periods of time. 
The depolarizer in this cell is silver chloride. The positive 
electrode is silver and the negative electrode zinc. The open- 
circuit voltage is 1.0 volt and the maximum current which it 


can give is from 0.5 to 1.0 ampere. These cells do not deteri- 
orate ordinarily when standing idle. The ampere-hour ca- 
pacity of this cell is small. 

Closed circuit cells are intended for use where a continuous 
flow of current is desired. Such cells must be free from polari- 
zation and must possess large ampere-hour capacity. Railway 
signaling and ordinary telegraphy with wires are typical ex- 
amples of this type of service. The gravity cell has been ex- 
tensively used for these purposes. It consists of a copper elec- 
trode in a saturated solution of copper sulphate, above which 
is a lighter solution of zinc sulphate surrounding a zinc elec- 
trode. The voltage of this cell is about 1 volt, but it has con- 
siderable internal resistance. Caustic-soda cells are now more 
commonly used for this purpose, since they have a much lower 
internal resistance and require less attention. Zinc plates form 
one electrode, the other being copper and copper oxide, which 
serves as the depolarizer. The electrolyte generally used is a 
20 per cent solution of caustic soda (sodium hydroxide). The 
working voltage of this battery is from 0.6 to 1.0 volt, depend- 
ing upon the rate of current discharge and the length of time 
that it has been in service. When these cells are exhausted, 
they may be renewed by preparing a new electrolyte and insert- 
ing new elements, which are usually assembled as a single unit. 
This battery is a development of the Lalande battery. 

Leclanche cells have elements similar to the ordinary dry cells, 
but are frequently referred to as " wet " cells in contrast to the 
dry cell. The electrolyte is a solution of sal ammoniac con- 
tained in a glass jar. They are made in various forms and are 
intended for bell ringing and other light and intermittent service. 
A cheaper form, commonly called the carbon-cylinder battery, is 
also used for similar purposes. This consists of a zinc rod and 
cylinder of carbon without depolarizer, in the solution of sal 
ammoniac. The voltage of such a cell is about 1.4 volts and it 
can yield several amperes momentarily. It polarizes rapidly, but 
the gas collecting on the carbon cylinder has opportunity to 
diffuse during periods of idleness. Other forms of primary 
cells are of less importance and will not be discussed here. 

For bell ringing and similar work in which alternating current 
can be used, batteries are sometimes replaced by small trans- 
formers rated at only a few watts, which are connected to the 


a. c. electric-light supply and deliver about 10 volts at their 
secondary terminals. (See Sec. 58.) 

20. Storage Cells. — Storage cells differ from the primary cells 
described above, since they may be charged and discharged many 
times without any renewal of the electrodes or electrolyte. 
When a storage cell is discharged, the current flows from the 
positive terminal to the external circuit and back to the cell 
through the negative terminal, as in the case of primary cells, 
which were described above. It is important to be able to dis- 
tinguish the positive terminal of the storage battery, particularly 
for charging purposes. It is frequently marked with a plus sign, 
or the letters POS, or a red spot of paint, or a red bushing 
around the terminal post. When the polarity of the battery can 
not be determined by any of these means, a voltmeter should be 
used to determine the polarity. 

The open-circuit voltage of a storage cell depends entirely 
upon its chemical composition and in no way upon the size or 
number of the plates. The capacity of a storage cell is usually 
expressed in terms of ampere-hours at a certain rate of dis- 
charge at normal temperature. If a cell is described as 100 
ampere-hours at the 5-hour rate, it means that the battery will 
deliver 20 amperes for 5 hours, the product of the hours and the 
amperes being 100 ampere-hours. If the battery is discharged 
more rapidly than this, the capacity will be proportionately less, 
and at lower rates of discharge it will be somewhat greater. 

Storage cells are usually connected in series as described 
above. The capacity of such a battery in ampere-hours is the 
same as that of a single cell, but the voltage is equal to the 
sum of the voltages of the individual cells. It is not desirable 
under ordinary circumstances to connect storage cells in 

There are two general types of storage batteries of practical 
importance. These are the lead-plate batteries, containing acid 
electrolyte, and the nickel-iron batteries, containing alkaline 

Lead batteries consist of lead plates immersed in a solution 
of sulphuric acid. The jar or container for portable batteries 
of this type is usually of a hard-rubber compound, but larger 
batteries, which are used in a fixed position, are generally 
contained in glass or lead-lined tanks. The lead plates for 










FOOT or 










Flu. 29. — Storage cell. Lead plate acid electrolyte type. 


the portable types of batteries are usually of the " pasted " 
variety. These consist of a flat frame or grid, which is made 
of an alloy of lead and antimony, into which the active mate- 
rials in the form of a paste made from lead oxides are 
pressed. The structure of the grid is such as to hold the 
active materials in place after they have cemented into a 
solid mass. Plates which are made in this way are then 
•' formed." This consists of a prolonged charge from a source 
of direct current, which oxidizes the plates intended for posi- 
tives until the active material of the plate is transformed into 
lead peroxide, which is the familiar brown material of the 
positive plate. The negative plates are reduced from the oxide 
condition of the paste to sponge lead, which is of a dull gray 
color. In making a cell, the required number of positive 
plates are welded to a connecting strap, forming the positive 
group. Similarly, the negative plates are made to form an- 
other group which will interleave with the plates of the posi- 
tive group. There is always one more negative than positive 
plate in the cell. To prevent a metallic connection within the 
cell, separators are used between the positive and negative 
plates. These generally consist of thin sheets of wood. In addi- 
tion to the wood separators, perforated or slotted rubber sepa- 
rators are sometimes used. A cell of the lead plate type, in 
which both kinds of separators are used, is shown in Fig. 29, 
page 68. The complete cells are joined together to form a bat- 
tery by connectors which are made of an alloy of lead and 
antimony. These connectors are welded to the terminal posts 
of the cells, but this process is usually referred to as " lead 

The nickel-iron batteries consist of plates that are made 
of steel grids. Positive plates have round tubes which contain 
a nickel oxide as the active material. The negative plates have 
thin rectangular pockets containing iron in a finely divided 
state. The electrolyte for these batteries is a solution of 
potassium hydroxide, to which certain other substances are 
added. The cells are contained in a steel can, which is elec- 
trically welded together. It is not practicable, therefore, to 
make repairs to these cells in the field. Fig. 30, page 71, 
shows the parts of a nickel-iron cell. The cells are connected 
together to form a battery by means of copper connectors that 


are nickel plated. These are attached to lugs having a taper 
which fits the terminal posts of the cell. These connectors are 
bolted and are not burned on, as in the case of the lead cells. 
Since the containers of these cells are electrical conductors, 
it is necessary that the cells be insulated from one another. 
This is accomplished by a special tray which holds the cells in 
place with space between each of the cells by means of sus- 
pension bosses on the sides of the cells. 

21. Electrical Characteristics of Storage Cells. — The ampere- 
hour capacity of a storage cell is the number of ami^ere-hours 
which can be delivered by the cell under specified conditions as 
to temperature, rate of discharge (i. e., current delivered), and 
final voltage at end of discharge. Thus the manufacturer may 
state that the capacity of a given storage cell is 100 ampere- 
hours at 25° C, when delivering a normal discharge current of 
20 amperes to a final voltage of 1.75 volts at end of discharge. 

Cells of the lead-acid type. — Cells of the lead-acid type have 
an open-circuit voltage of approximately 2 volts. The open- 
circuit voltage, however, does not indicate the state of charge 
of the battery. When a lead cell is being discharged at its 
normal rate, usually given by the manufacturer on the name 
plate, the voltage at its terminals gradually falls from approxi- 
mately the open-circuit value to about 1.75 volts, at which point 
practically the complete capacity of the battery has been de- 
livered. It is not desirable to continue the discharge beyond 
this point, except when the cell is delivering current at much 
more than the normal rate ; for example, at 10 times the normal 
rate of discharge it is permissible to continue the discharge until 
the voltage of the cell has fallen to about 1.40 volts per cell. 
The average voltage which the cell can maintain during dis- 
charge varies with the rate of discharge and the construction 
of the cell. The average voltage will be about 1.95 volts when 
discharging at the normal rate and 1.75 when discharging at 
five times the normal rate. As the cell discharges, the specific 
gravity of the electrolyte decreases. This is because lead sul- 
phate forms on both the positive and the negative plates in the 
process of discharging. It is possible, therefore, to estimate the 
state of charge of a lead-acid cell by the specific gi'avity of its 
electrolyte. This may be determined with a syringe hydrometer. 
The hydrometer is a float inclosed in a glass tube having a 



rubber bulb at its upper end, wbicb may be used to draw the 
electrolyte into the tube. The specific gravity of the electrolyte 
is ascertained by the position in which the hydrometer floats. 
For many types of portable batteries the cell is considered dis- 
charged when the specific gravity has fallen to 1.140. 

The nickel-iron cells have an open-circuit voltage which varies 
from 1.45 to 1.52 volts. When these cells are discharging, the 


Positive ^ole 

kle^ti've bote 
. .ndrjd robber 

Cell Cover 

rk^tive Gri 
VJ^tiVe f>ocKe^ 
B'n insulator 

Side InsuUtor 

stsci Conti 

cell bottom 

Cof>|>er wire 
Cell <,over 

Qldnd n'n^ 
Stoffin^fe, box ^SKet 

Weld tb Cover 
S^acin^ Wdsher 
Connecting rod 
Positive ^rid 
C\r\d se^aarvitor 
Seamless .stoel rir^s 

fosJtiVe tube^ 

du4>^ension hoa 

Fig. 30. — Storage cell of nickel-iron type having alkaline electrolyte. 

voltage falls gradually from approximately the open-circuit 
value to a final voltage which may be taken as 0.9 volt per cell 
at the normal rate, or as 0.8 volt at twice the normal rate. The 
average voltages during discharge of the cells are approxi- 
mately 1.14 volts per cell at the normal rate, or 1.05 at twice 
the normal rate. The state of charge of the nickel-iron cells 
can not be ascertained by the specific gravity of the electrolyte,, 
as in the case of the lead batteries. 


When storage cells are discharging, the voltage falls gradu- 
ally. The rate at which it falls depends on the current that is 
being drawn from the battery, its state of charge, and the kind 
of cell. The voltage of the nickel-iron cells falls more rapidly 
than that of the lead cells under similar conditions. For this 
reason when cells are used to supply, for example, the current 
to the filament of an electron tube (see Chap. 6), it is necessary 
to adjust the rheostat in the filament circuit occasionally. The 
lead cells are better suited to this purpose than the nickel-iron 
cells. If the latter are used, it will be necessary to readjust 
the current approximately every half hour under ordinary 
operating conditions. 

22. Charging and Maintenance of Storage Cells. — Direct cur- 
rent alone can be used for charging storage cells or batteries 
of either type. If alternating-current power only is available, 
it must be converted into direct current by means of a motor- 
generator set, or synchronous converter, or some type of recti- 
fier. Mercury- vapor rectifiers or a " tungar " rectifier are often 
used. The charging is generally done by the constant-current 
method ; that is, the charging current through the battery is 
held constant by an adjustable resistance at the normal rate 
specified on the name plate of the battery during the period 
of charge. The positive terminal of the charging circuit nmst 
be connected with the' positive terminal of the cell or battery. 
A failure to observe this rule may result in injury to the 
battery. A simple charging circuit is shown in Fig. 28. Dur- 
ing the period of charge the voitage at the terminals of the 
battery gradually rises, so that it is necessary to decrease 
the resistance which is in the circuit to maintain the current at 
a constant value. The amount of current which flows through 
the battery is dependent upon the difference between the volt- 
age of the battery and that of the charging circuit. It is neces- 
sary, therefore, that the charging circuit should have sufficient 
voltage to allow 2.5 volts for each lead cell or 1.7 volts for 
each nickel-iron cell in the battery. The period of charging 
ordinarily consumes from five to eight hours. During the later 
part of the charging period lead-acid batteries begin to gas 
freely, and it is usually necessary to decrease the charging 
rate to prevent excessive gassing and a rise in temperature. 
The finishing rate of charge, as this reduced current is called, is 


approximately 40 per cent of the normal charging rate. The 
nickel-iron batteries, on the other hand, gas throughout the en- 
tire period of charge and no decrease in the rate of charge is 
made. These batteries are completely charged under ordinary 
circumstances in seven hours. It is not advisable to charge 
nickel-iron batteries at less than the normal rate. In charging 
or discharging either type the temperature should not be 
allowed to exceed 110° F. 

The gases which are liberated during the charging period are 
oxygen and hydrogen. These gases form an explosive mixture, 
and it is dangerous to bring any open flame into the room where 
batteries are being charged. Good ventilation should be pro- 
vided. If the connecting wires to a battery under charge acci- 
dentally come into contact for an instant, the spark so formed 
may cause an explosion of the hydrogen and oxygen present. 
The gassing results in a loss of water in the cells, which 
must be replaced. For either type of battery it is desirable 
that this should be distilled water. AVhen it is impossible to 
obtain distilled water, ordinary drinking water may in most 
cases be used. Choking fumes sometimes observed when bat- 
teries are on charge are due to electrolyte sprayed into the at- 
mosphere by the bursting bubbles of gas. 

It is also possible to charge these batteries by what is called 
the " constant potential " or " tapering charge " method. For 
this purpose, the voltage at the terminals of the battery is 
maintained at a constant value throughout the period of the 
charge. The initial charging current may be very large, but it 
decreases automatically as the charging of the battery pro- 
gresses. At the end of the charging period the current will have 
fallen to a value considerably below that of the normal charg- 
ing rate. The time for a complete charge by this method is ap- 
proximately the same as when the cells are charged by con- 
stant current. The advantages of the constant potential method, 
however, are that a large percentage of the charge can be put into 
the battery during a short time and that the regulation of the 
charging current is automatic and may be adjusted to avoid 
most of the gassing of lead cells. For these the charging volt- 
age should be approximately 2.3 volts per cell at the terminals 
of the cell. For the nickel-iron cells 1.7 volts per cell is re- 
quired. To avoid too great a current at the beginning of the 


charge, a small resistance of a few hundredths of an ohm is 
sometimes put in series with the battery. The types of genera- 
tors suitable for charging storage cells are briefly discussed in 
section 102, page 223. 

During the process of discharge of a lead-acid cell, lead sul- 
phate is formed at both the positive and negative plates of the 
cell. If the cell is allowed to stand for a considerable time, this 
sulphate will gradually harden and become more difficult to 
reduce on the subsequent charging. When this has occurred, 
the cell is said to be " sulphated." Sulphation of lead cells is 
generally the result of neglect. It is desirable that a cell which 
has been discharged should be charged promptly. If it is not 
possible to restore a lead cell to its normal condition by charging, 
it may be possible to overcome the difficulty by pouring out the 
electrolyte and filling the cell with ordinary water, again charg- 
ing the cell. The nickel-iron cells may be left in a discharged 
condition without damage. 

Both the lead-acid and the nickel-iron cells show a temporary 
loss of capacity when allowed to stand idle for any considerable 
period of time. This loss of capacity is caused by local action 
within the cells, but they also become sluggish — that is to say, 
they will not give their full capacity after normal periods of 
charging. In such cases it is necessary to completely charge and 
discharge the cells several times to restore them to their normal 

The cells of both the lead-acid type and the nickel-iron type 
show a temporary loss of capacity at low temperatures. Be- 
tween ordinary room temperatures and freezing temperatures 
the cai)acity of the lead cells decreases nearly proportionately 
as their temperature is lowered. The nickel-iron cells, however, 
have a critical temperature which varies with the nite of dis- 
charge. Below this critical temperature the output of these 
cells will be small, but above the critical temperature prac- 
tically their full capacity can be obtained. The critical tempera- 
ture for these cells when discharged at the normal rate is slightly 
above the freezing point of water. If it is necessary to use 
storage cells at temperatures near freezing, the lead cell is to be 
preferred. In hot weather either type of cell may be used, but 
for the lead cell the specific gravity of the electrolyte should be 
somewhat reduced. 


The internal resistance of a storage cell of either kind is 
very small and for many purposes may be neglected entirely. 
The resistance increases toward the end of the discharge to 
more than double the resistance when fully charged. When such 
a cell is recharged, the internal resistance falls again to its 
original value if the temperature remains the same. The internal 
resistance of lead cells is less than for the nickel-iron cells 
of similar capacity. It is dangerous to short-circuit either type 
of cell, since excessive currents may be produced. 

The electrolyte for the lead-acid cells consists of chemically 
pure sulphuric acid and water. The specific gravity of this 
electrolyte varies somewhat with the type of cell and the use 
for which it is intended. Most portable cells, however, require 
an electrolyte having a specific gravity of 1.280. Electrolyte is 
to be added to the cells only in case of loss due to spilling, 
a cracked jar, or necessary replacement of all of the electro- 
lyte due to accumulated impurities. It should never be added 
merely to raise the specific gravity or to replace evaporation. 
When it is necessary to prepare this electrolyte, the water and 
the acid should be mixed by, pouring the acid slowly into the 
the water, stirring constantly. The water should never be 
poured into the acid on account of danger to the person making 
the mixture. This electrolyte should be prepared in an earthen- 
ware or glass jar and never in any metallic receptacle except- 
ing a lead-lined tank. 

The electrolyte for the nickel-iron cells usually consists of a 
\vater solution of potassium hydroxide, to which small amounts 
of lithium hydroxide and other substances have been added, in 
accordance M'ith the manufacturer's formula. Electrolyte for 
these cells should be obtained from the manufacturers. It may 
be obtained in either liquid or dry form. If it is in the dry 
form, it must be dissolved in pure water, in accordance with 
the directions on the package. The electrolyte in these cells 
does not change in density as the cells are charged and dis- 
charged, but a gradual diminution of the density is observed 
when they have been in use for a long time. When first pre- 
pared, the electrolyte should have a density of about 1.220. 
The electrolyte should be renewed when the density has fallen 
to 1.160. In some cases sodium hydroxide has been used as 


the electrolyte for these cells. This is a cheaper material, but 
the potassium hydroxide electrolyte is to be preferred. 

The Bureau of Standards has issued Circular 92, " Operation 
and Care of Vehicle-Type Batteries," which contains additional 
information on tliis subject. The care and use of both the acid 
and the alkaline types of storage cells are treated in Signal 
Corps Training Pamphlet No. 8. (See p. 576.) 

E. Electric Circuits. 

23. Current Flow Requires a Complete Circuit. — In order to 
maintain a steady flow of current, there must be a continuous 
conducting path. This path is called the " electric circuit," and 
it must extend out from the generator and back to it again. 
The amount of current which flows will be larger as the re- 
sistance of the circuit is less. If some part of the circuit is 
made of very high resistance material, the current which is 
maintained is relatively small. The complete circuit consists 
of two parts, (a) the external part of the circuit, which con- 
nects the poles of the battery or dynamo outside; and (&) the 
internal part of the circuit, which is made up of the liquid 
conductor of the battery or the wires in the dynamo. When 
the wire of a complete circuit is cut and the ends separated, 
the circuit is said to be opened or broken. If the ends of the 
wire are again joined, the circuit is said to be closed. 

Current Value Does not Vary Along the Cireuit.—TYie begin- 
ning student often has the idea that a current may start out 
from a source at a given strength and then in some way be- 
come used up or dwindle away as it goes on along the circuit. 
This is entirely a wrong conception and, at the outset, it must 
be understood that in simple circuits for steady currents, in 
which we are dealing with resistance only, the current has the 
same value at every point in the circuit which is under con- 
sideration. As an illustration of this, consider the circuit of 
Fig. 31, made up of a battery or dynamo G, a lamp e, and a 
resistor R. If the circuit is cut at a, b, c, or at any other 
point, and a current-measuring instrument (an ammeter) in- 
serted, it will indicate the same value of current. What this 
value may be is determined of course by the voltage applied 
and the total resistance in the circuit, but whatever its value, 


it is constant throughout the circuit. This is not necessarily 
the case with a.c. circuits, whicli liave distributed capacity 
effects, especially with the high-frequency alternating currents 
used in radio communication. (See Sec. 139.) But for the 
ordinary low-frequency alternating currents used commercially 
for lighting and power, the current has practically the same 
value in all parts of the circuit. 

The same idea may be applied to a circuit such as that shown 
in Fig. 32. The total current / divides at a into two parts, 
ii and h. The sum of these components is exactly equal to /. 
In other words, whatever current flows up to the point a, flows 
away from there. Also the currents ii and f- unite again at & 
to form the current /, which has the same value as before. 

Another important law is that the sum of the voltage drops in 
every part of the circuit, including the generator, is equal to 
the emf. of the generator. This has already been explained 
in connection with Ohm's law. Section 16. 

24. Series and Parallel Connections. 

(a) Resistances in Series. — If several resistors are connected 
as shown in Fig. 33, so that whatever current flows through 
one of them must flow through all the others, they are said to 
be in " series." The single equivalent resistance which may 
replace the entire group without changing the value of the cur- 
rent, is equal to the sum of the separate resistances. This may 
be proved as follows. The voltages across Ri. 7?2, Rs, etc., may 
be represented by Ei, E2, E3, etc. We may then write 

E 2=1^2! 

Since the over-all voltage between a and h is the sum of the 
voltages across the separate parts of the circuit, we may write 
for the total voltage E, 

=IR (18) 

w^here R replaces the sum of all the terms in the brackets and 
is seen to be the sum of the separate resistances. 



If a number of equal resistances are connected in series, we 
may write for the equivalent resistance of the group, 

R=nr (19) 

where n is the number and r is the resistance of each, ^yhen 
resistonccs are connected in senes, it must be remembered that 
the current throuf/h each resistance is the same and the total 
voltage is subdivided among the various parts of the circuit. 
(&) Resistances in Parallel. — If several resistances are con- 





^\AA/ vVVVvVV\,^ 1 








+l'l"l'_ A' 



tlectric Circuit. 

Divided Circuit 






ItRi \"t 


WW — 






_E , 


jtAncoS in P<ardllcl 

nected as shown in Fig. 34, so that only a part of the current 
passes through each resistance, they are said to be connected in 
** parallel " or " multiple." The voltage E between points a and 
h is the same over any branch. We may then write, from 
equation (11), 





Since the total current must be the sum of the three branch 
currents, we may add the throe equations and 



E Ri R2 R3 



From equation (9) it appears that tlie voltage divided by the 
current gives the resistance, hence the left-hand member of equa- 
tion (20) is the reciprocal of the equivalent resistance, or j^- 


Two resistances in parallel occur so often in practice that it 
is well to consider this case further. Solving equation (21) 
for R when there are only two component resistances we have. 

Thus, two resistances in parallel have a joint or equivalent re- 
sistance, given by the product of the resistances divided hy 
their sum. 

When there are a large number of single resistances, all of 
the same value, in parallel, it can be shown that the equivalent 
resistance of the group is given by 

R = - (23) 

where r is the value of one resistance, and n is the number of 

^Yllen resistances ore connected in parallel it must he remem- 
bered that the voltage across ah, Fig. 3Jf, is constant, and the 
total current is subdivided among the several hranches.^ 

(c) Batteries in Series and Parallel. — It is frequently neces- 
sary, when using batteries, to increase the effect which a single 
cell can produce. This is done by connecting the cells in any one 
of three ways : 

1. In series. Here the + side of one cell is connected to the — 
side of the next one, and so on for all the cells. (Fig. 37.) 

2. In parallel. In this case all the + terminals are connected 
together and all the — terminals are connected together. 
(Fig. 38.) 

^Exercise 1. — A current of 42 amperes flows in a circuit. Fig. 35, 
land divides into three parts in the three branches, of resistance 5 
53904° — 22 6 



3. In a combination of series and parallel groups. Several 
groups of cells in series may be connected in parallel, Fig. 39, or 
several groups of cells in parallel may be connected in series. 
(Fig. 40.) 

The proper combination to use in any given case is dependent 
upon circumstances, but in general a series arrangement builds 

5 ohms 


I 5 Vo/tS 

r» 1 ohm 

S ohms 

^A 6 obms / 

Fig 35 
Resistances connected in Rirailel 

Fig. 36 
Resistances connected in 

up voltage, but at the same time it increases the internal resist- 
ance, while a parallel arrangement, by decreasing the internal 

'ohms. 10 ohms, and 20 ohms, respectively. Find the current in each 

Solution. — The total resistance R between a and b is given by 

R 5 ^10^20 

r> 20 , 
iJ— -=- ohms. 


The RI drop between a and & Is, from equation (10), E=jX 42=120 
volts. The several currents may then he calculated from Ohm's law. 

• 120 „, 
ij=-^=24 amperes. 

120 ,„ 
tio= T7r=12 amperes. 

123 „ 
t'.o=-2«=6 amperes. 

Exercise 2. — A battery of internal resistance 1 ohm and 15 volts 
emf. is sending current through a circuit with resistances as shown in 
Fig. 86. Find (1» the total current. (2) the RI drops across resis- 
tances marked 1, 4, and 5 ohms, (3) the currents through the resistances 
marked 1, 4, and 5 ohms. 



resistance, permits greater current to flow. If we represent the 
number of cells by n, the emf. of each cell by E, the internal re- 
sistance of one cell by r, and the external resistance by R, we 
may write Ohm's law for each of the above cases. 
For series arrangement, 

^ nE 





Cells in Series 

FtQ -yr 


J- ; . -J. ; i ; p 

Cells in f5»rAlle/ 

FlQ :2)6 

Three Series Groups ir> Parallel 


Three Pdrdllef Group's in 5eries 

Fiq ^O 

For parallel arrangement. 





For n cells in series in each group, and m such groups in 


~r^ (26) 




If it is desired to build up a large current through R with a 
given number of dry cells, especially when their internal resis- 
tance has become relatively large through age, a series arrange- 
ment may actually cause the internal resistance to increase 


faster than the voltage. Hence, adding cells in series would 
result in a decrease of current. The best use of a given number 
of cells to produce a stated current, under fixed external circuit 
resistance, can only be determined by a careful application of 
Ohm's law and the above equations, having the entire circuit in 

In general the largest current from a given number of cells 
will be obtained when they are so grouped that the internal re- 
sistance of the battery is equal to the external resistance of the 
circuit. Batteries will be connected in series when the external 
resistance is large, and in parallel when the external resistance 
is small. In lighting systems, with many incandescent lamps in 
parallel, the lamp resistance is large compared to the line re- 
sistance, and very nearly the full voltage is realized at the 
lamp socket. 

25. Divided Circuits. The Shunt Law. — Electric circuits are 
frequently arranged so that the total current is subdivided, and 
made to flow through two or more branches in parallel. As 
shown in Fig. 41 the total current / divides into two parts, 

* Exercise. — Assume a battery of two dry cells in series, each cell 
having an omf. of 1.5 volts and an internal resistance of 0.3 ohm. 
Each battery then has an emf. of 3 volts and an internal n^sistance of 
0.6 ohm. Suppose that the external resistance in the circuit is 0.2 
ohm, and that a current of 6 amperes is to be established. 

Solution. — If we try one battery, Ohm's law gives 

This is not enough current, so we try two batteries in series, 



2^1 2 '=^-^ ampere"?. 

The current is still too small and it is seen that although the voltage 
has been doubled, the current has only been increased by about 14 
per cent. Trying three batteries in series, 


=4.0 amperes. 

0.2 + 1.8 

This is still too small and only represents an increase of 20 per 
cent, although the voltage was increased threefold. We will now try 
an arrangement of two batteries in parallel, 

7= ?rH^=6.0 amperes. 



ii and ia, wliicli flow in branches ri and Vn, respectively. When so 
arranged, either branch is called a shunt (side track or by-pass) 
with respect to the other. The voltage between points a and & 
is of course the same over either of the branches. We may then 


. E 

Dividing (a) by (&) we have 




Hg. 41 5Jiu.r)t Circuit 


MeAaoremen'T of Currervt by RjtenTio meter 

riQ ^■•i 


5irnt>lc Potentcomoter 

FiCi 4Z 

The currents in the two branches are inversely proportional 
to the resistances of their respective paths. This relation is 
called the " shunt law." In other words, it means that the 
branch of lower resistance carries the larger current, and the 
branch of higher resistance carries the smaller current. 

This law is of constant application in electric circuits. Sup- 
pose that the only ammeter available is one with a scale range 
of 0-5 amperes, and suppose that a current of 50 amperes has to 


be measured. The shunt hiw at once suggests that we may pro- 
ceed as follows : With 50 amperes flowing in the main circuit, 
and with 5 amx)eres as the safe current through the ammeter, 
a shunt s must be provided capable of carrying the rest of the 
current or 45 amperes. We may then write from equation (27), 

ia 5 s 

ZrvrT (28) 

where r is the resistance of the ammeter, s is the resistance of 
the shunt, fa is the current through the ammeter, and is is the 
current through the shunt. 

Then *="q ^ 

Thus to carry the required amount of current, the shunt re- 
sistance must be one-ninth of that of the ammeter. 
Equation (28) can be written 


1+^ = 1+-, and 

Hence if we write / for the total current v+^s, 



The factor — — - is called the " multiplying factor " of the 

shunt, and is in the above case equal to 10. 

26. The Potentiometer.^" — The potentiometer is primarily 

an arrangement of circuits for measuring potential difference or 

voltage. With the aid of certain accessories it can be used for 

measuring voltages over all ranges, and by means of Ohm's 

law these measurements can be applied to the determination 

^^ The word " potentiometer " is used here in its original sense, mean- 
ing an arrangement of circuits for measuring potential difference. In 
apparatus catalogues and in textbooks on radio circuits the word is 
often inaccurately used in the sense of a voltage divider. (See 
Sec. 15.) 


of a wide range of current values. A uniform homogeneous 
wire, usually a meter or more in lengtli (Fig. 42), is stretched 
between binding posts on a baseboard, by the side of a grad- 
uated scale. In series with this wire is a constant source of 
current, usually a storage battery WB and a variable resistor 
R. From equation (10) it is clear that by properly adjusting 
R the voltage between A and B can be varied through wide 
limits. Let us assume that (1) the end A is connected to 
the + side of the battery WB, (2) the resistance of AB is 
uniform from end to end, and (3) the current through AB 
is constant and of such a value that the RI drop along the 
wire is about 2 volts. If a standard cell, of voltage E (about 
1.0183), has its + pole connected to the point A, a certain 
point Ci can be found, such that when contact is made at this 
point, the galvanometer g (see Sec. 60) will show no deflection. 
The absence of deflection on the galvanometer means that the 
RI drop in the wire AB up to the point Ci is just equal, and 
opposed to the voltage of the standard cell. The distance Aci 
may be represented by di. Now let some other cell E', whose 
voltage is to be tested, be put in place of the standard cell E. 
If the voltage of this cell does not exceed the RI drop in AB, 
another point Co can be found, for which there is no current 
through the galvanometer. The distance Ac2 may be called d2, 
and the RI drop over this length of wire is just equal and op- 
posed to the voltage of the cell E' to be tested. Since the RI 
drops along the wire are directly proportional to the lengths, 
we may write 



£'=4 (30) 


This simple form of the apparatus is only capable of measur- 
ing a voltage not much greater than that of the standard cell. 
If very much higher voltages are to be measured, the high volt- 
age is put across the terminals of a voltage divider (Sec. 15), 
and some definite fraction of it is then measured against the 
standard cell, as described above. 

Also, any range of current can be measured by means of the 
potentiometer. The current to be measured is passed through 


11 standard resistance ab of known value R, Fig. 43. This is so 
chosen that the RI drop across it lies within the voltage range 
of the potentiometer. The determination of current then con- 
sists in measuring the voltage across ah in terms of the stand- 
ard cell, and calculating the current by Ohm's law. 

27. The Wheatstone Bridge, — This is a simple circuit for 
n-.easuring an unknown resistance in terms of a known re- 
sistance. The method depends upon the fact that in a branched 
circuit, Fig. 44, the voltage drop from a to c must be the same 
over the path ahc as it is over the path aclc. It then follows 
that for any point b which may be chosen on the upper circuit 
ohc there must be some point d on the lower branch, such that 
there will be no difference of potential between it and the point 
h. The point d can be found by connecting one terminal of a 
galvanometer at b and moving the contact point connected to 
tlie other terminal along the lower wire until there is no de- 
flection. This means that there is no current flowing, and 
hence no potential difference between b and d. When the points 
b and d have been located in this way, it can be shown that 
there is a simple definite relation between the resistances of the 
four arms of the circuit. (See Fig. 45.) 

If /p is the current through the top branch and It is the cur- 
rent through the bottom branch, then the voltage drop between 
a and b is rJv, and is equal to rjt, the voltage drop between 
a and (/. Hence 

ri Ip=r^I„ and -} = / 

'3 ■'p 

Likewise it is seen that 



Ip=ri It, and ^=y 

'4 -^p 

»-4 = ^3^ (31) 

If three of the resistances are known, the fourth, r*, can be 
easily calculated from this equation. 

In practice the branch adc may be made from a long, uniform, 
and homogeneous wire, in which case it is not necessary to 
know the resistance values. If the portion abc is such a wire, 


the ratio of the length h and h of the segments will be the same 
as the ratio of the resistances. The equation (31) may tlien be 

^4=^3 -=^'3 r 
'1 n 

28. Heat and Power Losses. — In Section 7 it was shown that 
when current flows through a resistance, heat is generated in 
it. It is important to understand that this effect does not refer 
to heating the resistor to a definite temperature, but rather it has 
to do with the generation of heat at a definite rate. This rate 
may be expressed in joules per second, calories per second, 
watts, or horsepower. When the rate of supply of heat due 




1 b "2 

^/ (r^ \^ 


^ © y^ 


Fig. 44 


T / 

Fig. 45. 

5imple Branched Circuit. 


of the Wheatstone Bnc/ge 

to the electric current i^ just equal to the rate of loss of heat 
by conduction or radiation, then the temperature becomes con- 
stant. The final temperature of any resistance coil through 
which current is passing depends upon its surroundings. If 
it is open to the air, radiation is more free. In coils which are 
inclosed, the temperature may rise rapidly and unless care is 
taken, the insulation may be softened or even burned. 

When the heat is dissipated at as fast a rate as it is pro- 
duced, so that the temperature of the resistor remains con- 
stant, the resistance becomes constant. 

Equation (2) is W=RPf (2) 

Since from Ohm's law, /= -^ we may write 


W=R'^,t=j^t (32) 


Again substituting 

«\'e liave 

x? = -jp> 

W=^=EIt. (33) 

These three equations will give the energy in joules when 
amperes, ohms, volts, and seconds are used. 

Power is the time rate of change of energy. If the three 
equations above are divided by the time t, we have the corre- 
sponding three equations for power. 


P = j = Rr- . (34) 

P=§ (35) 

P=EI. (36) 

Exercise 1. What power is required to operate 1,000 incandescent 
lamps, each of which requires I ampere and 110 volts? 
First solution. — From equation (36), each lamp requires 

For 1,000 lamps — 


J X 110=55 watts. 

1000X55=55,000 watts 

=55 kw. 
746 watts=l horsepower, 

Necond solution. — The resistance of each lamp is given by 

ie=-^= 112= 220 ohms. 

Using equation (34) 

P=220 X 5=55 watts for 1 lamp. 
For 1000 lamps — 

p=1000 X 55=55 kw. 

Exercise 2. — An instrument has 1210 ohms resistance in its coils, 
and a voltage of 110 volts is impressed. Calculate the rate of dissipa- 
tion (watt-loss) in the coils. 



F. Capacity. 

29. Dielectric Current. — So far, only steady currents and their 
flow in conductors have been considered. In a perfect insu- 
lating material a steady current can not flow. If an electromo- 
tive force is applied betvreen two points of an insulator, a 
momentary flow of current takes place which soon ceases. The 
current flow is very different from that in a conductor. If a 
very sensitive indicator of current g, Fig. 46, is connected 


FiQ 47 



LlecTnc Strain or Dl5t>laceme-T 

Simple Circuit iwitn , 

tondenser .V/.^ J ////M///////f^ 



Conitrocti on oif 
Fixed Condenser 

FlQ 46 

into the circuit, it shows a sudden deflection when the key is 
closed. This deflection soon drops to zero. The momentary 
flow of electricity is due to the production of a sort of electric 
strain or " displacement " of electricity. This is resisted 
by a sort of elastic reaction of the insulator that may be 
called electric stress. On account of this reaction of the 
electric stress, the electric strain due to a steady applied emf. 
reaches a steady value, and the current becomes zero. When 
the electric strain is subsequently allowed to diminish, a cur- 
rent again exists in the opposite direction. A current of this 
kind, called a " displacement current," exists only when the 
electric strain or displacement is changing. When considering 


the existence of electric strain or displacement in an insulating 
material, the material is called a " dielectric," and the displace- 
ment current is sometimes called a " dielectric current." 

We do not think of this electric displacement as being due to 
the actual passage of matter, on which the charge is carried 
from one plate to the other, nor even from one molecule to 
another Mithin the substance. It is rather as if, in each mole- 
cule, a positive charge is moved to one end and a negative 
charge to the other. Then with all the positive charges point- 
ing in one direction, the effect is that a certain change has been 
transmitted clear across the dielectric. An illustration may 
aid in making this idea clearer. In a dense crowd of people a 
sudden push or shove on one person will be sent through from 
person to person. Energy is transmitted, and yet no single 
person has passed all the way across. 

When a dielectric is in the electrically strained condition 
it possesses potential energy in the "electrostatic" form. (For 
a brief discussion of energy, see Circular 74, p. 9.) 

30. Condensers. — Displacement is produced in a dielectric by 
placing the dielectric between metal plates and connecting a 
battery or other source of emf. to these plates. Such an ar- 
rangement consisting of metal plates separated by a noncon- 
ducting material is called a condenser. Thus in Fig. 47, A and 
B are the metal plates of the condenser. The dotted lines 
indicate the directions of the electric strain or displacement. 
The plate from which the displacement takes place is called the 
positive or -f plate of the condenser. Conversely, the other 
plate is called the negative or — plate. The dielectric may 
be air or other gas, or any solid or liquid that is not a con- 
ductor. When the battery is connected to the condenser a 
displacement current begins to flow, continuing until the elec- 
tric displacement reaches its final or steady value. The dis- 
placemiMit produced depends upon (a) the voltage applied to 
the condenser and (b) the kind of dielectric. A continuous or 
direct current can flow only in conductors. An alternating cur- 
rent, in which tlie direction periodically changes sign, can 
flow also in condensers in the form of a dielectric current. 
(See Sec. 56.) In this case, the electric strain or displacement 
reverses its direction with every reversal of the current. The 
existence of the electrtc strain or displacement in the dielectric 


is equivalent to the presence of a certain quantity or charge of 

For a given condenser, its charge Q is found to be directly 
proportional to the applied voltage E. This relation may be 

"•"""" Q=CE (37) 

where C is a constant. For any given condenser the value of 
this constant is seen to be the ratio of the charge to the volt- 
age, or Q 

C=| (38) 

This constant C is called the " capacity " of the condenser. 
The unit of capacity is the " farad," which is defined in Ap- 
pendix 2, page 549. This unit is too large for practical purposes, 
and it is usual to use the microfarad, which is one one-millionth 
of a farad, and the micromicrofarad, which is one one-millionth 
of a microfarad. 

The capacity changes when different dielectric materials are 
used. If the plate area is increased, the capacity increases in 
direct ratio, and as the plates are brought closer together, the 
capacity increases. (Formulas for calculating the capacity of 
condensers are given in Circular 74, p. 235, and also in this 
book in section 32, p. 96, and section 170, p. 384.) 

Charging of Condensers. — During the brief time in which the 

charge is accumulating in a condenser, the voltage -7^ due to 

this charge is increasing. This voltage tends to oppose the ap- 


plied or charging voltage. When q has become equal to E, the 

charging process comes to an end. It will be noticed that 
equation (37) does not contain a time factor; therefore the 
same amount of charge is stored in a condenser whether it is 
built up slowly or quickly. However, the rate of building up 
the charge depends upon the value of the capacity and resis- 
tance of the circuit. The larger the product of the factors C 
and R the greater is the time required to arrive at any given 
fraction of the applied voltage. This product CR is called 


31. Dielectric Properties. — A simple experiment will show tliat 
the charge accumulated in a condenser, for a given voltage and 
distance apart of the plates, depends upon the kind of dielectric 



material. A pair of plates with dry air between them is 
charged by a certain emf., and the quantity or amount of 
charge is measured by some suitable means. If now a slab of 
paraffin be inserted between the plates, it is found that for the 
same voltage the charge is increased. Denoting the capacity 
with air by Ca and the capacity with paraffin by Cp, we may 


where K is a. constant. By simply changing the dielectric mate- 
rial, and without changing the geometric arrangement of the 
plates, we find that the capacity has been increased. Air is 
commonly used as the standard of comparison, and the factor 
K is called the " dielectric constant "" of the material. The 
dielectric constant of any substance may then he defined as the 
ratio of the capaHty of a co)idenser using tJiis substance as the 
dielectric, to the capacity of the same condenser irith air as the 
dielectric. This ratio is seen to be the factor by which the 
capacity of an air condenser must be multiplied in order to find 
the capacity of the same condenser when the new substance is 
used. Some values are given below. 





Hard rubber 


Paper, dry 

Paper (treated as used in cables). 

Porcelain, unglazed 







Wood, maple, dry 

Wood, oak, dry 

Moldedinsulating material, shellac base 

Moldedinsulating material, phenolic base ("bakelite"). 

Vulcanized fibre 

Castor oil 

Transformer oil 

Water, distiUed 

Cottonseed oil 

Values of 

4 to 10 

4 to 8 
2 to 4 
2 to 3 

5 to 3. 
5 to 4.0 

5 to 7 
to 4. 2 


to 3. 7 



7 to 10 

to 4. 5 

to 6.0 

4 to 7 
to 7. 5 

5 to 8 





» Sometimes called also " inductivity " or " specific inductive ca- 


A wide variation is seen in tlie values given for some sub- 
stances. Tlie different grades and kinds of different materials 
vary considerably in many of their physical properties, includ- 
ing their electrical properties. For instance, there are a very 
large number of kinds of glass made for different purposes, 
having very different properties. Many substances absorb a 
small amount of water very easily, and in some substances the 
presence of a small amount of water will considerably increase 
the dielectric constant. The value of the dielectric constant 
also depends on the kind of voltage applied and the manner in 
Avhich it is applied. If the current is supplied by a source o-f 
direct current, such as a battery, the values of the dielectric 
constant found when the condenser is charged slowly will 
differ considerably from the values found when the condenser 
is charged rapidly. If the voltage applied is from a source of 
alternating current, the values of the dielectric constant may 
differ considerably from the values for direct current. This is 
particularly true if the alternating current has a very high 
frequency, such as is used in radio communication. For accu- 
rate results the conditions under which the material is to be 
used must be stated. 

Dielectric materials are not perfect insulators, but do have a 
very small electric conductivity. A condenser will permit a 
very small current to flow through it continuously when a volt- 
age is applied to its terminals, and it will discharge itself 
slowly if allowed to stand with its terminals disconnected. 
This is called the " leakage " of the condenser. Materials differ 
greatly in this respect. A pair of plates with dry air as di- 
electric will retain the charge almost indefinitely after the 
voltage is cut off, while in some paper condensers the charge 
disappears by leakage in a few minutes. 

If an emf. gives a condenser a certain charge when applied 
for a short time and a greater charge when applied for a longer 
time, the dielectric is said to possess " absorption." There is a 
gradual penetration of the electric strain into the dielectric 
which requires time. When the terminals of a charged con- 
denser are connected by a conductor, a current flows and the 
condenser discharges. The charge which flows out instantane- 
ously upon discharge is called the " free charge." With some 
dielectrics, if the terminals are connected a second time, an- 
other and smaller discharge occurs, and this may be repeated 


several times. This so-called residual charge is due to the 
absorbed charge, and indicates a slow recovery of the dielectric 
from the electric stress. In condensers rnade with oil or well- 
selected mica for the dielectric, absorption is small. It is larger 
with glass, and very troublesome with bakelite and similar 
materials. After charging such a condenser with a high volt- 
age, the absorbed charge continues to be given up for a long 
time. Absorption is accompanied by the production of heat in 
the dielectric. This represents a loss of energj\ 

The ratio of the free charge of a condenser to the voltage 
across its terminals is called the " geometric capacity." Any 
measurements of capacity which make use of a prolonged time 
of charging yield values larger than the geometric capacity. 
Measurements made with high-frequency alternating currents 
give values which approach closely to the geometric capacity. 

Summary. — An elastic body is distorted or strained by placing 
it under the action of a stress ; and the effect produced is 
measured in terms of the flexibility of the material. A dielec- 
tric substance is strained electrically by placing it under the 
action of an emf., and the effect produced is measured in terms 
of the capacity of the condenser. It is of interest to note that 
the capacity of an electric condenser is directly analogous to 
flexibility or stretchability of an elastic body. 

32. Types of Condensers. — In order to increase the capacity 
of a condenser, we may — 

1. Increase the area of the plates. 

2. Diminish the distance between the plates. 

3. Use a substance of larger dielectric constant. 

In general, condensers are classified in two groups, as they 
may be designed, respectively, for (a) low voltage — less than 
500 volts, or ( 6 ) high voltage — several thousand volts. Increas- 
ing the plate area tends to increase the bulk and weight of the 
condenser. Bringing the plates very close together makes neces- 
sary the use of a substance of high dielectric strength if the volt- 
age is high. For low-voltage service, where large capacity is 
essential, the condenser plates are made of tin foil with thin 
sheets of mica or paraffined paper between them. The sheets 
are piled up as shown in Fig. 48, page 89. The dielectric layers 
are represented by aa, and the two sets of conducting plates by 
bb and cc, respectively. These are pressed into a compact 



form and held in place by a clamp and the composite stack is 
saturated and sealed with melted paraflBn or wax. If the con- 
denser must withstand a very high voltage, the plates will be 
more widely separated, and usually air or oil is used as the 
dielectric. If it is desired to have the capacity of the condenser 
variable instead of fixed, the construction usually takes the 
form shown in Fig. 49, page 9.5. Two sets of interleaved plates 
are insulated from each other, and one set is mounted so that 
it can be rotated with respect to the other. Such a condenser 




Electric Stndkin or Uis^ldcemanT 

Par<j||ef WiVe Antenna 

can be calibrated so that the capacity corresponding to any 
angular setting of the rotating part is known. Condensers used 
in radio circuits are represented by certain symbols. These 
symbols may be found in Appendix 3, page 5.53. 

It is not always necessary that the conducting plates in the 
condenser should be of sheets of metal. The earth is a con- 
ductor and frequently replaces one plate in the system. A wire 
stretched on a pole line forms one plate of a condenser, and the 
other plate may be the neighboring return wire of the circuit, or 
it may be the earth itself. Several wires in a connected group 
will have more capacity with respect to the earth than a single 
wire. Such a condenser is the radio antenna. (Fig. 50.) The 
53904° — 22 7 


conducting core of a submarine cable forms one plate of a con- 
denser, the insulating material is the dielectric, and the sea 
water is the other plate. Similarly in a telephone cable, paper 
is the dielectric, and any single conductor of the cable may be 
regarded as one plate, the other plate being the adjacent wire 
of the pair or the lead sheath of the cable itself. The great 
length of such wires and cables gives them large surface and 
hence large capacity. A mile of standard sea cable may have a 
capacity of about 3 microfarad. A mile of standard telephone 
cable should not have capacity of more than about 0.08 micro- 
farad. The capacity of a pair of No. 8 copper wires, 1,000 feet 
in length and 12 inches apart, is about 0.0032 microfarad. Two 
square plates 10 cm. on a side, separated by 1 mm. of dry air, 
have a capacity of approximately 100 micromicrofarads. 

In radio apparatus, particularly in the more sensitive types 
of receiving apparatus, very small capacities may be of much 
importance, such as the capacity between two short adjacent 
wires, or the capacity between a connecting wire and the walls 
of the room or other adjacent object. A sphere 1 inch in 
diameter has a capacity to the walls of an ordinary room some- 
what over 1 micromicrofarad, and as small a capacity as this 
may be of importance in the design of radio apparatus. 

The capacity of a condenser composed of two parallel metal 
plates of the same size and shape, separated by a uniform 
dielectric, is given by the formula 



where C is the capacity in micromicrofarads, / is the thickness 
of the dielectric layer between the plates in centimeters, S is 
the surface area of one side of one plate in square centimeters, 
and K is the dielectric constant of the dielectric layer. For 
air the value of K is 1, for the kinds of glass ordinarily used 
the value of K is from 7 to 8, for mica K is about 6, for par- 
affin K is about 2.5, and for most ordinary substances the 
value of K lies between 1 and 10. (See Sec. 31, p. 92.) This 
.same formula can be used for a parallel plate condenser hav- 
ing the two plates of different size, providing the area of the 
smaller plate is used for .S' in the formula. For further infor- 
mation regarding the calculation of capacity, reference should 



be made to Circular 74 of the Bureau of Standards, page 235. 
See also section 170 in this book. 

33. Electric Field Intensity. — Consider the air condenser 
shown in Fig. 51, having an emf. E applied across its terminals. 
The emf. is the cause of the electric strain or displacement 
which is in the direction shown by the dotted lines. The emf. 
between the plates of the condenser is equivalent to a force 
acting at every point of the dielectric, which would cause a 
body having a charge of electricity to move. This is called 
the electric field intensity and is defined as the force per 
unit charge of electricity. The space in which this field 
intensity acts is called an electric field. The value of the 
electric field intensity at any point inside tlie condenser shown 

r\o 5Z 

FlCi.53 >^c — .► 

E.lectric rielci between Two 
0|>f>OJif«ly CK^r^ce/ DcxJi'ea 

' I f f * ' > ' 

I ! T 1 > ! 

> I 1 
I I I 
( • I 

I 1 ' 

! I : 

EJectric Field About Vertical 

in Fig. 51 is the ratio of the emf. across the condenser to the 
distance between the plates. Electric field intensity £ is thus 
given by 


where E is the emf. between two points in the dielectric a 
distance d apart. £ is commonly expressed in volts per centi- 
meter. It is a quantity of importance in connection with elec- 
tric waves. 

The electric field in the condenser of Fig. 51 is the same 
everywhere in direction and in value. This is called a uniform 
field. There are many other kinds of fields. The electric field 
about two small unlike charges is shown in Fig. 52. Another 
example is given by two bodies, one of which is a long vertical 


wire and the other is a conductor extended in a horizontal 
direction. These amount to two conductors separated by a 
dielectric (air), thus fulfilling the definition of a condenser. 
Suppose the lower body is the earth itself, w^hich is a con- 
ductor. The field about the system will be represented by 
Fig. 53. This represents the form of condenser and electric 
field in the case of the radio antenna. 

84. Energy Stored in a Condenser. — The electric strain in the 
dielectric of a charged condenser represents a store of energy. 
The amount of energy stored in this way is found as follows. 
The work done in placing a charge in a condenser is the product 
of the charge by the voltage between the plates. Suppose a 
condenser is charged by applying to it an emf. which begins 
at a zero value and rises to E volts. The increase in voltage 
is uniform, and hence the average voltage is ^ E. The energy 
stored in the condenser is the product of this by the charge, 


W=h QE (40) 

Since Q=CE, from equation (37), we may write 

W=^ CE^ (41) 

The work is expressed in joules when the capacity is in farads 

and the emf. is in volts. A capacity of 0.(X)1 microfarad 
charged with an emf. of 20.0(X) volts has a store of energy 

given by 

Tr=*^^X20.0002=0.2 joules 

Fr<»m equation (41) it appears that time does not enter into 
the energy equation. For a given condenser charged to a given 
voltage it requires the same total amount of energy, whether 
rhe charge is acquired slowly or rapidly. 

The total amount of work done in charging a condenser 
divided by the time, gives the rate at which energy is supplied ; 
that is, the power supplied. This may be written, 

P=^ CE'N (42) 

where t is the time in seconds required to complete the charge, 
and .V is the number of charges completed in one second of 



time. If the condenser in the above problem is charged by a 
generator giving an alternating emf. with a frequency of 500 
cycles per second, the power becomes 

P=i C^^V=0.200X 1000=200 watts. 

It will be noted that the condenser is charged and discharged 
twice in every complete cycle of the a.c. generator ; also that E 
is the maximum emf. 

35. Condensers in Series and in Parallel. — Just as it is some- 
times found convenient to combine resistances into series or 
parallel groups, so it is often desirable to combine condensers. 
The capacity of the group, however, is not calculated the same 
way as in the case of resistances. 



Corideniera in Parallel 


Condensers in .Series 


Condensers in Parallel. — Fig. 54 shows three condensers con- 
nected in parallel. The condensers are all under the same im- 
pressed emf,, and they accumulate charges proportional to 
their respective capacities. It has been stated in Section 30 
that capacity is proportional to plate area. Connecting con-, 
densers in parallel is equivalent simply to increasing the plate 
area. If Ci, Co, Cs, etc., represent, respectively, the capacities of 
the condensers of the group, and if C represents the equivalent 
capacity of the entire group, we may then write 

C=C\-\-C,+ C,+ ■ ■ ■ (43) 

Parallel connection of condensers always gives a larger capacity 
than that of any single member of the group. 

Condensers in Scries. — If several condensers are connected 
as shown in Fig. 55 they are said to be connected in series. 
In finding the equivalent capacity of such a group, it must be 


kept ill mind that the same charge is given to each condenser, 
and that the total voltage E is subdivided among the condensers 
in direct ratio to their capacities. Using symbols as above we 
may then write 

or since in general E=j^ 

C Cj L2 C3 

"Whence 7^=7s-+7^+7=r+ • • • (44) 

Series connection of condensers always gives, a smaller 
■capacity than that of any single member of the group. (See 
problems below. ) 

1. A condenser has a capacity of 0.014 microfarari, and it is 
•cliarged with an emf. of 30,000 volts. 

Find (a) the charge in the condenser, (&) the energy stored, (c) the 
power exp^^utled when charged by a oOO-cycle a. c. generator. 

2. A condenser is built up of 15 parallel and circular plates. Each 
plate is 20 cm. in diameter and the separation is 1 mm. Transformer 
■oil is used as a dieletric Calculate the capacity. (See sections .'U, 32, 
pages 92-96, and Bureau of Standards Circular 74, page 235.) 

3. Three condensers have capacities of 0.02, 0.20 and 0.05 micro- 
farad, respectively. Find the equivalent capacity, (a) when they 
are all in series; (b) when they are all in parallel. 

G. Magnetism. 

36. Natural Magnets. — One of the forms in which iron is 
found in the earth is the black oxide of iron (chemical for- 
mula Fe304) called magnetite or magnetic iron ore. A piece of 
this substance is called a '* natural magnet," and it has two 
very remarkable properties as follows : 

(a) If a piece of it is dipped into iron filings the filings 
will adhere to it. 

(6) If a piece of it is suspended by a silk thread, or by a 
thin untwisted cord, it will set itself with its longer axis very 
nearly in a north and south direction. 

37. Bar Magnets. — A small rod of iron or steel which is 
brought near to a piece of magnetite, or which is rubbed on it 



in a certain way, shows the same properties, and is said to be 
" magnetized." If the rod or bar is made of rather hard steel, 
the effect persists after the iron ore has been taken away, and 
the magnetized rod is tlien called a " permanent magnet," or 
simply a bar magnet. These permanent magnets may l)e made 
in the form of straight bars of round or square section, usually 
with the length rather large as compared to the diameter. 
They are also often bent into various shapes, a common form 
being the horseshoe or U-shaped magnet. 

Magnets may also be made by passing an electric current 
through a coil of insulated wire which surrounds the rod. 
(See Fig. 56.) If the rod is made of soft iron, it is only mag- 
netized as long as the current flows. It is then called a tem- 



^X FIQ.57 

Kd^neti-sm by ihe Electric 


Pivoted Mi^ne+ic 

porary magnet or an " electromagnet." Examples of electro- 
magnets are seen in induction coil and buzzer cores, in tele- 
graph sounders and relays, and in telephone receivers. Elec- 
tromagnets are very useful because the magnetism is so easily 
controlled by variations in the current strength. If the bars 
are of hardened steel, the magnetism due to the current re- 
mains after the current ceases and a permanent magnet is the 

A slender magnetized steel rod mounted carefully on a pivot 
(Fig, 57) will turn very nearly into the north and south posi- 
tion, and is called a " compass needle." It is used by sailors 
and surveyors for determining directions. The end which 
points north is called the north-pointing or simply the " north 
pole." The other end is called the " south pole." 

38. The Magnetic Field. — If a compass needle is placed at 
various positions near a large bar magnet, it changes its direc- 
tion as shown in Fig. 58. This shows that in the space all 



around the inajrnet there are forces which act on magnetic 
poles. If iron lilinirs are sprinkled on a level sheet of paper 
which lies over the magnet, the filings arrange themselves as 
shown in Fig. 59. Each little particle of iron acts like the 
c(»mpass needle and points in a detinite direction at a given 
position. These direction lines, called " magnetic lines of 
force," all appear to center in two points near the ends of the 
bar magnet. These points are called the " poles " of the mag- 
net. Two magnetic poles are said to be alike when they both 
attract ()r botli repel the same pole. If one attracts and the 

no se> 



/ < ' \ "^^ ■*=^''4,'- / ' > \ 

I » \ ■•-_ _---,'/ I 

^ -- - / 

LirtCA of force Aroond A txsp ma^n«T .jncj 

^oAitions of e*f>(orir\^" needle 

5cmf>lc theory ©f" 
LArthis magnetic freW 

Md^rteti'c field about a bar m<4^net as ihown 
by iron film^s 

other repels the same pole, they are said to be unlike. Like 
poles repel each other and unlike poles attract each other. It 
is then easy to determine which is the north and which is the 
south pole of a bar magnet by means of the direction in which 
the north pole of a compass needle points. 

The region all about a magnet, in which these forces on the 
poles of magnetic needles may be detected, is called the " mag- 
netic field." The intensity of a magnetic field may be defined 
in terms of the force which acts on a given magnetic pole, or 
it may be defined in another way, as described in a following 
paragraph. The dire<'tion of a magnetic field is defined as the 
direction in which the north pole points. 


The earth has a magnetic field ahout it which is represented 
by Fig. 60. This field is similar to that which would exist 
about a bar magnet placed within the earth with its ends at 
the magnetic North and South Poles of the earth. 

39. Magnetic Flux and Flux Density. — The arrangement of the 
iron filings in Fig. 59 shows that there is a greater effect at 
some points than at others. It also suggests that the lines of 
force may be thought of as similar to stream lines in a moving 
fluid. From this point of view there is said to be a magnetic 
flux through the space occupied by the magnetic field. This is 
represented by lines drawn closer together where the field is 
strong and farther apait where the field is weak. The magnetic 
field must not be thought of as made up of filaments, like a 
skein of yarn, because it really is continuous. However, elec- 
trical engineers represent a magnetic flux by drawing one line 
through the field for each unit of the flux. The number of such 
lines through each square centimeter of the field perpendicular 
to the lines is the " magnetic induction "'or " flux density " per 
square centimeter. A magnetic field has a flux density of one 
line per square centimeter when the unit of magnetic flux is 
distributed over a square centimeter of area, taken perpendicu- 
lar to the dii-ection of the flux. 

40. The Magnetic Field About a Current. — It has already been 
pointed out in Section 3 that there is a magnetic field about a 
wire in which a current is flowing. Experiments with the 
compass show that this magnetic field has lines of force in the 
form of concentric circles about the wire. These circles lie in 
planes at right angles to the axis of the wire. If the wire is 
grasped by the right hand with the thumb pointing in the 
direction of the current, the fingers will show the direction of 
the magnetic field (Fig. 10). This field extends to an indefi- 
nite distance from the conductor, but for points farther from 
the wire the effect becomes more feeble, and the more sensitive 
must be the apparatus for detecting it. If the current stops, 
the magnetic field, together with its effects, disappears. When 
current is started through the wire, we may think of the mag- 
netic field as coming into being and sweeping outward from 
the axis as a center. This disappearing and rebuilding of the 
magnetic field as the current decreases and increases will be 



made use of in Section 46, in explaining some Important prin- 
ciples which apply in radio circuits. 

41. The Solenoid and the Electromagnet. — If the wire which 
carries a current is bent into a circle, the mascnetic field is of 
the form shown in Fig. 61. At the center of the circle the field 
is uniform only for a very small area. If many turns are 
wound close together in what may be called a bunched wind- 
ing, the intensity of the magnetic field is increased in direct 
proportion to the number of turns. When the wire is wound 





CircuUr Coil 




Md^ncTic Field of vSofenoiW 

closely with many turns, side by side along the surface of a 
cylinder in a single layer, the coil is called a " solenoid," Fig. 
62. In this case, the magnetic field is nearly uniform for a 
considerable distance near the center of the coil, and the 
solenoid has the properties of a bar magnet. This is seen by 
comparing the magnetic fields of Figs, 63 and 59. The intensity 
of the field and the magnetic flux density within the solenoid 
depend entirely upon the strength of the current and the num- 
ber of turns of wire per centimeter. The same magnetizing 
effect can be secured with many turns and a weak current, or 
with a few turns and a strong current, provided only that the 
product of wire turns times amperes of current is the same in 
each case. This product is called the " ampere-turns." In 


round numbers the magnetizing field strength, represented by 
the symbol H, is given by 

g^5/ ampeTe-tu j:Ds\ 

4 \length m cm./ ^ ^ 

If / is the current in amperes, N the total number of turns on 
the solenoid, and I the length of the solenoid in centimeters, the 
accurate formula may be written " 

4 NI 

42. Magnetic Induction and Permeability. — If the space 
within the solenoid is filled with iron, the magnetic flux lines 
are very greatly increased. This is due to a property of iron 
called magnetic " permeability." To say that iron is more per- 
meable than air means that the magnetism is stronger when 
iron is present than it would be if the space were filled with air 
alone." Permeability varies according to the quality of the 
iron, from a few units to a few thousand. For example, to say 
that the permeability of a certain sample of iron is 1,000 means 
that the magnetic flux through 1 cm. of cross section of the iron 
is 1,000 times as great as the flux through the same area 
before the iron was present. The total magnetic flux through 
an iron core within a magnetizing coil, divided by the area of 
cross section, gives the " magnetic induction," which is repre- 
sented by the symbol B. We may denote total flux through the 

iron by 0i, then 

ct>,=BA (47) 

where A is the area of cross section of the iron core. If the in- 
tensity of the magnetizing fleld within a solenoid is denoted by 
H, then the total magnetic flux through the solenoid is given by 

(p. = HA (48) 

" For proof of this formula see Circular 74, p. 15. 

" Time is required for the magnetization to travel inward from the 
surface to the axis of the iron core. Hence, if the current is rapidly 
reversed in direction, the magnetic wave started by one-half cycle 
does not have time to travel inward appreciably before the reversed 
half cycle recalls it and starts a wave of opposite sign. As a con- 
sequence the magnetism is confined to the outer layers of the iron 
core. For this reason iron is not as effective in increasing the num- 
ber of flux lines in high-frequency circuits as it is with steady cur- 
rents or low-frequency currents. 


where .4 is the area of cross section and 0a is the total flux 
tlirough the air core. The permeability is defined as the ratio 
of B to H. 

It is important that the student should remember that the 
magnetic induction depends upon (a) the number of ampere- 
turns and (&) the property of iron called permeability. The 
number of ampere-turns is under the control of the operator. 
The permeability depends upon the quality of the iron itself. 

If the current in the windings is reversed, the direction of 
the magnetic field is also reversed. The student should learn 
at least one rule for remembering the relation between the 
direction of the current and the direction of the magnetic flux. 
Two such memory helps are here given. 

(a) If to an observer looking at one end of a solenoid the 
current appears to flow in a clockwise direction (i. e., in the 
direction of the rotation of the hands of a clock), the end next 
to the observer is the south pole. 

Another way of stating this rule is to look along the direction 
of the lines of magnetic flux through the solenoid (from south 
pole to north pole) and the current is flowing in a clockwise- 

(b) Grasp the solenoid with the right hand so that the fingers 
point along tlie wires in the direction in which the current is 
flowing. The thumb then points to the north pole: that is, the 
thumb points in the direction of the magnetic flux inside of the 
solenoid which is from south pole to north pole. 

The student may verify this relation by applying to Fig. 61 
the thumb rule for the direction of the magnetic field about a 
straight conductor carrying a current, as stated in section 4, 
page' 30. Thus in Fig. 61, if it is assumed that in the half turn 
shown the current is flowing from the to]) of the figure to the 
bottom, the north pole is on the right of tlie turn. In Fig. 63, 
the current flows in at the bottom of the solenoid and out at 
the top, and the north pole is at the top of the figure." 

"Apply oarh of the above rules to Fiff. 62. Also wind an experi- 
mental solenoid with a few feet of wire, connect it to a dry cell and 
mark in some way the direction of current through the windings. 
Test its polarity with a compass, remembering that liljp poles repel 
and unlike poles attract. 


43. The Force on a Conductor Carrying Current in a Magnetic 
Field. — If two different magnetic fields are brought together in 
the same space, with their directions parallel, a force is always 
developed. If the lines of magnetic flux are in the same direc- 
tion, the two fields mutually repel one another, and if the flux 
lines are in opposite directions the two fields will be drawn to- 
gether. When a current flows in a wire which is at right angles 
to a magnetic field, a force will act on the wire. A rule which 
will help the student to remember the direction of the motion, 
together with the directions of current and field, is the so-called 
" left-hand rule." Extend the forefinger of the left hand in 
the direction of the magnetic field, and hold the middle finger 
at right angles to it in the direction of the current. The ex- 
tended thumb, held at right angles to both the other directions, 
indicates the direction of the motion. Note that this rule 
calls for the use of the left hand. Compare this with the right 
hand rule of Section 63. 

When the wire which carries the current is at right angles to 
the direction of the magnetic field, the pushing force on the wire 
is equal to the product of the current, the intensity of the mag- 
netic field, and the length of wire which lies in the magnetic 

If the wire makes some other angle with the direction of the 
magnetic field, the direction of the force is still the same as 
for the right angle position, and the value of the force is 
.smaller. In the single instance that the direction of the current 
coincides with the direction of the magnetic field the force is 

This push on a single wire is in most cases small, but by 
arranging many wires in a very intense magnetic field, very 
large forces may be obtained. The powerful turning effect of 
an electric motor depends upon these principles. ( See Sec. 96. ) 

H. Inductance. 

44. The Linking of pircuits with Lines of Magnetic Flux. — 
There is always a magnetic field about an electric current. 
The lines of magnetic flux are closed curves and the electric 
circuit is also closed. The lines of magnetic flux are then 
thought of as always interlinked with the wire turns of the cir- 


ciiit. ( See Fig. 64.) The number of flux lines through a coil will 
depend upon the current, and any change in the current will 
change the number of linkings. If there are two turns of wire 
the circuit will link twice with the same magnetic flux, and so, 
for any number of turns, the number of linkings increases with 
the number of turns. Let represent the number of magnetic 
flux lines, N the number of linkings and n the number of wire 
turns. Then it is seen that the number of linkings is always 
given by 

N=n<p ' (49) 

A change in A' may be brought about by (a) a change in 0, 
due to a change in the current or (b) a change in the number 
of wire turns. Again the loop of wire, Fig. 65, not now con- 
nected to any battery, may be placed near a bar magnet, or a 
solenoid which has current flowing in it. Some of the flux lines 
will pass through the loop. The number of these flux lines, 
is I'epresented by </> as before, and every turn of wire will link 
with the flux lines. Then the number of linkings is given by 

N=n(p (50) 

which is the same expression as in the other case. 

The number of flux lines may be changed by changing the 
number of wire turns or by changing the number of flux lines 
through the loop. The latter may be done by rotating the loop, 
or by moving it with respect to the magnet. If a solenoid is 
used, the change can be made by variations in the current 
through its coils. 

45. Induced Electromotive Force. — Whenever there is any 
change in the number of linkings between the magnetic flux 
lines and the wire turns, there is always an emf. induced in 
the circuit. If the circuit is closed, a current will flow. This 
is called an induced current. Some of the ways in which this 
is accomplished are described in the following paragraphs. 

1. A bar magnet is pushed into a closed coil of wire, Fig. 66. 
During the time the magnet is moving there will be indications 
on the galvanometer r/ that current is flowing. When the mag- 
net is drawn back, away from the coil, a current is induced in 
the opposite direction. The direction of this induced current 
will always be such as to oppose the change to which it is due. 



That is, if the magnet is approaching the coil, the current will 
flow in AB so that A is a north pole, and hence the magnet 
will be repelled. If the key A: is open, the induced current can 
not flow. If it is closed, an induced current does flow, and 
sets up a magnetic field about the coil. It can be shown that 
more work is required^-to move the magnet with respect to the 
coil when the key is closed than when it is open. These facts 
are expressed in the law of Lenz, which states that whenever 
an induced current arises, by reason of some change in Unkings, 
the magnetic field about the induced current is in such a direc- 


Fl<^ 65 


^' / • \ \ ^ 

Lines of •force of Solenoid ' ! inV4"<i. wi+K circuit i^b 


" ^ ^ \ 



/ MA'Xne'^^ tKrVsT- 4rttcr coil^Of wiro'^ induces enrf. 

tion as to oppose the change. A helpful, mechanical illustra- 
tion of Lenz's law is seen in the effort necessary to move a 
stationary body. Owing to the mass of the body, a force is 
necessary to start it, and if one tries to move it suddenly he 
will experience a considerable reacting force. This reacting 
force will be greater the more sudden the change in the motion 
of the body. Similarly in the electric circuit, the induced emf. 
will be greater the more sudden the change in the number of 

2. The same effects as those described in (1) may be secured 
if the bar magnet is replaced by a solenoid carrying current. 



3. The effects may also be produced by two solenoids fixed 
in the position shown in Fig. 67. If a current is started in one 
of them, .1, there will be a current induced in the other, whicli 
will continue to flow as long as the current in A is increasing. 
If the current in A becomes steady, there is no current induced 
in B. If the current in A falls off, the induced current in B 
is reversed in direction. In all cases it must be remembered 
that the magnetic field about the induced current tends to op- 
pose the change that is causing the induced current. 

)Vhen a currenT'h startea or 
stopped m circuit A, an emf 
is induced in circuit B. 

Current stopping m A 
induces a current in B. 



^ O 

Current starting in A induces 
a current in B. 







Fig 70. 

Circuits A and B have 
mutual inductance. 

4. A further example of induced currents is found in the case 
of two straight wires. Fig. 68, close together. If the electric 
current stops (Fig. 69), starts, or varies in one of them in any 
way, there are corresponding induced currents in the other. 
This case of parallel straight wires is seen in certain telephone 
lines where cross talk occurs, or where there is interference 
from a.c. power lines. The ordinary telephone pole line has 
several pairs of parallel wires mounted on a single cross arm, 
and for purposes of minimizing cross talk it is general practice 
to transpose at frequent intervals the two wires composing a 

I^'DUCTA^'CE. 111 

pair, so that over any considerable distance the enif. induced 
by adjacent wires acting on a transposed pair is zero. Although 
we think of the straight and parallel portions of the circuit, we 
must not overlook the fact that these are only portions of com- 
pletely closed circuits. 

The magnitude of the mduced emf. in all of the above cases 
depends upon the time rate of change of llie number of Unk- 
ings. This may be expressed by the equation 

where t is the time in seconds in which the change )?0 takes 
place. This is the basic principle of dynamo-electric machinery. 
46. Self Inductance. — With a single circuit carrying current, 
as shown in Fig. 64, the magnetic flux <p which threads through 
the circuit (and hence the number of linkings .V) is directly 
proportional to the current strength. This fact may be ex- 
pressed by the formula 

N=L[ (52) 

where L is called the " self inductance." or simply the '• in- 
ductance" of the circuit. 

The value of L depends upon the number of wire turns, upon 
the shape and size of the turns, and upon the permeability of 
the medium about the circuit. For air the permeability is 1. 
The inductance does not depend upon the current which is 
flowing, except when iron is present. By coiling up a piece 
of wire in many turns and introducing it into the circuit, the 
inductance of the circuit may be greatly increased. In that case 
the inductance is said to be concentrated. It must not be over- 
looked that the entire circuit has inductance. This may be 
distributed more or less uniformly throughout the circuit. 

The self-inductance L is measured in units called " henries." 
A henry is the inductance in a circuit in which the electro- 
motive force induced is one volt when the inducing current 
varies at the rate of one ampere per second. In practice other 
smaller units are also used — the millihenry, which is one one- 
thousandth of a henry ; the microhenry, which is one one- 
millionth of a henry ; and the centimeter of inductance which is 
one one-thousandth of a microhenry. Methods of computing in- 
53904°— 22 8 


ductance in a few special cases are given in section 170. A 
single layer coil wound on an empty cylindrical tube 5 inches 
in diameter, 11 inches long, having a total of 150 turns, has an 
inductance of a little over one millihenry. 

If a piece of wire is connected to one terminal of a dry cell, 
and tapped on the other terminal, a very slight spark may be 
seen in a darkened room. If a coil of many turns of wire is 
included in series with this cell, the same process of tapping 
will show brilliant sparks, particularly if the coil has an iron 
core. The explanation of this lies in the fact that the cell 
voltage of about 1.5 is too feeble to cause much of a spark. 
However, when the large inductance is included in the cir- 
cuit, there is a large number of Unkings between wire turns 
and flux lines. If these flux lines collapse suddenly, as they do 
when the circuit is broken, there will be a large change in the 
number of Unkings taking place in a very small interval of 
time. From equation (51), this means that a large voltage 
will be set up. This principle is made use of in ignition appa- 
ratus and spark coils of various types. According to Lenz's 
law, the induced emf. will be in such a direction as to oppose 
the change which causes it. In this case, when the circuit is 
broken, the change is from some value of current / to zero. 
Therefore the induced emf. will be in the same direction as the 
original current, and will try to keep the current flowing. On 
the other hand, when a battery is being connected to an induc- 
tive circuit by means of a switch, the rising current will estab- 
lish a set of magnetic flux lines which will, as they grow, 
induce an emf. which tends to keep the current from rising. 

47. Mutual Inductance. — Consider a circuit AA, Fig. 70, with 
a current / flowing through it. The magnetic flux through .1 
is directly proportional to /, and that part of the total flux 
which interlinks with a near-by coil B is also proportional to 
/. This means that the total number of interhnkings N, be- 
tween flux lines that arise in the A circuit, and wire turns of 
the B circuit, is proportional to the current / in the circuit A. 
This fact may be represented by the equation 

N=}fl (53) 

where M is the constant of proportionality. This factor M is 
called the " mutual inductance " of the two circuits. When 


currents are started, stopped, or varied in coil A, the mutual 
inductance shows itself by an emf. induced in coil B. The 
induced emf. may be calculated by 

E=My (54) 

where /' is the amount by which the current in the A circuit 
varies in the time t. Mutual inductance is necessarily meas- 
ured in the same units as self-inductance. It causes a transfer 
of electrical energy between two circuits which have no elec- 
trical conducting path between them. 

The mutual inductance of two given circuits depends on the 
size and construction of the circuits themselves, their distance 
apart, their relative positions in space, and the nature of the 
material between them. All of these factors necessarily affect 
the magnetic flux interlinked with both circuits. The mutual 
inductance falls off rapidly as the distance between the two 
circuits is increased. When two solenoids have their axes in 
the same straight line their mutual inductance is the largest 
for that spacing, while if the axes of the solenoids are at right 
angles their mutual inductance is much smaller. If the axes 
are parallel but not in the same straight line, the mutual 
inductance will also be somewhat smaller than if they were 
in the same straight line. In Fig. 70 the two loops of wire have 
their axes in the same straight line and are very close to- 
gether, and hence their mutual inductance is a maximum. If 
there is iron between the coils, it has a shielding effect and 
reduces the magnetic flux linked with both circuits, and hence 
reduces the mutual inductance. 

Two or more coils intended to be used as self-inductances 
are often connected into the same circuit. In such cases the 
fact must be taken into consideration that the various coils 
have mutual inductances also, and if accurate values of induc- 
tance must be used the various coils should be so placed that 
their nmtual inductances are so small as to be negligible, or 
the mutual inductances should be taken into account. If other 
circuits are in operation near by, it is also important that their 
mutual inductances receive consideration, 

A familiar example of the effect of mutual inductance is the 
" cross talk " often experienced between telephone lines which 


run parallel on the same poles, or the " Inductive disturbances" 
experienced on a telephone line which runs adjacent to an 
electric-power line. 

^Mutual inductance is of particular importance in radio cir- 
cuits. The phenomena of mutual inductance are the essential 
principles involved in the operation of many different types of 
electrical apparatus, of which some are considered in the fol- 
lowing pages. 

For further information regarding self-inductance and mu- 
tual inductance, the reader may consult Bureau of Standards 
Circular No. 74. 

48. Energy Relations in Inductive Circuits. — In mechanics it 
is well known that a piece of matter cannot set itself in motion 
and that energy must be supplied from outside. So in the elec- 
tric circuit a current cannot set itself in motion, and energy 
must be supplied by some form of generator (source of emf.). 
It has already been explained how a magnetic field arises about 
electric circuits. When this field collapses or disappears, the 
energy stored in the field is returned to the circuit. It can be 
shown that the energy thus associated with a magnetic field is 
given by the equation 

W=hLr (55) 

where / is the value of the current and L is the self inductance. 
The student who is familiar with the laws of mechanics will 
note that this e<iuation is quite similar to that for kinetic energy 
of a moving body 

Kinetic energy=^ms^ 

where m is the mass of the body and s is its speed. 

Illustration of Inductance. — When a nail is forced into a piece 
of wood the mere weight of the hammer as it rests on the head 
of the nail will produce but little effect. However, by raising 
the hanmier and letting it acquire considerable speed, the 
kinetic energy stored is large, and when the motion ef the ham- 
mer is stopped this energy is used in forcing the nail into the 
wood. In the electric circuit a cell with its small emf. can 
cause only a feeble spark. By including a piece of wire with 
many turns in the circuit, however, energy is stored as shown 
in equation (55). A small current will enable a large amount 
of energy to be stored in the magnetic field, if L is large. Then 


when the circuit is broken and the field collapses, this large 
amount of energy is released suddenly, and a hot spark of con- 
siderable length is the result. 

The close relations between capacity, inductance, and resist- 
ance will be more fully discussed in Chapter 3. 

I. Alternating Current. 

49. Reactance. — A steady current in a circuit meets no other 
hindrance than the resistance of the circuit. If the current 
changes, this is no longer true. If the circuit has inductance, 
the current is opposed by the emf. induced by the variation of 
the current. (See Sec. 46.) If a condenser is present, this is 
constantly charging or discharging as the current changes, and 
it exerts a controlling influence on the passage of the current. 
If both inductance and capacity are included in the circuit, 
they tend to offset each other in their effects, but usually one 
or the other exerts a predominating influence, with the result 
that there is added to the resistance an extra opposition to the 
current, which is known as the " reactance." 

The more rapid the changes of the current the greater the 
induced emf. in a circuit and consequently the greater the in- 
ductive reactance. On the contrary, the reactance of a con- 
denser is less, the more rapidly the current varies, as can be 
understood when we reflect that the greater the number of 
charges and discharges of the condenser performed each second 
the greater the total quantity of electricity which flows around 
the circuit in that interval — that is, the greater the current. 
In general, the reactance of a radio circuit is very much 
greater than the resistance. 

To calculate the current in a radio circuit, then, it is neces- 
sary to know how to calculate the reactance and how to com- 
bine it with the resistance, in order to determine the total 
hindrance or " impedance " to the current. Since the reactance, 
however, depends upon the way in which the current is vary- 
ing, it is evident that this must be definitely specified in each 
case. The problem can not be solved for all imaginable kinds 
of variation of the current. Radio currents, however, belong 
to the general class of alternating currents, and for these the 
theory is rather simple. In the following sections is given a 
brief treatment, not of general alternating current theory, but 



merely of those alternating current principles which are essen- 
tial to an understanding of the actions in radio circuits. 

50. Nature of an Alternating Current. — An alternating current 
is one in which electricity flows around the circuit, first in one 
direction and then in the opposite direction, the maximum value 
of the current in one direction being equal to the maximum 
value in the other. All the changes of current occur over and 
over again at perfectly regular intervals. 

Sine Wave. — To get an insight into the nature of such a cur- 
rent, suppose a case where the alternations occur so slowly 
that we may follow the changes of current with an ammeter. 
In the table below are given values of the so-called " sine-wave 
current " at successive equal intervals of time. The maximum 
value is taken as 10 amperes. 




Current , 










- 2.59 




2.59 1 


- 5.00 




5.00 ! 

1 15 

- 7.07 

1 27 



7.07 1 


- 8.66 






- 9.66 




9.66 1 








- 9.66 






- 8.66 




8.66 ! 


- 7.07 ' 




7.07 1 


- 5.00 






- 2.59 









The ammeter in such a case would creep slowly up to a 
maximum indication of 10 amperes, return gradually to zero, 
reverse its direction and build up to a value of 10 amperes in 
the opposite direction, then decrease to zero again, build up 
again in the original direction, and so on. It is, of course, to be 
understood that the current assumes in turn all possible values 
between zero and the maximum value (10 amperes in this case), 
and that the current has the same value throughout the circuit 
at every moment. The current in this case, as well as that of 
a steady current, may be regarded as like the flow of an in- 
compressible fluid. The emf. is, however, to be regarded here 
as a variable electric pressure, which acts first in one direction 
and then in the other. 



The values of current in the preceding table are plotted in 
Fig. 71 as ordinates (vertically), and the corresponding lengths 
of time elapsed since the start, as abscissas (horizontally), and 
a smooth curve drawn through the points enables one to de- 
termine what is the value of the current for any moment lying 
between any two of those which are included in the table. It 
is to be noted that the changes of current repeat themselves. 
Thus in the table the current is the same at 1 sec. and 25 sec. 
after the start; at 7 sec. and 31 sec, etc. The interval of 24 
seconds in this example is the " period " of this alternating 
current. The current passes through a complete " cycle " of 
changes in one period. 

'Sine V/Ave 


A current like that just treated is the same as that which 
would be produced in a circuit attached to a coil revolving very 
slowly in a uniform magnetic field. (See Chap. 2, Sec. 74.) 
The motion has been assumed slow in order that the changes 
can be followed with ordinary direct-current instruments. In 
order to represent the current developed by an ordinary low- 
frequency alternating-current generator, we must, however, 
imagine the coil to revolve more than a thousand times more 
rapidly. Thus the usual a. c. lighting circuits carry currents 
whose period is only about -g-V second. The current passes 
through complete cycles each second, that is, its " frequency " 
is 60 cycles per second. Ordinary alternating-current gen- 
erators can not use magnetic fields which are entirely uniform, 
so that the current obtained never passes through its changes 
in exactly the same way as the ideal sine current pictured in 


Fijr. 71. Tlie difference is, however, usually so small in well- 
designed machines that it does not need to be taken into account. 

The frequency of radio currents is enormously greater than 
Ihe usual low-frequency alternating currents. In order that 
Fig. 71 may properly represent a radio current, we must sup- 
pose a whole cycle to be completed in, say, loooo iyg ^o i o o^o o a 

51. Average and Effective Values of Alternating Current. — In 
just the same way as we have analyzed alternating current by 
imagining it to change slowly, it is possible to get an insight 
into complicated movements, like the throwing of a ball or the 
galloping of a horse, by running a motion-picture film of the 
action so slowly that the separate pictures on the film can be 
examined one at a time. 

When a direct-current annneter is traversed by an ordinary 
alternating current, the changes of current are altogether too 
rapid to be followed by the needle of the instrument. It can 
only take up an average position corresponding to the average 
of all the values through which the current passes during a 
cycle. However, since the current passes through the same 
values in one direction that it does in the other, the average 
value during the cycle must be zero. That this is the case can 
be shown by connecting a direct-current ammeter into an alter- 
nating-current circuit. The ammeter needle stands still at zero 
or else merely presents a blurred appearance while standing at 
zero. The same remarks apply to the use of a d. c. voltmeter 
in an a, c. circuit. 

A. C. Voltmeters and Ammeters Indicate Effective Values. — 
Alternating-current voltmeters and ammeters may be of several 
different types (hot wire, dynamometer or electrostatic, see 
Sec. 60), all of which, however, give a deflection in the same 
direction, whichever the direction of the current. The force on 
the moving portion of such an instrument is at every moment 
proportional to the square of the current through the instru- 
ment. When an alternating current passes, the average de- 
flection taken up by the pointer is therefore proportional to the 
average of the squares of all the values of current during the 
cycle. For a true sine current, the average of the squares of 
all the values of current during the cycle can be shown to have 
a value of one-half the square of the maximum value. 


Equivalent Direct Current. — The heating effect of a current 
is, at every moment, proportional to the square of its value at 
that moment. The average heating effect of an alternating 
current must, therefore, be proportional to the average of the 
squares of all the values' of the current during the cycle, or 
must be proportional to one-half the square of the maximum 
current. The same heating effect would, of course, be pro- 
duced by a steady current, whose square is equal to the average 
of the squares of the alternating current taken over the whole 
cycle. That is, the " effective current " is equal to the value 
of the direct current which would produce the same heating 
effect in the circuit in question. Since its square is equal to 
one-half the square of the maximum value, the effective value 
of the current is 

^^ /(maximum^ • (5^^ 

or equal to the maximum value divided by V^ . This is the 
same as the maximum value multiplied by 0.707. 

The effective current in the table above is 7.07 amperes, and 
this would be the current indicated by an a.c. ammeter in the 
circuit, although the current varies between 10 amperes in one 
direction and 10 in the other. The same heating effect would 
result if a direct current of 7.07 amperes were sent through 
the circuit. Likewise, an a.c. voltmeter will always read the 
effective value of the voltage, which is equal to the maximum 
voltage multiplied by 0.707. 

52. Circuit with Resistance Only. — Let us imagine a circuit 
with resistance R ohms, and w^ith such small inductance and 
capacity that they may be neglected. Let us suppose, further, 
that sine wave alternating emf. is applied to the circuit. At 
every moment, the current will be found by dividing the emf. 
at that instant by the resistance of the circuit. The current 
is zero at those moments w^hen the emf. is also zero, and is a 
maximum when the emf. is a maximum. In fact, the changes 
of current keep step with those of emf. The current and emf. 
are said to be "in phase" or to have "zero phase angle." 
Since the effective values of emf. and current are each the 
same fraction of their respective maximum values, the effective 


current / will be calculated from tbe effective emf. E by the 

/=f (57) 

That is, in this special case, Ohm's law holds, even when the 
current is alternating. An ordinary incandescent lamp circuit 
approximates this ideal circuit. 

The power in the circuit is, at every moment, equal to the 
product of the values of current and emf. which hold at that 
moment. The average power taken over the whole cycle is 
equal to the product of the effective current by the effective 
emf., that is, average P=IE. The power is used up in the 
circuit entirely in heating the resistance R. 

53. Phase and Phase Angle. — The values of current given in 
the table above are those which hold for certain definite 
moments in the cycle of change of the current. Each time the 
cycle is repeated the same values are run through, and any 
chosen value will be reached at a perfectly definite fraction 
of the way through the cycle. Each maximum in the positive 
direction, for example, occurs just one-quarter of a cycle after 
the preceding zero value. The points A in Fig. 71 have the 
same phase, although each is in a different cycle from the 
others. The current has the same value at the points C as 
at A, but points C are not in the same phase as A, since at A 
the current is increasing, and at C it is decreasing. 

The phase is, then, a certain aspect or appearance, occurring 
at the same definite part of each succeeding cycle. Difference 
in phase is nothing more than difference in position in the 
cycle. It is best referred to as difference in time, expressed as 
the fraction of the length of a cycle. Thus, the difference of 
phase of points B and 0, Fig. 71, is one-quarter of a cycle ; that 
of points B and D one-half cycle, etc. It is also customary to 
express difference in phase as an angle. A difference of phase 
of one complete cycle is regarded as equivalent to the angle 
of a whole revolution or circumference, that is, to 360°. One- 
quarter cycle is accordingly 90°, and two points mth a differ- 
ence of phase of one-quarter cycle are said to have a difference 
of phase of 90°, etc. 

The idea of phase angle is useful when two emfs. are acting 
In the same circuit or when the current and the emf. which pro- 



duces it do not pass through their maxima at the same moment. 
Fig. 72 shows the waves of emf. and current in a circuit where 
the emf. and current differ in pliase by about one-eighth of a 
cycle ; i. e., they have a phase angle of about 45°. 

When a circuit has resistance but no inductance or capacity, 
the emf. and current are in phase or the phase angle is zero. 
Their waves, shown in Fig. 73, pass through zero at the same 

f\Q.lZ And current curves \A*itS 
4 difference, of |3h<aae of ■^S' 

FlO. lA 

Two em^. corves m of>f'o»ite And current ourves m 


A '\ 

\ / 


/ ^'^ / 


1 \» 
/ ^ 




. T5 


-*— <S 


ourreot \n 

(nduttive circuil" 

moments and reach their maximum values at the same mo- 
ments. The case of opposite phase shown in Fig. 74, in which 
two emfs. are represented, is such that, although they pass 
through their zero values at the same moments, at other times 
one is always acting in the opposite direction to the other. 
Their phase angle is 180°. 

In any series circuit where the reactance is not zero the 
applied emf, and the current have a difference of phase. 

54, Alternating Current in a Circuit Containing Inductance 
Only. — Such a circuit would be approximately represented by 


one with a large inductance coil wound with such large wire 
that only a very small resistance would be offered to the cur- 

If an alternating emf. is applied to the circuit, an alter- 
nating current flows, and the changes of the current induce an 
emf. in the circuit which is greater, the greater the inductance 
and the mure rapidly the current changes ; that is, the greater 
the frequency of the current. 

The current / changes most rapidly at the points A, B, and C, 
Fig. 75, where it is passing through zero value. The induced 
emf. must therefore be a maximum at those points. Since it 
always opposes the change of current, it must be at its maxi- 
mum negative value in the figure at the points of the axis, A 
and C, and at its positive maximum at point B. At points D and 
E, the current does not change for a moment, so that the in- 
duced emf. must be zero at those times. It is not difficult to 
show that when we have a sine alternating current there is also 
a sine alternating emf. induced as shown in curve e, Fig. 75. 

In this kind of a circuit, this induced emf. has to be over- 
come at each moment, but the applied emf. is not requisitioned 
for any other service. Accordingly, the applied and induced 
emfs. are at every moment equal and opposite. The applied 
emf. wave is therefore given by curve r, Fig. 75, drawn with 
its vertical heights just equal and opposite to those of curve e. 
It is evident that the current lags one-quarter of a cycle in its 
changes behind those of the applied emf. The current is said, 
therefore, to lag 90° in phase behind the applied emf. 

The effective value of the induced emf. can be shown to have 
the value 2Tr fIJ, in which / is the frequency, L the inductance 
in henries, / the effective value of the current in amperes, and 
7r=3.1416, or nearly St. An effective applied emf. E, therefore, 
will produce a current whose effective value is 

Inductive Reactance. — The quantity A'=27r/'L is known as the 
reactance of the inductance coil. It is larger the greater the 
frequency and the greater the inductance, as would be expected, 
and has a considerable value in many cases. The reactance is 
measured in ohms. As an example, suppose a coil of 0.1 henry 


at 100,000 cycles per sec. The reactance is X=6.283X 100,000 X 
0.1=62,830 ohms. That is, such a circuit throttles down the 
current as much ns a resistance of 62,830 ohms would do. 
There is this difference, however, between the effects of an in- 
ductance and a resistance, that no energy is dissipated in heat 
in an inductance. In one-half of the cycle, energy is taken 
from the circuit, it is true, but this is stored up in the mag- 
netic field around the coil, and in the next half cycle the mag- 
netic field collapses on the coil and gives the energy back to the 
circuit. Thus in the long run energy is neither gained nor 
lost in the circuit. 

It is general practice to use the symbol w to represent the 
quantity of ^irf, since the quantity '2wf very frequently occurs in 
problems involving alternating currents. (See Circular 74, page 
22.) Using this abbreviation, equation (58) may be written 

55. Circuit Containing Inductance and Resistance in Series. — 
It is, of course, impossible to arrange a circuit which has abso- 
lutely no resistance. In addition to overcoming the induced 
emf., a portion of the applied emf. has to be employed to force 
the current through the resistance of the circuit. Thus if the 
current at any moment is passing through the value i, the emf. 
necessary to force the current through the resistance is Ri, 
and that which is overcoming the induced emf. is Xi, so that 
the value e which the applied emf. has at that moment is 
e—Ri+Xi. This equation shows the simple and obvious con- 
nection between the value of the current at any instant and the 
corresponding instantaneous value of the emf. which is produc- 
ing it. However, it cannot be used to calculate the effective 
current from the effective applied voltage, for the reason that 
the two emfs. Ri and Xi are not in phase. When the former 
is passing through zero value the latter is at its maximum, and 
vice versa, so that the sum of the two emfs. has a raaxinmm 
value less than the sum of their individual maximum values. 

This is in line with the results of the following experiment : 
Let a coil of inductance L be joined in series with a resistance 
R, and let three voltmeters a, b, and c be applied, as shown, 
Fig. 76, to measure the emf. between the points A and B, B and 



€, and A and C. The voltages measured by the voltmeters are 
effective values, and it is found that the reading of c is not 
equal to the sum of the readings of a and &, as would be the 
case with a direct current. 

The voltmeter a gives the emf. RI and the voltmeter h the 
emf. XI, where / is the effective value of the current, which 
would be measured by an a. c. ammeter in the circuit. Analy- 
sis shows that the reading E of the voltmeter c is represented 
by the hypotenuse of the right triangle whose sides are RI and 
XI. See Fig. 77-a. 

^, -'-€)---.. 


Circuit v>/'irh in<Juct*nce t^nd resistUnee 


f=»6o 1-2 L»cxl E-lo 


FiC5. -11 

for cincoi't K»vin^ resistance 

in Fia.l9 

e.- (oo f-feo 

L » O.I ii-io 

The effective applied emf. E in such a case is therefore re- 
lated to the voltages RI and XI by the equation (relation 
between sides and hypotenuse of a right triangle), 

E^=(Riy-\-{Xiy=I%X^-\-R^) (59) 

Accordingly the effective value of the current produced by the 
effective applied emf. E is 





Impedance. — The quantity -y/x^+R^ is known as the " im- 
pedance " of the circuit. It takes the place in alternating-cur- 


rent theory of the resistance in Ohm's law. It is related to the 
resistance and reactance as the sides of the right triangle, 
Fig. 77-b. 

As an example, suppose in Fig. 78 that L=0.1 henry, i?=10 ohms, 
f=60 cycles per second. Find what applied emf. is necessary to cause 
an effective current of 2 amperes to flow. 
RI=20 volts 

X =6.283X60X0.1=37.7 ohms 
Jr7^75.4 volts. 
The applied emf. must therefore be by (59) 

^=V(20)-+ (75.4)==78.0 volts. 
The reverse problem is to find what current will flow in the circuit 
when a given emf., say 100 volts, is applied. The impedance is 
^i22 + Z2=V(10)2+ (37.7)2=39 ohms. 

Therefore the current will be oq~o=2.56 amperes. The emf. on the re- 
sistance is 2.56X10=25.6 volts and that on the reactance 2.56X37.7^ 
96.5 volts, so that the voltage triangle is that given in Fig. 79. 

Poiver Factor. — The power dissipated in heat in this circuit 
is of course /"i?= (2.56) "X 10=65.5 watts. The product of the 
effective current and effective voltage is 100X2.56=256 ''volt- 
amperes." To obtain the dissipated power from this product, 

65 5 
it is therefore necessary to multiply by -^^ =0.256. Note that 


this is the same as r— — ^ The number which it is necessary 

39 ohms 

to multiply into the product of volts and amperes in order to 
get the power is called the " power factor." The power factor 
of the above circuit is 0.256. A circuit with resistance only 
and no inductance or capacity has a power factor of 1. A reso- 
nant circuit (see Chap. 3) is another example of power factor 
equal to 1. The power factor in other cases always lies be- 
tween zero and one. The power in any circuit is calculated, 
then, by the formula 

P=EIF (61) 

the power factor being given by the general formula 

_ resistance ,^^. 

F=. J (62) 

impedance ^ 

56. Charging of a Condenser in an Alternating Current Cir- 
cuit. — A steady emf. is not able to pass a steady current through 



a condenser. When the circuit is tirst closed, a charging cur- 
rent flows into the condenser, until the voltage between tlie 
plates of the latter has risen to the same value as the applied 
voltage. If the voltage is removed and the circuit completed 
by a wire, a discharge current flows out of the condenser in the 
opposite direction to the charging current. The discharge 
ceases when the plates of the condenser have no potential differ- 
ence. (See Sec. 30.) 

With an alternating emf. in the condenser circuit, an alter- 
nating current is constantly flowing into and out of the con- 
denser to keep the voltage between the plates equal to the 

Picj.60 A 
/ \ 

Current in con 

\ ' 


~ "i 


* e.,L a 

. /' \ \ / ^ 


on Coil dnd condenjcr 

\ / 

\ V/' / 


Circui't vs'V 

Fia.&t ^^ 

anc« Tn'dnjsjlei, 
rvJ C 



instantaneous value of the applied emf. The current is largest 
at those moments when the applied emf. is changing most 
rapidlj' ; it is zero at the moments when the emf. is for a mo- 
ment stationary at its maximum values. If curve e, Fig. 80,' 
represents a sine alternating emf., it can be shown that the 
charging current curve will be like curve i ; that is, the charg- 
ing current is 90° " ahead " of the applied emf, in phase. 
(Contrast this with the relations in the inductive circuit.) 
The charging current will, in general, be greater the greater 
the capacity C, and the greater the frequency of the emf. 

Rcartancr of Condcnncr. — Analysis shows that the effective 
value / of the charging current is I=^2wfCE. The reactance of 
the condenser is accordingly 





where C is the capacity in farads. This shows that the re- 
actance of the condenser is greater, the smaller the capacity 
and the lower the frequency. (Contrast with the reactance of 
an inductance.) The reactance, as before, is measured in ohms. 
As an example, we find that the reactance of a condenser of 
0.1 microfarad at 60 cycles is 


=26,500 ohms. 


At 100,000 cycles, the reactance is only 15.9 ohms. From this 
it appears that the condenser offers much less obstruction to 
flow of current at high frequency than at low frequency, and 
hence, that a given alternating emf. causes a much larger cur- 
rent flow if the alternations are rapid than if they are slow. 



'- ' ) 

Pul.Sd"ti'n^ Current 

5*.Ti^le Trans-former 

No energy is dissipated in a perfect condenser. Energy is 
stored in the dielectric of the condenser while it is being 
charged, but this is all restored to the circuit w^hen the con- 
denser discharges. Actually, no condenser is perfect, although 
well designed air condensers may be regarded as essentially so. 
Heat is always dissipated to a measurable extent in condensers 
with solid dielectrics. The condenser acts as though a certain 
resistance were joined in series with it. The actual value of 
this assumed series resistance depends upon the capacity and 
the frequency, as well as. upon the nature of the dielectric. It 
is less, the greater the capacity, and in general inversely propor- 
tional to the frequency. 

57. Circuit Containing Capacity, Inductance, and Resistance 
in Series. — When an inductance and capacity are joined in series 
and subjected to an alternating emf., the current through 
them both is the same, and the emf. on the condenser is X^i and 
that on the inductance X^i, where the instantaneous current 
53904°— 22 9 


has the value i, X^ is the reactance of the coil and .Y^. the 
reactance of the condenser. The curves for these voltages 
may be derived by combining the curves of Figs. 75 and 80. 
The curves X^^i and X^i, Fig. 81, show that at every moment 
the voltage on the condenser opposes that on the inductance. 
The circuit acts as though it possessed a single reactance equal 
to the difference of the reactance of the coil and the reactance 
of the condenser. If the latter is the larger the circuit be- 
haves like a condenser circuit, and if the coil has the greater 
reactance, the circuit behaves like an inductive circuit. 

The Effective values of the voltages in the circuit are shown 
in Figs. 82-a and b. The impedance is found by combining 
the resistance and the resulting impedance in the triangle dia- 
gram of Fig. 82-c. The value of the impedance is evidently 

^=V/2'+(Xl-Xc)2 (64) 

58. The Alternating Current Transformer. — A very important 
application of the principle of mutual inductance is the alter- 
nating-current transformer. The transformer is a particular 
kind of device for securing nmtual inductance between two cir- 
cuits. In most cases, the purpose of using the transformer is to 
change or transform alternating current of low voltage and 
comparatively large current to alternating current of higher 
voltage and smaller current, or vice versa. 

A transformer used to deliver an output of higher voltage 
than the input is called a " step-up " transformer. A trans- 
former used to deliver an output of lower voltage than the 
input is called a " step-down " transformer. 

The fact that a. c. voltages can be easily stepped up or stepped 
down by the use of a transformer, while a change from a low 
d. c. voltage to a high d. c. voltage requires rotating machinery 
which is much more expensive (see Motor Generators, Sec. 102, 
p. 223), constitutes one of the great advantages of alternating 
current over direct current for the electrical transmission of 
power. The use of d. c. voltages even as high as 10,000 volts is 
unusual, and involves many difficulties. A. c. voltages exceed- 
ing 100.000 volts are in regular use on long transmission lines. 
The electrical transmission of power over anything but com- 
paratively short distances would, in fact, be practically impos- 
sible without the use of alternating currents and the trans- 


former. In Chapter 2 there are discussed various types of 
dynamo-electric macliinery for generating electric currents, both 
d. c. and a. c. There are many practical operating conditions 
which limit the voltage which can be generated by a machine 
designed for generating either a. c. or d. c. For a given trans- 
mission line transmitting a certain amount of electilcal power, 
the electrical power loss in the line is, of course, proportional 
to the square of the current, and, therefore, in general, in- 
versely proportional to the square of the voltage of transmis- 
sion. Thus, in transmitting 10.000 kw, at 500 volts the line 
loss will be about 100 times the line loss in transmitting 10.000 
kw, at 5,000 volts. The use of high voltages for transmission 
is therefore very important. The great increase in efficiency of 
transmission at high voltages much more than compensates for 
the difficulties in insulation. 

Const ructi 071. — An alternating-current transformer consists of 
two coils of wire so placed as to have appreciable mutual in- 
ductance. In nearly all transformers in use for the electrical 
transmission of power, as on electric lighting lines, the wire for 
both coils is insulated, and there is additional insulation be- 
tween the two coils. In most cases the coils are wound so that 
they have a common iron core, which greatly increases their 
mutual inductance. The iron core is not a solid piece of iron, 
but is composed of thin sheets or laminations. The winding 
or coil to which the input power is delivered is called the 
" primary " and the winding which delivers the output to the 
load circuit is called the " secondary." A simple transformer 
is shown in Fig. 83, in which the path of the magnetic flux is 
entirely through iron. This is called a " closed-core " trans- 
former. A closed-core transformer of a type used in radio appa- 
ratus is shown in Fig. 181, page 355. In some transformei-s the 
path of the magnetic flux is partly through air ; such a trans- 
former is called an " open-core " transformer. The induction 
coil, which has various applications outside of radio communica- 
tion, such as in the ignition system of automobiles, is a particu- 
lar kind of open-core transformer. An induction coil is shown in 
Fig. 188, page 363, In some transformers there may be no iron 
core ; these are called " air-core " transformers. Air cores are 
often used for transformers for high fi'equencies, such as the 
frequencies employed in radio communication. The mutual 


iiuliictance of tlio windinjis of an air-core transformer is neces- 
sarily comparatively small. At low frequencies only small 
amounts of power can be conveyed from one circuit to another 
by air-core transformers. 

It can be shown that if h is the effective value of the current 
in the primary, M the mutual inductance, and f the frequency, 
the effective value of the emf induced in tlie secondary will be 

In Section 119, page 267, the use of ''coupled circuits" in 
radio communication, and various kinds of " coupling:," includ- 
ing " inductive coupling," are discussed. The transformer is 
a device for obtaining such " inductive coupling." 

Operation. — Assume that the primary is connected to a source 
of a. c. supply, and that the terminals of the secondary are not 
connected. The primary winding with its iron core is then 
simply an inductance coil of high inductance which offers a 
very large impedance to the voltage applied to the primary. A 
certain small current will flow in the primary, which is the 
"no load" or "open circuit" current, and is also sometimes 
called the " magnetizing current." The magnetic flux in the iron 
core must be of such a value that during a second the num])er 
of changes in flux linkages at the applied frequency is sufficient 
to induce in the primary winding a back electromotive force 
practically equal in magnitude to the applied voltage. 

Assume now that a load is connected to the secondary 
terminals. A current will flow in the secondary circuit due to 
the emf induced in the secondary winding. The current will 
at each instant flow in the secondary winding in such a direc- 
tion as to tend to cause a magnetic flux in the core in a direc- 
tion opposite to the direction of the flux caused by the current 
now flowing in the primary winding. As long as the voltage 
applied to the primary is maintained constant, the flux actually 
existing in the iron core must be of sufficient magnitude to 
induce in the i»rimary winding a back emf substantially the 
same as the applied voltage; that is, the effective value of the 
flux over a cycle must remain sul)stantially constant under the 
varj'ing conditions of load. In order to maintain the flux 
constant, the current flowing in the primary winding must 
increase to a value such that the increase in the primary ampere- 
turns is sufficient to overcome the opposing magnetic effect of 


the secondary ampere-turns. Considering the primary winding 
by itself, the effect is as though the iron had suddenly become 
less permeable. That is, the effective inductance of the pri- 
mary winding, considered by itself, drops to a value sufficient 
to permit enough primary current to flow to maintain the flux 
substantially constant. "When the secondary is delivering the 
full current for which the transformer is rated, the effective 
inductance of the primary becomes quite small. 

When the usual type of transformer for commercial fre- 
quencies is delivering its rated load, the primary current is 10 to 
50 times the small current taken by the primary when the 
secondary is not connected. As has been stated the magnetic 
effect of this primary current flowing when the transformer is 
under load is almost entirely counteracted by the opposing 
magnetic effect of the secondary current. 

Occasionally the secondary may be practically short-circuited, 
perhaps by accident, and in such cases the primary winding 
may be called on to carry a large current for a short time. 
Such short circuits not only make severe demands on the 
electrical system but produce large mechanical forces acting on 
the windings themselves, tending to move the coils with respect 
to each other. 

If ?h represents the number of turns in the primary winding, 
and 112 the number of turns in the secondary winding, and /i 
represents the increase in the primary current due to a current 
I2 flowing in the secondary, then with a constant voltage applied 
to the primary : 


If El represents the emf induced in the primary, and E2 repre- 
sents the emf induced 'in the secondary, 

722 ^2 

Thus if the primary has 100 turns and the secondary 1,000 
turns, and an emf of 200 volts is applied to the former, an emf 
of 2,000 volts will be induced in the latter, and if the primary 
current is 50 amperes the secondary current will be 5 amperes. 


Leakage. — All of the magnetic flux due to the current flowing 
in one winding and linked with that winding is not also linked 
\^'ith the other winding. The path of a certain part of the flux 
is through the air, outside of the core. This part of the flux 
due to one winding wliicli is not linked with the other winding 
is called its " leakage " flux. In well-designed transformers this 
leakage flux is quite small. The leakage flux obviously is not 
effective in transferring energy from one winding to the other. 
Leakage may be reduced by offering to the magnetic flux a 
complete path of high permeability. One way to do this is to 
use a closed core, so that the path of the magnetic flux is 
entirely through iron ; in the open-core transformer part of the 
path of the magnetic flux is through air, and considerable leak- 
age necessarily results. Another way is to use a core of large 
cross section, so that the iron is worked at low flux densities. 
Leakage is also reduced by bringing the coils close together 
and making them approach coincidence. This may be done by 
winding one winding right on top of the other; very little 
magnetic flux can then be linked with one winding and not 
with the other. 

Losses. — The transformer is one of the most efficient kinds of 
electrical apparatus. The efficiency of well-designed trans- 
formers is usually from about 94 to 98 per cent, according to 
size, the larger units being the more efficient. There are " cop- 
per " losses in primary and secondary windings, equal to the 
resistance times the square of the current. There are " eddy 
current " losses due to the currents induced in the iron core. 
If the iron core were solid, currents would be set up in the 
whole cross section of the core in the same plane as the plane 
of a turn of winding. By using thin sheets of iron the path of 
the eddy currents is reduced, and hence the eddy-current loss. 
At comparatively low frequencies the eddy-current loss is pro- 
portional to the square of the frequency and also to the square 
of the thickness of the sheets or laminations. At radio fre- 
quencies other effects must be taken into consideration, and 
these relations do not hold, (See the papers referred to at the 
end of this section.) At high frequencies it is important to 
have the laminations as thin as possible. In transformers for 
commercial frequencies the thickness of the laminations is 


usually between 0.010 inch and 0.030 inch. If a solid core were 
used in a transformer for handling any considerable amount of 
power, enough heat might be quickly evolved by the eddy cur- 
rents in the core to destroy the unit. There is also another loss 
in the iron, called the " hysteresis " loss. Hysteresis losses are 
caused by reversals of the magnetism of the core and represent 
the energy required to change the positions of the molecules of 
the iron core. At comparatively low frequencies hysteresis 
losses are directly proportional to the frequency and are greater 
the higher the flux density at which the iron is worked. 
Hysteresis losses at radio frequencies are discussed in the 
papers mentioned at the close of this section. The sum of the 
eddy-current losses and the hysteresis losses is known as the 
" core losses " or " iron losses." The core losses occur as long 
as a voltage is applied to the primary and are nearly the same 
whether the secondary is delivering a load current or not. The 
current taken by the primary when the secondary circuit is 
open supplies these losses in the iron. It is therefore very 
important to design transformers so that the eddy-current losses 
and hysteresis losses are small. This is particularly important 
in transformers which are connected to the line all the time 
but supply a load during only a small part of the day, as trans- 
formers on electric-light systems, and is less important on 
transformers supplying full load secondary current all day, as 
transformers in a power house. These losses are discussed 
further in connection with dynamo-electric machinery in Sec- 
tion 78, page 172. 

The cores of most transformers and other apparatus for al- 
ternating currents are now made of silicon steel instead of soft 
iron or a mild steel. One advantage of silicon steel is that 
when subjected to heat it does not age appreciably ; that is, 
its permeability does not decrease with use. Ordinary soft iron 
will age rapidly with heat. Therefore a transformer with core 
of silicon steel can' be operated at a higher temperature than a 
transformer with soft-iron core. Another important advantage 
of silicon steel is that its ohmic resistivity for electric currents 
is much higher than soft iron, and therefore in a given trans- 
former the eddy-current losses will be less with a silicon-steel 
core than with a soft-iron core. The permeability of silicon 
steel is about the same as the permeability of the soft iron 


which has been used for transformers. Practically all core 
transformers used for radio apparatus, for either transmitting 
or receiving, have cores made of silicon steel. 

Cooling. — The losses represent electrical energy converted 
into heat. Some means must be provided for dissipating this 
heat, or the temi>erature of the transformer may rise until it is 
destroyed. Small sizes, including most of those found in radio 
stations of moderate size, may be cooled by simply being exposed 
to the air. The exposed surface of the windings must be suffi- 
cient to dissipate the heat. In larger sizes an air blast may 
be blown through the transformer. Large transformers are also 
cooled by immersing the windings in oil, which is kept cool by 

If a tap is brought out from an intermediate point of the 
winding of an inductance coil, a part of the voltage applied at 
the terminals may be tapped off between one terminal and the 
intermediate tap. This can be considered to be a transformer 
in which one winding serves as both primai'j' and secondary. It 
is simple and cheap, but has the disadvantage that the two 
windings are not insulated and the voltage to ground of the 
high-voltage winding also exists in the low-voltage circuit. Its 
use is confined for the most part to small sizes. This device is 
often called an " auto-transformer." 

For bell ringing and similar work in which low-voltage al- 
ternating currents can be used, use is now made of small trans- 
formers rated at only a few watts, which are connected to the 
a. c. electric supply and deliver about 10 volts at their secondary 

In radio apparatus the load on the secondary of a trans- 
former usually includes a capacity. It may become desirable 
to adjust the system consisting of the a. c. generator, trans- 
former, and secondary condenser so that the impedance of the 
primary circuit is a minimum ; that is, so that the condition of 
"re.sonance" exists. (See Sec. 109, page 234.) This arrange- 
ment is called a " resonance transformer," and is discussed in 
Bureau of Standards Circular 74, page 230. With such an ar- 
rangement it is possible to obtain very high voltages. One type 
of transformer employing resonant circuits is sometimes called 
a " Tesla coil " and may be made to produce spectacular high- 
voltage effects. 


On closing the primary switch when a transformer is first 
connected to the line a relatively very large current may flow 
for an instant, its magnitude depending on the state of mag- 
netization in which the iron was left when the transformer was 
last disconnected from the line. This momentary current ob- 
tained on closing the primary line switch may in some cases be 
perhaps 10 times the primary rated full-load current and may 
blow the fuses in the primary line. 

Radio-frequency transformers. — Transformers used for al- 
ternating currents of radio frequencies usually have air cores ; 
that is. no iron is employed, as has been stated. If an iron core 
is used, very thin laminations are employed. At radio fre- 
quencies, the effectiveness of iron in increasing the magnetic 
flux is riot as great as at low frequencies, the eddy currents . 
contributing to this effect.*' ( See also footnote, Sec. 42. p. 105. ) 
Transformers for radio frequencies are shown in Figs. 197, 198» 
199, pages 372-374. Small radio-frequency transformers are 
used in electron tube amplifiers. (See Sec. 196, p. 482.) Small 
transformers with iron cores, for frequencies up to perhaps 
3.000, are also employed in electron tube amplifiers. 

A common use of a transformer with radio frequencies is to 
obtain an alternating current from a pulsating current. For 
example, in the use of electron tubes for amplifying received 
signals, Section 196, page 479, pulsations are produced in the 
plate current, above and below its normal steady value. By 
passing the plate current through the primary of a transformer, 
an amplified alternating emf. is obtained in the secondary, and 
this emf. is applied to the grid circuit of a second electron tube, 
and so on. If curve a, Fig. 84, represents a pulsating current, 
the latter may evidently be regarded as compounded of a 
steady current (dotted line) and an alternating current. The 
steady current has no inducing effect in the transformer, but 
the alternating part induces an alternating emf. in the 
secondary circuit. 

^^ Information regarding the magnetic properties of iron at radio 
frequencies may be found in the following papers in the " Proceedings 
of the Institute of Radio Engineers," C. Nusbaum, vol. 7, p. 15, Feb., 
1919 ; M. Latour, vol. 7, p. 61, February, 1919 ; L. T. Wilson, vol. 9, 
p. 56, February, 1921. 


J. Measuring Instruments. 

From what has gone before, it will be plain that the presence 
of an electric current can be known by such effects as the pro- 
duction of heat, magnetic action, or chemical changes. All of 
these effects are greater with a strong current than with a weak 
one, therefore all can be used to give an idea of the magnitude 
of a current. Instruments have been invented which take ad- 
vantage of each of those effects, but some are more conveniently 
used than otliers. Those about which the student of radio 
particularly needs to know are based on two effects of the 
electric current ; the magnetic effect and the heating effect. 

Such instruments can be used either to indicate the current 
in amperes flowing in a circuit, in which case they are called 
ammeters, or to indicate the potential difference in volts be- 
tween two points, in which case they are voltmeters, 

59. Hot-Wire Instruments. — Currents of radio frequency are 
generally measured by means of instruments which depend on 
the heating of a wire or strip of metal. They are therefore 
called " thermal " ammeters. These are again divided into 
two main classes, the expansion and the thermocouple instru- 
ments. The first takes advantage of the lengthening of a metal 
wire or strip when it is heated. Fig. 85 illustrates the principle. 
The current to be measured flows along the wire AB, which is 
of a material having sufficient resistance to cause it to become 
hot. In heating, it stretches somewhat. That permits it to be 
pulled aside by the spring *S acting through the thread T. The 
latter passes around the shaft P, and by turning it causes the 
pointer to move over the scale a greater or less distance, de- 
pending on the current in AB. The scale is graduated (marked 
off) in amperes so that the position of the pointer shows 
ilirectly how large the current is. 

The thermocouple type of ammeter ^^ utilizes the fact that 
when the junction of two dissimilar metals is heated, an emf. 
is developed (see Sec. 15). A pair of metals used for this pur- 
pose is called a " thermocouple." The value of the emf. de- 
pends on the combination of metals and ordinarily increases 
directly as the temperature is increased, 

'« Such instruments are made by the Weston Electrical Instrument 
Co. and the Roller-Smith Co. 


In Fig. 86, the thermocouple consists of the two wires c and 
d, and their junction is in contact with the hot wire AB, in 
which the radio-frequency current is flowing. The emf. pro- 
duced by the heat at the junction is applied to G, an instru- 
ment of the type shown in Fig. S8 below, and causes a pointer 
to deflect ; the millivoltmeter G responds to the direct current 
sent through it by the emf., as will be explained in the next 

It is to be noted that the heat due to a given number of 
amperes of alternating current is the same as that of an equal 
number of amperes, direct current. In fact, the effective value 

FlQ (55 / \ FlO.£>S 

Hot wire 
Prip>cit>le of Therm<»l Annma1"er 

Princible of ThermAf • v -tl 

Am merer usm^ hx.)MnAi«rt '^ - r 

in amperes of an alternating current is defined as equal to the 
value in amperes of the direct current which will produce the 
same average heating effect in a given conductor under exactly 
similar conditions. (See Sec. 51.) The emf. produced at the 
junction does not depend on the direcion of the current in AB 
but merely on the amount of heat produced. This emf. is 
always in the same direction ; it can therefore be measured by 
a d.c. instrument. Thus the combination is useful for meas- 
uring high-frequency currents. 

The heat developed varies as the square of the current, and 
the emf. of the thermocouple varies, quite closely, as the heat 
developed, so the indications of ammeters of the thermal type 
change, practically, as the square of the current. Consequently 
the scale is not uniform, being more open at the upper end than 
at the lower. 


In Fig. 86 the tliermoooiiple is made to appear separate from 
the rest of the instrument; in commercial ammeters the ther- 
mocouple and the indicating instrument are placed inside the 
same case, and the scale is made to read the amperes in the 
radio-frequency circuit. 

When a hot-wire instrument is needed for currents of more 
than a few amperes, it is not practicable to build it with a 
single heating wire. This is true both for expansion and for 
the thermocouple type. Several hot wires or strips are there- 
fore used, arranged cylindrically so that the radio currents 
divide equally among them. Then, either the effect on one 
of them alone is used to operate the indicating mechanism, or 
if thermocouples are used, the emfs. of several can be com- 
bined in series, so that their effects are added. 

On some of the older radio equipments, instruments are 
found which are incorrectly called wattmetei's. They are, as 
a matter of fact, simply ammeters in which the scale instead 
of being marked in amperes is marked proportionally to the 
square of the number of amperes. They are properly called 
"current-square meters." 

60. Magnetic Instruments. — While the heating effect of the 
current is used for measurements at radio freciuency. the mag- 
netic effect is the one utilized in most instruments for direct cur- 
rent and for low-frequency alternating current. The simplest 
and most conmion instrument for measuring direct current de- 
pends upon the force between a permanent magnet and a wire 
carrying current. 

7). C. MiUiammeter. — Fig. 87 represents a rectangular coil C 
of tine insulated wire between the poles NS of a permanent 
magnet." The coil consists of a number of turns wound on a 
light metal frame, which is pivoted in jewel bearings somewhat 
like those of a watch. iS/Sf are spiral springs resembling the 
hairspring of a watch but somewhat heavier and made of 
material that is nonmagnetic and a better electrical conductor 
than steel. They serve the double purpose of conducting the 
current and controlling the position of the coil. is a cylin- 
drical piece of soft iron that serves as a good magnetic path 
between N and »9, and causes a strong and uniform magnetic 

" Instrumonts with a movable coil in the field of a permanent magnet 
are called the " moving-coil " type. 



field to exist in the spaces between JV and O and between O 
and >S'. 

Assume that A and B are connected to a source of emf., so 
that current flows as indicated by the arrows. In the portion 
of the coil next to the N pole of the magnet the current flows 
downward in each turn of wire. The direction of the magnetic 
fleld is always from N toward S. Bv the " left-hand rule " 

-^ ^^ ^ 

F\a 61 


Pri'ncr}>le of the Milhammetep 







Princijial Parra^of ^C Voltmeter 
And Ammeter 

(Sec. 43), it is seen that the force on the wires is toward the 
front (out of the paper). On the side of the coil near the (S^ 
pole the current is up ; that side tends to be pushed toward 
the rear (into the paper). As a whole, therefore, the coil tends 
to turn on its pivots. This motion is opposed by the springs, 
and for each strength of current, there is some position of the 
coil in which the force due to the current and the force due to 
the springs balance. A pointer can therefore be attached to 
the coil so as to indicate, by its position over a scale, the current 
in amperes, in the coil. With the strong magnets, delicate 


parts, and iBne workmanship found in good instruments, it 
takes only a very small fraction of an ampere to move the 
pointer over its entire ransre; the scale may he graduated in 
thousandths of an ampere and the instrument used as a " mil- 
liammeter." Also, with certain modifications to be described 
presently, the instrument can be used to indicate millivolts, and 
is then called a " millivoltmeter." 

The arrangement of the parts of such an instrument is shown 
in Fig. SS. Attaclied to the ends of the permanent magnet MM 
are the soft iron pole-pieces XS, and between them is the cylin- 
drical soft iron core O, mounted on supports not shown in the 
sketch. This arrangement provides a strong and uniform mag- 
netic field in the narrow gap G. The coil C is free to turn in 
this gap, which is wide enough merely to allow the necessary 
clearance, P is the upper spiral spring, above the top of the 
coil. The other one is under the core 0. The pointer is a thin 
tube of aluminum, flattened at the end. The whole is inclosed 
in a dust-tight case, with a glass over the scale. From the de- 
scription it should be evident that abuse, such as setting the 
meter down with a jar, or applying excessive currents, will 
ruin it. 

Moving Coil Galvanometer. — For very delicate measurements, 
where even a milliameter is not sensitive enough, the pivots 
and springs are done away with and the coil is suspended by 
a long, fine wire or strip, which conducts the current to it and 
at the same time opposes the turning effort due to the current. 
Another fine wire at the bottom provides the other connection 
to the coil. If the suspension wire is fine enough and the coil 
has many turns, such an instrument, called a " moving coil 
galvanometer," can be used to measure currents less than a 
millionth of an ampere. No pointer is used; a tiny mirror, 
attached to tlie coil, changes the direction of light reflected from 
it as the coil turns. 

Ammeters. — An instrument of the type of Fig. 88 can be built 
only for small currents, otherwise the coil and other parts 
would be so huge as to be unwieldy. For larger currents the 
scheme of Fig. 89 is used. The current in .4. is to be measured. 
S is a short resistor called a " shunt," consisting of one or 
several strips of a special alloy large enough to carry the 


The current divides, most of it going through S, because its 
resistance is small. A little of it flows through the millivolt- 
meter M, of which the resistance is large compared with (S^. 
This current in M, though small, is a perfectly definite fraction 
of the total (Sec. 25) ; therefore, if we know how great it is, 
we can know at once how great the total is. 

For example, if the resistance of /S is 0.01 ohm and that of M 
is 0.99, then the current divides in the same ratio, the larger 
part flowing in the path of smaller resistance. Out of every 
unit of current 0.99 flows by way of <S and only 0.01 passes 
through the millivoltmeter. The total is 100 times as great as 
the current in M. If the resistances are 0.001 and 0.999, then 
the total is 1,000 times as great. The small current in the 
meter is an accurate measure of the much larger current in A; 
for any one shunt the scale is therefore made to read directly 
in amperes of total current. 

The number of amperes giving full scale deflection is also 
stamped on the shunt. It should agree with the scale of the 

Instruments of moderate range, say up to 75 amperes in one 
type, may be had with the shunt built in, concealed within the 
case. The binding posts are then of massive brass, with good 
sized holes for attaching wires. 

Aside from avoiding rough treatment, or connecting it to 
carry a greater current than it is built for, the chief precaution 
in using an ammeter is to connect it as shown in Fig. 89, page 
139, and not as in Fig. 90, which connection would cause its 
instant destruction. That is, the circuit is interrupted at some 
point and the shunt (or the instrument as a whole if it is self- 
contained) is inserted. If not a self-contained instrument, the 
millivoltmeter should then be connected to the terminals of the 
shunt after the latter has been securely connected in the circuit. 

Voltmeters. — The type of movement used in ammeters is also 
used in voltmeters, but the latter are connected to the circuit 
in a different way, which involves certain differences between 
the instruments. 

In Fig. 90, A and B represent two wires connected to the ter- 
minals of a battery. It is desired to measure the difference of 
potential, in volts, between them. M is an instrument like that 
of Fig. 88 and K is a wire of such great length and small 



diameter that its resistance is sufficient to l^;eep the current sent 
through the instrument within proper limits. In one very 
well-known make this resistance is around 15,000 ohms for a 
meter reading up to 150 volts. 

The current flowing through the instrument, by Ohm's law, is 
equal to the volts between A and B divided by the resistance of 
R plus M. Any change in the voltage will cause an exactly pro- 
portional change in the current in the instrument. Therefore 
it is possible to graduate the scale directly in volts. As a 
matter of fact, for ordinary voltages. R is usually wound on 

'^] F1Q.90 


Princijsle of Voltmeter Connection 

ha. 92 

Irvclined Coil Tyt>e M<ste.p 

MA^^notic Vane Ty^ft Meter 

spools or thin, mica cards which occupy little space and are 
fastened permanently inside the case of the instrument, out of 
the way of the user. He has merely to connect one binding 
post of the instrument to each of the two points in question. 
The pointer indicates on the scale the voltage between them. 
The main precautions to be taken in using a voltmeter are (1) 
never to connect it between points of higher voltage than the 
scale will indicate, even for an instant; (2) not to shake or 
otherwise roughly handle it; (3) always connect the positive 
terminal of the voltmeter to the positive side of the circuit. 

The resistance of a voltmeter may be made sufficiently low, 
without introducing serious sources of inaccuracy, to permit of 


its being used to measure small fractions of one volt, in fact 
one standard form is made to give full scale deflection on 0.02 
volt. Such instruments are graduated in millivolts and are 
called " millivoltmeters." Even when it is used as in Fig. 89, 
p. 139, to measure current, there are reasons why the instru- 
ment should have some resistance besides that of the copper 
wire m the coil. This accounts for the statement, made in 
connection with that figure, that M is a milli voltmeter. 

Ammeters and voltmeters can readily be distinguished, not 
only by the marking of the scale, but by the terminals. Those 
of an ammeter are large, and made to receive fairly thick 
wire ; those of a voltmeter are smaller, having insulating caps ; 
the screw threads are fine, and it is evident that they are made 
to receive only thin wires, as is to be expected because a volt- 
meter takes a very small current, usually less than 0.01 ampere. 

Other Types of Instruments. — For low frequency a.c. measure- 
ments, instruments with a permanent magnet can not be used, 
and the thermal type has not had as wide application as those 
types which make use of the magnetic effect of the current on 
a piece of soft iron. 

Fig, 91 illustrates the principle of one soft iron type. Cur- 
rent flowing around the coil C magnetizes the thin iron strip F, 
which is fixed in position by a stationary support. In the 
same way it magnetizes the other strip M, which is movable, 
being supported from the same shaft that carries the pointer P. 
The tops of both strips are at any instant of the same polarity, 
and the bottom edges of both are of the opposite polarity to this 
(but of the same polarity to each other). They therefore repel 
each other ; the strip M moves to the right, and the pointer turns 
with it. The motion is opposed by spiral springs, as in Fig. 87. 

If an instrument of this type is to be used as an ammeter, 
the coil is made of a few turns of large wire; if it is to be a 
voltmeter, many turns of fine wire are used and a resistance R 
is placed in series with the coil, inside of the case, as in Fig 90. 

It will be seen that such an instrument will respond to alter- 
nating currents, for when the current reverses, the magnetiza- 
tion of both of the iron vanes reverses at the same time, so they 
continue to repel each other. 

Another w^ay of utilizing the magnetic effect is shown in 
Fig. 92. The coil is inclined, and a little iron vane, also in- 
53904°— 22 10 


clined, is carried on the pointer spindle. When the pointer is 
lield in the position Pi by the controlling spring, the vane does 
not point in the direction of the axis of the coil. The current 
sets up a field and magnetizes the vane which then tends to set 
itself along the axis of the coil, turning the spindle in doing so, 
and moving the pointer against the force of the spring to some 
position P2. The difference between ammeters and voltmeters 
of this type is the same as in the preceding form. 

K. Wire Telegraphy and Telephony. 

6Qa. Wire Telegraphy. — An ordinary wire telegrapn system 
consists simply of an electric circuit connecting two stations 
and simple equipment inserted directly in the line at each sta- 
tion. The same kind of equipment is generally used at each 
station, and communication can be had in either direction. On 
short lines the equipment of each station consists of a " key " 
and a " sounder " connected in series in the line. The key is 
a simple device for rapidly opening and closing the circuit 
and is so constructed that it can be conveniently and rapidly 
operated by hand. There is only a small clearance between the 
contacts of the key. When the key is not bemg operated and 
is up in its normal position the circuit is open. At all times 
when no signals are being transmitted at a given station the 
terminals of the key are short-circuited by a switch. The 
sounder is an electromagnet with an armature so mounted, 
close to the poles of the electromagnet on a pivoted arm, that 
the armature moves through a small distance when the current 
passes through the magnet windings. The end of the arm 
moves between two fixed stops, which may be screws. The arm 
moves in accordance with the current impulses on the line, cor- 
responding to the opening and closing of the key at the distant 
station, and the contact of the end of the arm with the stops 
causes a click both when contact is made with the lower and 
with the upper stop. Signals are transmitted by means of 
depressing the key to make " dots " and " dashes." A dot is 
made by depressing the key for an instant ; a dash is made by 
holding the key down a little longer. A dash is equal in length 
to three dots. Messages are transmitted by a " code " or ar- 
rangement of groups of dots and dashes representing the letters 


of the alphabet. The code used on hind lines in the United 
States is the " Morse " code. On the Continent of Europe land 
lines use the " Continental " code or " International Morse 
code." This code is used throughout the world in radio teleg- 
raphy. The International Morse code is given in Appendix 7. 

In ordinary practice there is only one wire between two sta- 
tions, and one terminal of the station apparatus at each end 
is connected to the earth, through which the return current 
flows. Ordinarily a number of intermediate stations are cut 
in on a telegraph line at points between the two terminal sta- 
tions. Telegraph lines are usually operated as closed circuits — 
that is, current is flowing through the line at all times except 
when the line is actually in use for transmitting signals. The 
power for operation may be supplied by a closed-circuit battery, 
such as a battery of " gravity " cells, or by a direct-current 
generator. On all except short lines the line current is not 
strong enough to operate a sounder directly so that signals can 
be read, and a relay is connected in the line. The operation of 
the relay by the line current opens and close-s a local circuit 
which operates the sounder. 

The telegraph system here described represents the simplest 
case. In actual practice many modifications may be made. 
Signals may be transmitted and recorded at high speed by auto- 
matic apparatus. There are very few operators who can copy 
as many as 50 words per minute, but with automatic apparatus 
several hundred words per minute may be transmitted. With 
suitable apparatus it is possible at one time to transmit several 
messages over the same wire without one message interfering 
at all with the others ; this is called " multiplex " telegraphy. 
Many other modifications may also be found. For further in- 
formation see " Telegraphy," by T. E. Herbert, or " Modern 
Land and Submarine Telegraphy," by G. S. Macomber. 

60b. Wire Telephony. — In ordinary telephony the voice itself is 
electrically transmitted oyer wires and reproduced at a distant 
point. The essential parts of a simple telephone system are ( a ) 
a device called the " transmitter." by means of which sound vi- 
brations cause corresponding variations of an electric current. 
(b) a device for changing the electric current variations back 
into the corresponding sounds, and (c) an electric circuit for 
connecting the two devices. 


In the telephone exchanges in use in hirge cities the con- 
necting circuit and switching apparatus are very intricate. 
In some cities automatic switching equipment is in use for 
connecting subscribers at the central office. This equipment 
operates automatically directly under the control of the calling 
subscriber, without an operator at the central office, and may be 
very elaborate. 

MicropJwne Transmitters. — The device -by means of which 
sound vibrations cause corresponding variations of an electric 
current is usually the carbon microphone transmitter. This 
type of transmitter is a speech-controlled variable resistance, 
and its operation is based on the fact that the resistance of 
carbon varies wath pressure changes. A low voltage, as from 
a battery of a few cells, is connected to opposite sides of a 
small cup containing carbon granules. The pressure on the 
carbon granules is controlled by the position of a metal dia- 
phragm on which the sound is impressed. 

Fig, 93a shows a telephone transmitter of a type which is in 
general use throughout the United States, called the " solid- 
back " transmitter. This name is used be*cause the cup con- 
taining the carbon granules is supported on a solid back which 
consists of a metal bar attached at its ends to the case of the 
transmitter. In the figure D is the diaphragm, usually an 
aluminum disk about 2^ inches in diameter. T is the solid 
back, on which is mounted the metal cup B, containing the 
carbon granules C. At the back of the cup is a small hardened 
carbon plate E, which serves as one electrode of the carbon 
microphone. At the front is another very hard carbon plate F, 
which serves as a lid for the small metal cup. The diameter 
of this plate is a little less than the diameter of the inside of 
the cup, but the cup is completely closed by a flexible mica 
disk, which is attached to the rim of the cup and to the 
carbon disk. This carbon lid or cover forms the second elec- 
trode of the transmitter. The button L attached to the 
carbon plate F is maintained in contact with the diaphragm 
by a metal spring S, which serves also to damp the vibrations 
of the diaphragm. The space between the carbon cover F and 
the back electrode E is nearly filled with carbon granules, and 
the electrodes E and F are so insulated that the electric cur- 
rent in the transmitter circuit, in passing from one electrode 



to tlie other, passes through the entire mass of carbon grannies. 
The two wires leading to the transmitter are connected to the 
binding posts G and H. The metal face K of the transmitter 
is made heavy to prevent excessive vibration, and the exposed 
metal parts are usually insulated from the current-carrying 
parts. In practice it is not usually found desirable to have 
the transmitter extremely sensitive, because outside noises are 

Fig. 93a. — Microphone transmitter. 

then transmitted, and it is therefore difficult to understand the 
speech. The current through the usual type of microphone 
transmitter is about 0.2 ampere, and the power consumed in the 
transmitter is about 2 watts. 

The microphone transmitters used in radiotelephony at the 
present time do not differ essentially from those used in wire 
telephony, and, in fact, the identical transmitter usually fur- 
nished by operating telephone companies can be used for radio- 


Telephone Receiver. — The device by means of which the va- 
riations in the electric current reproduce the corresponding 
sounds is the telephone receiver, which is made in a variety 
of forms. The type of receiver shown in Fig. 93b, called the 
" watchcase " receiver, is often used in wire telephony, and is 
almost universally used in both radiotelegraphy and radiotele- 
phony. Two watchcase receivers are commonly used together, 
connected by a metallic " headband," constituting a " head set." 
In Fig. 93b, T is a cup which is the case of the receiver. This 
cup may be metal or hard rubber or a composition. In the 
bottom of this cup a permanent magnet of horseshoe shape is 
placed ; the ends of this permanent magnet are shown at HH. 
To the ends of the permanent magnet are attached the bent, 
soft-iron pole pieces NP, SQ. The earpiece E is usually hard 
rubber or a composition and is threaded to the cup C. Around 
each pole piece a coil of fine insulated wire is wound, forming 
the windings MM. These two windings are usually connected 
in series, so that the received current passes through both 

In some instruments for use with feeble currents the wire is 
very fine and the two coils contain some thousands of turns, 
sometimes as many as 10,000 turns. In the ordinary standard 
receiver the number of turns is, roughly, about 1,000. The re- 
sistance measured with direct current of a receiver for wire 
telephony may vary considerably, but for the standard receiver 
is usually about 100 ohms. A receiver designed for the very 
feeble currents sometimes used in radio communication may 
have a d. c. resistance of 8,000 ohms, and seldom has a resistance 
of less than 1,000 ohms. The coils of a receiver, particularly 
those designed for radio work, have considerable inductance, 
and at high frequencies the impedance in ohms of the coils of 
the receiver may be many times the resistance of the coils meas- 
ured with direct current. The larger the number of turns used 
the greater is the magnetic effect in the receiver for a current of 
given strength. The use of telephone receivers in radio com- 
munication is discussed in Section 180. 

Above the pole pieces and very close to them is a thin cir- 
cular soft-iron disk D, called the " diaphragm." The diaphragm 
of a -receiver can be seen through the hole in the center of the 
earpiece. The distance between the pole pieces and the dia- 



phragm is important in determining the sensitivity of tlie 
receiver; in standard instruments this distance is about 0.003 
inch. The permanent magnet pulls the diaphragm toward the 
pole pieces a certain distance, which depends upon the flexi- 
bility of the diaphragm. The variations in the current in the 
receiver windings, corresponding to the sound vibrations of 
the voice spoken into the transmitter, produce corresponding 
variations in the magnetic field of the pole pieces, and the 
diaphragm moves in accordance with these variations and 
reproduces the voice spoken into the transmitter. 

Fig. 93b. — Watch case telephone receiver. 

It is possible to use a telephone receiver as a transmitter. 
With a circuit containing only two identical sensitive telephone 
receivers and no battery, the same instrument can be used 
alternately as receiver and transmitter by the person at each 
end of the line, and speech thus transmitted. This was, in fact, 
done in the early days of telephony, but the currents so gen- 
erated by using the receiver as a transmitter are so feeble that 
other devices are now used for practical purposes. 

Operation. — Words spoken into the transmitter vary the pres- 
sure on the carbon granules, and hence the resistance between 
the transmitter terminals and corresponding variations in the 
output current of the transmitter are thus produced. The 
nature of the electric current transmitted by the wires leading 
to the receiving station depends upon the auxiliary apparatus 
used with the transmitter. The electric current passing be- 


tween ^^e stations is often a feeble alternating current having 
a frequency from perhaps 100 cycles per second to 3,000 cycles 
per second, considerably higher than the frequencies used for 
commercial lighting purposes. (See Sec. 50.) These frequen- 
cies, in fact, correspond to the frequencies of the sound waves 
impressed upon the transmitter diaphragm. Thus the note 
" middle C," which corresponds to a sound wave having 256 
vibrations per second, causes an alternating current having a 
frequency of 256 cycles per second. It should be noted, how- 
ever, that the wave forms produced by speech or by musical 
sounds are by no means as simple as the sine wave shown in 
Fig, 71. In the case of some kinds of telephone systems the 
wires may transmit a pulsating direct current of several tenths 
of an ampere, whose pulsations correspond to the impressed 
sound waves. The electrical transmission of speech is more 
fully described in connection with radiotelephony. (See Sees. 

Speech transmitted by telephone instruments is not entirely 
natural, because the vibrating parts, both electrical and me- 
chanical, of the telephone equipment used produce distortions 
during the transmission of the sound. In the early days of 
telephony, when the causes of distortion were not well under- 
stood, serious effects of this kind occurred when talking over 
veryshoit distances. At the present time it is possible to talk 
from New York to San Francisco by wire. This result has been 
attained only after years of experience and investigation and 
the development of instruments involving principles only re- 
cently discovered. Successful transmission over such long 
distances requires many refinements in the design of every 
device used. 

It is possible at the same time to transmit both telegraph 
and telephone messages over the same line; such a line is 
often called a " composite " line. 

With the currents used in ordinary telephony, it is pos- 
sible at the same time to transmit three telephone messages 
over two pairs of wires by adding at each end a " phantom " 
circuit, which is an additional circuit balanced across the two 
main circuits through suitable impedances. For information 
regarding phantom circuits, see the books mentioned in the 
next paragraph. The operation of a telephone system so that 


one pair of wires carries more than one message is called 
" multiplex telephony." Besides the use of the phantom circuit, 
multiplex telephony can be attained by the use of alternating 
currents of the high frequencies used in radio communication. 
(See Sec. 212.) 

For further information regarding wire telephony, the reader 
may consult G. D. Shepardson, " Telephone Apparatus " ; K. B. 
Miller, "American Telephone Practice " ; or H. R. Vandeventer, 
" Telephonologj." In a book by David P. Moreton, " Drake's 
Telephone Handbook," may be found an elementary exposition 
of the principles of telephone apparatus, and detailed informa- 
tion regarding practical methods of construction and operation 
of various kinds of telephone systems, which may be of par- 
ticular interest to the beginner. 

Circular 112 of the Bureau of Standards, " Telephone Serv- 
ice " (1921), gives detailed information regarding the opera- 
tion of various kinds of telephone systems, and will be found 
valuable for reference. 



61. Generators and Motors. — In the preceding chapter some 
laws of electric and magnetic circuits are discussed, and at- 
tention is directed to the relations between electric currents 
and magnetic fields. In the present chapter certain practical 
applications will be described, in which use is made of all those 
laws, but which are based particularly on three experimental 
facts, namely, that — 

1. When a conductor is moved across a magnetic field, an 
emf. is induced in the conductor. 

2. When a current flows in a conductor in a magnetic field, 
a cross-push is exerted on the conductor. 

3. When a current is sent around an iron core, the core is 

The forces involved are not necessarily small, as is some- 
times imagined, but may run into hundreds or even thousands 
of kilograms. Such forces can be used for power applications 
on a large scale, by means of machinery, called ** dynamo- 
electric " or, for short, *' electrical " machinery. 

Electric machines are used for conversion of power from 
mechanical to electrical form, or vice versa. If driven by some 
sort of prime mover like a steam engine, gas engine, or water 
wheel, they convert mechanical power into electrical power and 
are called " generators." If supplied with current and used to 
drive machinery, vehicles, or other devices, thus converting 
electrical power into mechanical power, they are called 
*' motors." 

While there are various types of motors and various types 
of generators, the difference is more in the use than in the 
construction or appearance; in fact, the difference between 
most motors and the corresponding kinds of generators is so 
slight that the same machine can be used for both purposes 
with no changes, or only minor ones. Electric machines may 
be built for either direct or alternating current. 



A, The Alternator. 

62. Production of Emf. by Revolving Field. — It was pointed 
out in Chapter 1, Section 45, that the motion of a conductor 
across a magnetic field causes an electromotive force in the 
conductor. This is true whether it is the conductor or the 
magnetic field that actually moves; the essential thing is that 
there shall be relative motion of one with respect to the other. 

One way in which such relative motion may be secured is 
illustrated by Fig. 94. Suppose the magnet NS is made to 
rotate continuously in a vertical plane about the axis mn. The 
loop of wire ab is stationary. Its ends are connected to some 
external part of the circuit X. As the field from the N pole 
sweeps across a, an electromotive force is induced in it to the 
right and at the same time an electromotive force is induced 
to the left in h by the passing of the S pole. Thus the emf. 
produced tends to send a current in a clockwise direction 
around the loop ab, as indicated by the arrows. 

When the magnet has made half a revolution the poles have 
exchanged places with respect to a and b and the electromotive 
forces are counter-clockwise around ab. As the magnet con- 
tinues to be rotated, there are thus two pulses of electromotive 
force (and of current if the circuit is closed) in opposite direc- 
tions for each revolution of the magnet. The device described 
constitutes a simple " alternating-current generator " or " alter- 

63. Direction of Emf. — The direction of the electromotive 
force induced in a straight conductor moving across a magnetic 
field can be determined by the " right-hand rule." This rule as 
generally stated assumes that the magnetic field is stationary 
and that the conductor moves across the magnetic field. Using 
the 7'ight hand, the thumb, the first finger, and the second finger 
are so placed that each is at right angles with the other two, 
the first finger being extended directly out. Then if the thumb 
is pointing in the direction of motion, and the first finger is 
pointing in the direction of the magnetic lines of force (from 
north pole to south pole), then the second finger will point in 
the direction of the induced emf; that is. in the direction in 
which the induced current will flow. 



If the magnetic field is moving, and ttie conductor stationary, 
the rule is readily applied by recalling that the relative motion 
is the essential thing. Thus in Fig. 94 the effect of having the 
north pole move toward the reader, passing the conductor a. 


Production of alterrvitm^ 
" ' ' y rotating ma5/i«J' 

> i- 

(t) »- 

One cycto 


(i) ThoijSAr>dT-hi,'<»f «iV»"*>'^ 




k15 rriA^ne'f' 
mn ftptis. Abool" which it revoWea 
Ab it.ition<jr^ \oa\> o'f Wire 
y.Z.'b.A ^uocassive t>oaiti'on3 of t4 


/i!Tern.itrn^ electro rnot"ive 
jor<ic A\ ZS cyc(«s pc seoond 

Fia. 9fe 

AItC'>»Ti'\i, omf. by fr>oft/f>oUr ■fi«l<d 

is the same as if the conductor were to move away from the 
reader, passing pole N. 

A similar left-hand rule can be used for determining the direc- 
tion in which a straight conductor carrying a current will move 
if placed across a magnetic field. Using the left hand, the 


thumb, the first finger, and the second finger are so placed 
that each is at right angles to the other two, the first finger 
being extended directly out. Then if the first finger is pointing 
in the direction of the magnetic lines of force and the second 
finger is pointing in the direction in which the current is flow- 
ing, the thumb will point in the direction in which the con- 
ductor will move. 

The reader may compare these rules with the rule for the 
direction of the magnetic field about a straight conductor carry- 
ing a current, as stated in Section 4, page 30, and with the 
rule for the polarity of a solenoid stated in Sec. 42, page 106. 

64. Emf. Curve. — If the electromotive force is called positive 
when to the right in a, and negative when to the left, the 
changes in it may be shown by a curve like Fig. 9-5. Successive 
moments of time are taken along the horizontal axis, and the 
corresponding electromotive forces are shown by the height of 
the vertical ordinates. When the north pole is in position 1, 
Fig, 94, no emf, is induced. This is shown by the point marked 
1, Fig, 95. A short time afterward, in position 2, Fig. 94, a 
certain maximum emf. is induced, shown by point 2 on the 
curve. When the pole has moved to position 3 the electro- 
motive force has decreased to zero, and in position 4 it has 
reached a negative maximum. It then decreases again to zero 
and the whole series is repeated. 

A curve like the one in Fig. 95 is often called an electromotive 
force curve or wave. 

The emf. curves generated by commercial alternators have a 
variety of shapes, but ordinarily they are not very different 
from sine curves, and for reasons given in Chapter 1 are usually 
treated as such. 

65. Cycle, Period, Frequency. — A regularly recurring series of 
values of electromotive force, from any point in the series to 
the corresponding point in the next series, is called a " cycle." 
The portion of the curve in Fig. 95 from 3 to 7 represents a 
cycle ; similarly, the portion from 2 to 6. The time required for 
one cycle is the " period." The number of cycles per second is 
called the " frequency." 

In American commercial practice, 60 and 25 cycles per second 
are the most common frequencies for alternating current cir- 
cuits. The corresponding periods are -gV ^.nd ^V of a second. 


Other frequencies, for example, 50 cycles, are used in Europe. 
For certain purposes in radio telegraphy, 500-cycle generators 
are used. Quite recently, special machines have been developed 
for generating frequencies as high as 100,000 cycles per second, 
to be applied directly to the radio circuits. This frequency cor- 
responds to a radio wave length of 3,000 meters.^ 

66. Multipolar Magnets. — To produce a frequency of 60 cycles 
per second by the use of a single magnet with two poles re- 
quires a speed of rotation of 60 revolutions per second. Such 
a speed is not practicable for large machines. To get 500 cycles 
would i*equire 500 r. p. s., or 30,000 r. p. m. (revolutions per 
minute). By arranging a number of similar north and south 
poles alternately, as in Fig. 96, and providing corresponding 
conductors, a lower speed of rotation may be used. As in 
Fig. 94. the magnet is supposed to be made to rotate, while the 
conductors a. b. c, d, e, f remain stationaiy- 

When the upper north pole is coming toward the reader, 
electromotive forces will be induced in the several conductors 
in the direction of the arrows. The conductors are all con- 
nected in series, except between f and «., where connection is 
made to an external part of the circuit, X. All are in the same 
relative position to the several magnetic poles ; their electro- 
motive forces are equal, and in the case shown, the total is six 
times as great as the electromotive force in any one conductor. 

For every revolution of the magnet, each conductor is passed 
three times by an X and three times by an -S pole. Each pair 
of poles gives rise to a cycle, so for each revolution there are 
three cycles of emf. in the conductors. Thus, for a given speed, 
the frequency is three times as high as it would be if there were 
but one pair of poles. 

67. Field and Armature.— The magnets {NS, in Fig. 96. p. 116) 
which produce the magnetic field of an alternator are called 
the " field magnets." If there is but one north and one south 
pole, the machine is said to be " bipolar " ; if there are several 
pairs of poles the machine is " multipolar." 

The conductors in which the electromotive forces are induced 
constitute the " armature winding." The winding is supported, 
usually by being embedded in slots, well insulated, on an iron or 

1 Wave length is explained in Sec. 125. High-frequency alternators 
are described in Sees. 95 and 173. 



steel core called the " armature core." Winding and core to- 
gether constitute the " armature," though this term is also used, 
loosely, when the armature winding alone is meant. 

68. Coil-Wound Armature.— The electromotive force devel- 
oped in one conductor of an ordinary generator is only a volt 

Fig. 97.— Windings partially assembled in a 25-cycle synchronous motor. 

or two, not enough for practical use. Armature windings, 
therefore, consist of a large number of conductors, usually com- 
bined into coils (see Fig. 97) of several turns each, which are 
pushed into slots in the face of the armature core and then 
connected by soldering. The joints have to be carefully covered 
with tape or other insulating material. 



The coils are made of copper wire covered with insulation 
(usually cotton) wound to the proper shape on a form, wrapped 
with tape, and finally covered or impregnated with an insulat- 
ing compound. The core slots are often lined with tough, heavy 
paper or fiber. After being placed on the core, the coils are held 
by wedges of fiber or wood driven into the tops of the slots. 

The core is built up of thin, flat sheets of soft iron or steel, 
ring-shaped, with teeth on the inner edge.^ See Fig. 98. 
Enough sheets are stacked up to make a cylinder of the length 

Fig. 98. — Laminations partly assembled, making up the armature core 
of a skeleton frame alternator. 

desired. Occasionally a separator is included to provide air 
ducts through the core for ventilation. The three dark rings 
around the core in Fig. 97 show where the ducts are. The 
teeth are carefully lined up, and the spaces between them be- 
come the troughs or slots for the windings. 

How the emf. increases and decreases in such a winding can 
be studied from Fig. 99. Here the coils are drawn as if the 
armature were unrolled and opened out flat. The magnet poles 
are supposed at the given instant to be over the rectangles 

2 See section 78, p. 173. 



marked N and S*. Each of the numbered lines in the figure may 
represent either a single conductor or one side of a coil. Only 
a portion of the armature winding is represented. 

Imagine the poles in Fig. 99 to be moving toward the right, 
the conductors Ij 2, 3, etc., remaining stationary. Starting at 
the instant when a north pole is just approaching conductor 1, 
and a south pole conductor 5, electromotive forces will be in- 
duced in the directions shown by the arrows. As conductors 2 
and 6, 3 and 7, etc., are reached, additional electromotive forces 
are induced. The maximum comes when the N pole covers 1, 
2, 3, and 4, and the /S pole covers 5, 6, 7, and 8. After that the 


f\Q. loo 

To show Add iti'on cf^ emf. In 
Joccesai'vo coil* 

A -au-mAt>jr« Cora <5- &ir>A^ 

CT- bole core T- j5ole tifa 

D- t>ol« shoe t- Armditune Teeth 

E- +\e.\<i rin^ 5- " slot's 

resultant electromotive force begins to decrease, falling to zero 
and then beginning to increase in the opposite direction. In 
this manner an alternating emf. is gotten in which the changes 
occur gradually as conductors get into or out of the magnetic 
field one by one, or at least coil by coil. In addition the edges 
of the poles are usually tapered off ("chamfered") to ;nake 
the changes still smoother. 

69. Concentrated and Distributed Windings. — Sometimes all 
the turns for one pair of poles are combined into one coll, 
which is put into a single pair of large slots, one for each pole. 
Such a winding is a "concentrated" winding. (See Fig. 103.) 
When the portion of the core under each pole face contains a 
number of slots in which the coils are placed, the winding is 
" distributed." (See Figs. 97, 99, 100.) 

53904°— 22 11 



Fig. 101-A-B (C and 
KVA., 900-R. P. M. 

1. Stator frame. 

2. Complete rotor. 

3. Shields. 

4. Journal boxes. 

5. Oil rings. 

6. Stator winding. 

7. Stator leads. 

8. Cable tips for leads. 

D on opposite page).— Alternating-current generator, 150 
, 60-cycle. Single phase. Dismantled parts listed below. 

9. Oil gauge. 

10. Oil hole cover. 

11. Shaft. 

12. Pole shoe. 

13. Collector ring. 

14. Field coil. 

15. Cap screws for holding 

shields to frame. 

16. Journal box set screw. 

17. Twin unit brush 

holder, with brushes. 

18. Dust cap. 

19. Dust washefr. 

20. Rotor leads. 

21. Rotor lead cable tips. 

22. Brush stud. 



70. Magnetic Circuit. — It is important to get an understand- 
ing of the magnetic path in an electric machine. Various shapes 
are possible, but an understanding of one makes all others easy. 
Fig. 100 is a diagram indicating the parts of a typical mag- 
netic circuit, with their names. It is not intended to show 
details of mechanical construction. The fine lines in the upper 
part of the figure show the path of the magnetic flux for one 


pair of poles. The paths for the other poles are similar. The 
armature conductors are placed in the slots ss. 

71. Field Excitation. — Thus far nothing has been said as to 
how the magnetic field is produced. While permanent mag- 
nets might be used, they are not satisfactory for practical 
purposes, except in the very little machines called " mag- 
netos." " Electromagnets are therefore used. The poles are 
fitted with coils or spools of wire, usually of a large number of 
turns, through which direct current is sent from some external 

The coils are connected to a pair of metallic rings, called 
" slip-rings " or collector rings, which are in contact with con- 
ducting strips, called " brushes," connected to the source of 
current. As the entire field structure rotates, current is 
brought to the coils through the sliding contacts of the sta-. 
tionary brushes with the revolving slip-rings. 

The source of direct current is usually a separate small 
direct-current generator, which when used for this purpose 
is called an " exciter." If used for one alternator alone its out- 
put will range from 1 to 3 per cent of the rating of the alter- 
nator. When the alternator is very small, like those used in 
the Signal Corps portable radio sets, the exciter is larger by 

72. Stator and Rotor. — When it is desired to refer to the sta- 
tionary and rotating members of a dynamo-electric machine 
without regard to their functions the former is called the 
" stator " and the latter the " rotor." 

73. Arrangement of Parts. — A good idea of the parts of a re- 
volving-field alternator is obtainable from the pictures in Fig. 
101, which show a complete machine, as well as views of the 
most important parts. The general view shows how the parts 
fit together. 

Through the holes in the ventilated iron frame of the stator 
the outside of the core is visible. On the inside of the core 
the laminations can be dimly seen. The two dark rings which 
seem lo divide the core into thirds are ventilating ducts. 
Where the windings lie in the slots they are concealed by the 
wedges, but the ends of the coils are in plain view. Note that 

" A discussion of the principles of the magneto may be found in 
Bureau of Standards Scientific Paper No. 424 ; 1922. 



the coil ends are given a twist to make a neat construction. 
Tlie four terminals at the left of the stator indicate a two- 
phase machine (Sec. 75). 

The right-hand end shield shows one brush holder in place, 
to the left of the bearing; the little hole to the right of the 
bearing is for the stud on which the other brush holder (lying 
in front) is to be mounted. 

The brushes of one set slide on one collector ring, and those 
of the other set on the other ring. Two brushes are used in 
each set, in this particular machine, in order to have a large 
and reliable contact. The ends of the cables leading to the 
brushes are in view on the right of the complete generator. 

1 ^ 

L- b— r 

FlQ.. Vo'i 

R f^ 

Production of AlternATin^ ernf. by revolving coil 
As - Field mA^net RR. -Collector ri'n^a 

Ab- Loot> oj v^i're C>C> - DrovShes 

On the rotor the pole shoes are noticeable, held on by six 
screws. One of the connections between field coils is seen be- 
tween the upper pole shoe and the one just in front of it, near 
the center of the shoe. The massive ring to which the pole 
cores are attached is also visible. There are two collector 
rings close together, though it is a little difficult to distinguish 
them in the picture. 

74. Other Forms of Alternator. — Thus far we have considered 
alternators of which the field magnets revolve, while the arma- 
ture is stationary. That is the construction generally used on 
large machines, one reason being that it makes the armature 
easier to insulate. But it is also possible to have the field mag- 
nets stationary while the armature is made to revolve. Small 



The principle is sho^^'Tl in 

machines are often built this way. 
Fig. 102. 

The magnetic field occupies the space between the poles N 
and (S of the stationary field magnet. The turn of wire ab is 
made to revolve about a horizontal axis in this magnetic field. 

Fig 103. — Circuit diagram of revolving-armature alternator. A, arma- 
ture ; F, frame ; P, poles ; R, collector rings ; B, brushes ; TT, termi- 
nals of field circuit ; XX, leads to external circuit. 

When a is passing under the A^ pole, coming toward the reader, 
the electromotive force in it is to the right, and that in b 
which is cutting through the same field (the direction of the 
magnetic flux is from the N pole into the S pole), but moving 
a^vay from the reader is to the left. Current will therefore 


flow in the turn of wire, and by way of the collector rings and 
brushes in the external circuit, as shown by the arrows. 

When the loop has made half a revolution, a is passing in 
front of the S pole and the electromotive force in a is toward 
the left. In b it is toward the right. In the external portion, 
X, of the circuit the flow of current will then be opposite in 
direction to the arrows. The continued rotation of the loop 
thus causes an alternating current to flow in the circuit. 

The simple bipolar magnet of Fig. 102 may be replaced by a 
multipolar electromagnet consisting of a massive cylindrical 
frame called the " yoke," from which poles project radially in- 
ward. Direct current is sent through coils or spools on the 
magnet poles. The same kinds of windings are used for the 
revolving armature as are used for the stationary kind ; the 
only difference is that they are put on the outside instead of 
on the inner face of the core. 

A machine in which the fleld magnets are stationary, while 
the conductors, in which the electromotive force is induced are 
rotated, is said to be of the " revolving-armature " type. A 
diagram of such a machine, used in one form of radio pack set, 
is given in Fig. 103.^ The armature winding in this case is of 
the concentrated type. A picture of a generator very much like 
it appears in Fig. 122. 

It has previously been shown that, when the field is made to 
revolve, slip-rings have to be used in the field circuit. Simi- 
larly, when the armature is the part that revolves, there must 
be slip-rings in the armature circuit to provide connection with 
the external portion. Such rings are shown at RR in Fig. 102. 

Inductor Alternator. — Another type of alternator is of especial 
interest in connection with radio telegraphy. It is called the 
" inductor alternator," and is used particularly for the genera- 
tion of continuous high-frequency currents, say, around 100.000 
cycles per second, but is also used for lower frequencies. 

8 The little machine to which this diagram applies has 18 field poles 
and 18 armature teeth, runs 3,333 r. p. m., and generates current of 
500 cycles frequency. It is designed for an output of 250 volt-amperes, 
to be used in a field radio pack set. The windings are shown only in 
diagram ; actually the field coils average 250 turns each ; the armature 
coils 19 turns each. The sketch is practically to scale, except the col- 
lector rings, which are drawn smaller so as not to conceal the arma- 
ture. The whole diameter across the frame is about 15 cm. (6 in.). 



The principle on which sucli machines operate is illustrated 
in elementary form in Fig. 104. The field magnet and the arma- 
ture are both stationary, A considerable gap separates the 
armature core from the faces of the field poles. In this gap are 
masses of iron, /, free to revolve in a plane perpendicular to the 
plane of the paper about the axis mn. These masses of iron 
are called " inductors." Imagine them made to revolve by an 
external force. When the inductors are in the position shown, 
between N and Ci, and (S and C2, there is a certain magnetic 
flux, due to the d. c. excitation. When the inductors are not 
in that position, there are long air gaps in the magnetic circuit. 

FlQ. 104 

Fia. io5 

Production o-f A,IternaTtn^ em^ by 

moving Iron Inductor 
FJ5 - Poles of itAtioridry «lectromd^net 
C|C2- Cores o'f ^titioriAr^ arnvitvre 

Production of 2-f>K«^a<S em|i. 

t\U -Coils in Which <il 
1 1 - Moving nrvisies of 
revolved •about <aAi\5 rnn 

'■ irar\('ir,3ucto'S) 

which have a very much smaller permeability than the iron con- 
ductors. The fiux is consequently less. The increase and de- 
crease of magnetic flux in the coils A A sets up an alternating 
emf., because any change in the flux inclosed by a circuit sets 
up an emf. in the circuit (Sec. 45) in the one direction while 
the flux is increasing, and in the opposite direction while it is 

In this type of alternator, the passing of each mass or 
inductor causes a complete cycle of emf., whereas with alter- 
nators of either the revolving field or the revolving armature 
.type it requires the passage of two poles to cause a cycle. 

75. Polyphase Alternators. — Suppose that in Fig. 94, p. 154, 
another loop similar to ab, but entirely independent of it, were 


placed at right angles to ab, as shown at cd in Fig. 105. The 
rotation of XS would induce in the second loop an alternating 
emf. identical with that in the first, having the same fre- 
quency and the same series of values. The sole difference 
would be that they would reach corresponding points in the 
cycle at different instants of time, for at the moment when 
the poles were in line with the conductors of one loop, and 
it was having maximum emf. induced, the other loop would 
have none. 

Suppose the emf. wave of the first winding is given by curve 
I, Fig. 106. Then curve II will represent the emf. of the other 
winding. The two curves are first shown separately and then 
combined into one diagram. They are alike in shape, showing 
that the two emfs. go through the same series of values, but 
II is always a quarter of a cycle behind I (see Sec. 53). Sup- 
pose the distance — 4 represents ^^ second. Then whatever 
happens in I, at any instant, happens in II just x^^ second 
later. This is expressed by saying that there is a " phase dif- 
ference " of a quarter cycle between them, or that the two 
emfs. differ in phase by a quarter cycle. 

Two emfs. which differ in phase by a quarter of a cycle are 
said to be in quadrature. A generator giving sucb a pair of 
emfs. in quadrature is called a " two-phase " alternator. The 
two windings considered separately are called "phase wind- 
ings," or, somewhat loosely, the " phases."' Either one may 
be thought of as phase I and the other as phase II. 

It will now be plain why the pictures of Fig. 101, show four 
terminals at the left. Two belong to one phase and two to the 

There may be more than two phases ; in fact, modern power- 
generators usually have three phase windings. 

Definitions. — A machine for a simple alternating current is 
called a " single-phase " machine. Generators used exclusively 
for radio communication are generally single-phase. 

A machine for alternating current of two or more phases is 
called a " polyphase " machine ; polyphase generators are either 
two-phase or three-phase, almost without exception. They are 
used for power purposes. 

Arrangement of Windings. — An idea of the way the windings 
of a polyphase generator are arranged may be obtained by re- 



ferring back to Fig. 99. Suppose another winding to be added 
identical with the one shown, but occupying the spaces left 
vacant by the first winding.* As the magnet poles move along 
the windings come into play alternately. 

Notice that in a single-phase generator half the surface of 
the armature core has to be left vacant. In a polyphase gen- 

E-mj Curves -^or 1 {jKasx? circuit' 
X Curve "Jor one ^h<is>e 
U. Curve for other ^H^se 

Cvrv«s Jor ttire«-)>K<i»e cmj. 



star orY 

star or Y 

Three f>lvise connec.t"ion5 

erator, on the contrary, the windings may cover the entire 
surface, and usually do. 

Next, suppose the two-phase windings were each made nar- 
rower, leaving space for a third winding just as large as each 

* The reader who has diflSculty in imagining the second winding may 
trace on transparent paper the winding shown and may then slide the 
paper to one side by the proper amount. 


of the first two. AVe should then have three phase windings, 
and a given field pole would pass them one after the other. 
Tlius would be produced three emfs. differing in phase by equal 

By properly selecting the terminals, the three emfs. would 
follow one another as represented in Fig. 107, and it will be 
seen that now the difference between them is one-third of a 
cycle. In the time of one cycle each of the three comes to a 
positive peak one after the other. The emf. curves are shown 
in Fig. 107. The emfs. are often spoken of as differing by 120°. 

It might be expected that a three-phase machine would have 
six terminals. As a matter of fact, the phases are usually so 
connected in the machine that three terminals are sufficient, as 
illustrated in Fig. 108. The three coils stand for the three 
armature windings. When joined as in the upper sketch, they 
are said to be connected in " delta " ; when one end of each coil 
is brought to a common junction as at in the middle figure 
they are connected in " Y " or " star." The lower figure is the 
same as the middle one, in that terminals 2, 4, 6 are all joined 
together and 1, 3, 5 are connected to the line wires A, B, C. 
By changing the position on the paper the connections are made 
to look simpler. 

The scheme of connections is ordinarily of no interest to the 
operator, except in case of trouble, and cannot be determined 
without a close examination. The wires by which the connec- 
tions are made are carefully wrapped and tucked away at the 
end of the armature, concealed by an overhanging part of the 
frame or by the end shield, which has to be taken off before the 
connections can be traced." 

5 Discussion of this subject can be found in any textbook on alter- 
nating-current machinery. See, for example, Timbie and Higbie, " Alter- 
nating-Current Electricity. First Course," pp. 114-128 ; Franklin & Esty, 
"Elements of Electrical Engineering" (2 ed.), vol. 2, pp. 98-116. 


B. Alternator Theory, Losses, and Efficiency. 

76. Equations for Frequency and Emf. — The frequency of the 
emf. generated by an alternator of the revolving-field or revolv- 
ing-armature type is given by the equation : 

/=% or/=|^ (65) 

where f = frequency in cycles per second. 
p = number of poles. 
n = revolutions per second, 
^'^revolutions per minute. 

The passing of each pair of poles. -^ in number, gives rise to 

one cycle. If there are n revolutions per second, the number of 

cycles per second is therefore o" X^. The second form of the 

equation is given, because the speed is commonly given in revo- 
lutions per minute. 

For example : What frequency will a 12-pole alternator give when 
running at 5000 r.p.m. ? 

With 12 poles each revolution gives 6 cycles. In a minute there will 
be 6X5000=30,000 cycles. In a second there are 30.000^60=500 
cycles. The machine gives 500 cycles per second. By the second 
formula we get the same answer 

^ 12X5000 ^^^ 

/= — J2o — =500 cycles per second. 

For tlie inductor type the frequency is the same as the num- 
ber of inductors which pass a given point per second. Thus 
40 teeth at 25 r.p.s. give 1000 cycles per second. The inductors 
are usually in the form of teeth, somewhat like gear teeth, that 
project from the revolving part. 

The emf. generated in an alternator depends on how much 
magnetic flux is cut by the conductors per second. Increasing 
either the magnetic flux from each pole, or the number of poles 
that pass a given conductor in a second, or the number of con- 
ductors connected in series (so that the effects in them are 
added together) increases the emf. of the machine in a corre- 
sponding way. This may all be stated in one equation. 


E=(pNfJc (66) 

where £"= effective volts (Sec. 51), as shown by a voltmeter. 

0=magnetic flux per pole, in maxwells or " lines of mag- 
netic force." 

iA'= number of turns of armature winding connected in 

/= frequency in cycles per second. 

7i-=a multiplier that depends on the arrangement of the 
winding and certain mathematical relations not 
necessary to consider here." 

77. Dependence of Driving Power on Current. — The power con- 
sumed in an electrical circuit at any instant is proportional to 
the emf. and also to the current. It is therefore proportional 
to their product. If the current is made to flow by means of a 
generator, and if the generator is driven by an engine of some 
sort, the power that has to be developed by the engine evidently 
depends upon the power used in the circuit. It is worth while 
to trace the reason why increased current in a generator calls 
for more power from the engine that drives it. 

Let the simple loop in Fig. 102 be made to rotate at constant 
speed by any " prime mover " suitably governed. This prime 
mover may be anything that vt^ill make the loop go around — a 
man turning a crank, a gasoline engine, a steam engine, an 
electric motor, etc. At the instant wiien the loop is in the 
plane of the paper, and a is coming toward the reader, an emf. 
is being induced in it, in the direction of the arrow. If the 
circuit is closed, a current flows in the same direction. But it 

^ The student who has some previous knowledge of electricity will see 

that if 2f poles pass a conductor per second, the average flux cut per 

second is 2fX<f>- To generate 1 volt requires passing 10^ lines of flux 

per second. Hence the average volts per conductor are 2fx 4-10^. 

Each turn consists of two conductors in series, so we multiply by 2. 

The voltmeter reads not average but effective volts. For sine waves 

the effective volts are 1.11 times the average, so we multiply by 1.11. 

Collecting all the numbers it is seen that ^ in the formula stands in 

2 X 2 X 1.11 4 44 
part for ^^ — "^"^8 ■■ ' — or ^Qg . It also includes a factor, not greater than 

1, depending on the kind of winding used, because if the winding Is 
distributed, the emfs. in the various turns do not rise and fall together 
(there is a difference in phase), and this must also be taken into 

1 72 I) V N A .vro-ELP:CTRrc machin ery. 

JH known (see Sec. 4'.^) uIkti a conrluct.or, carrying a 
current, i« in a ma^nef.k- |j<|r], tht- coruhictor tenrls to move 
acroHH the field. The foro- on tlu' ♦•ondiiff.or is proportionni to 
the strenj(th of the field uu<[ t(; the eurrent. Tho direction of 
tlif? forr-e is ;,'iven hy the loft-hand ruh*.^ Apr>lyin;< tJie left- 
h;ifi<l ni]<- to 'oridijetor «, It Is hccji t)j;it th'^ fojv(. (>fj jt, is away 
from the reader, opposite to the din^otion in uhieh the con- 
ductor iH hoinj? driven, ho tiuit the wire is harder to push than 
It would be if there were fio ^urrr-nt. Tlw. j^reater the current 
In the conductor the greater must be tiie force exerted to drive 
It arounrl, nnd therefore the greater must be tiie power (ievel- 
or^^d by the prime mover In Iceepin;? up. a ^iv<'n sf)eed. The 
Hame reawniirit^ Mf)plj<'l to ft «hows tiuit it. ;i'-t.s uitJj a in opfjos- 
In^ rot;ition. 

78. Losses. — <)i the Mieflianir-ai f-ncrtry HiijijWii'I ton. ^'<'ri'-r;itor 
by Its prime mover, not nil ;if)f)cnr>: iti elc-trifjil form in tli<i 
circuit. Some Is unavrjidjihly transformed intr> Iieat, nnd thus 
lost for practical purposes. 'J'iie lo.sses, whuh may he culled 
power loHHes or ener^ losses, may be classified as — 

1, Mechanical losses. 

2, Copper losses. 

3, Core losses. 

Mechanical Iohhch are thos^? due to friction in lli<- hearings, 
friction at the brush conta<^'ts, find frjrti(,n h(;tw(!en the jjir and 
the movln;( part of tiie machine, comtnonly called windij^e. 
Thf! latter Is not important in low-sx)eijd machines, but be- 
comes prominent in the caw? of very iiiirh-spec-d generators. 
Generators of the kind we fire (iLscussIng urf; driven at nearly 
coBstant speed, .so the rnechjini'-nl loss^^s do not depend rnucii (tu 
the load, whether large or small, 'i'hcy do depend very greatly 
on the condition of the b<*aringH nnd brushes. Some points 
regarding the care of machines in this respect are glv<'n at the 
end of this chapter, In Section 1')^;. 

Copper loHHCH fjre due to the flow of current ngjiinst the re- 
sistance of the field and armature windings. 'Jh»-y an? tiiere- 
fore divided Into two parts, fi<lfl fofjfjer loss and amuiture 
copfK-r loss. The forrnf r i jI .<> ';iil"l ' < ' itatlon loss." Since 

' Thfr fhijrrih, fitr(-i\nK*'f, arid friWIrll*- nnt^f-r, all ;if r\nh\. uui^U'M, /{ivinjf, 
rftHpw'tlv*'ly, thfr <\\r('c\.\(}UH of rnoflon, flux, and ^-urr'-nt. H»rfc H<»c. 63, 
p. 153. 


tlio fiold t'(»ils hnvo rosislniu'o (iisu;illy hi.Lih) somo ho;ii is 
produced as the necessary eiirreiit t'i>r inas::iietization is made to 
llow throuirh Ihein. Like all heat losses due to eiirrent in a 
eondU('i«)r. (he heMtinsr is proiHU'tiouMl (o (he square oi' (he enr- 
ren(, IxMUir in watts. 

ir=/fVx»r (07) 

where h is the cnrrent in amperes in (lie (ield eoils and Rt is 
(he resis(!nu'e ol' (he whole held t'ireuit. 

To livt the same terminal voltage at the armatnre. when (he 
<'nrren( in (he lat(er is lar.ire. recinires more maimetization (han 
when the arm.-Hnn^ enrren( is small. This in tnrn reqnin^s 
nu>i-e held t'nrnMh. henee (he held eop[ier h^ss. or e\i'i(a(ion 
loss, is somewlial iireaita- at larue U»ads (han at small loads; 
(hat is. i( varies somewhat with (he load. 

l.iki^ (lu^ held Ickss. the armalnrt^ t'opiun* loss is ol' tlie l^R 
type: i( varies as the sipian^ o\' \\\o armatnre enrr(MH. and 
tluM\H"oi*t^ as \ho s»niari^ o[ \\\o U>ad on the etMUM'ator. The 
armatnn^ resistanee is made as small as is expedient. In a 
lariio .mMitM'ator it may he only a small frae(U>n of 1 ohm. bnt 
(lu> loss dm^ to the urc^il cairrent ueiun-ated ^\ ill mw (>rtlu>less 
be eonsiderahle. 

("()/•(" losses, or losses in {\\o m.aunetit' eirrnit. are oi two 
elasses. dne ti> " hysteivsis '" and •'eddy cnrreiits.' Hysteresis 
l(»sses are eanseil hy the rapid revtM'sals o\ the maiiiietism of 
the armatiu'i' eor(\ l\aeh mttliH'idt^ ot" the ^'ore may he reuarded 
as a tiny ma.irnet. aitd when the mau'neti'/ation of the eore is 
i'hanu'iMl in dirin-tion (he mi>UHuU^s have \o be pulled annmd 
auainst (lunr nuniial ma.irnede a(trai'ti(>ns. It takes eneru:y 
t(> aci'omplish this. In an tMeetrie maehini^ there is a donhU^ 
reversal dnrinu' each r.xcle. This makes mai\y reversals i>er 
seeond anil nnpiires eonsitlerahU* power. 

iMldy enrriMits ari^ little iMi\'trie enrrents imbued in (he iron 
sheets of which tlu' armamrt^ eert^ is made up. The thinner 
the sheets the smaIU>r are the rnrrents: in I'art. it is btH'anse o( 
tUo K\U\\ enrrents (hat \\\o eort^ has to be lanunated. 

HcMh hysteresis and eddy onrrtMits produce heat in (he core, 
and in prodncinu lu>ai thc.\ ns<' up power which has to be I'nr- 
lushed hy (he prime mover. ThertM'ore they are wastefnl. and 
the designers of elci'tric machinery plan to ktvp them as small 


as possible. Core losses in transformers have been briefly 
discussed in Section 58, page 132. 

No specific statement can be made regarding the magnitudes 
of tbe various losses described in tbe preceding paragraphs, 
because they depend on many factors, such as the size, the operat- 
ing speed, and special features of design. But in order to give the 
reader some idea, it may be said, roughly, that at fuil load, for 
generators of the usual types, the mechanical or frictional losses 
may range from 6 per cent for a 1-kw. machine to 1 per cent 
for the 1,000-kw. size : the excitation loss, from 6 to 1 per cent ; 
the armature resistance loss, from 4 to 1 per cent ; and the core 
loss, from 4 to 2 per cent. 

It will now be clear why the allowable power output of a 
generator has a limit. Usually machines are heavy enough 
to give a large margin of strength, but they can not well be 
made large enough to allow for the heat produced by severe 
overloads long continued. The increased current causes heat 
to be produced more rapidly, and the temperature rises. High 
temperature is injurious to the insulation. For example, it is 
found that cotton should not be continuously heated as hot 
as the boiling point of water. Cotton is the usual insulation for 
the copper wires used in machinery. If the insulation is spoiled, 
the current can follow other paths than those it should, and 
the machine is ruined. 

79. Rating; Name Plate Data. — Practically all electrical appa- 
ratus, whether for alternating or for direct-current generator, 
motor, or other device, is designed for certain definite condi- 
tions of operation. It is standard commercial practice to at- 
tach firmly to every electrical machine before it leaves the fac- 
tory a brass information tag called a " name plate." This 
usually gives the serial number by which the machine can be 
identified ; tells the maker's name ; states whether the machine 
is a generator or a motor ; what is the maximum continuous 
power output ; whether for direct or alternating current ; if 
alternating, for what frequency and how many phases ; at what 
speed j.t is to be operated ; at what voltage ; the maximum cur- 
rent for continuous operation. Some of these items are at 
times omitted, but most of them are essential. A person who 
wishes to become familiar with electrical machinery should 
form the habit of examining the name plate of every machine 


to which he has access and note the differences in size, con- 
struction, and nse. 

It has been previously said that electrical power is measured 
in watts (or kilowatts, " kw.," when large). In a direct-current 
circuit watts are the product of volts times amperes. With 
alternating current something else has to be taken into account, 
and to get the average power we must multiply the volts-times- 
amperes by the " power factor." * We might expect to find a.c. 
machines rated in watts or kilowatts, but if we look at the name 
plate of a generator we are likely to find the letters " kva." 
(kilovolt-amperes). That is, instead of actual v/atts the per- 
missible output is expressed as a product of amperes times volts 
divided by 1000. The reason is plain, if we remember that the 
whole question of what an electric machine will stand hinges 
altogether on the heating. 

Tlie heating of the field coils and armature core depends 
upon the voltage generated, because that is determined by 
the strength of the magnetic field, which in turn depends on the 
current in the field coils. The heating of the armature conduc- 
tors is determined by the armature current ; whether or not 
that is in phase with the emf. makes no difference. The total 
heating, then, depends on the volts and the amperes, regardless 
of the power output, which may be large or small, depending 
on the phase relation between the two. 

Direct-current generators are usually rated in kilowatts 
and, as just stated, alternating-current generators in kilovolt- 
amperes. Motors, either d.c. or a.c, are often rated in units of 
horsepower (1 horsepower =746 watts). When an a.c. motor is 
rated in horsepower, a particular power factor is', of course, 

80. Efficiency. — The ratio of the useful output of a device to 
its input, is called its " eflaciency." 

In all kinds of machinery it is impossible to avoid some 
losses of power, so the output is less than the input and the 

8 Power factor is, in fact, the number by which we must multiply 
volt-amperes to get true watts. (See Sec. 55.) It is commonly ex- 
pressed in per cent. It can not be over 100 per cent and is usually less. 
It depends entirely on the sort of circuit that happens to be connected 
to the generator, since this as well as the generator itself controls the 
phase difference existing between volts and amperes. 

53904°— 22 12 


efficiency is less than 100 per cent. It is lower for small elec- 
trical machines than for large ones, and for a given machine 
it varies with the extent to which the machine is loaded. Cer- 
tain losses go on regardless of the load ; those are the mechani- 
cal losses, field excitation, and core losses. Others increase 
with the load ; the armature copper loss rapidly, some addi- 
tional core losses and a portion of the excitation loss more 
slowly. When the output is small, most of the power input 
is used up in the constant losses, and the efficiency is low. 
With very large outputs the variable losses become excessive, 
again lowering the efficiency. For some intermediate load, 
usually not far from the rated load given on the name plate, 
the efficiency is a maximum. At full load, and for the usual 
designs, it may range from SO per cent for a 1-kw. generator to 
95 per cent for a 1000-kw. generator. 

81. Regulation. — Electric generators are, with few exceptions, 
intended to be operated at constant or nearly constant speed. 
Assuming that the speed is constant, and that the field excita- 
tion is also constant, the generated voltage would likewise be 
constant, regardless of the current output, if it were not for 
certain disturbing influences. A generator operating under 
these conditions is often called a " constant potential " or " con- 
stant voltage " machine. 

The current output depends on w^hat is going on in the ex- 
ternal circuit. In a city it might depend on the number of 
lamps turned on. In the case of a generator supplying energy 
to a spark gap, it would depend largely on the adjustment of 
the gap. The term " load " is commonly used in this connec- 
tion. Sometimes it means the devices themselves, which are 
connected to the Ime, and sometimes the current taken by them. 
There is generally no trouble in knowing which is meant. 

Suppose we have a certain voltage generated when the load is 
zero. Then, if the machine is made to supply current to a cir- 
cuit, the voltage at its terminals will in general be lowered and 
the greater the current, the more will the voltage be reduced. 
The term by which the behavior of a generator is described in 
this respect is called the " regulation." It is found by subtract- 
ing the voltage at full load from the voltage at no load, dividing 
by the full load voltage and multiplying by 100 to get the result 
in per cent. 


Expressed as a formula — 

Regulation = (-^^^—M X 100 per cent. - 

where T\,= voltage at no load and 
Ff=voltage at full load. 

A small percentage regulation means that the voltage remains 
very nearly constant when the load is changed. 

82. Armature Impedance and Armature Reaction. — There are 
two reasons why the voltage of a generator is lower when it is 
supplying current than when it is not supplying current, even 
if the speed is entirely steady and the direct current flowing 
around the held magnets is the same. 

(n) The armature windings are bound to have some resist- 
ance and some reactance. It requires an emf. to send current 
through the armature, therefore. This emf., called the arma- 
ture impedance drop, has to be subtracted from the emf. gen- 
erated to get the emf. left to send current through the external 
circuit. The greater the current, the greater the armature im- 
pedance drop and the less the emf. left for the external circuit. 

(b) The armature winding and core ccmstitute an electro- 
magnet. When current flows in the windings, the magnetic 
held caused by it is combined with the magnetic field due to 
field .strength, with consequent decrease in armature voltage, 
since tlie resultant magnetic field is what determines the gen- 
erated emf. 

The change in the field flux by reason of the current flowing 
in the armature is called "armature reaction." Armature re- 
action occurs in direct current as well as in alternating current 
machines, and in motors as well as generators." 

83. Effect of Power Factor on Regulation. — The reduction of 
terminal voltage due to the current flowing in the armature 
depends not only on the magnitude of the current but also on 
its phase relation to the emf., which is indicated by the power 
factor. A lagging current causes a greater reduction in ter- 
minal voltage than the same number of amperes in phase, the 
effect increasing with the lag. Thus, at 80 per cent power factor 

" Swoope, p. 362 ; Rowland, p. 230 ; Franklin and Esty, " Dynamos 
and Motors," p. 256. 



it may be twice as great as at 100 per cent. Conversely, a 
leading current, such as is taken by condensers, improves the 
regulation, so that the terminal voltage may actually be higher 
when current is flowing than when there is none. 

Fig. J 03 
Field Rheostat 
JLetters correspond m the ttvo figures 
PP -Binding posts A - Contact JTrm 

SS - Contact studs R - Resistance wire 

Scheme of connections of Alternator. 
E - Exciter Armature F- Alternator f/eld corls 

R ~ Alternator field rheostat A -Alternator armature. 

84. Effect of Speed on Regulation. — Since the emf. is propor- 
tional to the rate of cutting of flux, it follows that fluctuations 
of speed are attended with proportional fluctuations of voltage, 
provided the field excitation is not changed at the same time. 


85. Voltage Control. — The simplest way to control the voltage 
of a generator is by adjusting the strength of the magnetic field 
by means of the field current. For this purpose an adjustable 
resistance is inserted in the circuit of the latter, called a field 

One kind consists of a quantity of wire of an alloy having a 
comparatively high resistance, mounted on insulating supports 
in a perforated iron box with a slate face, or embedded in an in- 
sulating enamel. A handle is provided for making contact with 
any one of a number of brass studs attached to the resistance 
wire at various points, so that more or less of it can be in cir- 
cuit. Terminals are provided for connecting the rheostat to the 
field circuit. Fig. 109 shows the principle. 

The place of the field rheostat in the scheme of connections is 
seen in Fig. 110, which represents the stationary armature and 
revolving field of an alternator, with arrangements for supply- 
ing current to the alternator field from the exciter E, current 
being controlled by the field rheostat R. 

Small alternators for field use in radio telegraphy are often 
used without a field rheostat. The voltage is kept steady enough 
for practical purposes by driving the machine at the right speed. 

C. Direct-Current Generators. 

S6. Commutation. — Fig. 102, page 16.3, illustrates the principle 
used when alternating currents are generated by revolving an 
armature in a stationary magnetic field. But if each end of the 
loop is connected to a half cylinder of metal (0, Fig. Ill), on 
which rests a stationary brush B-f or B — , then as the loop is 
revolved the connection to the external circuit is reversed every 
half revolution, and the pulsations of current are always in the 
same direction. The reversing device is called a " commuta- 
tor." The brushes must be so set that the reversal of connec- 
tions occurs at the instant when the current in the loop is zero 
and about to reverse. 

Thus in the figure, a is near the 2V i>ole, and if it is coming 
toward the reader the emf , will be toward the right. At that 
instant the current will flow out through the segment in con- 
tact with, the upper brush to the external circuit; that is 
the upper brush is +. After a quarter revolution the conductors 
will be moving along the flux and not cutting across it, so 



there will be no emf. Each brush will be just in the act of 
passing from one segment to the other. 

After a half revolution from the position shown b will have 
exchanged places with a. Now the emf, in & will be toward the 
right, and current will flow out to the external circuit through 
B-\-. Thus the same brush is always positive. In the external 
circuit the current always flows in the same direction, though 
in the armature conductors the current is alternating. 

piO. Ill 

ProdycTi'on of uni-direoTional ennf. by revolvir^ coil with commoMTor 
NS - M<aXn«1" C- Commute Tor, two Se^menTa 

ab- Revolving loofj o^ Wife E>>-, 6pu.5hes 

X - External circuit 

Fig ll^ -...-'' 

^e.<:d"ifrc<ition o^ current. 
Me^dtive hdlf -Wdve Z changed Te> fjositiv* hdilf -wAVe 3 

If an emf. curve similar to Fig. 95, p. 154, were plotted for this 
circuit, with time measured along the horizontal axis, and volts 
at any instant along the vertical axis, the result would be 
somewhat lilie Fig. 112. Instead of a positive and a negative 
half wave there would be two positive halves, the negative 
being rectified by means of the commutator. 

Again, as with alternators, the need of higher emfs. tlian 
can be developed by a single loop and of more effective utiliza- 
tion of the material make necessary the use of coil-wound 


armatures and multipolar field magnets. With a commutator 
consisting of only a few segments, say as many segments as 
there are magnet poles, the current would still be pulsating. 

To get a steady, practically constant emf., commutators are 
used having many segments — several hundred in the case of 
large generators and motors, and usually not fewer than 20 
or 30 even on very small machines for 110-volt circuits. Such 
a commutator consists of bars of copper, slightly wedge-shaped, 
separated by thin insulating sheets of mica, the whole as- 
sembled in the form of a cylinder held together by strong end 
clamps. The segments are insulated from the clamps by 
suitably shaped rings, usually of molded mica insulation. Con- 
nections leading to the armature conductors are soldered into 
slots in the segments, which commonly have lugs or " risers " 
for the purpose, extending upward at the end toward the 

87. Ring and Drum Windings. — Armature windings fall into 
two broad classes, called " ring " and " drum " windings, ac- 
cording to the way the conductors are mounted on the core. In 
the first of these the wire is laid on the outside and passed 
through the hollow space inside of the core, being threaded 
through and through nuich as a napkin ring or a bridle ring 
might be covered with string. 

Ring windings are scarcely ever used nowadays. Modern ma- 
chines have windings of the type shown in Fig, 113, called 
" drum " windings. The conductors are all on the outer face 
of the core, and the two branches of a turn lie under adjacent 
poles of opposite polarity. These two features are characteristic 
of all kinds of drum winding. In the kind illustrated in the 
diagram, starting with commutator segment 1, we pass up to 
conductor &, which at the instant shown is under a »S pole. It 
is connected at the back of the armature to i, which lies under 
a N pole and is soldered into segment 2. Starting at 2, we 
have d under the edge of the S pole back-connected to k under 
the edge of the N pole ; k is attached to segment 3. Continuing 
in the same way all around the armature we finally have 16 
loops connected to the 16 commutator segments. It will be 
understood that an actual machine has a great many more turns 
in the armature winding and a larger number of commutator 



At the four segments marked + or — contact is made with 
brushes leading to the external circuit. By the " right-hand 
rule"" the emf. in conductors under the N pole is toward the 
back end, so current flows into the armature at segment 3. The 
brush on that segment is therefore negative. The brush at 
segment 7 is positive, because there the current flows out of 
the armature. Similar reasoning applied to the conductors 
under the a9 poles leads to the same result as to polarity of 




Scheme oj -4 - t^o!<= Drorn Wi.ndin^ 

\,7,3 .etc . CommoTATof a>e-2j'^*^'^ '1 "*■ ~ Loo<it'ior\ of broihes 

3,b,c. , etc. . Arm«sitijre c-orvcJocTor^ ^J,S>. - Fi<sl<J bol«5 

the brushes, which are thus seen to be alternately, one positive 
and the next negative, as we go around the commutator. If 
a machine having more than two sets of brushes is examined, 
it will be found that all the positive brushes are joined by a 
heavy conductor and all the negative brushes by another. Then 
one connection is made from the group of positive brushes to 
the external circuit, and one from all the negative bnishes. 

In speaking of alternators, the actual construction of arma- 
tures was described ; that is, the use of machine-wound coils in 
slots in the face of a laminated core. D.c. armatures are made 

10 See section 63, p. 153. 

Fig. 114 (upper) — Method of assembling commutator segments. Fig. 
115 (middle) — Commutator and armature core assembled showing 
risers. Fig. 116 (lower) — Armature complete with windings con- 
nected to risers. 



the same way except that the ends of the coils are soldered to 
the commutator segments." 

The main steps are shown in Figs. 114, 115, and 116. The 
first shows the copper segments, with their sheets of mica be- 
tween them, assembled in the form of a ring and held together 
by a firm temporary clamp. The next picture shows the com- 
mutator fastened on the front end of the armature core. The 
*' risers " are to be seen coming up from the ends of the seg- 
ments for connection to the armature coils. On the core, built 
up of thin laminations, note the teeth, slots, and three rows of 
air ducts for ventilation. The last picture shows the coils in 
the slots of the core. Their ends have been soldered to the 

88. Excitation: Separate, Series, Shunt, Compound. — While 
alternators require d.c. from a separate source for their field 
excitation, direct-current dynamos usually excite their own 
fields. Depending on the scheme of connections between the 
armature and the field coils, this gives rise to several arrange- 
ments, all of which are of practical importance. In this dis- 
cussion we leave out of consideration the " magneto," which 
depends for its magnetic field on a group of permanent magnets. 

Fig. 117 shows the several ways of exciting the field magnets, 
and incidentally illustrates the conventional symbols generally 
used for an armature and for field windings. In this sort of 
diagram no attempt is made to draw a picture of the machine. 
A whole set of field coils, for example, is represented by a single 
coil, the armature and brushes by a single circle" and two 

Separate. — The first sketch indicates that current for the field 
coils comes from a source, like a battery, entirely independent 
of the armature. Such a machine is said to be " separately 

Shunt. — The next indicates that the current from the arma- 
ture divides ; some goes to the load circuit, some to the field 
coils : the two unite again and flow back into the armature at 

^^ Brief information on the care of commutators and proper position 
of brushes is given at the end of this chapter in Sec. 106, page 227, on 
" Common Troubles." 

^ Note difference from alternator, which has two circles, representing 
slip rings. 



the brush of opposite polarity. When the current from the 
armature divides, a portion flowing through the field winding, 
the machine is spoken of as a " shunt generator." Only a small 
fraction of the total current which a machine is able to generate 
continuously is required for shunt field excitation ; it may be 
5 or 6 per cent for a 1-kw. generator, and as little as perhaps 
2 per cent for a 100-kw. generator. 



S>a ^ ra ts 


Lo<»d Various rnocfes of 

exciting d. c.jXjeneiaTors 
A -•irmatore 
F- Fin« wire orshonT- 
■Ai«ld windinj? 
5 - Series -field 
wi nd I n^ 










Shunt field windings consist of many turns of fine wire (in- 
sulated, of course). There may readily be 2000 or 3000 turns. 
For instance, the little exciter for the .500-cycle audio-frequency 
generator described on page 195 is a direct-current shunt gen- 
erator. Each of its two field coils has 2800 turns of wire about 
0.25 mm. (0.01 in.) in diameter. Using this great quantity of 
fine wire has two consequences ; because of its high resistance 
it lets only a small current flow : because of the large number of 
turns this small current sufiBces to produce the desired magneto- 
motive force (which depends on the "ampere turns"). 


Series. — When the whole current from the armature flows 
through the field coils, the generator is " series excited." Two 
ways of representing a series generator are shown in Fig. 117. 
Heavy wire is used for series coils. They have to carry the full 
current output of the machine ; if fine wires were used, the 
excessive heat produced would destroy the insulation. The 
necessary ampere turns are secured by virtue of having a large 
number of amperes and comparatively few turns of wire. 

Compound. — When a generator is provided with two sets of 
field coils, one of fine wires connected in shunt and the 
other of a few turns of heavy conductor connected in series with 
the armature, it is called a " compound wound " generator, or 
more commonly just a " compound " generator. Two ways of 
representing it are shown in Fig. 117. 

89. Characteristics of Terminal Voltage. — Why are so many 
different kinds of connection used for field excitation? Ordi- 
narily the load on a generator will vary. By this we mean that 
there are changes in the number of devices switched on ; lamps 
may be turned on or off, or motors started and stopped. Such 
changes of load automatically affect the terminal voltage of the 
generator, but they affect it differently, according to the kind 
of field excitation used. 

To see why the effects differ, in each case consider the dy- 
namo driven at a steady speed without load. Then imagine the 
load (current through the armature) to be successively in- 
creased. If sepai;ate excitation is used a certain emf. is gen- 
erated at no load. When current flows in the armature some 
of this emf. is used up in sending the current through the re- 
sistance of the armature itself. There is also another effect, 
due to " armature reaction," " which weakens the magnetic field. 
Both increase as the armature current increases. Hence the 
terminal volts are less when the armature current is large, 
than when it is small. Curve a, Fig. 118, shows this graphically. 
The load current in amperes is plotted along the horizontal axis, 
the terminal volts along the vertical axis. The greater the cur- 

"Armature reaction is explained in Sec. 82 and in texts on electrical 
engineering (See Franklin and Esty, "Elements of Electrical Engineer- 
ing," vol. 1, p. 151 ; Franklin and Esty, " Dynamos and Motors," p. 
176 ; Timbie and Higbie, "Alternating Current Electricity, First Course," 
p. 394 ; Sheldon and Hausmann, " Dynamo Electric Machinery " (9th 
ed.), vol. 1, pp. 110-121. 



rent, the lower the voltage. The difference between no load 
and full voltage shown in the diagram corresponds to a regu- 
lation '* of some 8 per cent, and applies to rather large ma- 
chines, say of 100 kw. or more. For a smaller one the difference 
would be greater. 

When shunt excitation is used the reduced terminal voltage 
sends a reduced current through the field coils, so the magnetic 

<i 1 ^ 

_^ — ' l^^^""^^^ 


"*"^ -----^ '^1^ 


^ a 




y^ 1 ~-*.*.,k 


y^ 1 ^^**"*^ 


c/ ! ''* '^ 


y^ 1 ^^ 


X ' \ 


/ i * 

/ -Ol ' 

/ -• y 



/ — t 


/ ^\ .'"''' 


/ _----""'"' 

/ — -s. " "'" " 

/ — " "'"'''' " 1 

•' ,' M So IS ,^a r{S 

LoAd, Percent o| rated Amf>«sres 


^eUtion between Current Out^>ut and Terminaf Volt's 

& - For AejaarAtely exoitsd ^^enerafbr 

D- For ihunT (JEjeneralisr 

c.- For Series ^ener<a+or 

Ci~ For Corrijaou'nd ^er>ere>1bf 

flux is weaker, the greater the armature current. Hence the 
terminal voltage falls off more than it does with separate ex- 
citation. Thus curve &, Fig. 118, droops more than curve a. 
The dashed part shows how the voltage falls off when the ma- 
chine is greatly overloaded. 

With series excitation, the condition is very different. When 
no current flows, only the weak residual magnetism of the iron 
is available, and the emf. generated is consequently very small. 

1* Defined in Sec. 81. 


Curve c shows it by starting only a very little above the zero 
value. If current is taken from the machine, this current, flow- 
ing in the field coils, strengthens the magnetic field and so 
causes a greater emf. to be generated. The greater the current 
taken by the external circuit, the gi-eater will be the voltage. 
Hence curve c rises. 

In the compound generator the two effects are combined. De- 
pending on the relative proportions of the two windings, the 
voltage at full load may be made equal to that at no load, or 
greater, or less ; the latter is rare. Curve d, Pig. 118, is for a 
generator somewhat " over-compounded." If the full load volt- 
age were the same as the no load voltage, the generator would 
be " flat-compounded." 

In examining a generator, it is usually impossible to deter- 
mine whether the field coils are of fine or thick wire without 
tearing them open, because they are protected with wrappings 
of tape, hard cord, or other covering. To distinguish between 
shunt and series coils is, however, quite easy by looking at the 
connections. Those between the shunt field coils on the differ- 
ent poles are small because they have to carry only a small 
current, those between the series coils are heavy, consisting 
of thick, wide straps of copper on the larger generators. 

90. Emf. Equation. — It has been stated that the emf. devel- 
oped in a conductor depends on the rate of cutting the mag- 
netic flux ^^ and is equal in volts to the number of magnetic 
lines of force cut per second, divided by 10 ^ On an armature 
a number of such conductors are connected in series and their 
emfs. are therefore added. Thus in Fig. 113, the conductors 
which would have to be traversed in going from one brush on 
the commutator to the next through the armature constitute 
one such group. There are three other similar paths, and these 
four paths are all in parallel, so the resulting emf. is the same 
as that of one path alone, but the current that goes to the 
external circuit is the sum of the currents in the four paths. 
Let A^=the number of conductors in series. 

^?=number of revolutions per second (not per minute) 
of the armature. 

/)=number of magnetic poles. 

0=magnetic flux per pole. 

15 Chapter 1, Section 45. 


Then the flux cut per second by any conductor is nXpX(p lines. 
Dividing by 10 * gives the average volts. If there are A^ con- 
ductors in series, the total emf. is 

£=^^><£g^ volts. (68) 

This formula shows that the voltage of a generator can be 
changed by changing the speed n, the flux»0, the number of poles 
p, or the number of conductors N. The last two, of course, are 
fixed once for all when the machine is built ; the first two can 
be changed quickly by the operator, and afford practical means 
of controlling the voltage. 

This formula means exactly the same thing as the one given for 

induced emf. in Chapter 1, namely that E=—j-' It is merely nec- 
essary to note that if nXp poles are passed per second, then the time 
required to cut the flux <i> is only ^^ th of a second; this takes the 
place of t in the denominator; or what amounts to the same thing as 
dividing by , we multiply by nXp. The reason for the factor 

71 Xp 

10^ in the denominator has been explained. 

91. Voltage Control. — The practical way of controlling the volt- 
age of separately excited, shunt, and compound generators is by 
having an adjustable resistance, called a "field rheostat" (Fig. 
109), in circuit with the fine wire (shunt field) coils. The 
points R in Fig. 117, show where such a rheostat might be put 
in the circuit of each machine. 

92. Effect of Varying Speed, — A rise or fall of speed causes 
the emf. of a separately excited generator to rise or fall in 
about the same proportion. In shunt and compound generator^ 
the effect is greater. That is why engines for driving such 
generators have to have good governors, if a steady voltage is 
W' anted. 

Because of these characteristics, each type of generator has 
its special uses. For instance, the exciter for the a.c, generator 
of a radio field set is a simple shunt generator, because the load 
does not change much. The shunt generator is good also for 



charging storage batteries. Incandescent lamps need a very 
steady voltage that is not changed when some of them are turned 
on or off. A compound generator meets this requirement. 

Voltage Regulators. — Various devices have been developed for 
maintaining the voltage of a generator constant with varying 
generator speed and varying conditions of load. A simple type 
used with a shunt generator is shown in Fig. 118-a. The 
shunt field winding of the generator is shown at S. The 
voltage regulator proper consists of an electromagnet with two 
windings V and ir, a vibrating armature .1 normally held back 








///( \\m 


A ^ 



by a spring G, and a noninductive resistance R. The two wind- 
ings of the magnet are wound so as to oppose each other; the 
winding T' is called the " voltage " winding, and may have more 
turns than the " reverse " winding W. The voltage winding V 
is connected across the voltage to be regulated, which is the 
voltage across the terminals of the generator. The tension of 
the spring G is adjusted so that when the line voltage is normal 
the armature A is just held against the contact C, and the 
shunt field is then connected directly across the line. If now 
the line voltage increases, the armature is pulled away from 
the contact C, and the current to the shunt field must pass 


through the noninductive resistance R or the winding W. The 
current through the shunt field is therefore decreased, and hence 
the line voltage is decreased. If it were not for the winding TT, 
the armature would be held over with the contact C open until 
the line voltage had dropped sufficiently so that the spring 
would pull the armature back. The reverse winding W, how- 
ever, accelerates this action. Winding W is connected across 
the resistance R, and part of the shunt field current passes 
through W. The magnetic field due to the current through W 
opposes the magnetic field due to the current through the 
voltage winding T', a)id the armature is therefore pulled back 
and contact C closed more quickly. A little time is required 
for the current to build up in the inductive winding W, and the 
magnetic effect of the current through W lags a little behind 
the effect of introducing the non-inductive resistance R into the 
circuit. In operation this type of voltage regulator is continu- 
ously chattering, and gives good regulation. A voltage regulator 
of this type is now supplied with some generators used in 
Signal Corps sets. There are also various other kinds of voltage 
regulators in general use. 

D. Special Alternators for Radio Use. 

93. Audio Frequency and Radio Frequency. — Alternating cur- 
rents are generated at various frequencies, covering a remarkably 
wide range. Depending on their application, the frequencies in 
practical use fall into three well-defined classes : 

(a) Commercial frequencies, which nowadays generally mean 
25 or 60 cycles per second. 

(b) Audio frequencies, which are usually around 500 to lOOQ 
cycles per second but may extend as high as 10,000 cycles per 

(c) Radio frequencies, usually between 20,000 and 2,000,000, 
but extending in extreme cases down to perhaps 10,000 and up 
to three hundred million cycles per second. 

Commercial frequencies are used for lighting and power. The 
great machines in the central stations which supply our cities 
with current operate at these frequencies. 

Audio frequencies are those conveniently heard in the tele- 
l^hone. When alternating currents are sent through a telephone, 
53904°— 22 13 


tlie diaphragm of the latter vibrates. Tlie vibrations are heard 
as sound. The more rapid the vibrations, the shriller the tone. 
Vibrations at the rate of 4,000 or 5,000 per second give a shrill 
whistle, while the lowest notes of a bass voice have somewhat 
under 100. If a 500-cycle generator supplies current to a spark 
gap and the spark jumps once on the positive and once on the 
negative half-wave, then at the receiving station the signal is 
heard in the telephone as a musical tone of 1000 vibrations per 

Radio frequencies occur in the circuits of radio apparatus, for 
instance, in an antenna. They are too rapid to cause a sound 
in a telephone which can be heard by the human ear. They 
may be generated by dynamo-electric machines of highly special- 
ized construction, but are usually produced by other means. 

94. Audio-Frequency Generators. — To show how the methods 
described in the preceding sections are applied in actual genera- 
tors, a few typical machines used in radio sets will be briefly 
described. Whether or not these are of the latest design is not 
important. Changes of detail are constantly being made, but 
they do not affect the principles used and can be readily under- 
stood after the workings of similar machines have been grasped. 
The examples of machines here given will also illustrate how the 
form of generator and the auxiliaries used with it are influenced 
by the source of power available for driving it. 

The generator is only one part of a unit for converting energy 
into the electrical form. The other part dei^ends on the source 
of energy available ; it may be heat derived from coal or gaso- 
line ; it may be falling water, moving air, human muscles, or a 
charged storage battery. 

Crank Driven. — The field radio pack set furnishes an example 
of a self-contained generating unit driven by hand. These sets 
have been changed somewhat from time to time and can there- 
fore be described only in a general way. The generator is 
cylindrical in shape and is entirely incased, including the ends, 
in a metal shell. At one end of it is a flywheel for equalizing 
the speed. At the other is the train of gears, running in oil and 
inclosed in a housing, through which power is transmitted from 
the crank shaft to the generator shaft. The crank shaft is 
turned by means of a pair of cranks. 


The alternator ^^ is a 250-watt, 500-cycle machine of the revolv- 
ing armature type. The exciter " is built in with the alternator, 
so that the two have but one frame and one set of bearings, and 
the same shaft carries both armatures. Near one end, on op- 
posite sides of the shell, is a pair of holes giving access to the 
d.c. brushes which bear on the commutator of the exciter ^^ 
and near the other end are similar holes for the a.c. brushes 
that bear on the collector rings. The crank is turned at the rate 
of 33 to 50 r.p.m., depending on the machine (that is, the date 
of the model), and the generators make 3.300 to 5,000 r.p.m., 
the cranks being geared to them at a ratio of 1 to 100. 

The diagram and data of Fig. 103 apply to the alternator of 
such a set, the armature having 18 teeth, the same as the num- 
ber of field poles. To get 500 cycles it must make 8,333 r.p.m 
which corresponds to a crank speed of about 33 r.p.m. 

The connections are shown in Fig, 119. The field coils of the 
exciter are connected directly to the brushes. The circuit to the 
alternator field coils passes through a receptacle Pi on the side 
of the machine. A two-wire cable can be plugged in at this point 
for the sending key. While the key is closed, field current flows 
and a.c. is generated in the armature. Another receptacle P2 
provides for connecting the alternator armature to the trans- 
former from which current is supplied for the spark. 

In view of the high speed at which these generators run (some 
make 5,000 r.p.m. ) the brushes have to fit very smoothly and the 
bearing surfaces, particularly the d.c. commutator, have to be in 
good condition. For ease of turning, they should not be pressed 
in harder than necessary ; on the other hand, unless the contact 
is good the set fails to operate satisfactorily. The most common 
troubles, electrically, are due to a dirty commutator, poor brush 
contacts, or to turning the brushes in replacing them, so that 
the curve of the brush does not match the curve of the com- 

GasoUne-Engine Driven. — Hand power is not practical, except 
for very small generators, since a man can develop only about 

18 See Fig. 103, page 164, and foot note, page 165. 

" A little generator of d.c. for the field coils of the alternator. See 
Sec. 71. 

" The commutator is described in. Sec. 86. 



one-tenth of a horsepower if he has to keep it up for more than 
a short time. One of the most convenient sources of larger 
power is the gasoline engine. It is particularly suitable for 
isolated stations, or for the more powerful portable sets, like 
the field radio tractor sets. Detailed information about any 
particular set is supposed to be furnished with the set, but cer- 
tain features are likely to be common to all. 

FiQ. 119 

Connec-Tions of ^cKSeT 
D - exciter Arrrksture 
C5-A-C genenaTor " 
LP - E-Xciter -field 
AF- iLlterndtbr -field 
Pi Pz~^^S co"nec-tions 
K - ^endin^ Ke^ 
T - Coil o| transformer 


E.x.field rheo 


S<:heme. 0+ connection of <a Tr«3ictor jet ^cnerciTor 
<And eXciTer 

The speed of rotation of the alternator is almost always much 
higher than that of an engine; it is therefore stepped up by 
pulleys and belts, or sprockets and chain, or gears, the smaller 
pulley or sprocket or gear being on the generator shaft. 

The generator may be of any of the three possible types pre- 
viously described; for example, one of the permanent Signal 
Corps stations uses an inductor alternator (Sec. 74) ; one kind 


of tractor set also has the inductor type ; another has the re- 
volving armature. If it becomes necessary to open the ma- 
chine it is easy to discover which type it is. If the rotor, or 
revolving part, has no windings at all, then we are dealing with 
an inductor alternator ; if the circuit leading to the transmitting 
apparatus (not necessarily the key, because that may be in the 
field circuit) comes from the slip-rings, then the revolving part 
must be the armature. 

In one of the sets of this latter type the alternator and its 
exciter are two separate machines, connected by a coupling so 
that both revolve together. A frequency indicator in front of 
the chauffeur guides him in controlling the speed of the engine 
so as to maintain the right frequency — 500 cycles per second. 
The combination is chain driven from the main tran«imission. 
The same engine that drives the truck is used to furnish power 
for the generator, the one or the other being thrown in as de- 

The following name-plate data of this particular set will 
illustrate some of the statements made in earlier sections : 

Generator frequency, 500 cycles ; poles, 30 ; kva., 2.5 ; open 
circuit volts, 245 ; terminal voltage at full load, with key 
closed, 110 ; 2 kw. at 0.80 p. f . ; 2000 r. p. m. 

Exciter, shunt tjrpe : poles, 2 ; load volts, 110 ; load amperes, 
2.7 ; 0.3 kw. 

From the speed, 2000 r. p. m., and the stated number of poles, 
30, each revolution gives 15 cycles and the cycles per second 

will be — ^ =500, which checks with the figure given. 

From the full load voltage, 110, and the rating, 2.5 kilovolt- 

amperes or 2500 volt-amperes, the full load current is ' ~ 

or 22.7 amperes. The product of volts, amperes, and power 
factor gives power in watts, thus 110X22.7X0.80=2000 watts, 
2 kw. The great difference between the volts on open circuit, 
245, and volts when loaded, 110, shows that the armature has a 
liigh impedance. It must not be assumed that this loss of volt- 
age is all due to resistance, and so represents a waste of power. 
Much of it is due rather to the demagnetizing action mentioned 
in Section 82, which causes a reduction in the effective mag- 
netism, and therefore in the emf. generated. 


The sclieme of connections in Fig. 120 shows that the exciter 
voltage can be controlled by means of the exciter field rheostat. 
This, in itself, would govern the 500-cycle voltage fairly well, 
but a second control is provided in the generator field rheostat. 
High-resistance connections between each machine and the 
ground provide a leakage path for high voltage charges and 
prevent their accumulation. 

Fan Driven. — Audio-frequency generators have an important 
application in furnishing current for communicating from air- 
planes. Fan motors have been used as a source of power, 
though it has been objected that they increase the head resis- 
tance of the plane. There is no theoretical reason w^hy any tj-pe 
of self-contained generator might not be used, but because of 
the high rotative speeds obtainable with fans and the need of 
lightness, special machines have been developed with the fan 
mounted directly on an extension of the shaft. One recent 
form is described on page 203. 

Motor Driven, by A.C. Motor. — When electric current is to be 
had, but not at the desired frequency, use may be made of a 
combination of a motor, adapted to the circuit that is available, 
and a 500-cycle generator. Such a combination is called a 
*' motor-generator set." For use with 110-volt, 60-cycle alter- 
nating current, sets are built using the same sort of generator 
(with built-in exciter) described in connection with hand-driven 
apparatus. Mounted on a common bedplate with it is an a.c. 
motor. The shafts are connected by a flexible coupling. 

Except for the mechanical connection between the shafts, the 
two machines are entirely independent. Electrically there is no 
connection. The motor is designed to run automatically, at the 
proper speed for the generator, or perhaps it would be better 
to say that there are certain definite speeds at which 60-cycle 
a.c. motors have to run, and the generator has such a number 
of poles that it gives the desired frequency when driven by a 
motor operating at one of these speeds. Voltage control of the 
generator is secured by means similar to those shown in Fig. 

Motor driven, by D. C. Motor. — When direct current at 110 
volts is available the arrangement is somewhat different. The 
exciter is unnecessary, because current for the field coil of 
the alternator may be taken directly from the line. It is then 



possible to combine the generator and a 110-volt, direct current, 
shunt motor (see Sec. 97) into a very compact unit. The two 
armatures are on the same shaft and the two frames are joined 
in one structure. 

Fig. 121 represents such a unit, whicli is sliown partly disas- 
sembled in Fig. 122, The generator happens to be of the same 

Fig. 121. — Small 500-cycle motor-generator set (2500 r.p.m. ; 24 poles 
on stator ; 24 teeth on rotor; 110 volts; 3.2 amp.; 0.35 kva.). 

1. Field terminals. 

2. Collector rings. 

3. Armature terminals. 

4. Shaft of both units. 

design as that shown in diagram in Fig. 103, but being built 
for nearly 50 per cent more power it is somewhat larger, has 
more poles, and runs at a correspondingly lower speed to give 
the same frequency. The two armatures are seen on their 
common shaft; the collector rings are near one end and the 
commutator near the other. 



One scheme of connections for such a unit is seen in Fig. 123, 
which shows tlie d. c. motor connected to its line by way of a 
switch and starting box/® The rheostat sliown in circuit witli 
the motor field, MF, may be omitted. Its purpose is to give con- 
trol of the motor speed,^" if such control is desired, in order to 
get some definite frequency quite accurately in the a. c. circuit. 
From the d. c. line, connection is made also to the generator 
field winding, the flow of current being controlled by another 
rheostat which determines the magnetization and, therefore, 
the generator voltage. Thus the generator frequency may be 
governed by means of the motor field rheostat and the voltage 
by the generator field rheostat. 

Motor-Driven Inductor Alternators. — Thus far in this part 
of the chapter attention has been centered on revolving armature 
generators. It is equally feasible to generate 500-cycle cur- 
rent by means of inductor alternators. Fig. I'Zi represents 
a motor-driven inductor alternator for conversion from direct 
to alternating current at 500 cycles. The table following gives 
the data as taken from the name plate. 

Fig. 122. — Motor-generator set of Fig. 121 partly dismantled. 

1. Motor brushes. 

2. Motor field windings. 

3. Motor field poles. 

4. Motor field j'oke. 

5. Terminals of motor field wind- 


" Described in Sec. 97. ^o How this is done is explained in Sec. 97. 



5KAFT. DC (Mf TOR} ^ND^. 


sKAfj. a.c7(5e mckat oib$kno. 

^£S £Nt>- 5ftteiO J&BEaiglN&. 

Fig. 122 (continued). — Motor-generator set of Fig. 121 partly dismantled. 

6. Motor armature core. 

7. Commutator. 

8. Generator armature windings. 

9. Generator armature core. 

10. Collector rings. 

11. Motor armature windings. 

12. Generator brushes. 

13. Generator field windings. 

14. Generator field yoke. 

15. Terminals of generator field 


16. Ventilating fan. 


Name plate data for motor-generator shown in Fig. 124- 

A. C. gener- 

Volts ; 120 

Amperes I 7. 3 

Revolutions per minute 2500 

Rating I 1 h. p. 

Shunt field amperes 0. 4 

Cycles per second 

Here again the two distinct machines, motor and generator, 
are combined in a single compact unit. The armatures are on 


FlQ 113 

s e>. 



ConnecTions of mt^r -h^crxareitor- Toi" conversion from DC- To C^.C- 
/V\ _ Motor drmdTure E.( - Motor -^lelcsl rheostAf 

(J _Cje.ncr,jror armdture. E2-Q«"ef^^or field rhcoflTAl" 

5- fe — Motor sldkrTini box 
OF— O«nerdtor -field windin> 

one shaft and the two frames are made into one structure, 
though openings are left for ventilation. These, as well as 
other openings at the ends of the machine, are screened to keep 
out foreign material, while permitting a free flow of air for 
cooling. The generator frame is cast in the form of a cy- 
lindrical shell. At each end is inserted a laminated armature 
core, with teeth projecting radially inward, on which the arma- 
ture winding is placed. Between the two armature cores is the 
field winding, a single large coil which fits inside the cylindrical 
shell, where it is rigidly held in place. This coil produces a 

Fig. 124. — Inductor alternator type motor-generator set. 

Generator armature coils, first 

Generator armature coils, sec- 
ond row. 

Generator field coil. 

4. Terminal box. 

5. Inductor teeth. 

6. Brass disks. 

7. D. c. motor armature. 



magnetic flux parallel with the shaft. The armature winding 
is in two groups, one on each core. Each group consists of 12 
coils, and the coils are all connected in series. 

The portion of the set so far described is stationary. The 
rotor is a solid cylindrical core, at each end of which is a ring 
of 12 teeth projecting radially outward. The core is mag- 
netized by the stationary field winding previously mentioned. 
To trace the magnetic circuit, begin at the core. One end of it 
is N, the other /S. The flux passes out through all the rotor 
teeth at the iV end, across the air gaps, into the adjacent stator 
teeth, through the corresponding gap into the rotor teeth at 
the /S* end, and thence into the central core again. As the rotor 
is made to revolve, the teeth are alternately in line with the 
armature coils, then opposite the spaces between coils. The 
flux through the coils consequently pulsates, and alternating 
emfs. are induced. 

So far as the diagram of connections is concerned. Fig. 123 
applies to this case quite as well as to the preceding one, for 
the shunt motor and generator field are supplied with direct 
current in either event, and alternating current flows from 
the alternator armature, whether that be revolving or sta- 

Self-Excited Inductor Alternator. — A very novel construc- 
tion has lately been worked out for fan drive on airplanes. A 
simplified diagram of it is given in Fig. 125. from which the 
electrical and magnetic circuits may be traced, and the prin- 
ciple of its operation may be followed. For the moment, 
ignore the windings on the rotor. The machine is then seen 
to be an inductor alternator. The a.c. winding is on the 16 
stator teeth, each tooth and its adjacent slot spanning ^ of 
the circumference. These teeth, in groups of 4, form four 
polar projections. 

The polar projections are made to have opposite polarities 
around the stator, so that there are two N and two S poles, 
by means of direct current sent through the field coils F, each 
of which consists of a large number of turns. The field coils 
are all connected in series to the source of direct current, to be 
mentioned hereafter, but the connections are omitted from the 
sketch to avoid having so manv lines. 



When the rotor is made to revolve, the flux through the stator 
teeth pulsates, and alternating emfs, are induced in the coils 
encircling them. By symmetry, whatever happens in any one 
coil is also going on at the same time in eleven others. The 







^,-— ■ — " 









1 \\^^ 


^ 1 




w^ 1 













A' -^ 













Fig. 125. — Soif-excited inductor type alternator. (4500 r.p.m. ; 75 
volts; 5 amp., 900 cycles per second.) A, terminals of a.c. windins , 
B, brushes for taking d.c. from commutator ; C. commutator seg- 
ments ; F, d.c. field coils ; J, inductors ; T, stator teeth. 

passage of the inductor across a pair of consecutive, oppositely 
wound teeth gives rise to one cycle. The generator here repre- 
sented is intended for operation at 4500 r.p.m. and at that 
speed, with the 12 inductors as shown, gives a frequency of 900 
cycles per second. 


Besides having on it the inductors for the alternator, the rotor 
also functions as a d.c. armature. That accounts for the wind- 
ings shown on the rotor. How such an armature generates 
direct currents is explained in Section 87. For present pur- 
poses it suffices to say that the armature consists of a large 
number of turns, wound, of course, for four poles ; each turn 
spans three teeth. In the diagram the connections have been 
simplified for purposes of illustration, and the number of com- 
mutator segments shown is much smaller than on the actual 
machine. Connections, not shown in the figure, are made be- 
tween the field coils and the four brushes, two positive and two 
negative. The brushes are shown in the diagram on the in- 
side of the commutator, for clearness ; actually they are on the 
outside. The direct current from this armature is what ener- 
gizes the field coils. 

It will thus be seen that the rotor serves two entirely distinct 
purposes : 

1. It carries the inductors for the a.c. generator, which has 
stationary field and armature coils. 

2. It carries the d.c. armature, which corresponds to the ex- 
citer in other machines. 

9.5. Radio-Frequency Generators. Alexanderson High-Frequency 
Alternator. — It is possible to construct an alternator of the in- 
ductor type which will directly generate a frequency as high 
as 200,000 cycles per second. In order to secure this fre- 
quency, it is necessary that 200,000 inductor teeth pass a given 
point every second. This result can be attained only by having 
a great many teeth on the rotor and driving it at a very high 
speed. In a 2-kw., 100,000-cycle generator the rotor has 300 
inductors and makes 20,000 r.p.m. With a rotor having a 
diameter of about 1 foot, this design allows about one-eighth 
inch for each slot and tooth together, and even with this design 
the peripheral velocity of the rim is approximately 12 miles 
per minute. 

The rotor consists of a steel disk with a thin rim and a much 
thicker hub shaped for maximum strength. Instead of having 
teeth on the edge, slots are cut on each side of the rotor very 
near the edge and may not extend entirely through the rotor 
disk. The spokes of steel which remain form the inductors, 
and a solid rim of steel is left. To cut down the friction of the 



air at the high speed at which the disk is operated, the slots are 
filled with a non-magnetic material such as phosphor bronze, 
finished off smoothly with the face of the disk. 

The armature conductors are laid zigzag in small straight 
open slots in the flat face of the btator core, this face being per- 
pendicular to the shaft. Fig. 126a shows a cross section of a 
part of a small Alexanderson alternator. C is the rotor disk, 
and A the field windings. The armatures are shown at B, and 

Fig. 126a (left). — Section of Alexanderson alternator, showing rotor. 
Fig. 126b (right). — Front view of armature used in 200 kw. Alexan- 
derson alternator. 

the armature conductors, which are carried in laminations, at 
E. The field flux passes through the' iron frame D, the lami- 
nated armature, and the disk. The slot filled with non- 
magnetic material is shown at F. The usual air gap is 0.015 
inch, so that a very slight defect in construction -will cause 
a serious accident. 

In the radio station at New Brunswick, N. J., there is an 
Alexanderson alternator having a rated output of 200 kw. 
generated at a frequency of about 22,100 cycles per second when 
the alternator is running about 2,170 r.p.m. Similar alterna- 


tors are in use at Tuckerton, N. J., and Marion, Mass. In 
this alternator the rotor disk runs between two laminated 
firmatures, which are cooled by water circulation. The rotor 
disk of the type of alternator used at New Brunswick is shown 
in Fig. 120c: this rotor weighs about 5.500 pounds. Fig. 126b 
shows one-half of the armature of an alternator of this type 
complete and shows the leads from the terminals of circuits 
embedded in insulation. In this half of the armature there 
are 32 armature windings, and each circuit generates about 

Fig, 12Gc. — Rotor of 200 kw. Alexandersou alternator. 

130 volts on open circuit and carries a current of 35 amperes 
under normal load. In the complete armature there are 64 wind- 
ings, and the current generated by these 64 windings is collected 
in an air-core transformer which has 64 independent primary 
windings, and the single secondary winding delivers the entire 
output of the alternator. Tl>e voltage at the terminals of the 
secondary winding when the alternator is operated at normal 
speed is about 2,000. 

The construction of the high-frequency alternator requires 
many refinements in alternator design and very fine workman- 
ship. Since a slight defect may have serious consequences, very 
careful operation of these alternators is essential. The use of 


(he high-frequency alternator in radio communication is de- 
scribed in Section 173. For further information regarding the 
Alexanderson alternator the reader is referred to : E. F. W. 
Alexanderson. General Electric Review, volume 16, page 16, 
January, 1913; Proceedings A. I. E. E.. volume 38, page 1077, 
October. 1919 : Proceedings Institute Radio Engineers, volume 
8, page 263. August. 1920 ; General Electric Review, volume 23. 
page 794, October. 1920 : E. E. Bucher, General Electric Review, 
volume 23. page 814, October, 1020: A. X. Goldsmith. Radio 
Telephony, page 117 : and to United States Patents Nos. 1008577 
and 111CHJ26. 

French Designs of High-Frequency Altern<itors. — Bethenod 
and other French engineers have designed high-frequency alter- 
nators in which the practical difficulties of making the very 
small slots are lessened by utilizing several alternators mounted 
on one shaft to do the work of one. and in each alternator there 
are placed only a fraction of the needed poles. Thus, if three 
alternators are used, in passing around the periphery the suc- 
cessive poles are found by passins: from one alternator to the 
next, and two of every three ix)les are omitted in each alter- 
nator. The pole of each alternator is displaced with reference 
to the corresponding poles of the other two alternators a dis- 
tance of one-third of the pole pitch. The space left by the 
missing poles permits placing the coils more easily. Modi- 
fications permit simplifications in construction, so that the as- 
sembled unit does not really consist of three separate units. A 
description of this type of altei-nator is given in a paper by 
M. Latour, Proceedings Institute Radio Engineers, volume 8, 
page 220. .Tune, 1920. Two 500 kw. alternators of this tj-pe are 
being installed in a new high-power station under construction 
at Sainte-Assise. near Paris. 

GoJfJschmidt Alternator. — A principle not previously men- 
tioned in connection with electrical machinery is utilized in 
the generators of certain German high-power stations. Advan- 
tage is taken of the building up of large currents by electrical 
resonance (see Sec. 109) in the rotor and stator circuits of the 
machine itself, as well as of the multiplication of frequency by 
the interaction of the currents in the stator and rotor windings 
on each other. These alternators differ from the Alexanderson 
alternator in that the high frequencies are not directly gen- 

53904° — 22 14 



erated, but are built up in circuits associated with the alterna- 
tor, which are often called " reflector circuits." A very brief 
description of this type of alternator will be given here. For de- 
tailed information the reader is referred to A. N. Goldsmith, 
Radio Telephony, and to papers which have recently been pub- 
lished in German periodicals devoted to radio communication. 
(See also Bureau of Standards Circular 74, p. 224.) 


-=- -5 6" §^ stater 



Fij. JZ7. 




Circuit of 

Without undertaking to give the proof here, it may be stated 
that when a rotor is revolved, and at the same time alternating 
currents are made to flow in the rotor at a frequency corre- 
sponding to the speed of rotation and to the number of poles, 
then, due to these currents, pulsations take place in the strength 
of the magnetic flux of the machine at double the frequency of 
the alternating currents. 

The circuits (in simplified form) are shown in Fig. 127. 
Imagine /S to be the stator winding, energized by some source of 
direct current, such as a battery B. In the magnetic field due 
to the stator there is revolved a rotor, represented by the coil R. 


Suppose it is revolved at such a speed tliat tlie alternating emf. 
induced in R has a frequency of 10,000 cycles per second. By 
way of the slip-rings this emf. is impressed on the circuit 
C3Z/2C4, which is tuned (Section 110), so that, when the induc- 
tance of R is taken into account the natural frequency is the 
same as that of the emf. Then heavy currents will flow in the 

According to the statement made above, pulsations will take 
place in the magnetic flux at the rate of 20,000 per second. 
These will induce a 20,000-cycle emf. in /S. If the inductances 
and capacities SC1L1C2 are chosen for resonance at that fre- 
quency, large currents will flow in the stator at the same time 
with the steady current from the battery. These high-frequency 
currents are prevented from flowing through the battery by the 
high inductance L. 

The 20,000-cycle stator currents cause a 20,000-cycle pulsation 
of the magnetic flux in which the rotor revolves, and when the 
rotor revolves in this pulsating field it gives rise to a triple- 
frequency emf. ; that is, 30,000 per second in the illustration 
chosen. The condenser C5 has such a capacity that the circuit 
RC3C5 resonates to that frequency, and the 30,000-cycle currents 
in the rotor, in view of the rate of rotation of the latter, cause a 
40,000-cycle pulsation of magnetic flux with respect to the 
stator windings. That in turn induces a 40,000-cycle emf. in /S. 
Remembering that the antenna A and the ground G constitute 
a condenser (see Sec. 137), which has the same relation to the 
stator circuit that O5 has to the rotor circuit, it is seen that by 
proper tuning the circuit SCiAG can be made to resonate at the 
final frequency. 

Thus by providing suitable circuits, it is possible to get a fre- 
quency four times as great as that corresponding to the actual 
speed and number of poles of the machine. 

The principle has been explained as though the machines 
were bipolar. Clearly, that would necessitate extraordinary 
speeds. Instead, the large generators used in transatlantic 
service have 360 poles and are driven at 4000 r. p. m. by 250- 
li. p. motors. The fundamental frequency is therefore 12,000, 
which is quadrupled as has just been explained, giving 48.000 at 
the antenna. To secure satisfactory operation the finest sort of 
workmanship is necessary in building them. 


The Goldschmidt alternator which has just been described 
has inside of the machine a means for stepping up the fre- 
quency. The Goldschmidt machine, in units suitable for high- 
power stations, usually operates at a speed of about 4.000 r. p. m. 
An alternator of the Goldschmidt type was formerly in use at 
Tuclierton, N. J. The use of the Goldschmidt type of machine 
is at present decreasing. 

Telefunken Alternator. — The " Telefunken " type of high-fre- 
quency alternator is at present extensively used in Germany, 
and an alternator of this type was installed at Sayville. Long 
Island. In the Telefunken type, the device for stepping up 
the frequency to two to four times the generated frequency is 
a separate unit outside of the machine, and is somewhat simi- 
lar to a transformer in construction. Telefunken alternators of 
a size suitable for use at high-power stations usually operate at 
a speed, of about 1.500 r. p. m., and this slower speed as com- 
pared with the speed of the Goldschmidt machine is an im- 
portant advantage. For further information regarding the 
Telefunken alternator and the device for stepping up the fre- 
quency which is used with it, see A. N. Goldsmith, " Radio 
Telephony," and L. B. Turner, " Wireless Telegraphy and Tele- 

E. Motors. 

96. Uses of D. C. and A. C. Motors. — It has already been noted 
that an electric motor is almost identical with a generator in 
structure, but its function is reversed ; it converts electrical 
power into mechanical power. It is important to have the 
motor suited to the kind of circuit on which it is to be used ; 
a. c, or d. c, the right voltage, etc. Common voltages are 110 
to 120; 220 to 240; 500 to 550; also, for a. c, 440. Lower 
voltages are used on battery circuits. A. c. motors,, like gen- 
erators, may be single phase, two phase, three phase, etc. ; and 
d. c. motors may have series, shunt, or compound excitation. 

97. D. C. Shunt Motor. — If a shunt generator is used for charg- 
ing a storage battery and the engine is shut off, the generator 
will continue running, provided the battery is large enough, 
but an ammeter in the circuit shows that the current has re- 
versed. The battery is discharging and the generator is run- 
ning as a motor. The action is explained by the fact that 



when a current is sent through a conductor in a magnetic field 
there is a force that tends to push the conductor across the 
field (see Sec. 43). The left-hand rule gives the directions. 

Consider the simple loop in Fig. 128, between the poles NS 
of an electromagnet. If the wires + and — are connected to 
a source of direct current, the iron will be magnetized. At the 
same time current flowing in the direction of the arrows in 
the loop causes a force toward the front in the conductor near 
the N pole and a force toward the back in the conductor near 
the S pole. The loop turns. The effect of the commutator is 

Fia. \z& 

Princifsle oj 
^hunt Motor 

J I I ij 

to make the rotation continuous by making the proper connec- 
tion to the conductors as they come into place. 

By a line of reasoning very much like that for the d. c. gen- 
erator, we can pass from this simple case to that of a four-pole 
drum-wound motor, illustrated in Fig. 129. The directions of 
current and rotation are shown by arrows. 

Limiting Speed. — It might be expected that a shunt motor 
would speed up indefinitely, but actually it soon comes to a 
definite speed, and then continues to turn so fast, but no faster. 
As soon as the armature begins to rotate, it generates an emf. 
according to the right-hand rule.^ This action is exactly the 
same as in a generator. 

-^ See Section 63, page 153. 



The emf. generated is opposite to tlie direction of current 
shown by the arrows, and is for that reason called a " counter 
electromotive force." The faster the armature turns the 
greater the counter emf. becomes. It cannot turn so fast that 
the counter emf. is as great as the line voltage, because then 

Fig. 129. — Diagram of circuits of a 4-pole shunt motor. 

the two would balance ; there would be nothing to make the 
current flow through the armature, and consequently no pull 
to keep it turning. For example, suppose the armature resis- 
tance of a certain motor is 0.25 ohm, and suppose that a current 
of 4 amperes in the armature furnishes just enough jjuU to keep 
it rotating. If the speed is high enough to make the counter 


emf. 109 volts when the line voltage is 110, the current is 4 am- 

Next, suppose the motor is driving machinery that calls for 
five times as great a pull. The speed falls off a little. When 
it has fallen enough to make the counter emf. 105 volts, the 
current is 20 amperes.^^ If that is enough to drive the load, the 
speed will be steady at the new rate. So by changing its speed 
a very little the motor automatically takes more or less cur- 
rent, but always just enough to drive its load. 

The magnets are always of the same strength, regardless of 
load, because the current around them depends only on the line 
volts and the resistance of the field coils. It is entirely inde- 
pendent of the current in the armature. 

Comparison of Generator and Motor Actions. — In both gen- 
eiator and motor we have an emf. developed in the armature by 
rotation in a magnetic field. Also in both we have currents 
which cause a pull on the armature conductors. If the machine 
is to act as a generator, its armature must be driven at such a 
speed that its emf. is higher than the voltage at its terminals, 
due to emfs. in other parts of the circuit. Then current flows 
with the emf. This current causes a back-drag on the arma- 
ture and makes it harder to turn. If the machine acts as a 
motor, its emf. is lower than that of the circuit to which it is 
connected. The current flows against this motor emf,, now 
called a counter emf.. and causes a forward pull on the arma- 
ture which keeps it turning. 

Starting Box. — The resistance of a motor armature is small. 
The counter emf, developed by rotation is what keeps the cur- 
rent from becoming excessive. When the motor is first con- 
nected to the line it is not rotating and there is no counter 
emf. Some other way must be found to keep the current mod- 
erate. The simplest way is to put resistance in series with 
the armature^* and then gradually reduce it ("cut it out") 
as the armature gains speed. The resistance is usually in 

E 1 

22 f= p~- r= 110-109=1 volt. jR-0.2oohm. 7= ^25= 4 amperes. 

=3^=110-105=5 volts. i?=0.25 ohm. 7='^-^=20 amperes. 

2^ The field excitation is not cut down, but is of full strength from 
the start. 



the form of wires or grids, mounted in a ventilated iron box, 
tlie whole known as a "starting rheostat" or "starting box." 
Various forms are used ; Fig. 130 shows the connections in one 
type. The parts drawn in solid lines are supported on an in- 

'^N r^N i' ^\'' V \'' '« /'"' ." p 
W hO 6 6 (S y L'-' 

Fia. i3o 

start ir^ bo a -[or ohunt motor 

L- Connection To line F- Connection to shunf •J-iela 
(^-Connection To <^^maTu^e . 



\\ r""=» 










-^ dl / 

^^ shunt 

_ 1^ 

} rnoTor 

Connectiorvs oj ahonl" motor and starting box 

sulating face plate, commonly slate. The internal connec- 
tions are drawn in dashed lines. Fig. 131 shows how the 
starting box is connected between the fused main switch and 
the motor. 



When the resistance is all cut out the iron strip A' comes 
against the electromagnet M, and the handle is held in place. 
If the switch (Fig. 131) is opened, or the line becomes "dead " 
for anv other reason, the magnet ceases to hold K, and a 


D- -, 


^ ' 

. A A / 
6 6 6 

^ A I 





r- — - 






starting box witW Two 'line" termmdls 

L+,L~, li'nc Terminafs f- Connection to shunT field 

A— Connection To <irmdTure 



<>l I F A 

'' S^ < Switch (_+ u- 


box ^ 

Pia. \2>5 


Connections Tor o 3hunT rnoTor and sTarTin^ 
box with Two line Terminals 

spring *S' (Fig. 130) pulls the handle back against tlie bulfer B, 
thus protecting the motor against injury in case the current is 
turned on again. 

Some starting boxes have four terminals. The internal con- 
nections of one box of that kind are shown in Fig. 132. and the 


connections to the motor in Fig. 133. Tlie extra terminal is 
marked L — . It is needed because tlie electromagnet for the 
'' no voltage release " is connected directly across the line, the 
high resistance Z being contained in the box to keep the current 
for it small. 

Connections to a starting box must be made according to the 
way the terminals are marked on the box. They are almost 
always stamped with letters or with the words " line," " field," 
" armature." but will not always be found at the places shown 
in Figs. 130 and 132. 

At the motor the circuits are often brought out on a terminal 
board after the fashion of Fig. 134. Care must be taken not to 
get them confused, for example, by connecting the field in place 
of the armature, or by making the sort of mistake sho\Aai in the 
right-hand diagram (marked "wrong") of Fig. 134, where the 
"A" terminal of the starting box is wrongly connected to the 
junction of armature and field, and the " — Line " is wrongly 
connected to the armature alone. Wrong connections are bound 
to cause trouble. 

Starting and Stopping. — The proper operations for starting 

1. See that handle of starting box is in the " off" position. 

2. Close switch (see Figs. 131, 133). 

3. Move starting handle to first contact. Armature should 
begin to turn. If it fails, open the switch at once, for some- 
thing is wrong — perhaps a faulty connection, loose contact, 
blown fuse, excessive overload, wrong brush position, etc. 

4. As armature gains speed, move handle over contacts, one 
step at a time. Move slowly if load is great, taking if neces- 
sary as much as 30 seconds. When the load is slight and the 
motor small, a few seconds may suffice. 

The operation for stopping is : Open main switch. In a few 
seconds the handle should snap back sharply. If it fails, move 
it back by hand and look for dirty contacts. Sometimes wiping 
the contact studs and putting on just a trace of vaseline will 
cure the trouble. 

Very small motors, rated at a fraction of a horsepower, are 
often connected directly to the line without a starting rheostat 
by simply closing a switch. 



Reversing Direction. — In the diagram (Fig. 134) the mains 
are marl^:ed + and — . As a matter of fact, it makes no practi- 
cal difference if the one marked + is really — , and vice versa. 
The motor rims in the same direction. It can be reversed by 
taking olf the two connections at F (left-hand diagram. Fig. 
134) and interchanging them. Care must be taken that the 
brushes rest on the commutator at the right place and point 
the right way for smooth running, as described in Section 106. 

Speed Regulation and Control. — For reasons given under the 
heading " Limiting speed " a shunt motor generally runs a 
little more slowly when loaded (driving machinery) than when 
running free. Tlie change of speed is called the " speed regula- 
tion." For most motors the regulation is good, the change in 

speed between no load and full load being only 5 per cent or 
less. Shunt motors are therefore often called " constant speed " 

This supposes that the voltage applied to the motor is con- 
stant. If it is too low, the speed falls off, as well as the power 
which the motor can develop. If it is too high, the motor will 
overspeed somewhat and is likely to overheat and to spark in- 
juriously at the commutator. The speed can be changed, if 
necessary, by several methods. Only two will be described. 

A resistance in series with the armature circuit only (not the 
joint line to armature and field) will reduce the speed. The 
conductor must be large enough to carry the armature current 
without overheating. The ordinary starting rheostat will not 
serve, as it is not made large enough for continuous duty. It 
would quickly overheat. Sometimes special rheostats are pro- 


vided for starting, which are large enough to be left in circuit 
continuously. They are then usually marked " Regulating rheo- 
stat, for continuous duty." 

The objection to this scheme is that it wastes power and that, 
if the load changes, the speed changes, too. It has the advan- 
tage of being simple. 

A resistance in series with the shunt field winding increases 
the speed. This seems contradictory. The explanation is that 
when the field current is reduced the magnetism is weakened. 
The conductors have to move faster to generate about the same 
counter emf. as before, and since this counter emf. is always 
nearly as great as the applied voltage the speed has to increase. 

The objection to this method is that the motor may overspeed 
and burst the armature by centrifugal force if too much re- 
sistance is used in the field circuit. There is also danger of 
damaging the comnmtator by sparking. It is not wise to raise 
the speed more than 10 or 15 per cent above that marked on the 
name plate unless the operator is very sure no harm will follow. 

98. D. C. Series Motor. — The field coils of a motor may be made 
of thick wire and connected in series with the armature, so that 
the same current flows through both. It is then called a 
" series " motor. The difference in connections, compared with 
a shunt motor, is the same as for the corresponding kinds of 
generator. (See Fig. 117.) Series motors differ in their be- 
havior from shunt motors in two important ways. They do not 
operate at constant speed, but run very much more slowly when 
heavily loaded ; and at the lower speeds they develop a large 
turning force. They are therefore used on street cars, for crank- 
ing gasoline engines on automobiles, and similar duty where 
high turning effort is wanted for starting a load. 

Suppose there is some current, say, 5 amperes, flowing in arma- 
ture and field coils. Now imagine the load to increase until the 
current is 10 amperes. Two things happen. If the magnetism re- 
mained the same, the doubled armature current would cause 
double the pull. But the magnetism does not remain constant. 
When the current doubles, the field magnetism increases, be- 
cause the 10 amperes flow in the field coils as well as in the ar- 
mature. Thus the doubling of the armature current and the in- 
creased magnetization combined make the pull much more than 
double. Also the stronger field would make the counter emf. 


automatically increase if the speed remained unchanged. But 
this is impossible because the counter emf. must always be a 
little less than the line voltage, else no current will flow to 
keep the motor going, so the speed must fall off. 

The turning force mentioned above is called " torque." From 
the explanation just given, the torque of a series motor at 
starting is seen to be great, because at starting the speed is low 
and the armature current large. The less the load, the higher 
the speed. If the driving belt slips off, a series motor, unless it 
is quite small, can overspeed enough to wreck itself. Series 
motors are therefore direct connected or geared to the driven 
machinery. Shunt motors, on the contrary, will not overspeed 
and belts may safely be used. 

Speed Control. — The only way of controlling the speed of a 
series motor that need be mentioned here is by using a rheostat. 
Except for small motors, one is needed anyway for starting. If 
large enough it can be left in circuit to keep down the speed. 
Of course, this is wasteful, because the heat produced in the 
rheostat uses electrical power. 

99. Other D. C. Motors. — Connected like compound generators 
(Fig. 117), compound motors are used for special purposes, but 
the worker with radio equipment is not likely to run across 
them, and for that reason they are not treated here.^^ 

100. Combination A. C. and D. C. Motors. — Reversing the cur- 
rent in the line to which a series motor is connected has no 
effect on the direction in which the armature turns. If the cur- 
rent is reversed in the field coils alone the magnetism is reversed 
and the armature turns the opposite way. Reversing the cur- 
rent in the armature, too, makes a second reversal of force : that 
is, the armature turns as it did at the beginning. This is still 
true when the reversals ^are so rapid that the current is truly 
alternating, so the same motor can be used for a.c. and d.c. But 
in that case some special construction is necessary ; for example, 
the magnets are built up of laminations instead of being in a 
solid piece. 

101. Alternating Current Motors. — Induction Motors. — When 
the terminals of any coil are connected to a circuit, the cur- 

2' Compound motors are explained in Rowland, p. 126 ; Franklin and 
Esty, " Dynamos and Motors," p. 144 ; Timbie, " Elements of Electric- 
ity," p. 221. 


rent sets up a magnetic field in and around the coil. When 
a number of coils are arranged in the form of a stationary 
two-phase or three-phase armature^® and connected to a cor- 
responding two-phase or three-phase power circuit, there comes 
the remarkable result that the alternating currents flowing in 
the coils produce inside of the armature a magnetic field which 
rapidly and continuously revolves. The iron core and the 
copper coils are both stationary; only the magnetism changes. 
If the changes of current are made slowly a compass needle 
placed in the open space within the armature w411 spin just as 
if it were directed by an imaginary magnet with its poles sliding 
along the face of the armature. 

Next, let an iron core with suitable coils on it be placed in- 
side this armature, on a shaft, so that it can turn. The revolv- 
ing magnetic field cuts across the conductors of this movable 
" rotor " ; that sets up emfs. ; currents flow, and now we have 
conductors with currents in them in a magnetic field. Conse- 
quently the rotor begins to turn. It speeds up until it turns 
nearly as fast as the moving magnetic field. How fast that is 
depends on the construction of the stationary armature and the 
frequency (cycles per second) of the alternating current sup- 

The machine just described is an " induction " motor." Its 
parts are called the stator (stationary part) and rotor (part 
that revolves) just as in an alternator. Nothing has been said 
about any connection between the rotor and an external electric 
circuit. In the simplest form of induction motor there is no 
such connection. The rotor is dragged around magnetically at 
a practically constant speed. A pulley on the rotor shaft can 
be used with a belt to deliver power to some other machine. 

An induction motor can be considered to be a particular kind 
of a. c. transformer in w^hich the secondary winding and the 
secondary core are allowed to revolve with respect to the 
primary, and the secondary winding is short circuited. In the 
transformer the position of the secondary is fixed, and the emf. 
induced in the secondary w^inding causes a current to flow 

^See also Sec. 75. 

-^ For furtlier explanation of action see Timbie and Higbie, " A. C. 
Machinery, Second Course," pp. 429-449 ; Franklin and Esty, " Dynamos 
and Motors," pp. 340-362 ; Rowland, pp. 252-270. 


which delivers electric power in the secondary circuit. In the 
induction motor the emf. induced in tlie secondary causes a 
current to flow in the short-circuited secondary winding, and 
this secondary current causes the secondary to revolve and 
deliver mechanical power. 

In some forms of induction motor there are connections be- 
tween the rotor, which in that case has slip-rings, and an 
external circuit. But the external circuit is not a power circuit ; 
it merely consists of resistances for controlling the motor speed. 

The terms " squirrel cage " and " wound " are often used to 
describe rotors ; the first means the simple kind with conductors 
of plain bars of metal and no slip-rings or other moving con- 
tacts ; the second means the kind having coils like an armature, 
and, commonly, slip-rings. 

If one of the connections to a three-phase induction motor is 
opened, leaving only two attached, the rotor continues to turn. 
Two wires can supply only a simple a. c. (single phase), so it is 
evident that an induction motor can be used on a single phase 
circuit. But it will not start on a single phase without a 
special starter. 

Like d. c. motors, those for a. c. have to be operated at about 
the voltage for which they were built. In addition, they have 
to be connected to a line of the right frequency. Then they run 
at certain definite speeds, which are nearly as high at full load 
as when running free. On 60-cycle circuits the common speeds 
for small motors are a little under 1800, 1200, and 900 r. p. m. 

Starting. — Small induction motors are started by simply con- 
necting them to the right kind of power circuit by a switch, 
double-pole (two blades, for two wires) for single phase, three- 
pole for three-phase, and four-pole for two-phase motors. With 
polyphase (two or three phase) motors, this produces the re- 
volving magnetic field as previously explained. With single 
phase the action is different. It was said, earlier in this sec- 
tion, that an induction motor will not start on one phase, but 
will continue if started somehow. One way might be to give 
it a start by hand. Generally, that is not a practical method. 
A second way is to use a '* phase splitter." That merely means 
that the current goes through the stator by two paths in parallel, 
one having more inductance or capacity than the other. In- 
ductance in any branch of a circuit causes a phase-lag in that 


branch. The armature must have two sets of coils, and if the 
currents' in them differ as to phase, the motor starts as a sort of 
two-pliase machine. After it gets up to speed, one winding (tlie 
"starting" winding) is disconnected. That may be done by 
hand, a special two-way switch being provided with a starting 
and a running position or there may be an automatic centrifugal 
cut-out in the motor.''^ 

A third way is by " repulsion motor " action. Then the rotor 
has a commutator and brushes, like those for d. c. The stator 
is connected to the supply line, the rotor is not. The brushes are 
connected together by a short-circuiting conductor. When cur- 
rents flow in the stator, other currents are induced in the rotor ^ 
and it begins to turn. At the proper speed, a centrifugal device 
short-circuits the commutator and so converts the machine into 
a simple induction motor. At the same time, the brushes are 
lifted automatically, to reduce friction. 

Larger three-phase motors are started by applying a fraction 
of full voltage, obtained by a combined transformer and double- 
throw switch known as a " compensator."^" 

Synchronous Motors. — In Sections 73 and 74 there have been 
described briefly several forms of alternators, and their use as 
generators of alternating current. If two alternators of identi- 
cal construction are driven at the same speed, they may be con- 
nected in parallel to supply the same distributing line. If now 
the supply of mechanical power to one alternator is cut off, as 
by slipping off the belt, that alternator will usually continue 
to operate as a motor, taking power from the other alternator. 
An alternator operating as a motor in this way is called a 
" synchronous motor," and may be either single phase or poly- 
phase. It is not at all necessary that a synchronous motor be 
of the same size as the generator supplying it ; a number of 

"® Split phase starting is described in Timbie and Higbie, " A. C. Elec- 
tricity, Second Course," pp. 510-512. 

29 gee Timbie and Higbie, "A. C. Electricity, Second Course," p. 514 ; 
Rowland, p. 270 ; Franklin and Esty, pp. 383, 386 ; Standard Hand- 
book, p. 542. 

3" For details and other methods of starting, see Timbie and Higbie, 
"A. C. Electricity," p. 454 ; Franklin and Esty, " Dynamos and Motors," 
p. 360 ; " Standard Handbook for Electrical Engineers," pp. 520, 1292, 
1293 ; A. S. McAllister, "Alternating Current Motors " ; C. E. Magnus- 
son, "Alternating Currents." 


small synchronous motors can be driven by one large generator. 
Synchronous motors are much less used in practice than induc- 
tion motors. Synchronous motors of large size have particular 
applications. The single-phase synchronous motor will not start 
itself, except by the use of special starting devices, some of 
which are similar to those described for starting the single- 
phase induction motor. The synchronous motor must operate 
at exactly the frequency of its supply, and if it falls out of 
step for any reason it will usually stop. The synchronous motor 
must operate at the same speed at any load, while the speed of 
the induction motor varies with the load. By adding a commu- 
tator to the synchronous motor it becomes a " synchronous con- 
verter " or "rotary converter." (See Sec. 103.) The construc- 
tion of one kind of synchronous motor is shown in Fig. 97, page 
157. For further information see A. S. McAllister, Alternating 
Current Motors. 

F. Motor Generators and Dynamotors. 

102. Motor Generators. — When electric current is to be had, 
but not in the form needed, the change is made by transformers," 
rectifiers, motor generators or dynamotors, according to circum- 
stances. The first named change a. c. at one voltage to a. c. at 
another voltage at the same frequency. The second change a. c. 
to pulsating d. c. Tlie last two are used for changing a. c. at 
one frequency to a. c. at another frequency or to steady d. c, or 
the reverse ; also for changing d. c. from one voltage to another. 

The most easily understood way to make the change is by the 
use of a suitable combination of motor and generator, built for 
the same speed and mounted on a common base, the shafts being 
coupled together. Such a combination is a " motor generator." 

Motors and generators have been described. The combina- 
tion brings no new ideas. Each part can be thought of by itself, 
without regard to the other. Examples of such machines have 
been given.^^ In radio practice they are used particularly for 
battery charging and for supplying spark and arc circuits. 

Battery Charging. — Motor generators for battery charging are 
used where the supply is a.c, or d.c. at the wrong voltage. In 
the latter case if the d.c. voltage is too high, a rheostat may be 

31 Described in Sec. 58. ^2 Sg^. 94, Figs. 121, 122, 124. 

53904° — 22 15 


used, but it wastes power. When several low-voltage batteries 
have to be charged, they may be connected in series and the 
power wasted in resistance thereby reduced. 

The generator of a battery charging unit is usually shunt- 
wound. The voltage of a storage battery rises as it gets charged. 
Also, at the beginning it is allowable to use a larger current 
than toward the end of the charge. The voltage of a shunt 
generator is lower when it is delivering a large current than 
when the current is small.^^ Therefore such a generator, con- 
nected to a discharged battery and given the proper setting, 
produces a large current which gradually decreases as the bat- 
tery voltage rises. It is also possible to use a compound gen- 
erator, so designed that the voltage is substantially constant, 
whatever the current within the limits of the machine. In that 
case the initial rate of charging the battery is higher than when 
a shunt generator is used, but falls off in the same way. A 
high rate of charging at the beginning cuts down the time re- 
quired for the whole process, and is therefore desirable, pro- 
vided it does not injure the battery. Modern portable batteries 
will stand charging in this way and compound generators may 
consequently be used. The proper treatment for a given bat- 
tery must be learned from instructions pertaining to that par- 
ticular form. 

Motor generators are used also for connection to ordinary 
lighting circuits (about 110 volts) to get 500 or 600 voits d.c. 
for arc transmitters,^* or for connection to such circuits or to 
low voltage storage batteries to get a.c. at 500 to 900 cycles 
for use with transformers in audio-frequency spark transmit- 
ters.^^ Motor generators may also be used for supplying 300 or 
more volts to the plates of electron tubes used for generating 
undamped alternating currents of radio frequency. ( See pages 
491, 498.) Such alternators and motor generators have been 
described in Section 94. 

103. Rotary Converters. — If connections are made to a pair of 
collector rings from opposite sides of a two-pole d.c. armature, it 
will generate alternating current. At the same time, direct cur- 
rent can be taken from the commutator. In that case the ma- 
ss Shown in Fig. 118. ^ See Sec. 174. ^ See Sec. 154, page 354. 


chine is a " double current generator." If not driven by an 
engine, but connected to a d.c. circuit, it operates as a shunt 
motor and can be used to generate a.c. Operated on a.c. as a 
motor, it delivers d.c. When used for such conversion it is 
called a rotary converter. When an a.c. generator is used as a 
synchronous motor (not an induction motor) it requires d.c. for 
field excitation and operates at the exact speed (called "syn- 
chronous " speed), corresponding to the frequency of the supply. 
The d.c. for the rotary converter field comes from the commuta- 
tor. On the other hand, when such a converter is used to gener- 
ate a.c, the frequency depends on the speed of rotation of the 
armature, which can be controlled as previously described for 
the shunt motor. When a rotary converter is used in this way 
for converting direct current into alternating current, it is said 
to be operated as an " inverted rotary." 

The rotary converter has the advantage of accomplishing in a 
single machine what the motor-generator does in two. Its dis- 
advantage is that the voltage at the generator end depends 
entirely on the voltage supplied to it as a motor, the effective 
value of the a.c. voltage in the case of a single-phase converter 
being about 71 per cent of the d.c. voltage, slightly more or less, 
depending on the direction of the conversion. Thus, if operated 
on a 10-volt storage battery, it would give about 7 volts a.c. In 
radio communication it is desirable to have a machine which 
will deliver a.c. of a frequency of 500 cycles when supplied with 
d.c. from a storage battery. Small rotary converters can not 
be designed to supply a.c. of a frequency anywhere near as 
high as 500 cycles. Either the speed or the number of com- 
mutator segments would have to be increased beyond reason. 

Instead of single phase, rotary converters can be built for 
two-phase or three-phase currents, the former by four connec- 
tions equally spaced on the armature and four rings, the latter 
by three connections and three collector rings. The statements 
made for bipolar machines are equally true for multipolar 
rotary converters, if it is understood that each ring has as 
many connections to the armature as there are pairs of poles. 

The rotary converter, or " synchronous converter," is really 
a synchronous motor to which a commutator has been added, 
but the design of rotary converters requires a number of modi- 
fications from synchronous motor design. In external appear- 



ance a polyphase rotary converter resembles a direct-current 
g:enerator with a conspicuously large commutator and an auxili- 
ary set of collector rings. 

104. Dynamotors. — Rotary converters cannot be used for 
changing direct current at one voltage to d.c. at another voltage. 
The most compact machine for that purpose is the " dyna- 


\o V. 

Fia. 13)5 



PynAmoTbr connecTiona for co'^ver3ion "from lo to 3oo Volta 



Doy ble cwrrenl* ^enerATor 
•for low and hi^h Voltage 


5- 5hunT colli 

D- Differential colls 

Re^- - AulbmaTic r^uliTor 

motor." An application which will occur to the radio student 
is the securing from batteries giving only 10 or 12 volts of the 
300 or more volts required for supplying the plate potential of 
electron tubes used as generators of radio-frequency alternating 
current. ( See Fig. 135. ) In the dynamotor two separate arma- 
ture windings are placed on a common core. One acts as a 
motor, the other as a generator. There is but one frame and 


one set of field magnets. The two windings are connected to 
commutators at opposite ends of the shaft. The ratio of volt- 
ages is fixed when the machine is built, so the output voltage 
depends on the voltage applied. The field coils receive current 
from the same source as the motor armature. 

105. Double- Current Generators. — A dynamotor can be driven 
by mechanical power as a generator, and can then deliver d. c. 
at two different voltages. Such machines have been designed 
for fan drive on airplanes, the low and high voltages being 
used for the filament and plate currents, respectively, of 
electron tube transmitters. 

To get constant voltages, in spite of the varying speed at 
which the armature is driven, the field flux must be weakened 
as the speed rises. Current taken from one commutator is 
sent around the field coils, supplying the main magnetization. 
A weaker current from the other commutator is sent around the 
opposite way, giving a differential effect. (Fig. 136.) If the 
speed rises, and consequently the voltage, the current in the 
second winding is made to increase considerably by a sensitive 
automatic regulator. The flux is therefore reduced, counter- 
acting the effect of the rise in speed. 

106. Common Troubles. — Electrical machinery is subject to the 
same troubles as other machinery, such as rough, gritty, dry 
or tight bearings, bad alignment, sprung shaft, etc., which show 
themselves by heating, taking excessive power, and vibration. 
The bearings must be clean and smooth. Care must be taken 
never to spring or jam the shaft. There must ahvays be enough 
oil of good quality in the oil wells to keep the bearings 
thoroughly lubricated. Most generators and motors are oiled 
by means of brass rings that ride on the shaft and dip into the 
oil and carry it up as they turn. Sometimes these are injured 
in taking the machine apart ; then they do not turn properly ; 
the bearing runs dry and heats. 

Some machines have ball bearings. They should run very 
easily, but are subject to the same troubles as a bicycle bear- 
ing, such as broken balls, grit, adjustment too tight. In gen- 
eral if a bearing gets too hot to be borne vrith the hand, it 
needs attention ; the trouble is likely to grow woi*se, until 
finally the shaft binds firmly and cannot be turned. The job 


of getting it free again may then be a very tedious and trouble- 
some one. 

Anotlier point of friction is at tlie brushes. If they are 
pressed in too firmly, they rub harder than necessary. They 
should be fitted smoothly so as to give the fall area of electrical 
contact, then excessive pressure will not be needed. They 
should be only tight enough to make good contact and prevent 
sparking or flashing. When carbon brushts are working prop- 
erly, the metal surface on w^hich they rub becomes finely 
polished, and wears down very slowly. This is particularly 
noticeable in the case of copper commutators on direct current 

Besides those of a mechanical nature there may be electrical 
troubles, some requiring expert attention, others easily found 
and. cured. The most common electrical troubles are caused by 
loose, wrong, or missing connections, and dirt. 

Connections (usually accidental) that allow current to pass 
by a piece of apparatus, instead of flowing through it, are 
called " short circuits." They are a common source of trouble. 

A systematic way of hunting troubles is as follows : 

1. Make or find a circuit diagram, unless you are thoroughly 
familiar with the connections and are positive they are right. 
In drawing diagrams follow each branch of the circuit from the 
source (+ terminal of battery or generator armature) com- 
pletely around (through the — terminal) to the place of begin- 
ning. Remember that no current will flow in a circuit or in any 
part of a circuit unless there is a difference of potential in it. 

2. Trace the wiring according to the diagram. 

3. While tracing, see that — 

(a) Fuses are good, if any are in circuit. 
(&) Connections are clean and good. 

(c) Contact is not prevented by insulating caps of binding 
posts or insulation of wire. 

(d) Wires do not touch, making short circuits. 

(e) There are no extra wires or connections. 

if) There are no breaks in wire inside of the insulation. 
This occasionally happens with old lamp cord. The broken 
place is very limber, and can be pulled in two more readily 
than a sound place. 

4. Look for defects in the apparatus itself. 


In a generator, besides loose connections, electrical troubles 
easily remedied are, for d.c. : 

5. Failure to generate emf., caused by — 

(a-) Brushes not in the right place. On nearly all d.c. 
generators of reasonably modern construction, the proper posi- 
tion for the brushes on the commutator is nearly opposite the 
middle of the field poles, or slightly forward (in the direction 
of rotation) of that point. The exact location, found by trial, 
is that which gives sparkless commutation. Brushes are set 
right at the factory, and should be left as they are, unless there 
is good reason to believe that they have since been shifted. 

(6) Brushes not making good contact because of bad fit or 
too little pressure. Test by lifting them slightly, one by one, 
to detect loose springs ; also try pressing brushes to commuta- 
tor with dry stick. Remedy by working line sandpaper back 
and forth, sharp side out, between comnmtator and brush 
(holding it in such a way that the toe of the brush is not 
ground off) or by tightening brush springs, as needed. 

Brushes are designed, either to press against the commutator 
squarely, pointing toward the center of the shaft, or, more 
commonly, to trail somewhat as an ordinary paint brush might 
trail if held against the commutator. However, there is also 
in very satisfactory use a form of holder by which the brushes 
are held pointing against the direction of rotation. Instead 
of sliding up or down in a box they are pressed against a 
smooth face of brass by springs. 

(c) Field connections reversed. 
. 6. Sparking, when caused by 

(a) Roughened commutator; cured by holding fine sand- 
paper (not emery) against it while running. 

( & ) Brushes shifted ; for remedy see 5, above. It is very im- 
portant that all brushes be at the proper points. This means, 
for example, that if the brushes are supposed to touch at four 
points, spaced a quarter way around the commutator, they 
shall actually be exactly a quarter of a circumference apart, as 
tested by fine marks on a strip of paper held against the com- 

7. Heating of commutator due to brush friction. Reduce ten- 
sion of springs. 


In a. c. generators look for — 

8. Loose connections and bad contacts at brushes. Position 
of brushes on rings is immaterial, as there is no commutation. 

In d. c. shunt motors, motor-generators, or dynamotors, the 
simple troubles are : 

9. Failure to start, or starting suddenly with speed quickly 
becoming excessive, due to wrong connections. ( See Sec. 97. ) 

10. Sparking, caused by excessive load or wrong brush posi- 
tion. (See 5 and 6 above.) The proper position for motor 
brushes is slightly backward (against the direction of rotation) 
of the center of the field poles. 



A. Simple Radio Circuits. 

107. The Simplicity of Radio Theory. — The principles of alter- 
nating currents developed in Chapter 1 are applicable to radio 
circuits. Radio currents are merely very high frequency alter- 
nating currents. The fundamental ideas of sine waves (Sec. 
50) apply to what are known as continuous or "undamped 
waves." " Damped waves " also behave in many ways like 
sine waves; for some purposes slight modifications of the sine 
wave theory are needed. These are treated in Part B below. 

The frequencies of alternation of radio currents are very high. 
Ordinary alternating current power circuits use frequencies from 
25 to 60 cycles per second. The lowest radio frequencies, how- 
ever, lie above some 10,000 cycles per second, and the upper 
limit may be put at perhaps 300,000,000 cycles per second. Such 
an enormous difference in frequency should naturally give rise 
to some differences in the behavior of radio circuits as distin- 
guished from low-frequency alternating current circuits. 

In low-frequency a.c. circuits the prhicipal opposition to 
the flow of currents through the wires connecting the vari- 
ous machines and other parts of the circuit is the resistance 
of the wires. It is only in unusual cases that the inductance 
and capacity of the connecting wires requires consideration in 
low-frequency a. c. circuits, although the inductance of the 
windings of generators, motors, and transformers is important. 
The inductance and capacity of every part of a radio circuit are 
usually of much more importance than the resistance. 

The reactance of such small inductances as are provided by 
a few turns of wire is of importance, and condensers whose 
small capacity would very effectually prevent the flow of ordi- 
nary alternating currents readily allow the passage of radio 
currents. The mutual inductance effect of one circuit on another 
is much greater, when radio frequencies are used, than is the 




case with ordinary alternating current circuits. The enormous 
frequencies used in radio work give rise also to much larger 
skin effect (see Sec. 117, p. 263), eddy currents, and dielectic 
losses than would be the case if the same circuit were worked 
at low frequency. 

Furthermore, measuring instruments commonly used for alter- 
nating current work are, for the most part, unsuitable for use in 
radio circuits, or require modified methods of connection. In- 
struments whose indications depend upon the heating effect 
(Section 59) are, in general, suitable for radio work. Direct 
current instruments may also' be used, but in connection with 
rectifying devices. The telephone receiver, so useful in low 
frequency work, requires a rectifier also. At low frequencies 

' ■ 1 


F J a 1^1 




Simple Series CircuiT 





the diaphragm of the receiver vibrates with the current, giving 
an audible singing note of the same frequency as the alternat- 
ing current. Radio currents execute their changes, however, 
altogether too quickly to be followed by the telephone directly, 
and even were it possible for the diaphragm to vibrate so rap- 
idly, the sound produced would be of too high pitch to be 
heard by the ear. It is found to be necessary, therefore, to 
break up the radio currents into groups of rectified waves. 
Each group gives a single impulse to the diaphragm, and if the 
impulses follow regularly with sufficient rapidity a musical note 
is produced. 

108. The Simple Series Circuit. — The simplest form of radio 
circuit is one having resistance, inductance, and capacity in 
series, as in Fig. 137. An alternating emf. is supposed to be 
applied at E, 


In Chapter 1, Section 57, page 127, it has been shown that the 
value of the current produced in a circuit, to which an alter- 
nating emf. is applied, may be calculated by the equation, 

^ emf. 

Cur rent =■ 


If the effective value of the emf. is used here, the equation 
gives the effective value of the current. (Sec. 51, p. 118.) 

The impedance Z depends not only on the resistance R, but 
on the reactance X of the circuit as well. (Sees. 55, 57.) For a 
sine wave of applied emf, 

Z--=R-^-X'' (69) 

That is, the square of the impedance is found by adding the 
squares of the resistance and the reactance. The impedance 
can therefore never be less than the resistance, and may be very 
much greater. If the resistance in the circuit is very small in 
comparison with the reactance, the impedance is practically 
equal to the reactance. The impedance is measured in ohms. 

As has been pointed out (Sec. 49), the reactance is the opposi- 
tion offered to the current by an inductance or a capacity. The 
reactance, in ohms, of an inductance coil is equal to 2ir times the 
frequency, times the inductance in henries. For a capacity, the 

reactance, in ohms, is equal to ^ .^ (Sec. 56), in which / is the 

frequency and C is the capacit.v in farads. In their reactive 
effects an inductance and a capacity tend to offset one another, 
so that the total reactance of an inductive coil and a condenser 
in series is found by taking the difference of their individual 

It is general practice to use the symbol w to represent 27r 
times the frequency (27rf), since the quantity 27rf very fre- 
quently occurs in problems involving radio circuits. (See Cir- 
cular 74, p. 22.) Using this abbreviation, the reactance of an in- 
ductance may be written wL, and the reactance of a capacity 

may be written — t^- 



Example. — Let us calculate the reactance of the combination 
of a coil of 500 microhenries inductance in series with a con- 
denser of 0.005 microfarad capacity at several different fre- 


cycles per 


Reactance of 



Reactance of 



Total react- 




100, 700 


316. 23 

-316. 23 





The table shows at a glance that the reactance of the coil is 
small at low frequencies, increases as ihe frequency rises, and 
becomes very considerable at the higher frequencies, such as 
occur in radio work. 

The behavior of the condenser is just the reverse. At the 
lowest frequency it offers a very large reactance, but at radio 
frequencies the impedance is vastly smaller. For very high 
frequencies the reactance would be negligible. 

In most radio circuits the resistance of the circuit can be kept 
as small as a few ohms. It is therefore obvious that only in the 
case of the 100,000 cycles, in the table, would it be necessary 
to take account of the resistance in calculating the impedance. 

For example, if i^=5 ohms, the impedance for the frequencies 
in the table above will have the values 530,000, 31,837, 6.5, 5 
and 3110, respectively. In all except the third and fourth cases, 
the difference between the reactance and the impedance is less 
than one part in a million of the total. 

It is thus apparent that in many cases the impedance of a 
circuit depends almost entirely on the reactance of the circuit. 
Only in those cases where the reactance is small is it necessary 
to take the resistance into account. 

109. Series Resonance. — It would seem at first sight, then, that 
radio circuits \\'ould offer for the most part a high impedance 
and that therefore very little current could flow, except with 
very large emf. This is in general true of any radio circuit if 
the frequency be taken at random. However, by properly ad- 
justing the value of the frequency, the reactance of the cir- 


cuit may be made zero. This is at once evident, wlien we 
remember tbat the inductive reactance increases with the 
frequency, while the capacitive reactance diminishes. At some 
definite frequency, then, the inductive reactance of the coil must 
have the same value as the capacitive reactance of the con- 
denser, and since they act against each other, the total reac- 
tance will be zero. 

This may be shown graphically. In Pig. 138 are plotted the 
curves A and B of the reactances of the coil and condenser, 
respectively, of the previous example. Frequencies are meas- 
ured along the horizontal axis and reactances along the vertical 
axis. The reactances of curve B are taken as negative to dis- 
tinguish between the opposing effects of the inductive and 
capacitive reactances. Curve C is obtained by taking the alge- 
braic sum of the reactances of curves A and B. It is the curve 
of resultant reactance in the circuit. For the particular values 
of C and L chosen in this example, the circuit acts like an in- 
ductive reactance at all frequencies greater than a value of 
slightly above 100,000 cycles, while below that point it has the 
character of a capacitive reactance. Furthermore for only a 
narrow range of frequencies, 99,000 to 103,000, perhaps, the 
reactance of the circuit is less than 10 ohms. For most fre- 
quencies the reactance is much greater than this. 

The frequency which makes the capacitive and inductive re- 
actances equal is called the" resonance frequency" of the cir- 
cuit, and the circuit is said to be in " resonance," or to be 
** tuned " to the frequency in question. It is important to be 
able to calculate the frequency for resonance. To do so, the 
condition must be fulfilled, that 

2^//^=^ (70) 


which shows that the frequency at resonance must be 

/= o ^ (71) 

Applying this relation to the example under discussion, and 
substituting therein L =0.0005 henry, C=iq9 farad, the reso- 
nance frequency is found to be about 100,700 cycles per second. 
The reactances of both the coil and the condenser at this fre- 









Frequencu— cycles per second. 

133. Variation of reactance with Freqaencu. 

/ •=■ soo microhenries 
C - COOS' microfarad's 



<£** 19.1 volts ^ \o 

"^ s 


tL % 

/t 11 

tt A^c 


tii trijT, 

f-f-f \-\-^/44ohm5 

2 tt X\ ^ 

cr t 44 ^ 

7 ^ t -t V 

^ bI U L ^ 

2 ft \ \ 

J- Z--, v4^.. L K 

r ^-j -\--" g.'^ohrr^ 

~ 7 t ^J\ 

y^\± \^^ 

.^^ /^4ohms. ^v ^- 

^^ ^^ 


2Z0O £300 2400 ZSOO 

Capaciia in micnmicrotarads. 
'Fiq.i'53. 'Resonance Curves 
for iSeries Circuit rvith 
Different J^esistances. 


Capacity in micromicrofarads . 
Fig. i^c^Fffect of Fes is- 
iance on the shape of 
the Peso nance Curiae 


quency are the same and have the value 316.2 ohms. This value 
may, of course, be calculated by using for f the value of the 

resonance frequency in either of the expressions 27r fL or ^ — -7^. It 

is of interest to note that each of these expressions for reactance 

reduces simply to -y-p, when the frequency has the resonance 


There exists, then, for any series circuit containing in- 
ductance and capacity a definite value of the frequency, for 
which the total reactance in the circuit is zero, and the im- 
pedance is simply equal to the resistance of the circuit. This 
frequency is called the resonance frequency, and the circuit is 
said to be in a condition of resonance. The impedance has its 
smallest value, and the current which flows in the circuit when 
the applied emf. has any value whatever has the largest value 
possible with that value of frequency. 

These facts may be readily verified experimentally by insert- 
ing in a simple radio circuit a suitable ammeter for measuring 
the current. If now the frequency of the applied emf. is gradu- 
ally raised, the current will at first be small and will increase 
very slowly as the frequency is increased. In the immediate 
neighborhood of the resonance frequency tlie current will sud- 
denly begin to increase rapidly for small changes of frequency, 
and after passing through a maximum will rapidly decrease 
again as the frequency is raised to still higher values. The 
results of such an experiment may be shown by a curve in 
which frequencies are measured in the horizontal direction, 
while the values of the current corresponding are plotted ver- 
tically. Since most instruments suitable for measuring radio 
currents give deflections proportional to the square of the cur- 
rent, it is customary to plot the squares of the current, or the 
deflections of the instrument, rather than the current itself. 
Such " resonance curves " are plotted in Fig. 139, and they 
show plainly the " resonance peak " of another circuit having 
different constants. (See p. 241.) 

On account of its great importance in radio work the phe- 
nomenon of resonance requires further study. To fix our ideas, 
let us suppose that a circuit whose inductance and capacity 
have the values already chosen in the previous example (500 


microhenries, 0.005 microfarad) has a resistance of 5 ohms and 
that an emf. of 10 volts is applied in the circuit. The maximum 
possible value of the current is found by dividing the applied 
voltage by the resistance, which gives 2 amperes. This cur- 
rent will flow when the frequency has the critical value of 
100,700 cycles per second. To study the distribution of emf. 
over the different parts of the circuit we have to remember 
(Sec. 55) that the emf, between any two points of the circuit 
has to have a value equal to the product of the current by the 
impedance between the two points. Accordingly the emf. be- 
tween the ends of the resistance is 2X5=10 volts, that on the 
coil is 2X316.23=632.46 volts, and the same emf. is found be- 
tween the terminals of the condenser also. 

The existence of such a large voltage on both the coil and the 
condenser explains how it is possible to obtain such a relatively 
large current through the large reactances of the coil and con- 
denser. The small applied voltage is employed only in keeping 
the current flowing against the resistance of the circuit, not for 
driving the current through the coil or condenser. To explain 
the presence of the large voltages on coil and condenser, it must 
be remembered, as was shown in Section 57, that when a current 
is flowing through an inductance and capacity in series the emf. 
on the inductance opposes that on the capacity at every moment. 
The sum of the voltages on the two is therefore found by sub- 
tracting their individual values. Since at the resonance fre- 
quency the emf. on the inductance has the same value as the 
emf. on the capacity, the emf. between the terminals of the two 
in series is therefore zero. 

Energy is supplied to the circuit by the source at a rate which 
may be determined (when the resonance condition has been 
established) by simply multiplying the emf. by the current. 
(Sec. 55, p, 123.) That is, in the present instance the power is 
10X2=20 watts. The x>ower dissipated in heat in the resistance 
may be calculated by taking the product of the resistance by 
the square of the current. (Sec. 51.) In this case it is 
5X2^=20 watts. The source, therefore, supplies energy to the 
circuit at just the right rate to make good the energj^ dissipated 
in heat in the resistance. After the current has reached the 
final effective value (2 amperes in this case) no further energy 
is supplied to the coil or condenser by the source, but their 


energ"y is simply transferred back and forth from one to the 
other without loss or gain in the total amount, nor is any out- 
side agency necessary to maintain this condition. 

In the above discussion of a simple series circuit, consisting 
of a resistance, an inductance, and a capacity in series, it has 
been assumed that the inductance coil was a pure inductance 
and that the capacity was a pure capacity — that is, that neither 
had any resistance and that the entire resistance of the circuit 
was concentrated in the resistance unit. In actual practice 
these ideal conditions can not be absolutely realized, althougli 
they may be very closely approximated. The inductance coil 
necessarily has a certain amount of resistance in which energy 
is dissipated as heat, and there may be other sources of energy 
loss in the inductance coil. The insulating material between 
the plates of the condenser constituting the capacity is not an 
absolutely perfect nonconductor, but allows a certain very small 
leakage current to flow, resulting in a small loss of energy as 
heat. There are also other sources of energy loss in con- 
densers." The effect of these energy losses in the condenser 
is equivalent to introducing additional resistance into the cir- 
cuit. With suitable design, the energy losses in both inductance 
coils and in condensers may be made very small. 

MecJianical Example of Resonance. — Many mechanical ex- 
amples of resonance might be cited. It is a well-known fact that 
the order to " break step " is often given to a company of 
soldiers about to pass over a bridge. Neglect of this precaution 
has sometimes resulted in such violent vibrations of the bridge 
as to endanger it. This is especially the case with certain short 
suspension bridges. 

When a shock is given to a bridge it vibrates, and the fre- 
quency of the vibrations — that is, the number of vibrations per 
second — is always the same for the same bridge, whatever the 
source of the shock. The frequency of vibration is analogous 
to the resonance frequency of the circuit. For if an impulse 
be applied to the bridge at regular intervals, tuned so that the 
number of impulses per second is exactly equal to the number of 

" A discussion of energy losses in condensers may be found in Bureau 
of Standards Circular No. 74 and in a paper by J. H. Dellinger, Pro- 
ceedings Institute Radio Engineers, vol. 7, p. 27, February, 1919. 
53904° — 22 16 


vibrations natural to the bridge in the same time, violent vibra- 
tions may be set up, although the individual impulses may be 
small. In fact, when the bridge is thiis vibrating the impulses 
need to have only just force enough to overcome the frictional 
forces and thus keep the vibrations from dying away. The 
much greater forces involved in the vibrations themselves cor- 
respond to the large voltages acting on the coil and condenser. 
The voltage on the condenser is of the same nature as the large 
forces which exist in the beams of the bridge when they are 
stretched, while the voltage on the coil corresponds to the very 
considerable nromentum of the moving bridge. The small force 
of the impulses given the bridge corresponds to the small 
applied emf. in the electrical case. 

If the vibrations of the bridge ever become so violent as to 
rupture it, it means that the beams have been stretched beyond 
their breaking point. Similarly the dielectric of the condenser 
may be broken by the emf. existing between its terminals in 
cases where the resonance current is too large. 

AlO. Tuning the Circuit to Resonance. — The practical impor- 
tance of resonance lies in the fact that it enables the impedance 
of a circuit to be made equal to the resistance alone. It must 
be remembered that the reactance of the small inductances in 
the circuit, which are unavoidable, becomes important at radio 
frequencies and may often be much greater than the resistance. 

This fact, taken in connection with the smallness of the emf. 
of incoming signals, would make it impossible to obtain any but 
minute currents in the receiving apparatus with inductance 
alone in the circuit. From this standpoint, the sole function of 
the tuning of the circuit to resonance is to offset the inductive 
reactance by an equal capacitive reactance, so that the im- 
pedance may be made as small as the resistance. 

The circuit may be tuned to resonance in three ways — 

(a) By adjusting the frequency of the applied emf. 

( b ) By varying the capacity in the circuit. 

(c) By varying the inductance in the circuit. 

Of these, the first case has already been treated, the other 
two find application in receiving circuits where the frequency 
of the incoming waves is beyond the control of the operator, in 
the use of coupled circuits and in the adjustment of the fre- 
quency of the waves emitted in certain methods of sending. 


The possibility of tuiiinj? a circuit is of course not confined to 
radio circuits, but is present also with ordinary alternating 
current circuits, and is becoming common in telephone work. 
However, at low frequencies the values of the inductance and 
capacity involved are relatively great, so as to make it incon- 
venient to vary their values in steps sufficiently small. Further- 
more, in low-frequency work the reactances of the coils likely 
to occur in the circuit are small, and the large quantities of 
power involved render the use of condensers relatively uncom- 
mon. The inductances and capacities used in radio work, on 
the other hand, are relatively small, and the construction of 
coils of continuously variable inductance ("variometers" or 
variable inductors) and of apparatus of variable capacity (vari- 
able condensers) offers no particular difficulties. 

From fornnila (71) it appears that it is the product of the 
inductance and capacity, rather than their actual values, which 
determine the resonance frequency. To tune a circuit to a 
given frequency, the inductance may be large or small, pro- 
vided only that the capacity may be so adjusted that the prod- 
uct of inductance and capacity shall have the value correspond- 
ing to the frequency assumed. (A table showing these varia- 
tions with the product of inductance and capacity is given in 
Appendix 5, p. 557.) 

111. Resonance Curves. — A resonance curve is a curve which 
shows the changes of current in a circuit, when changes are 
made which cause the resonance condition to be somewhat de- 
parted from. For example, the current (or square of the cur- 
rent) may be plotted for different values of the frequency 
somewhat above or below the resonance frequency. Or, the 
curve may show the change in current, when the capacity (or 
inductance) is somewhat raised and lowered with respect to 
the value which holds for the condition of resonance. Such 
curves are often determined experimentally, in whole or in 
part, on account of their value in calculating the damping of 
the circuit. (Damping is treated in Sec. 116 below.) Such, 
for example, are the curves of Fig. 139, in which are plotted 
the values of the current squared, to an arbitrary scale, for 
different values of the capacity of the variable condenser. The 
inductance of the circuit was fixed at the value 377 micro- 
henries. Three different curves were determined with the re- 



sistance in the circuit fixed at the vahies 4.4, 9.4, and 14.4 ohms, 

Sharpness of Resonance. — It was, of course, to be expected 
that the value of the current at resonance (height of the peak), 
should be greater, the smaller the resistance in the circuit, but 
attention needs to be called particularly to the sharpness of the 
curve with the smallest resistance and to the flatness of the 
curve with greatest resistance. This is the characteristic of 
resonance curves in general, and is a necessary consequence of 
the equations for the impedance. It may be shown still more 
clearly, if the scales to which the three curves are plotted are 
so altered that the peaks of the three curves have the same 
height. This has been done in Fig. 140. page 236. 

The same results may be seen by calculating the square of 
the impedance with different settings of the condenser and with 
different resistances in the circuit. The resonance frequency 
in this case was 169,100 cycles per second, which shows that 
with the inductance of 377 microhenries the setting of the con- 
denser at resonance is almost exactly 2,350 micromicrofarads. 
The reactance of condenser and coil at this frequency is 400.56 
ohms in each case. 

The following table shows the impedances for three different 
settings of the condenser when the resistance of the circuit has 
the three values corresponding to those of the curves. The 
squares of the currents are, of course, less in proportion as the 
squares of the impedances are greater. 

Setting of 

Impedance squared. 

For R=iA 

For E=9A 

For i?= 14.4 

2300 94. 1 
2350 19. 3 
2400 90. 




For the smallest resistance, the square of the current is about 
4.7 times as great at resonance as when the capacity is changed 
by 50 micromicrofarads in either direction. For 9.4 ohms in 
circuit the ratio is about 1.8, and for the largest resistance 
only about 1.35. These calculated ratios agree very well with 
the experimental values. The close connection of the shape of 


the resonance curve with its resistance points to the possibility 
of calculating the total resistance in the circuit from measure- 
ments of the resonance curve. For this method of measuring 
radio resistance see Circular 74 of the Bureau of Standards, 
Sections 49 and 50. 

The calculations here given, as well as an inspection of the 
curves of Fig. 139, show that the resonance curve is not sym- 
metrical. That is, the current has not the same value when the 
capacity is a certain amount less than the resonance value that 
it has when the value of the capacity is gi'eater by the same 
amount. The question of this lack of symmetry is treated in. 
the next section. 

Symmetry of Resonance Curves. — The curves of Fig. 138 
show the changes of coil reactance, curve A, and condenser reac- 
tance, curve B, together with the total reactance, curve C (their 
show the changes of coil reactance, curve .4, and condenser reac- 
tance, curve B, together with the total reactance, curve C (their 
its zero value (point Z, Fig. 138). The resonance peak (Fig. 
139) is, therefore, unsymmetrical also. That is, the current is 
not the same for two frequencies, one slightly higher than the 
resonance frequency, and the other the same number of cycles 
lower than the resonance frequency. The explanation is found 
in the shape of the curve of condenser reactance. 

The same lack of symmetry exists when the inductance and 
the frequency are held constant and the capacity is varied to 
obtain resonance, because the shape of the curve of condenser 
reactance in this case is the same as in the preceding. However, 
if the frequency and capacity are held constant, and the reso- 
nance condition is reached by varying the inductance, a sym- 
metrical resonance peak is obtained ; equal changes of the in- 
ductance above and below the setting for resonance will cause 
the current to fall to the same value. The difference of this 
case from the two preceding lies in the fact that curves of 
condenser and coil reactance and hence o^ total reactance are 
here straight lines. 

To summarize, then, the resonance curve is symmetrical when 
the tuning is accomplished by varying the inductance (C and. f 
constant), but is not symmetrical in the two other methods of 
tuning, viz, by varying the capacity (L and f constant) or by 
varying the frequency (C and L constant). 



112. The Wavemeter. — Tlie phenomenon of resonance enables 
one to obtain relatively large currents in a circuit to which only 
a small emf. is applied, provided only that the circuit is properly 
tuned. To determine when the condition for resonance is real- 
ized with a given frequency in a given circuit, or to measure the 
frequency at which a circuit of predetermined constants should 
be in resonance, use is made of the " wavemeter." This is the 
most important instrument used in radio measurements. It 
consists essentially of a series circuit, which includes an induc- 
tance and a capacity, both of which are of known values. Either 
•the inductance or the capacity may be of fixed value, while the 







Fia. 141 
Sim Isle WdVenneTer circuiT 




WdVemeTer witK coo)»(ee/ Indf'catoP 

h^Vin^ C4it=a<i"ty 
in >ii Pallet with 
Induclance * pesistsrw 

other will be variable. A hot-wire ammeter, thermo-junction, 
or other suitable device for measuring radio currents is in- 
serted, either directly into the circuit (Fig. 141), or, better, is 
coupled electromagnetically to it, the coupling being made as 
loose (Sec. 119) as will permit of a suitable maximum deflection 
of the ammeter (Fig. 142). 

If the frequency of the current in a given circuit is to be 
measured, the coil of the wavemeter circuit is placed near the 
circuit in question and the capacity of the wavemeter is varied 
until the indicating device shows that the current in the wave- 
meter circuit is a maximum. In making the final adjustment 
the wavemeter coil should be moved as far away from the circuit 


in question as is possible and yet provide a convenient maxi- 
mum deflection of the current-indicating device. 

From tlie known value L of inductance of the wavemeter coil 
and the capacity Cr, corresponding to the setting of the con- 
denser at resonance, the desired frequency may be calculated 
from equation (72), which gives 

What is generally desired, however, is not so much the fre- 
quency as the wave length (Sec. 125) of the electromagnetic 
waves radiated by the circuit. The wave length \ is connected 
with the frequency / by the fundamental relation 

X=j (73) 

in which c is the velocity of electromagnetic waves in space 
and has the value of 300,000,000 meters per second. Expressing 
Cr in microfarads and L in microhenries, as is commonly con- 
venient, the fundamental wavemeter equation giving the wave 
length in meters is 

X=1884VrC, (74) 

For example, if L=1000 microhenries and Cr=0.001 microfarad, 
the wave length emitted by the circuit is 1884 meters. 

A wavemeter is usually provided with a buzzer or some other 
auxiliary device by means of which oscillations may be set up 
in the wavemeter circuit. These will have a wave length 
which may be calculated by equation (74) from the inductance 
and capacity of the wavemeter circuit. By coupling any de- 
sired circuit with the wavemeter circuit an emf. is introduced 
into the former, when the buzzer is working, the frequency of 
which is the same as that existing in the wavemeter circuit. 
This frequency may be calculated by (74) from the known 
inductance of the wavemeter coil and the capacity correspond- 
ing to the setting of the condenser. If, further, it is desired to 
tune the circuit in question to the frequency emitted by the 
wavemeter circuit, it is only necessary to connect a detector 
and telephones in the circuit to be tuned, to cause the wave- 
meter to emit waves, and to vary the capacity or inductance of 


the circuit to be adjusted, until tlie sound of the buzzer in the 
telephones is a maximum. 

113. Parallel Resonance. — In the preceding sections it has been 
shown how to obtain the maximum current in a circuit for a 
given applied emf. The principle of resonance, utilized for this 
purpose, finds application also in the solution of the reverse 
problem of keeping currents of a certain frequency out of any- 
chosen part of a circuit without, however, preventing the passage 
of currents of other frequencies. To such an arrangement is 
given the appropriate name of a " filter." A filter consists es- 
sentially of an inductance coil, joined in paralled with a con- 
denser. This combination is interposed between the emf. in 
question and that portion of the circuit from which the unde- 
sirable currents are to be excluded. Any such combination of 
inductance and capacity, taken at random, will oppose currents 
of a single frequency only, whose value depends principally on 
the values of the inductance and capacity. To render such an 
arrangement effective against currents of a certain chosen 
frequency it is necessary to adjust the capacity and inductance 
to have a definite relation. The solution of this problem re- 
quires a knowledge of the principles of " parallel resonance.'* 

Fig. 143 shows a coil of inductance L and resistance R, joined 
in parallel with a condenser of capacity C The current / flows 
from the alternating source of emf. E through the main circuit, 
and at the branch point divides, a part Ii flowing through the 
coil and the remainder /c through the condenser. At every mo- 
ment the current / has a value which is the algebraic sum of the 
values of 7i and /c existing that same moment. Let us sup- 
pose, first, that the emf. E has a definite frequency, and that 
the inductance of the coil is invariable. Current-measuring 
instruments may be arranged to measure the three currents. 
If the capacity is varied continuously and the indications of 
the ammeters recorded, the following experimental facts will 
be observed. 

In general, the currents in the coil and condenser will be 
unequal, and the current / may be less than either. As the 
capacity is varied, the currents in the coil and condenser may be 
made to approach equality, and at the same time the main 
current will decrease. At length, for some critical value of the 


capacity, the main current will reach a very small minimum 
value, while the current in the coil and the condenser current 
are nearly equal. Further, each is many times larger than the 
main current. As the capacity is now varied still further, the 
main current begins to increase, and the coil and condenser 
currents are no longer so nearly equal. 

As an example, assume the inductance of a coil to be 1000 
microhenries and its resistance 2 ohms. An effective emf. of 10 
volts and a frequency of 71,340 cycles per second is applied. 
(This value of frequency was chosen, since it gives a minimum 
current /, with a condenser of almost exactly 0.005 microfarad.) 
The changes of the current in the main circuit, as the capacity 
is varied from 0.002 to 0.008 microfarad are shown in Fig. 144, 
in which values of the capacity are measured horizontally and 
values of the square of the current vertically. The latter values 
in the figure are multiplied by a million. The minimum current 
is not zero, but its value is only about 0.0001 ampere, a value 
whose square is too small to be easily distinguished in the figure. 
The corresponding currents in the coil and condenser are each 
about 0.02236 ampere. Their difference is only about TFo:F!nr 
part of this value, the condenser current being the larger by 
this minute amount. 

In practice, then, if we imagine some troublesome emf. to be 
introduced into the circuit at E (Fig. 143), by induction or other- 
wise, the employment of a parallel combination of inductance 
and capacity can be made to very completely prevent this emf. 
from causing currents to flow in the circuit, provided only that 
the values of inductance and capacity are properly chosen. And 
such a filter does not prevent the passage of currents of other 

If, for example, we suppose that the emf. E has a frequency 
of 100,000 cycles, in the above case the combination of 1000 
microhenries and 0.005 microfarad would allow 0.01549 ampere 
to flow in the main circuit. That is, this filter has 155 times 
as much stopping effect for currents of 71,340 cycles per second 
as for currents of 100.000 cycles, and for frequencies further 
away the effect would be greater. Filters of this kind are used 
in airplane radio telephone sets to remove noises produced by 
the electric generator used in the set ; for example, in the type 


SCR-68 sets. A similar filter is used in connection witli the 
Signal Corps buzzerphone. type EE-1.^ Filtei's are also listed 
in telephony on wires using modulated radio-frequency currents. 
(See Sec. 212.) Filters designed for this purpose may consist 
of an elaborate arrangement of a considerable number of in- 
ductances and capacities. 

The results of theory show that to filter out currents of a 
frequency /". the necessary relation between inductance and 
capacity is given in the following equation : 

The current in the main circuit is, imder this condition, 



In all practical radio circuits, hov.ever, the resistance of a cir- 
cuit is so small in comi>arison with the inductive reactance, that 
it may be neglected. The equation (75K under these circum- 
stances, goes over into the same equation that holds for series 
resonance, that is — 

Otherwise expressed, then, it may be stated that when the 
condition of parallel resonance is realizied, the loop circuit 
which contains the coil and condenser in series is very closely 
in a condition of series resonance. Recalling the fact that, in 
the series resonance condition, the emf. on the condenser is 
equal and opposite to that on the coil, it is easy to see that 
there is here a fiow of current back and forth between the coil 
and the condenser. Viewed from the main circuit (Fig. 143), the 
current in the coil is, at every moment, opposite to the condenser 
current, so that the main current, which is their algebraic sum, 
is at every moment merely the difference between the condenser 
and coil currents. These latter being nearly equal in value, we 
have the explanation of the existence of the relatively large cur- 
rents in the coil and condenser, when the main circuit is almost 
free from current. 

^ See Signal Corps Wire Communication Pamphlet No. 1 (see p. 576). 



The ideal filter would be one in which the resistances of the 
inductance coil and all the connecting wires in the two branch 
circuits were actually zero. In such a case, the condition for 
parallel resonance would be rigorously the same as for series 
resonance, equation (70), the condenser current would be ex- 
actly equal to the current in the coil, and absolutely no cur- 
rent would flow in the main circuit. The filter effect would hef 
perfect. No energy would therefore flow from the source E, 

1 — 


FlO. 144 












j i 

1 1 i 

-i 4 


i i 


i / 








i ! 



" 1 1 / 



1 ' / 

"i .1 U = I'25 m'icrohcnn'et 
T3 9 1 \ *^' 'o micro -m^d 

» 1 \. 




\ 71 



1 i / 



' 7 ' 



1 J 





! ' 


~t I 

/ ' ■ 



— ', — ' — ' — ' — 



' ' 

V, Maters 


\ / 

f^TAlIe! Resonance Cur\ 

o loo "too 3oo ^o< 

VariAtion of «»t>^drenT irducT^nce. 
o[<^ooil wiffi wave length 

but this would merely give the condenser an initial charge, and 
thereafter current would flow between the two branch circuits, 
even if the main circuit were removed. See Section 115, on 
free oscillations. 

In any actual case there must, however, be some resistance in 
the circuit, and the energj- for the heating in the resistance 
must come from outside. The emf. E must cause just enough 
current to flow in the main circuit to make good this loss of 
energy. It is easy to show that these conclusions follow also 
from the equations [ireviously cited. When the resonance 
condition is established, the main current and the emf. E are in 
phase, so that the power is equal to the product of the emf. E 


and the main current — that is, to -02^(0 — 7T^- ^^^ power 

lost in heating is equal to the square of the current in the coil 
multiplied by the resistance of the coil. The current in the 


coil is, however (Sec. 55), , , so that the power in 

heating has the value d2_i_/9 /-rv ' ^^ before. The fact that 

the main current should be zero, when the resistance is zero, 
is in line with equation (76) for /, and with the fact also that 
the heating must be zero in that case. 

Besides tuning the filter by varying the capacity, it is of 
course possible to obtain parallel resonance by varying the in- 
ductance instead. For a given coil and condenser, it is also 
possible to obtain parallel resonance by adjusting the frequency 
of the applied emf . It must be noted, how^ever, that when either 
the inductance or the frequency is varied, the conditions for 
minimum current in the main circuit are slightly different and 
are not the same as when the capacity is varied. These three 
conditions differ appreciably only when the resistance is large. 
For radio circuits, the resistance is usually so small that no 
difference can experimentally be detected between all these 
conditions for minimum current. For zero resistance, all three 
coincide and are expressed by equation (75). 

114. Capacity of Inductance Coils. — A coil used in radio cir- 
cuits can seldom be regarded as a pure inductance. While the 
capacities between turns of a coil are small, they approach the 
same magnitude as other capacities used in radio circuits. A 
coil is to be considered as a combination of inductance and 
capacity in parallel. It is found that the capacity Co of a coil 
does not change appreciably with frequency. Neither does the 
inductance itself, but the apparent or equivalent inductance La 
of this combination of inductance and capacity does vary with 
frequency as indicated by the equation 



in which the quantity a> is equal to 2'7rf. (See p. 123.) 
The variation with wave length is shown in Fig. 145. When 
the coil is the main coil of a circuit, it is usually desirable to 


introduce the emf. into the circuit by induction in the coil itself 
ratlier than in series with the coil. The capacity of the coil is 
then merely added to the capacity of the condenser. When 
the emf. is in series with the coil, one effect of the coil capacity 
is to increase the resistance introduced into the circuit by the 
coil and thus reduce the current. 

The capacity of coils frequently gives rise to peculiar and 
undesirable effects in radio circuits. Among these are effects 
caused by the capacities of those parts of a coil which are not 
connected in the circuit. The turns which are supposedly 
" dead " may actually produce considerable effect, both upon 
the resistance and frequency of resonance of the circuit. Thus, 
the capacity of the unused part 2 of the coil in Fig. 146 causes 
a second circuit to be closely coupled to circuit 1. This may 
cause the circuit 1 to respond to two frequencies and exhibit 
the other phenomena of coupled circuits described in Section 120 
below. (See also Circular 74 of the Bureau of Standards, 
Sec. 19 ; Bureau of Standards Scientific Paper No. 427, by 
G. Breit, " Some Effects of the Distributed Capacity Between 
Inductance Coils and the Ground " ; and also a paper by G. 
Breit, " The Distributed Capacity of Inductance Coils," Physical 
Review, vol. 17, pp. 649-677, June, 1921.) 

B. Damping. 

115. Free Oscillations. — Thus far it has been assumed that a 
constant alternating voltage has been applied to radio circuits, 
in which case the alternating currents produced are of constant 
amplitude. Such currents may be regarded as analogous to the 
forced oscillations which are produced in a mechanical system 
like a swing or a pendulmn, when it is acted upon by a force 
which varies periodically. The system is forced to vibrate with 
the same frequency as that of the force. 

It is, however, possible to produce oscillations of current in 
a circuit without the necessity of providing a source of alternat- 
ing emf. A common method is merely to charge a condenser 
and then to allow it to discharge through a simple radio circuit. 

This may be accomplished, for example, by the simple means 
shown in Fig. 147. By throwing the switch /S to the kft, the 
condenser C is charged by the battery E, but when the switch 
is thrown to the right, it is discharged into the circuit contain- 



ing tlie resistance R and the inductance L. If the resistance R 
is not too great, electric oscillations are set up which, however, 
steadily die away as their energj' is dissipated in heat in the 
resistance. As in Fig. 148, the current becomes less and less as 
the oscillations go on. 

To explain this action, we must follow more closely what 
takes place in the circuit from the moment when the condenser, 
charged up to a certain potential difference, is inserted in the 
discharge circuit. When the cojidenser starts to discharge it- 
self, a current flows out of it, and the potential difference of 
the plates decreases as a result. At the moment when the 
plates haA'e reached the same potential, current is still flowing 
out of the condenser. The current has energy and can not be 

F I Q. \^c 

Effect of disTribLfted cA^Acity 
in the unused Ti/rns of a co'i I 

F I 

q. 141 



s <; 

stopped instantly. In fact, to bring the current to zero value 
it is necessary to oppose it by an emf., and the amount of emf. 
necessary is greater the more quickly one wishes to stop the 
current. It is similar to the case of a moving body. On account 
of its motion the body possesses energy, and can not be brought 
to rest instantly. The greater the force which is opposed to it, 
the more quickly it may be brought to rest, but unless its motion 
is opposed by some force, it continues to move indefinitely with- 
out change of velocity. 

The flow of current from the condenser, then, does not cease 
w^hen the condenser has discharged itself, and, as a result, that 
plate which was originally at the lower potential takes on a 
higher potential than the other. The condenser is beginning to 
charge up in the opposite direction. The potential difference ol 
the plates now acts in such a direction as to oppose the flow 



of the current, which decreases continually as the potential 
difference of the plates rises. If the resistance of the circuit 
were zero, the current would be zero (reversing) at that mo- 
ment when the potential difference of the plates had become 
just equal to tlie original value. That is, the. condenser would 


Free osciIlaTi<sn5 with 
dif ferenT vaIuc* of the. 

. OecramcriX • ( 

be as fully charged as at the beginning, only with the potential 
difference of the plates in the direction opposite to that at the 
start. Now begins a discharge of electricity from the condenser 
in the opposite direction to the first discharge, and this dis- 
charging current flows until the condenser has become fully 
recharged in the original direction. The cycle of operations 
then repeats itself, and so on, over and over again. 


The action in the circuit may thus be described as a flow of 
electricity around the circuit, first in one direction and tlien in 
the other. The rate of flow (current) is greatest when tlie 
plates have no potential difference, and the current becomes 
zero and then begins to build up in the opposite direction at 
the moment when the potential difference of the plates reaches 
its maxamum. value. This alternate flow of electricity around 
the circuit flrst in one direction and then in the other is known 
as an " electrical oscillation." Since no outside source of emf., 
such as an a.c. generator, is acting in the circuit, the oscillations 
are said to be "free" oscillations. 

Mechanical free oscillations are well known. Such, for ex- 
ample, are the swinging of a pendulum and the vibration of a 
spring which has been bent to one side and then let go. In the 
case of the pendulum the velocity with which it moves corre- 
sponds to the value of the current in the electrical case, while 
the height of the pendulum bob corresponds to the potential 
difference of the condenser plates. When the bob is at its 
highest point its velocity is zero, corresponding to the con- 
denser when the plates are at their maximum potential differ- 
ence and no current is flowing. When the pendulum bob is at 
its lowest position it is moving most rapidly. Similarly, when 
the plates of the condenser have zero potential difference, the 
current flowing has its maximum value. The pendulum does not 
stop moving when it passes through its lowest point ; neither does 
the current cease at the moment when the condenser plates are 
at the same potential. The pendulum rises with a gradually 
decreasing velocity toward a point at the other end of the 
swing as high as the starting point. The current gradually 
decreases as the condenser charges up to an opposite potential 
difference equal to the original value. The return swing of the 
pendulum corresponds to the flow of current in the direction 
oposite to the original discharge. 

A pendulum .swinging in a vacuum and free from all friction 
would continue to swing indeflnitely, each swing carrying it 
to the same height as the starting point. Similarly, electric 
oscillations would persist indefinitely in a circuit — that is, they 
would be " undamped " if there were no resistance to the 

Actually, electric oscillations die down in a circuit and finally 
cease altogether, just as an actual pendulum will make shorter 


and shorter swings and finally come to rest. Since the occur- 
rence of free oscillations in a circuit presupposes no interfer- 
ence with the circuit from outside, the circuit receives no energy 
beyond that imparted to it at the moment when the oscillations 
begin. Thereafter the circuit is self-contained, and any loss of 
its energy in heat and electromagnetic waves reduces by just so 
much the energy available for maintaining the oscillations. 
This loss of energy goes on continuously and the oscillations die 
away to nothing. They are said to be " damped " oscillations. 

At the start there is a definite amount of energy present in the 
circuit, namely, the energy of the charge given the condenser. 
The amount of this energy depends upon the capacity of the 
condenser and the square of the potential difference between its 
plates (emf. to which it is charged). This energy exists in 
the dielectric of the condenser, which is in a strained condition 
due to the charge. As soon as the current begins to flow the 
condenser gives up some of its energy, and this begins to be 
associated with the current and is to be found in the magnetic 
field around the current; tliat is, principally in the region 
around the inductance coil. As the current rises in value under 
the action of the emf. of the condenser, energy is continually 
leaving the condenser and being stored in the magnetic field of 
the inductance coil. When the plates of the condenser have no 
potential difference, the whole energy of the circuits resides in 
the magnetic field of the coil and none in the condenser. 
Energy is then drawn from the coil as the current decreases 
and energy is stored up in the condenser as it is recharged. 

If the resistance of the circuit were zero and no energy were 
radiated in waves or dissipated in other ways, the total energy 
of the circuit would be constant. The energj'- dissipated in 
heat and electric waves is, however, lost to the circuit, so that 
the total amount of energy, found by adding that present in the 
condenser to that in the inductance, steadily decreases. Finally 
all the original store of energy given the circuit has been dis- 
sipated and the oscillations cease. 

The energy lost when a steady current is flowing In a circuit 
depends not only on the value of the current, but on the resis- 
tance of the circuit, and in a radio circuit this resistance is 
replaced by a somewhat larger quantity of the same kind, the 
"effective resistance." (See Sec. 117.) The greater the effec- 
53904°— 22 17 



tive resistance the greater the amount of energy dissipated per 
second when a given current flows. 

Ohm's law shows that to keep a current / flowing through a 
resistance R an emf. RI is necessary and this has to be fur- 
nished by the battery, generator, or other source. In an oscil- 
lating circuit the same is true, and that portion of the emf. in 
the circuit which is employed in forcing the current against the 
resistance is, of course, not available for charging the condenser 
or building up the discharge current. The changes of current 
in the circuit described above are thereby hindered, and the 
current does not rise to as great a value as it would in the 
absence of resistance. The maximum of emf. between the 
plates of the condenser is less each time the condenser is dis- 
charged, and thus the oscillations of the current die away. 

Vi'brdtron o|<=» 
in <a vise /riili11I!7l]i\ 

F»o ISO 



er-— .- 


Emf" induced in the cross section of A 
Conc/uctor cArr^^ir^ hii>\ frequency currenT 

A good analogy to damped electrical oscillations in a circuit 
is found in the vibrations of a flat spring, clamped at one end 
in a vise, and then bent to one side and released, Fig. 149. The 
spring vibrates from side to side with decreasing amplitude, 
until finally it comes to rest in its unbent position O. When the 
spring is bent energy is stored up in it — the energy of bending. 
On being released the spring moves and gains energy of motion, 
while the energy of bending decreases. If there were no fric- 
tion the loss of one kind of energy would be just offset by the 
gain of the other kind and the sum total would remain constant. 
The spring would move past the natural undisturbed position O, 
under the influence of its energy of motion, and would be 
brought to rest at a position just as far to the other side of O 
as was the starting point. 

Friction has, however, the effect of opposing the motion and 
causing a dissipation of energy in heat, and each excursion 
away from the resting point is smaller than the one preceding. 


Free oscillations, then, can take place in a circuit containing 
inductance and capacity. These would be undamped in the 
ideal case where the resistance can be regarded as zero. In all 
practical cases of free oscillations, however, the oscillations are 
damped. To produce undamped waves it is necessary to pro- 
vide some source of power to make good the energy dissipated 
in the oscillating circuit. Strictly speaking, undamped free 
oscillations are impossible in actual circuits. It is of impor- 
tance to study the effect of the resistance in determining the 
rapidity with which the oscillations die away. 

116. Frequency, Damping, and Decrement of Free Oscillations. — 
If the resistance of the oscillating circuit is constant it is pos- 
sible to calculate the period of the free oscillations in the cir- 
cuit and to find the rate at which the oscillations die away. If 
L, C, and R are. respectively, the inductance, capacity, and re- 
sistance of the circuit, then free oscillations in the circuit will 
have the frequency 

^^ (78) 

^ 2;rVrC 

This is known as the " natural frequency " of the circuit. Simi- 
lar considerations apply to the pendulum and vibrating spring 
discussed above. Each vibrates in a period natural to it. which 
depends upon the dimensions, material of the vibrating system, 
and the friction against which it moves. 


If it should happen, in any case, that the quantity -^— 

is equal to or greater than j-fi then free oscillations in the 

circuit are impossible; the current in the circuit does not re- 
verse its direction at all, but simply dies away. The circuit 
is said to be in the " aperiodic " condition ; that is, without 
period. Seldom do such cases occur in radio circuits. Usually 

i?2 1 

the quantity jri" instead of being larger than j-^ is very small 

in comparison with the latter. We may, therefore, as a rule, 
use without error as the expression for the natural period 


•^ 2ir-y/LC 

which is the same expression as for the frequency of the applied 


emf, necessary in order that the circuit shall be in the resonance 

The rapidity with Avhich the oscillations die away depends, 
not only on the resistance of the circuit, but on the inductance 
also. The greater ttfe resistance and the smaller the induc- 
tance, the more rapid is the damping and the rate at which 
the oscillations decrease. If the resistance, capacity, and in- 
ductance of the circuit have fixed values, it may be shown that 
each successive maximum of current is the same fraction of the 
preceding maximum as the latter is of the maximum imme- 
diately preceding it. If, for example, the second maximum is 
0.9 of the first, the third will be 0.9 of the second, etc. How- 
ever, instead of adopting as a numerical measure of the rate 
of decrease this ratio itself, it is found more convenient in the 
mathematical theory of damping to adopt the natural logarithm 
of the ratio of any maximum to the next following maximum 
with the current in the same direction, i. e., the logarithm of 
the ratio of two maxima one cycle apart. This number is 
known as the " logarithmic decrement," or " decrement," for 
short. This is the decrement per complete oscillation. 

In cases where the resistance of the circuit is not exceed- 
ingly large, the decrement is equal to tt times the quotient of 
the resistance by the inductive reactance of the circuit, calcu- 
lated for the natural frequency of the circuit. That is, the 

decrement is equal to 7r( - — -r=-),so that either increasing the 


resistance or decreasing the inductance will increase the decre- 
ment. The natural frequency being practically independent of 
the resistance, that is, equation (79) being sufficiently accurate, 
the capacitive reactance is equal to the inductive reactance. 
Thus the decrement is tt times the quotient of the resistance by 
the capacitive reactance at the natural frequency of the 

In a spark circuit the idea of logarithmic decrement is not 
exactly applicable. On account of the variable resistance of 
the spark, the oscillations fall off according to a different law 
than that just discussed. (See Circular 74, p. 230.) 

Examples of Decrements. — Fig. 148 gives a graphic idea of the 
dissipation of the oscillations in three cases where the decre- 
ments are 0.01, 0.1, and 1. These correspond to circuits of very 


small damping, moderate damping, and excessive damping, re- 
spectively. Each curve starts from the same value of current 
at the first maximum, and for each the natural period of the 
circuit is the same. The latter is represented by the horizontal 
distance. AB, BC, etc., in each. The difference between the 
curves is striking. In the case of a decrement of 0.01, the oscil- 
lations decrease only very gradually; this case approximates 
that of undamped waves. In the extreme case of a decrement 
of 1, the oscillations become negligible after only four or five 
periods. To cous*truct such curves the following simple method 
may be used : 

Assume a certain number of divisions in the horizontal di- 
rection to represent the period of the oscillations, for example, 
five. Then the curve must cross the horizontal axis every two 
and one-half divisions. Choose a convenient number of di- 
visions to represent the first maxinnim of the current, for ex- 
ample, ten. The curves DE (Fig. 148) are next drawn to scale, 
starting with the chosen value for the first maximum. The 
curves DE have the property that the height of the curve falls 
off by equal fractions of its value for equal horizontal inter- 

For instance, if the decrement is 0.1, we find, since 0.1 is the 

natural logarithm of 1.105, that the first maximum OD in the 

positive direction is 1.105 times as great as the next, PG, and 

so on for any two successive maxima in the same direction. If, 

therefore, we take OD=10 divisions, PG will equal-:pYo5~9.05 

9. 05 
divisions, RH will be -. -.^^ —8.19, etc. 

For all except large values the logarithmic decrement is 
practically equal to the fractional difference between successive 
maxima. Thus, for example, when the logarithmic decrement 
is 0.1 each maximum is approximately 0.1 greater than the 

Nuniher of Oscillations. — Although, strictly speaking, the 
oscillations never would become absolutely zero, they actually 
become negligible after a certain time. A knowledge of the 
logarithmic decrem-ent enables us to calculate how many com- 
plete oscillations will be executed before their amplitude has 


fallen below a certain fraction of the first oscillation. This 
number is greater the smaller the decrement. 

If, for example, we arbitrarily choose to find the number of 
oscillations which will be completed before the maximum of 
current will fall below 1 per cent of the value at the start, we 
ha^e simply to take the quotient of the natural logarithm of 
100 by the decrement. The natural logarithm of 100 is, near 
enough, 4.6. The number of oscillations is thus 4.6 divided by 
the decrement. Thus in the three cases given in Fig. 148 the 
numbers of complete oscillations will be 460, 46 and 4.6, cor- 
responding to the decrements 0.01, 0.1, and 1, respectively. 

The maximum possible value of decrement would be infinite, 
but the United States radio laws^ require that values greater 
than 0.2 shall not be used on account of the interference of 
highly damped stations with other stations. The number of 
complete oscillations calculated by the above rule is 23 for a 
decrement of 0.2. The ratio of two successive current maxima 
for a decrement of 0.2 is about 1.22. 

Effect of Decrement on Tuning. — The decrement of a trans- 
mitting set gives an approximate idea of its effectiveness in 
generating oscillations of a definite wave length, and in deliver- 
ing its energy at the wave length which it is desired to use. 
The smaller the decrement the sharper the tuning possible and 
the less the chance of interference with stations tuned to a 
different wave length. The reason for this is that with 
highly damped waves there are fewer radio-frequency oscilla- 
tions per wave train than with slightly damped waves, with the 
result that in the former case the tuning of a receiving circuit 
to the wave length of the emitted radio-frequency oscillations 
has less effect in determining how much current will be built 
up in that receiving circuit. Let us compare two wave trains 
having the same energy content, one being highly damped and 
the other only slightly damped. In the former there will be a 
smaller number of waves between the same relative values of 
amplitude in a wave train than in the latter, and the energy 
and the electric impulse in the earlier waves of the highly 

2 See the pamphlet Radio Communication Laws of the United States, 
issued by the Bureau of Navigation, Department of Commerce. Copies 
may be secured from the Superintendent of Documents, Government 
Printing Office, Washington, D. C, for 15 cents each. 


damped wave train will be greater than in the slightly damped 
wave train. Also the electric impulse in the successive waves 
of the highly damped train will differ considerably, while the 
electric impulse in the successive waves of the slightly damped 
train will be almost the same. The first wave of the highly 
damped train will have a large electric impulse and mil also 
have a considerably larger electric impulse than the one fol- 
lowing it. This first large electric impulse can be thought of as 
producing a large response — that is, forcing a current in a sys- 
tem which is not exactly in tune with it. Even if the second 
impulse should act on the receiving system at an instant such 
that its effect would tend to diminish the effect of the first, 
nevertheless since the first impulse was so much greater than 
the second the current in the receiving system would not cease 
on account of the counteracting effect of the second impulse. 
Hence if a highly damped wave train acts on any receiving 
circuit, that circuit will respond to the first incoming waves of 
the train and will maintain oscillations at the frequency to 
which the receiving circuit happens to be tuned. (See Impulse 
Excitation, Sec. 123.) In the case of the weakly damped wave 
train, each Impulse is comparatively small and has nearly the 
same impulsive force; the first impulse will produce a small 
response which could be annulled by the second impulse if it 
should act on the receiving system at an instant such as to 
oppose the effect of the first impulse. Since each impulse is 
small and has nearly the same value, the cumulative effect of a 
number of impulses must be utilized, which means that the 
transmitting and receiving systems must be closely in tune. 

In Fig. 148 the emitted wave train having a decrement of 0.1 
will cause an appreciable response only in such receiving cir- 
cuits as are approximately tuned to the radio frequency of the 
emitted wave. The wave train having a decrement of 1,0 will 
cause an appreciable response in nearly all receiving circuits 
which it has the power to affect at all by simply applying to 
them a series of impulses of the train frequency. A wave train 
having a decrement of 10 would have only one-half of an oscilla- 
tion of appreciable magnitude and would have no tuning prop- 
erties whatever in a receiving circuit. 

Thus, even if the total power of the oscillations be the same 
in both cases, a transmitter which sends out a certain number 


of waves trains per second, each wave train having 20 oscilla- 
tions of large amplitude at 600 meters, will be much more apt 
to interfere with a receiver tuned to 800 meters than if the 
transmitter sent out the same number of wave trains per sec- 
ond each of which had 100 oscillations of less amplitude at 
600 meters. 

This can be roughly illustrated by the familiar example of 
resonance in sound. Tuning forks usually persist a consider- 
able time in their vibration. This means that their vibrations 
are weakly damped and that any one single oscillation in the 
sound wave which they emit will have comparatively small 
energy content. If a tuning fork having a frequency of 512 
vibrations per second is to cause another tuning fork to respond 
by the action of sound waves, it is necessary that the two forks 
have nearly the same vibration frequency. However, the single 
blow with the hammer which started the 512 fork vibrating 
will also start a 900, 1200, or 3000 fork. The single blow with 
the hammer which would start all of these forks can be thought 
of as corresponding to the strong impulse of the first wave of 
a very highly damped wave train. 

Another illustration of this application of the principle of 
resonance is found in a suspended swing. A small child by 
feeble but well-timed impulses can gradually swing his play- 
mate high Into the air, providing friction is very small, that 
is, providing the hinges of the swing are well oiled. The swing 
will reach the greatest height if the frequency of the impulses 
is the same as the natural frequency which the swing would 
assume by itself if given a single strong initial impulse. If 
the hinges are rusty, it will be very difficult if not impossible 
to work the swing up to its full height by feeble impulses no 
matter how well timed ; this condition corresponds to the case 
of highly damped oscillations. If the hinges are .very rusty, 
it may be necessary to give an initial impulse sufficient to 
send the swing to its full height on the first swing; this corre- 
sponds to the case of impulse excitation, w^hich gives waves 
which will cause response in every receiving circuit which 
they reach at all without regard to the wave length to which 
the receiving set may be tuned. 

Mochdatecl Continuous Waves. — If a continuous or undamped 
radio-frequency wave, such as that produced by an electron 


tube generator, is modulated at a low frequency, as in radio 
telephony, it may cause interference over a wide range of 
tuning adjustments, behaving in this respect much the same 
as a damped wave of appreciable decrement. This effect is 
discussed in Section 206, page 514. 

C. Resistance. 

117. Resistance Ratio of Conductors. — When a steady emf. is 
applied between the ends of a conductor, the current quickly 
rises to the final Ohm's law value, and distributes itself uni- 
formly over the cross section of the wire. During the interval 
between the moment when the emf. is applied, and the moment 
of attainment of the final steady state, the current distribution 
over the cross section is not uniform. This effect is due to self- 
Induced emfs. in the cross section of the conductor. Suppose 
that a section be taken through the axis of a cylindrical con- 
ductor and that the applied emf. tends to produce a current in 
the direction of the arrow (Fig. 150). The magnetic lines in 
the cross section will be circles, in planes at right angles to the 
axis, and with their centers in the axis. In the figure, the lines 
will be directed out of the paper in the region above the axis 
and into the paper in the region below the axis. As the total 
current rises in value, the number of lines of force through any 
portions of the cross section, such as ABCD and EFGH, will be 
increasing, and by Lenz's law (Sec. 45) this change of field ^ill 
give rise to induced emfs. which tend to oppose the changes of 
the field. The directions of these induced emfs. will accordingly 
be those indicated by the small arrows, and it is easy to see 
that the increase of the current is aided in those portions of 
the cross section which lie near the surface of the conductor, 
and hindered at the portions nearer the axis. That is, the cur- 
rent reaches its final value later at the axis of the cross sec- 
tion than at points on the surface of the wire. On the other 
hand, if the circuit is broken after the distribution of current 
has reached the uniform state, the outer portions of the con- 
ductor will first be free from current. 

These effects may be accurately described by the statement 
that the current grows from the outer layers of the wire in- 
ward, and that the current inside the conductor attains the 


same value as that at the surface, only after a finite interval of 

When a rapidly alternating emf. is impressed upon the con- 
ductor, (a) the phase of the current inside the conductor lags 
behind that of the current at the surface by an amount which 
is greater the nearer the point is to the axis ; and ( b ) the ampli- 
tude of the current is largest at the surface and decreases as 
the axis is approached because sufficient time has not been 
allowed for the final steady value to be reached before the emf. 
was changed. This non-uniformity of current distribution in 
the cross section is known as the " skin effect," and it is equiva- 
lent to a reduction of the cross section of the conductor with 
consequent increase in its resistance. 

From these considerations, it will be seen that in addition to 
its dependence on the frequency, the skin effect will be more 
serious, the thicker the conductor and the greater the perme- 
ability and conductivity of the material of which it is composed ; 
for the thicker the conductor, the longer the interval which must 
elapse before a change in emf. will be felt at the center of the 
conductor and thus the greater the difference in the current 
density at different points of the cross section. With given 
dimensions, the greater the permeability of the wire, the greater 
the emf. induced in its mass. The better the conductivity, the 
less the ratio of the effective current to the value at the surface. 

A numerical calculation of the magnitude of the skin effect 
can be made only in a few special cases for which Circular 74, 
pages 299-308, should be consulted. Table 18 of Circular 74 
will enable one to see at a glance how great diameter of wire is 
allowable, in order that the increase of resistance due to skin 
effect shall not exceed 1 per cent of the direct current value. 
Such data are of use in estimating the size of wire suitable for 
a hot-wire ammeter, in order that its resistance may not vary 
in the range of frequency for which it is intended. For larger 
diameters of wire the effect increases rapidly, and cases where 
the high-frequency resistance is five to ten times the direct cur- 
rent value are not rare. These facts must be kept in mind when 
estimating the current carrying capacity of a conductor. The 
'* resistance ratio " is defined as the ratio of resistance at the 
frequency in question to the resistance to direct current. Then, 
for the same heating, the allowable current at the high fre- 


queiicy will be less in the ratio of the square root of the resis- 
tance ratio. 

In Appendix 4, page 556, is given a table of values of the 
resistance of various sizes of solid copper wire at a frequency of 
1,500.000 cycles per second. 

Since the skin effect tends to render useless for the carrying 
of the current the inner portions of the cross section of a wire, 
thin tubing, or a thin layer of good conducting material plated 
or welded on the surface of a poor conducting cylinder is a 
form of conductor suitable for carrying currents of radio fre- 
quency. In fact, tubing which is very thin in comparison with 
its radius has for the same cross section a smaller high- 
frequency resistance than any other single conductor. 

To reduce the skin effect, a conductor is often built up of a 
number of very fine conducting strands. The resistance ratio 
of such a combination is, however, on account of the mutual in- 
ductance of the strands, appreciably greater than the resistance 
ratio of one of the strands. To be effective, the strands should 
be placed as far apart as practicable, and the diameter of the 
individual strands should not exceed about 0.1 mm. The indi- 
vidual strands are usually enameled and the conductor is 
usually so constructed that each strand comes to the surface or 
very near the surface at regular intervals. If the individual 
strands are not enameled, a stranded conductor may at high 
frequencies have a resistance considerably greater than the 
resistance of the corresponding solid conductor. In a stranded 
conductor carrying radio-frequency current, in a given cross 
section different strands have different potentials, and if the 
strands are not enameled current will flow across contacts of 
appreciable resistance between individual adjacent strands, and 
energy will be lost as heat and the effective resistance of the 
conductor will be increased. The most effective form of 
stranded conductor, although expensive to make, is one where 
the strands are so twisted as to form a woven tube. For further 
particulars see pages 306-308, of Circular 74. 

Effective Resistance. — The resistance of a circuit at high fre- 
quency is never the same as the resistance measured by direct 
current. To define what is meant by the resistance at high fre- 
quencies, we have to divide the power lost in heating or other- 
wise dissipated, by the square of the effective current. This 


quotient is known as tlie " effective resistance " at the frequency 
in question. 

Tlie effective resistance of a circuit carrying currents of radio 
frequency may be very appreciably affected by the presence of 
neighboring conducting bodies. The energy of any eddy cur- 
rents which may be induced in the latter is drawn from the 
circuit in question, whose effective resistance is thereby in- 
creased. On account of the high frequency, this effect can be 
astonishingly large in good conductors and may be appreciable 
in the presence of such a poor conducting path as a painted 

Different portions of the same circuit should not be placed 
in close proximity. The mutual effects of the currents which 
flow in opposite directions in two parallel cylindrical w^ires is, 
for example, such as to cause the maximum current densities 
in the two cross sections to be shifted to points nearer the other 
conductor, with an increase in the effective resistance of each 
conductor above the value it would possess in the absence of 
the other. In other cases (p. 302, Circular 74) the effective 
resistance may be reduced by the presence of the other lead. 
An important example of the effect of the mutual inductance 
of neighboring conductors on their effective resistances is fur- 
nished by a system of parallel wires connected in parallel. In 
this case more current, at radio frequencies, flows in the outer 
wires than in the inner, and the differences may become very 
important. This is a point which cannot be overlooked in the 
design of hot-wire ammeters to carry large currents. 

118. Brush, Spark, Dielectric, and Radiation Resistance. — As 
has already been explained (Sees. 31 and 56), no dielectric is 
perfect. Some heating takes place in it, and w^e may artificially 
represent a condenser as equivalent to a pure capacity in series 
with a resistance. The introduction of a condenser into a radio 
circuit has therefore the effect of increasing the effective re- 
sistance of the circuit, and, except in especially designed air 
condensers, this effect cannot be neglected. Care needs there- 
fore to be taken that poor dielectric materials be kept away 
from regions of intense electric field. 

When operating condensers at high voltages, large energy 
losses may occur in the so-called brush discharge, and this 


effect will generally give rise to a very considerable increase 
in the effective resistance of the condenser. 

If a spark gap is included in a circuit, the resistance of the 
spark will have to be included in the total effective resistance 
of the circuit. This spark resistance depends upon a number 
of circumstances, and the laws of its variation are very com- 
plex. In general, a short spark gap has a larger conductivity 
per unit length than a long one. Thus a series of short spark 
gaps is better than a single one of a length equal to the sum 
of the lengths of the shorter gaps. The pressure and nature 
of the gas between the terminals also affect the resistance 
which is materially decreased with reduction of pressure. 
Further, the nature of the terminals and the constants of the 
remainder of the circuit all affect the spark resistance. 

Some of the power supplied to a circuit, which is carrying a 
radio current, is radiated from the circuit in the form of electro- 
magnetic waves (see Chap. 4). This may be regarded as the 
useful work obtained from the circuit, and for transmission 
purposes the power radiated should be made as large as pos- 
sible, in comparison to the power dissipated in the circuit itself 
and in its immediate surroundings. The power radiated at any 
frequency is found to be proportional to the square of the 
current flowing, so that the radiative effect may be regarded, 
artificially, as causing a definite increase in the effective resist- 
ance of the circuit. This fictitious resistance increase is known 
as the " radiation resistance," and is found to be directly pro- 
portional to the square of the frequency, or inversely propor- 
tional to the square of the wave length. 

D. Coupled Circuits. 

119. Kinds of Coupling. — When two circuits have some part 
in common or are linked together through a magnetic or an 
electrostatic field they are said to be " coupled." If two cir- 
cuits have an inductance coil in common (Fig. 151a), their 
relation is said to be " direct inductive coupling." If they have 
a condenser in common, their relation is said to be " direct 
capacitive coupling" (Fig. 151c). If they have a resistance 
in common, their relation is said to be " resistance coupling." 



If two circuits are mutually inductive (Fig. 151b) and have 
no part in common other than the mutual inductance, their 
relation is said to be " indirect inductive coupling," usually- 
called simply "inductive coupling." (For mutual inductance 
see also Sec. 47.) Sometimes the coupling shown in Fig. 151c 
is modified by using two additional condensers. Each circuit 
contains two condensers in series and one condenser in the first 
circuit is coupled to one condenser in the second circuit through 
a coupling condenser ; this is described as " indirect capacitive 
coupling." Mutual inductive coupling is used very extensively 
in constructing radio apparatus. It often happens that the 
two coils constituting a mutual inductance are so mounted that 
they also constitute the two plates of a condenser whose capaci- 

FlQ. 151 







Ty fees of cou^lini •, fd) direct coo^ I inV^ (t>) inducttve ooufilin^ 
(C) CAfa^ci'ti ve. coufslin^ 

five reactance is appreciable at radio frequencies, and in this 
case the effect of the coupled coils is a combination of inductive 
coupling and capacitive coupling. 

It is customary to denote as the " primary " that circuit in 
which the applied emf. is found, the other being regarded as the 
" secondary " circuit. When two circuits are coupled they re- 
act on one another so that the current in each circuit is not the 
same as would be the case were the other circuit absent. The 
extent of the reaction is, however, very different in different 
cases. Circuits are said to be "■ closely coupled " when any 
change in the current in one is able to produce considerable 
effects in the other. When either circuit is little affected by 
the other the coupling is regarded as "loose." The coupling 
between two inductively coupled circuits is changed by changing 
the distance between the two coupling coils. In general, increas- 


ing the distance between the two coils will make ttie coupling- 
looser, providing each coil is moved parallel to its original posi- 
tion. If the distance between the two coils is not changed, but 
they are moved so that the angle between their projected axes is 
changed, the coupling will also be made looser, since fewer lines 
of force are then linked with both coils. 

A more exact measure of the closeness of the coupling is given 
by what is called the "coefficient of coupling" (denoted by A:). 
Its value in the case of direct coupling (Fig. 151a) is given by 

If the total inductances of the circuits in Fig. 151b are denoted 
by Li and Lo, we have' for inductive coupling 

and for capacity coupling (Fig. 151c.) 


(Ca+C^)(Cb+C^) ^ " 

As the coupling is made very loose, k approaches zero as its 
limit ; for the closest possible coupling k would be unity. 

In equations (80) and (81) the values of M, La, L\^,Li, L2, 
must be expressed in the same units. In equation (82) the 
values of Og,, Ob, Cm must be expressed in the same units. 

The coupling of two direct coupled circuits may be increased 
by increasing the amount of inductance which is common to the 
two circuits, maintaining constant the total inductances 
(La+il/) and (Lb+J/) of the two circuits. To make the coup- 
ling of tlie inductively coupled circuits closer, their mutual in- 
ductance is increased by moving the coils nearer or by increas- 
ing the inductance of either coil. For example, the coefficient of 
coupling of an antenna may be increased by adding turns to 
the coil of the oscillation transformer, enough inductance being 
subtracted from the loading coil to keep the total inductance of 
the circuit constant. Capacitive coupling is closer, the smaller 
the common capacity Cm is in comparison with the capacities 
Ca and Cb- 


In some types of receiving apparatus the coupling condenser 
is connected in a different manner from tiiat shown in Fig. 151-c 
(see Sec. 177), and in that case the coupling is loosened by a 
decrease of capacity in the coupling condenser. 

The reaction of either circuit on the other affects, not only 
the value of the currents in the coils, as would be expected, but 
has an important influence on the frequency to which the cir- 
cuits respond most vigorously. This is explained in the fol- 
lowing : 

120. Double Hump Resonance Curve. — It may be shown (Sees. 
16 to 18 of Circular 74 of the Bureau of Standards) that the re- 
actance of either of the circuits, primary or secondary, is zero ; 
that is, the impedance is a minimum for two separate fre- 
quencies f and f", which are different from the natural fre- 
quences fi and f2, for which the primary and secondary circuits 
are in resonance when talien alone. AYith loose coupling f 
and f" differ little from fi and f^. With closer coupling, how- 
ever, the differences becomes very appreciable. If f be used to 
denote the lower of these two frequencies, then it may be shown 
that /' is always still lower than the lower of the two natural 
frequencies /i and f-, while the higher frequency f" is always 
higher than the higher of the two natural frequencies. In- 
creasing the closeness of the coupling has always the effect of 
spreading f and f" further apart. Furthermore, the difference 
between f" and the higher of the two natural frequencies is 
always greater than the corresponding difference between /' 
and the lower of the natural frequencies. 

These conclusions may be tested by means of a wavemeter. 
As has been already pointed out (Sec. 112), the current in- 
duced in a wavemeter circuit is a maximum when the wave- 
meter is tuned to the frequency of the exciting current. Sup- 
pose the wavemeter to be very loosely coupled to either the 
primary circuit or the secondary. Let the frequency of the 
current in the primary be varied by small steps and adjust 
the setting of the wavemeter for each frequency until the in- 
dicator shows a maximum current in the wavemeter circuit. 
If the settings of the wavemeter condenser and the correspond- 
ing deflections of the indicating instrument are plotted, a reso- 
nance curve is obtained which will show two humps or peaks 
corresponding to the frequencies f and f". The positions of 


the two humps will be found to be different for a second reso- 
nance curve, taken \\ith. a different coupling between the pri- 
mary and the secondary. The coupling between the wavemeter 
circuit and the circuit which is exciting it must be made as 
loose as practicable in order that the wavemeter circuit may 
not react appreciably on the other circuits and thus change 
their currents. 

A more direct method of showing the two frequencies is fur- 
nished by simply inserting a hot-wire ammeter or thermocouple 
in the circuit to be examined and noting tlie clianges in its 
readings as the frequency is continuously varied. 

In the case of the usual coupled radio circuits the two cir- 
cuits, primary and secondary, are adjusted independently to the 
same natural frequency ; that is, fi is made equal to U. 
When the coupling is made loose both f and f" approach the 
same value, f" from above and f from below, and at very loose 
coupling f' = f" = fi=f2. 

It might be supposed that in the special case where fi=f2 the 
currents in the circuits would be a maximum for a single fre- 
quency only, namely, at the value of f to which they are both 
tuned. Nevertheless, both experiment and theory show that 
each circuit, even in this case, offers a minimum impedance 
at two different frequencies, just as is found for the more 
general case. The two frequencies f and f" lie on either side 
of the value f, though not at equal intervals from the latter, 
the difference f" — f being always greater than f — f. 

When fi=f2 the effect of the coupling on the values of f 
and /" is shown by the simple relations. 

-^ ^/l+k' -^ -y/l-h 

If the coupling is made more and more loose, the two frequencies 
f and f" approach one another, and the two humps of the reso- 
nance curves finally merge and become indistinguishable from 
a single hump. (See also Sec. 165.) 

In the absence of a secondary current there is no reaction on 
the primary, which is no longer a coupled circuit, and will 
necessarily be in resonance at a single frequency only {f by 
hypothesis). The same remarks apply to the secondary when 
the primary circuit is broken. 
43904° — 22 18 


' The further treatment of coupled circuits naturally follows 
two different lines, according to whether the primary is excited 
by a sine wave of a definite frequency (producing oscillations), 
or whether the primary circuit is given a single impulse and 
then allowed to oscillate freely. (See Sec. 115, p. 251.) 

121. Forced Oscillations. — Forced oscillations of frequency 
/o will be caused when a sine-wave emf. of frequency fo is ap- 
plied to the primary of two coupled circuits. When the emf. is 
initially applied to the primary, the currents in the primary 
and in the secondary are at first very complicated, and con- 
sist of free oscillations of the two resonance frequencies of the 
circuits as coupled {f and f of the preceding section), sui^er- 
posed upon forced oscillations of the impressed frequency fo. 
The free oscillations quickly die away, and there remain sine- 
wave currents of frequency fo in both the primary and secondary. 

High-Frequency Transformer. — It can be shown that to obtain 
the maximum current in the secondary circuit a certain value 
of the coupling of the coils is necessary. If the coupling be 
made either closer or looser than this value the secondary cur- 
rent falls off in value. In general, the proper coupling for maxi- 
mum secondary current will depend upon the resistances of the 
primary and secondary and their reactances, and can be de- 
termined better by actual experiment than by calculation. For 
one important case, however, the values of the coupling and the 
maximum secondary current can be expressed very simply. 

If the primary and secondary circuits are separately tuned to 
the frequency of the applied alternating emf. E, the maximum 


possible secondary current has the value /2= „ /p~p where R^ 

and R2 are the primary and secondary resistances. The value 

of the mutual inductance (coupling) which gives the maximum 

secondary current may be calculated from the relation 2irfM= 

Ri R2. The primary current under these circumstances as- 

sumes the value /i=^^^-, which is one-half the resonance value 

of the primary current when the secondary is absent. 

These relations and the dependence of the secondary current 
on the coupling are illustrated in Fig. 152, which shows the 
changes of the secondary current as the mutual inductance be- 
tween the coils is varied. The resistances i2i=2.0 and 7^2=12.5 



ohms are assumed, and the secondary current is plotted in terms 
of its maximum value, which is taken as 1. The abscissas taken 
are not the mutual inductance itself but 27ufJ/, so that the 
curve is applicable to different frequencies, assuming, of course, 
that in every case the two circuits are tuned to the frequency 
in question. Maximum secondary current is, in this example, 
obtained for 27rn/=V2.0 X 12.5=5. Supposing, for instance, that 


i^eLiTive values cjp secondary currenTs 
LAP^esI v<ilue tiiKen A5 1. 
1 (^ 






























L . 






1 1 






i i 







tS" 5 15 lo 17 S IS ns lo 
Z-rrf M 

VAridtlon oj SecondApy corrcnt with The cou^IinX 

the frequency is 100,000, the coils must be so placed that their 


mutual inductance is 

■■, or 7.96 microhenries. 

27rX 100,000' 

Current and Voltage Ratios. — The current ratio (secondary to 
primary) in the high-frequency transformer, when adjusted to 

give maximum current, has been shown to be -*/^, so that, 

:n general, it may be increased by decreasing the secondary 
resistance or by increasing the primary resistance. 

The voltage ratio is in general more complicated. If the two 
currents are tuned to one another and to the impressed fre- 


qiiency, the voltage ratio (secondary to primary) approaches 
the value ^ / -J as the resistances in the circuits are made smaller. 


If the circuits are not tuned to the same frequency, but are 
closely coupled, the voltage ratio approaches the ratio of the 
number of turns on the two coils (when the resistance may be 
neglected), which is the case of the usual alternating-current 

Inductive coupling of transmitting sets is discussed in Section 
161, page 370, and types of transformers for high frequencies 
are described. Transformers used for radio frequencies gen- 
erally have air cores, that is, no iron is used. In the case of 
the small radio-frequency transformers used in electron tube 
amplifiers (see Section 196, page 481) an iron core is sometimes 
used, very thin laminations being employed. Devices of trans- 
former type, such as the Alexanderson magnetic amplifier (see 
Section 173, page 399) are used for controlling or modifying 
radio-frequency currents. 

122. Free Oscillations of Coupled Circuits with Small Damp- 
ing. — Suppose the condenser in the primary circuit is given a 
charge, and the primary circuit is closed directly or through a 
spark gap. If the secondary circuit is open, the primary will 
oscillate freely, the frequency of the current being given by the 

equation/i= , , the damping of the oscillations being deter- 

mined by the ratio ^ ,V ^^ treated in Section 116, page 257. 

As soon as the secondary is closed, the matter is complicated 
by the reaction of each circuit upon the other. An emf. is in- 
duced in the secondary by the changes of the primary current, 
and thereby a forced oscillation is started in the secondary. 
The secondary condenser is charged by this current and starts 
a free oscillation, whose period will depend on the constants of 
the secondary circuit. This latter wave will induce a forced 
oscillation in the primary, and similarly the oscillation which 
was forced in the secondary by the primary, will react on the 
primary, modifying the original oscillation in the primary which 
produced it. The oscillations in the primary will then further 
react on the secondary, and so on. 


Naturally, the result will be very complicated, but it is evi- 
dent that each circuit is the seat of two waves, one free and 
the other forced by the other circuit. Each of the waves which 
we have designated as free is, however, not entirely so, since it 
forces an oscillation of its own frequency in the other circuit, 
and has to supply the energy for this induced wave. This has 
the effect of modifying the frequencies of these waves from 
the natural values fi and f2 already treated. Of the two waves 
in the primary, the free wave has (with loose coupling) the 
greater amplitude, and the same is true of the secondary ex- 
cept that here the amplitudes of the waves are more nearly 
equal. With close coupling, the forced wave in the primary be- 
comes stronger, owing to the increased amplitude of the second- 
ary free wave. Finally, with very close coupling, those waves 
predominate the frequency of which is f. The frequency f" of 
the other waves lies so far above the natural frequency of either 
circuit that only feeble oscillations of this frequency are present. 

In general, therefore, the oscillations in both the primary and 
secondary circuits are compounded of two damped oscillations 
of different frequencies. It is of interest to study a little more 
closely the nature of the complex oscillations resulting from 
the superposition in a single circuit of the two oscillations of 
different frequencies. 

Damping Curves of Coupled Circuits. — Fig. 153 shows two 
sine waves A and B of equal amplitudes but of different fre- 
quencies. Curve C is obtained by taking the algebraic sum 
of the ordinates of A and B. It is seen to be a curve the oscil- 
lations of which alternately increase and die away. The fre- 
quency of these fluctuations is equal to the difference of the 
frequencies of the components A and B. The curve C passes 
through its zero values at nearly regular intervals of time, the 
length of the intervals usually being intermediate to the inter- 
vals between successive zero values for curve A and the inter- 
vals between successive zero values for curve B. In addition, 
however, curve C passes through zero at one extra point in each 
cycle of curve C, the intervals between this extra point and 
adjacent zero values being about one-half of the regular in- 
terval. This extra zero value occurs at the mid-point of the 
cycle of curve C, where curve -4. and curve B pass through zero 


at the same point, which is in the vicinity in which the ampli- 
tude of the oscillations of curve C is smallest. In Fig. 153 
curve C has ten zero values in a cycle, including the extra zero 
value at the mid-point of the cycle. It is also noticeable that 
the loops of the curve C are only approximately of sine shape. 

An exactly analogous case is furnished by the resultant sound 
wave coming from two tuning forks which are vibrating with 
somewhat different frequencies. The sound which is heard 
alternately increases and decreases in loudness, giving the phe- 
nomenon of " beats." The number of beats per second is equal 
to the difference in frequencies of the two forks. Thus, if two 
forks have frequencies of 259 and 255 vibrations per second, 
they combine to give a sound which beats four times per second. 

Beat phenomena in the reception of undamped waves are 
discussed in Section 205. p. 501. 

Production ot imSi 

Free oscillations in coupled circuits are damped, so that in 
addition to the alternate waxing and waning of the resultant 
oscillation, the energy of the oscillation as a whole dies away 
according to the laws already treated in Section 116. Fig. 154 
shows the nature of the damped oscillations in the primary 
and secondary circuits. The primary decrement is assumed to 
be 0.1 and that of the secondary 0.05. The two coexistent fre- 
quencies are supposed to have the ratio of 4 to 5. The curve of 
oscillations is in each case drawn as a full line. The dotted 
curves show the beating effect described above, while the dashed 
curves give an indication of the damping effect. It is notice- 
able that the primary current is passing through its maximum 
values at the moments when the secondary current is zero, and 
vice versa. Further, when the primary is passing through a 
period of intense oscillation, the secondary oscillations are 
small, etc. 



Another important conclusion which can be drawn from Fig. 
154 is that the energy of the coupled system is transmitted alter- 
nately from the primary to the secondary, and back again from 
the secondary to the primary. Thus, at certain moments the 

Primarij Oscillations. 

Fig IS4. 
Oscillations in Coupled Circuits. 
Decrement of Primary Circuit * 
Decrement of Secondartj Circuit - O.QS 
Patio of Freouencies -^ s to'4 

energy is entirely in the primary, at others entirely in the 
secondary, and at other instants partly in the primary and 
partly in the secondary. This transfer of energy, first in one 
direction and then in the other, shows that the primary and 
secondary play alternately the rOle of driving circuit. 


From the standpoint of radiation of energy, it is desirable to 
hinder the return of energy to tlie primary, after it has once 
been given to the secondary. Since the closed primary circuit 
is of such a nature as to radiate very little energy (see See. 
136), no useful purpose is served by the transfer of energy back 
to the primary, and some of the energy thus handed back is nec- 
essarily lost in heating in the primary. Further, the radiatioa 
of the energy of the secondary in waves of two different fre- 
quencies is undesirable. The receiving circuit can be tuned to 
give a maximum of current for either one of the incoming wave 
frequencies, but not for both at the same time. The partition 
of the radiated energy of the secondary in waves of two fre- 
quencies is therefore wasteful, since only that wave to which 
the receiving circuit is tuned is effective, while practically none 
of the energy of the other wave is usefully employed, and it 
may cause interference with other stations. 

For a further discussion of oscillations in coupled circuits, 
the reader may refer to Bureau of Standards Circular 74, and 
to a book by'G. W. Pierce, "Electric Oscillations and Electric 

123. Impulse Excitation. Cliienched Gap. — If by some means or 
other the energy of the primary circuit can be transferred to the 
secondary and then all connection between the circuits can be 
removed before any energy can be handed back to the primary, 
we may avoid the disadvantages just mentioned. In this case, 
the secondary will oscillate simply in its own natural frequency, 
and the loss of energy in the primary can be restricted to the 
short interval during which the primary is acting. By properly 
choosing the resistance of the secondary, the damping of the 
radiated wave may be kept small, and since only a single fre- 
quency is radiated, the advantages of close tuning of the receiv- 
ing circuit can be realized. Such a method of excitation is 
known as " impulse excitation," and is analogous to the me- 
chanical case where a body is struck a single sharp blow, and 
thereafter executes vibrations, the period of which depends 
entirely on the inertia and elasticity constants of the body 
itself, and not at all on the nature of the body from which the 
impulse has emanated. 



One means of obtaining an impulse excitation of the secon- 
dary is to insert so much resistance in the primary that its 
cuiTent falls away aperiodically (see Sec. 116, p. 257). This has 
however, the disadvantage that considerable energy is lost in 
the primary due to the heating of the rather large resistance 
of the primary by the initially rather large primary current. 


Quanch«el Primary OscillaTi'ons 

Oscillations oj Quenched 
Cjaja Circuits 

Primary PecremenT o i 
SeoondAry Decrement o-o5 

C'aconc^ary Oscilicitions 

A more satisfactory arrangement is the "quenched gap." By 
dividing the spark gap in the primary into a number of short 
gaps in series, the cooling effect of the relatively large amount 
of metal is available for carrying away the heat of the spark 
discharge. This is found to be sufficient, in the case of a 
pn^perly designed quenched gap, to prevent the reestablishment 
of a spark discharge after the first passage of the primary oscil- 
lations through their condition of maximum amplitude to zero, 
as at point D, Fig. 154. The secondary, at this moment, is the 
seat of the whole of the energy of the system and thereafter 
oscillates at the single frequency natural to it. The damping 
of the primary does not have to be made excessive, and the 


energj^ lost in the primary is restricted to tlie heating during 
the short interval before the quencliing of the primary oscilla- 

Fig, 155 shows the form of the oscillations in the two circuits 
for this case. The curves are the same as in Fig. 154 up to 
point D, after which the secondary curve is a simple feebly 
damped oscillation. The construction and operation of the 
quenched gap are treated further in Chapter 5. Section 156. 



A. Wave Motion. 

124. Three Ways of Transmitting Energy. — All of the ways of 
signaling between distant places operate by one or by a combi- 
nation of these three methods : 

(a) By a push or pull on something connecting the places. 
(6) By projectiles, 
(c) By wave motion. 

Thus think of all the ways in whicli you can arouse a dog 
asleep at the other side of a room. You can prod him with a 
long stick (method a). You can throw something at him. If 
you hit him, it is a case of method 5 ; if you miss him, the noise 
made when the missile hits the wall or floor may wake him, in 
which case we have a combination of methods & and c. You 
can whistle or call, using sound waves (method c). Any way 
that you can think of is an example of one of these three 

All these three methods are important in many different 
kinds of physical phenomena. In the study of radio com- 
munication, wave motion, the third method, is of particular 

12.5. Properties of Wave Motion. — Everyone is familiar with 
the to-and-fro motion of water at sea, which we call waves. 
When a stone is thrown into a quiet pond, ripples, or little 
waves, are produced, which spread out until they meet the 
shore, or die away. A moving boat creates a particular kind 
of wave. Waves can be produced by rocking a boat. Ocean 
waves may be 40 feet in height, while a ripple may be scarcely 

If a rope supported at one end is given an impulse at the 
free end, each point of the rope will have a to-and-fro motion 
and the rope has a \yave motion. 

Many of the most familiar phenomena of everyday life are 
caused by wave motion. Sound is transmitted by waves in the 



air. Light and heat are transmitted by exceedingly short 
waves. Our ears and eyes are detectors for particular kinds of 
waves. Earthquake disturbances are transmitted by waves in 
the earth. Air is the medium through which sound waves are 

When wave motion exists in a medium, each particle of the 
medium executes a series of to-and-fro motions, which are re- 
peated at regular intervals. If a particle at a given point is 
executing a certain series of motions, then at a later instant 
a particle farther along in the direction in which the wave is 
traveling will execute the same series of motions. The number 
of times in a second that the same series of motions is repeated 
by a given particle is the frequency of the wave motion. Fre- 
quency is usually represented by the symbol f. 

The instant after a stone is dropped into a pond, waves are 
formed in the immediate vicinity. (See the frontispiece.) 
These waves possess energy and are capable of doing work. A 
minute or two after the stone has been dropped the surface of 
the water at the spot where it was dropped will be calm again, 
but there will be waves at a considerable distance also possess- 
ing energy. Energy has been transmitted over this distance by 
means of wave motion. 

Every wave has a length. In the case of water waves the 
wave length is usually determined as the distance between the 
crests of two successive waves, and the wave length of any 
kind of wave can be determined in the same way. The alter- 
nate crests and troughs, though invisible in many types of 
waves, are present in all. If we use the term phase to mean 
the position at any time of a point on the wave outline, we 
can say in general that the wave length is the distance between 
two successive points in the same phase. It is common prac- 
tice to use the symbol \ (pronounced lambda) to represent wave 
length, usually expressed in meters. 

Waves of all kinds travel with a definite velocity. When a 
stone is dropped into a pool, a certain time elapses before the 
resultant w^ave reaches the shore. The distance traveled by 
the wave in one second is its velocity. If a fixed point is 
watched on the surface of a pool over which waves are moving, 
it is seen that a crest appears at that point a definite number 
of times every second ; this number is the frequency f. If we 


multiply /, the number of waves per second, by \, the length 
of each wave, we obtain the distance which the wave travels 
in one second, which is the velocity c/ In symbols, c^\f. 

Different kinds of waves liave frequencies which vary greatly. 
Large ocean waves may have a frequency of only about two per 
minute, and be a half mile in length. The waves of yellow 
light have a frequency of six hundred million million per second^ 
and a wave length of only one twenty-thousandth of a cen- 

The velocity of different kinds of waves varies greatly. 
Waves in water do not all have the same velocity. The long^ 
ocean wave just mentioned would have a velocity of over a mile 
per minute. Small ripples may have a velocity of from 10 to 
100 centimeters per second. Sound waves travel in air witli a 
velocity of about 330 meters per second, or about 1083 feet per 
second. The velocity of light waves in space is 300,000,000' 
meters per second, or about 186,300 miles per second. 

It has been demonstrated in many ways that radio waves are 
transmitted with the same velocity as light waves and the waves 
which constitute heat radiation, and that the three are the same- 
kind of waves, differing in frequency. Electric waves, including 
radio waves, light waves, and radiated heat waves, are all re- 
ferred to by the general term " electromagnetic waves." The- 
alternating electric currents used for commercial lighting have 
a frequency of 60 per second and may produce electromagnetic 
waves of that frequency. The electromagnetic waves used for 
radio communication have frequencies from about 10,000 to 
8,000,000 per second. Heat waves are electromagnetic waves 
having frequencies from about 5 million million to 200 million 
million per second. The electromagnetic waves which the eye 
perceives as light have frequencies from about 400 million 
million to 1000 million million per second. 

In the case of water waves the more the surface of the water 
is displaced by the waves from its position of rest the greater 
is the amount of energy which is being passed along. The 
amount of energy transmitted by water waves depends upon the 

1 Example. — What is the wave length of waves having a frequency 

of 100,000 cycles per second which travel with a velocity of 300,000,000' 

meters per second? 

, c 300,000,000 ^„„^ 
^^7^ 100,000 =3000 meters. 


height of the crests and the depth of the troughs. This is true 
of all kinds of waves. 

The greatest displacement from the position of rest that any 
point undergoes is called the amplitude of the wave. In speak- 
ing of water waves, we usually call the vertical distance between 
the crest and the trough the height of the wave, and this is twice 
the amplitude. In the case of sound waves, the distance through 
which each particle of air moves is very small. 

In general, we say that the energy in wave motion depends 
on the amplitude. The amount of energy in wave motion de- 
pends on the work which has to be done to produce the displace- 
ment. This is. in general, equal to the product of the resisting 
force and the distance moved. In the case of electromagnetic 
waves, including the waves used in radio communication, the 
resisting force is proportional to the distance moved. Hence the 
work done and the energy transmitted is proportional to the 
square of the amplitude of the wave. 

Waves have many different kinds of shapes or forms. In the 
case of water waves, everyone is familiar with the large variety 
of wave forms produced by different conditions. A simple 
wave form is the sine wave shown in Fig. 71, page 117. A 
simple sound, such as that produced by a tuning fork, may 
t)roduce an air wave having the simple sine wave form. Other 
sounds such as the notes emitted by musical instruments, and 
speech, produce air waves having much more complex wave 
forms. The wave forms used in radio communication may 
assume a wide variety of forms. (See Sees. 156, 172, 205, 206, 
pp. 360, 396, 501, 507.) 

Every wave has the properties which have been mentioned — 
w^ave length, frequency, velocity, amplitude, and wave form. 
In the case of waves which are always transmitted with the 
same velocity, such as electromagnetic waves, the wave length, 
frequency, and velocity have the relation c=\f, so that they 
are not independent properties. 

The kind of waves which will be produced by rocking a boat 
depends on the size, shape, and weight of the boat and how 
fast it is rocked. If a small boat is rocked rapidly, we get 
short waves. If a large boat is rocked slowly, we get long 
waves. Energy is required to rock the boat, and the boat is the 
device for radiating this energy as waves. In radio communi- 


cation tlie antenna is the device for radiating tlie electric en- 
ergy as waves. Long antennas are used in radiating long 
waves. The antenna is discussed in detail later. 

The short waves produced by rocking a small boat die out in 
a short distance. Longer waves produced by the motion of a 
large boat travel farther. Ocean waves may be half a mile 
in length, and travel hundreds of miles. In radio communica- 
tion it is also found that long waves travel farthest. 

When a train of waves due to a disturbance in a medium is 
transmitted tlirough that medium, the waves are said to be 
" radiated " through the medium, and the source of the dis- 
turbance is said to " radiate " the waves. Thus an antenna 
" radiates " electromagnetic waves. 

Much information concerning wave motion of interest to the 
student of radio communication is contained in the following 
books: J. A. Fleming, Waves and Ripples in Water, Air, and 
Aether ; J. A. Fleming, The Wonders of Wireless Telegraphy ; 
R. C. Maclaurin, Light ; D. C. Miller, The Science of Musical 

126. Wave Trains, Continuous and Discontinuous. — If a stone 
is dropped into a quiet pool of water, a " train " of waves is 
started which soon passes out from the starting point in all 
directions, leaving the surface behind it undisturbed. If a 
second stone is dropped just at the moment that the surface at 
the starting point has completed one up-and-down excursion, an- 
other wave train will start in phase with the first, and the two 
will form one train. If the process is repeated once after each 
complete vibration of the surface at the starting point, continu- 
ous waves are produced. Similarly, if we hold a vibrating 
body so that it touches the surface, continuous waves are pro- 
duced. By interrupting the vibrations of the body we can pro- 
duce interrupted or discontinuous trains of waves. Continuous 
waves are produced by an organ pipe when the key is held 
down. Discontinuous, " damped," waves are produced by a 
piano when a key is struck. 

Examples of these two kinds of wave trains are met with 
often. Thus the sound from a musical instrument where the 
strings are set in vibration by picking (as with a mandolin) is 
transmitted in discontinuous trains, while that from an instru- 
ment whose strings are bowed (as a violin) is transmitted by 


more nearly continuous waves. Similarly, in radio we have to 
do with both kinds, continuous waves being furnished by high- 
frequency alternators, the Poulsen arc, and the oscillating elec- 
tron tube, while discontinuous trains are given by condenser dis- 
charges in spark circuits. In these latter the amplitude of the 
waves diminishes steadil^^ in each wave train ; these are called 
'" damped " waves. Such waves are discussed in Section 115. 

B. Propagation of Waves. 

127. Wave Propagated by Elastic Properties of Medium.^ — In 
the case of ripples on the surface of water it is plain to the eye 
that the waves are transmitted by the passing on of the up-and- 
do"\Mi motion of the surface at the source. This is possible be- 
cause at the surface of the water the particles of the water are 
held together by forces which resist their displacement. When 
one particle is displaced its neighbors are dragged with it to 
some extent. In technical terms the medium of transmission is 
said to have " elastic " properties and the forces brought into 
play are said to be elastic forces. The velocity of the waves 
(ripples) depends on the nature and amount of these elastic 

In the case of sound weaves in air we do not ordinarily see the 
vibrations of the particles of the air. The vibrations are quite 
small and the waves travel so fast that only under quite unusual 
conditions can they be made visible. But the mechanism by 
which the energy is transmitted is found to be of the same kind 
as in the case of water ripples. By the delicate elastic connec- 
tions between neighboring portions of the air a vibration at one 
point is passed on to another. Sound waves are of another type 
than water waves only because the structure of air is different 
from that of w^ater. Hence the elastic reaction to displacement 
is different in the two media. This is the sole cause of the dif- 
ferences between any two types of waves. 

2 For further explanation of the radiation of electric waves, see J. H. 
Bellinger, Bureau of Standards Scientific Paper No. 354 ; W. H. Eccles, 
Wireless Telegraphy and Telephony ; J. A. Fleming, Principles of Elec- 
tric Wave Telegraphy ; G. W. Pierce, Electric Oscillations and Electric 
Waves ; S. G. Starling, Electricity and Magnetism, pp. 423-429 ; L. B. 
Turner, Wireless Telegraphy and Telephony. 



128. Properties of Electromagnetic Waves. — In the case ol 
electromagnetic waves, often called " electric waves," the dis- 
placements produced are of the kind already considered in the 
section on capacity (Sec. 29). The elastic reactions set up by 
such displacement currents can be found by the same laws which 
determine the electric and magnetic forces due to any current. 
It is beyond, the scope of this book to show the nature of these 
electrical elastic forces. It will be sufficient, however, to state 
that they are such as to produce waves in which (in free space) — • 

(a) The displacement (and the electric field intensity) are 
at risfht angles to the direction of motion of the wave train. 

' E-leclric lines of force ma 
The eleclric field and the Magnetic i cKAr^ed . plate condenser 
field are at rigKt a/i^aus and travel 
together fict i 56 

(6) The magnetic field intensity resulting from the displace- 
ment current is at right angles to the displacement and to the 
direction of the wave train. 

(c) The variations in the displacement (or the electric field 
intensity) and the magnetic field intensity are in phase. 

(d) The velocity of the waves is 300,000,000 meters per sec- 
ond, the same as the velocity of light (about 186,300 miles per 
second ) . 

These relations are shown in Fig. 156, where the curve 
marked E or D shows the variations in the electric field in- 
tensity or displacement, and that marked H the variations in 
the magnetic field intensity, the wave moving in the direction 
shown by V. 

53904° — 22- 



129. Modification of Waves in Free Space Near the Earth. — 
Such waves if started at a point in free space travel in all direc- 
tions with the same velocity. They may be modified in various 
ways as they proceed. Thus, if they pass into a region of dif- 
ferent dielectric constant, they are in general changed slightly 
in direction and partly reflected. Their energy is also absorbed 
to a greater or less extent in their passage through any medium. 
This absorption is greater for short than for long waves. In a 
perfect conductor no waves could be transmitted, since in such 
a medium there is no elastic opposition to the displacement of 
electricity. A perfectly conducting sheet would reflect all of the 
wave energy falling on it. However, a conductor parallel to the 
•direction of motion of a wave acts as a guide to the wave, 
through the action of currents induced in it by the varying 
magnetic field of the wave. It takes less energj^ from the waves, 
the better conductor it is. In the use of electric waves in radio 
communication all of these modifications occur and serve to ex- 
plain many of the irregularities of received signals. We can 
think of the space through which radio signals are sent as 
being bounded below by a sheet of varying conductivity (the 
earth's surface) and above — at a distance of from 30 to 50 
miles — by another conducting region. This upper region, where 
the air is much rarefied, is a fairly good conductor, owing to its 
ionization by radiations from the sun. The region in between 
these conducting layers is usually a good dielectric. Thus, 
this region acts more or less as a speaking tube does for sound 
Avaves, though its action is much more complicated. The 
^electromagnetic waves are set up near the earth's surface. They 
are partly transmitted as guided wave trains along the earth's 
surface, modified by refractions and absorption at its irregu- 
larities ; another part, however, goes off as space waves, which 
by reflections at the upper and lower layers of the conducting 
boundaries may recombine with the guided wave in such a way 
as either to add or subtract their effects, depending on circum- 
stances. In the daytime the upper conducting boundary will be 
les^s definitely marked than at night, on account of partial ioniza- 
tion of the air by the sun's radiations. Hence, there will be 
less reflection of the space wave in the daytime, and conse- 
quently the guided wave will not be assisted materially by any 
xeflected or refracted part of the space wave. In the night, 


however, when the upper boundary is more sharply defined, 
there is more reflection of the space wave, and in general sig- 
nals received at night are stronger than in daytime. Night 
signals are, however, more variable in intensity, particularly 
for short waves. This is especially true during the time when 
the sunset line is passing between two communicating stations. 
This is in general what we should expect, as the upper boundary 
would be quite variable under such circumstances. Clouds and 
other meteorological conditions would cause great variations in 
the sharpness of this boundary surface, and this may explain 
the rapid fluctuations in the strength of received signals often 

From all these considerations it can be seen that the condi- 
tions under which received signals will be most uniform in 
intensity are : 

(a) Transmission using long waves, 

(6) Transmission by daylight. 

(c) Transmission over short distances, 

(d) Transmission over uniform conducting surface of sea 

It is only under these conditions that the performance of 
different transmitting stations can be fairly compared. 

130. Difficulties in Transmission. — There are three principal 
sources encountered in practice wiiich make it difficult to re- 
ceive readable radio signals: (1) Interference from trans- 
mitting stations whose signals it is not desired to receive, (2) 
strays or static, and (3) the "fading" of the strength of the 
received signal. 

Interference from other transmitting stations can to a large 
extent be elhiiinated by selection of frequency (wave length), 
particularly by the use of transmitting apparatus which will 
radiate only a single wave length or a narrow band of wave 
lengths. Laws have been enacted which are designed to 
minimize interference from other stations. (See Appendix 6.) 
Interference from transmitting stations using even the same 
wave length as the station which it is desired to receive can 
also be reduced by directional reception and to some extent 
by directional transmission, which are discussed later. 

Strays are electrical disturbances giving rise to irregular 
interfering noises heard in the telephone receivers. They are 


also called " static," "atmospherics," " X's," and other names. 
Investigations have shown that there are many different 
causes for these stray waves, but have by no means completely 
explained their sources. In any particular case the possibility 
of getting a readable signal depends on the ratio of the strength 
of the signal to the strength of the static at that time. Experi- 
enced operators have stated that it is possible to copy messages 
when the strays were four times as strong as the signals, but 
much difficulty is often experienced when the strays are much 
weaker than this. The most common type of strays produces 
a grinding noise in the telephones; this type causes the most 
serious trouble. Another type, which produces a hissing noise, 
is usually associated with snow or rain. Near-by lightning 
produces a sharp snap. Another type consists of crashes 
similar to but stronger than the grinding noises first mentioned. 
By " stray elimination " is meant methods for increasing the 
ratio of signal strength to stray strength. 

Strays are usually much more serious in the summer than in 
the winter, and more serious in tropical latitudes than in more 
temperate latitudes. Radio communication in the Tropics pre- 
sents many special difficult problems. 

Strays are the most serious limitation on radio communica- 
tion. Transmitting stations of high power can be built, but if 
the strays are strong at a given time at the receiving station 
satisfactory communication can not be maintained, at least not 
with the ordinary types of receiving equipment. A great deal of 
careful investigation has been done to reduce the effects of 

The use in particular ways of the three-electrode electron 
tube (see Chap. 6) has resulted in considerably reducing the 
effects of strays as compared with the results obtained with 
earlier forms of receiving equipment.^ The use of sharply tuned 
receiving equipment and the use of a musical note in the trans- 
mitted signal will usually somewhat reduce the effect of strays. 

If the ordinary elevated type of antenna is used alone, a 
method for reducing strays which has given fairly satisfactory 
results has been the use of a receiving circuit having a pri- 
mary circuit containing considerable Inductance and having the 

3 The use of the beat method of reception, with continuous waves, is 
one of the most important ways of reducing strays. See Section 205, 
page 506. 


circuit containing the telephone receivers tuned to the audio fre- 
quency and loaded with considerahle inductance. 

The most satisfactory results in stray elimination have been 
obtained by the use of various kinds of directional receiving 
antennas — that is, antennas which receive most strongly signals 
which are transmitted from a particular direction. Such an- 
tennas are discussed later in this chapter and include not only 
particular forms of the ordinary elevated antenna but also the 
coil antenna and the ground antenna. The best results have 
been obtained by a combination of coil antennas and ground 
antennas.^ (See Sees. 150-152.) 

" Fading " or " swinging " is a rapid variation of the strength 
of signals received from a given transmitting station, the same 
circuit adjustments being used at the transmitting and receiv- 
ing stations. Fading is not usually observed at short distances 
from a transmitting station, but usually only at distances from 
the transmitting station which are at least some 10 or 20 per 
cent of the normal transmitting range of the station. Fading 
is observed particularly on short wave lengths, especially under 
400 meters, and is therefore most important in amateur com- 
munication and in communication with airplanes and other 
sijecial military applications. A certain transmitting station 
will be received with normal intensity for a few minutes ; then 
for a minute or two the signals will become much louder ; and 
then rapidly become much fainter and may become so weak as 
to be unreadable for a short time. Fading is usually observed 
particularly at night and usually only in transmission over 
land. Fading variations may be very rapid, with a period of 
about one second, or very slow, with a period of one hour or 
more. Transmitting stations located on the seacoast seem to 
fade more than inland stations. The principal method of avoid- 
ing transmission difficulties caused by bad fading is to increase 
considerably the wave length of the transmitting station, when 
this is possible. Fluctuations of the received signal resembling 
fading may sometimes be due to variations in the wave length 
or intensity of the transmitted wave, caused, for instance, by 

* Information regarding stray elimination is given in the following 
papers in the Proceedings of the Institute of Radio Engineers : A. H. 
Taylor, vol. 7, p. .337, August, 3 919; A. H. Taylor, vol. 7, p. 559, 
December, 1919; A. H. Taylor, vol. 8, p. 171, June, 1920; R. A. Wea- 
gant, vol. 7, p. 207, June, 1919 ; G. W. Pickard, vol. 8, p. 358, October, 
1920 ; L. W. Austin, vol. 9, p. 41, February, 1921. 


the position of the transmitting antenna being changed by wind. 
If the fluctuations are due to wave length variations and are 
not too rapid, it is possible to vary the tuning adjustments of 
the receiving set to follow the wave length variations.® 

C. Theory of Production and Reception of Electromagnetic 


To produce a train of waves of any kind a vibrating body is 
necessary. The vibrations of this body have next to be com- 
municated to a continuous medium, after which the elastic 
properties of the medium take care of the transmission of the 
waves. In the case of electromagnetic waves the vibrating 
body is an oscillating electric charge in a circuit (the sending 
antenna circuit), while the means by which these oscillations 
are communicated to free space can best be described in terms 
of the motion of the lines of force which, when at rest, are used 
to picture the field about electric charges as in Fig. 53. 

These lines are to be looked upon as lines along which there 
is a displacement of electricity against the elastic force of the 
medium. Thus they can not exist in conductors (in which no 
such elastic forces exist). Under the action of the elastic forces 
the displaced electricity is continually urged to return to its 
position of rest. In other words, there is a tension along the 
lines of force. In addition there must be a pressure at right 
angles to the lines of force, otherwise those lines would always 
be straight and parallel under the action of the tensions. These 
pressures can be thought of as arising from the repulsion be- 
tween the displaced charges of the same sign in neighboring 

Every alternating current has associated with it a magnetic 
field which can be considered to be the sum of two components 
having entirely different characteristics called, respectively, 
the " induction field " and the " radiation field." 

The induction field is the only one of importance in the opera- 
tion of the apparatus ordinarily used with alternating currents 
of commercial frequencies, such as 60 cycles. The alternating 

5 For further information regarding fading, see S. Kruse, Q. S. T., 
vol. 4, p. 5, November, 1920, and vol. 4, p. 13, December, 1920 ; 
Bellinger and Whittemore, Journal Washington Academy Sciences, vol. 
11, pp. 245-259, June 4, 1921. 


currents by which the ordinary transformer operates (see Sees. 
45 and 58) are due to the induction field. The cross tall?; often 
noticed between adjacent telephone lines is caused by the in- 
ductiou field. The action of the induction field on near-by 
circuits is often spoken of as " transformer action." If two 
coils are placed near together, interruptions in an alternating 
current passing through one coil will be reproduced in the 
other by the action of the induction field. The intensity of the 
induction field, due to a current in such a closed coil, decreases 
rapidly with the distance from the coil and is inversely propor- 
tional to the cube of the distance from the coil. Signals can 
be transmitted by the induction field, using alternating currents 
having frequencies from about 300 to 3000 cycles ; this is called 
" induction signaling." One of the applications of induction 
signaling has been to transmit signals from a submerged cable 
to a ship almost directly over the cable to aid the ship in finding 
its course. The induction field due to the ordinary type of ele- 
vated antenna is inversely proportional to the square of the 
distance from the antenna. The induction field is not important 
in the usual applications of radio communication. 

The radiation field is transmitted by wave motion. The 
intensity of the radiation field falls oif with the distance from 
a transmitting station, but is inversely proportional to the dis- 
tance, instead of being inversely proportional to the square or 
the cube of the distance. The induction field due to a current 
in a coil at a distance of 10 miles from the coil is only one one- 
thousandth of the strength of the induction field at a distance 
of 1 mile from the coil. The radiation field due to a current 
in a coil at a distance of 10 miles from the coil is one-tenth of 
the strength of the radiation field at a distance of 1 mile from 
the coil. For communication over any considerable distance, 
it is therefore necessary to make use of the radiation field. 

For the ordinary type of elevated antenna, the intensity of 
the radiation field is greater than that of the induction field at 
distances from the transmitting station exceeding the wave 
length divided by 6.28. 

The strength of the radiation field at a given point due to an 
alternating current in the ordinary type of elevated transmit- 
ting antenna is directly proportional to the frequency. When 
the coil antenna is used for transmitting, the strength of the 
radiated field is proportional to the square of the frequency. 


(See Sec. 134.) It is therefore necessary to use high fre- 
quencies to get a radiation field sufficiently strong to alloNV 
successful communication. With the ordinary tj*pe of ele- 
vated antenna, the radiation field at a given point due to an 
alternating current having a frequency of 1,500,000 cycles ( wave 
length=200 meters) would be 25.000 times as strong as the 
radiation field due to an alternating current having a frequency 
of 60 cycles. 

The above statements are for radiation in free space. In 
actual communication part of the energy of the radiated field 
is. however, absorbed in the surface of the earth or in the sur- 
face of the ocean as the wave travels. This absoi*ptlon effect is 
greater for high frequencies (see Sees. 129 and 134). It need 
not ordinarily be taken into account in short-distance work, but 
at distances greater than about 100 kilometers it becomes im- 
portant. For this reason it is not possible to indefinitely in- 
crease the strength of the radiated field at a given distance by 
increasing the frequency. (See Sees. 134-136.) 

The statement is sometimes made that a circuit carrying an 
alternating current of low frequency, such as 60 cycles, does not 
radiate. This is not really true; radiation does occur, but is 
of very feeble intensity. 

Another statement sometimes made is that an " open " circuit 
can radiate, while a " closed " circuit can not ; this is not true. 
All circuits are closed. Radiation from coils is described later 
in this chapter. 

For further information regarding radiation the reader may 
refer to Bureau of Standards Scientific Paper No. 354. 

131. Magnetic Field Produced by Moving Lines of Electric 
Displacement. — Consider what happens to the lines of force when 
a condenser is discharged. Before the discharge begins, the 
field is as shown in Fig. 157. Now. suppose a wire to replace 
the line flfec. thus discharging the condenser. The displace- 
ments previously existing along abc vanish, or. in other words, 
the line shrinks to nothing when the tension is relieved. But 
this, at the same time, does away with the sidewise pressure on 
the neighboring lines, which, since the pressure from the lines 
outside of them still remains, move inward toward the wire 
under the action of this unbalanced pressure. Their ends slide 
along the plates of the condenser during this motion, and when 
they come to the wire the displacements along their length 


vanish. This process continues until all the lines have van- 
ished and the condenser is discharged. 

Novr, while this is happening to the electric lines of force in 
the field, a current has been flowing in the condenser plates and 
the wire abc; also the magnetic lines of force which always 
accompany any current have sprung into existence and con- 
tinue to exist as long as the current flows. In the space between 
the condenser plates these magnetic lines of force will be 
directed up from the plane of the paper at right angles, both to 
the electric lines of force and to the direction of their motion. 
These two facts can be described in terms of the motion of 
the lines by saying that the motion of the ends of the elec- 
tric lines along a conductor causes a current to flow in it. 
while the motion of the electric lines at right angles to their 
own length produces magnetic lines of force in the other direc- 
tion, which is perpendicular to the direction of motion. If the 
motion of the electric line is parallel to its length, there w^ill be 
no magnetic field produced. From this point of view% what 
takes place in the medium is the cause of what takes place in 
conductors. The energy in the former (in the case we are con- 
sidering) appears in the latter as heat. 

132. Mechanism of Radiation from a Simple Oscillator. — Now 
consider what takes place when the discharge is oscillatory in- 
stead of in one direction. To fix our ideas, let us take the case 
of the simple Hertzian oscillator, the electrostatic field of which, 
before the gap becomes conducting, is shown in Fig. 158-i.® ( The 
field to the left is shown by dotted lines, in order to be able to 
keep track of each line clearly in its motion as shown in the 
following figures.) When a spark passes and the gap becomes 
conducting, the straight electric line of force represented by the 
straight line connecting the gap terminals vanishes and those 
from each side begin to move up under the unbalanced sidewise 
pressure as before. Here, however, when the ends of the first 
curved line to the right of the gap in Fig. 1.58-i reach the gap. 
we must suppose that it has sufficient momentum so that the 
ends cross and the middle portion travels across the gap. 
After t^^ o lines have done this, the state of things is as repre- 
sented in Fig. 1.58-ii. There will soon come a different state of 
things, however, owing to the shape of the lines. When the 

* See S. G. Starling. Electricity and Magnetism for Advanced Stu- 
dents, 2d ed. (1916), pp. 423-429, from which Fig. 158 is taken. 



ends get to the gap before the middle portion, as shown in Fig. 
158-iii, they will cross as before, and soon thereafter we will 
have the loop formed as in Fig. 158-iv. Now, at some timy as 
the ends continue to go up, this loop will break, forming two 
parts m and n, as shown in Fig. 158-v. This is because at that 
moment the angle of intersection becomes so acute that each 
part of the line will be moving parallel to its length, in which 
case neither half will have any magnetic field and, consequently, 
no momentum to carry them by each other. The process goes 
on as shown in Figs. 158-vi, 158-vii, and 15S-viii, the last of which 
shows the state of things w^hen one half oscillation has been com- 
pleted and the charges on the oscillator have been reversed in 
sign. A cylindrical sheet of lines of force has then been de- 
tached from the oscillator and is traveling outward. At this 


r^a. 135 

ElecThic field of a 
HerTjiarv OjcilUtordt 
different nvomeftTa duriiKO 
<a Kdilf cycle 

' moment those lines left attached to the oscillator have been 
stretched as far as their momentum can carry them, and they 
begin to contract again and repeat the process, provided the 
gap is still conducting. In the next half wave length another 
cylindrical sheet of lines of force will be snapped off, so to 
speak, and the process will continue until the energj^ lost as 
heat in the oscillator has exhausted the supply of lines which 
remain attached to it. These cylindrical sheets, as they spread 
out, become more and more nearly plane, the plane being per- 
pendicular to the motion away from the oscillator. During the 



process shown in Figs. 158-ii to 158-vii — tliat is, while the current 
in the oscillator is flowing upw^ard — the motion of the electric 
lines of force generate magnetic lines (not shown), which form 
circles around the oscillator running into the paper to the right 
and coming out on the left. These magnetic lines vanish at any 
point, when the electric lines of the attached field come to rest 
as in Figs. ]58-i or 158-viii. but continue with the moving electric 
lines of the radiated cylindrical sheet. When the cylindrical 





Fig. i39 Electric and JTlagnetic 
Fields of a Vertical Wire Ffntenna. 

sheets have moved so far that they can be considered practically 
as planes, then the magnetic lines also lie in these planes, but 
perpendicular to the electric lines and to the direction of motion. 
In the case of a simple vertical antenna, the mechanism of 
radiation is quite similar. In this case, however, since the 
lower end of the antenna is earthed, only the upper halves of 
tlie waves shown in Figs. 158-i to 158-viii are produced, so that 
the field looks like that shown in Fig. 159, where the electric 
lines are shown in elevation and the magnetic lines in plan, 
while in between is shown the wave form common to both. At 



any one point in space the lines approach and separate like 
a bellows. When the wave has progressed so far that the lines 
can be regarded as sections of planes, the state of things will 
be as shown in Fig. 160 for the electric lines, while the same 
figure will also represent the magnetic lines if rotated through 
90° about the line ox. Where the surface over which the waves 
travel is not a perfect conductor, the ends of the lines will be 
as shown in Fig. 161. 

The same method of picturing the process of wave production 
applies to other forms of radiating systems of either the open 
antenna or the closed coil type. (See Sec. 151, p. 330.) In all 


I I rill" I • 


1 1 III 1 1 



DiatorTion oj' Llectric Lines of Force in a 
Plane v\/Ave TnAvaliiiTt over<in im|>erfectly 
CowducTir^ sur^ce 


E.l«ctri<= Lines OJ Force inA 

E-leclnc. lines c(f Force Arriviryk, aI" A 
VerTioAl AnTennA 

kinds, loops are formed and detached in the same general way. 
In some of them the distribution of the lines of force is such as 
to favor the production of more such loops than in others ; this 
means that such an antenna will be a better radiator than the 

133. Action in Receiving. — The mechanism of the reception of 
waves by an antenna can be followed through in terms of the lines 
of force in an analogous manner. Thus, suppose the antenna to 
be located with respect to the incoming wave train as shown 
in Fig. 162. Then the upper ends of the lines as they arrive 
travel down the antenna, as shown in the dotted lines, and give 
rise to moving charges of electricity in the antenna, or the 
receiving action can be thought of in another way. As the ad- 
vancing waves sweep across the receiving antenna the electric 


field intensity along the antenna alternates in value. This is 
equivalent to an alternating voltage between the top of the 
antenna and the ground. A still different way of looking at 
tlie receiving action depends upon the principle that an enif. 
is induced in a conductor whenever there is relative motion 
between the conductor and a magnetic field. The moving wave 
has a magnetic field which sweeps past the antenna, and thus 
there is relative motion between the antenna and this mag- 
netic field, which results in an emf. in the antenna. This emf. 
is what causes the received current in the antenna. 

The reception of electromagnetic waves in a closed coil used 
in place of an antenna can be explained by the same prin- 
ciples. The explanation is somewhat difficult because of the 
differences of phase between those currents in different parts 
of the coil. For such antennas it is more convenient to think 
of the current as produced by the changing magnetic flux 
through the coil, due to the alternations of the magnetic fiehi 
associated with the wave. Either way of looking at it leads to 
the same result. (See Section 151, page 330.) 

D. Transmission Formulas. 

134. Statement of Formulas. — When the general ideas of wave 
production and reception discussed above are put into exact 
mathematical language, it is possible to deduce certain prac- 
tically useful formulas connecting the currents in the sending 
and receiving antennas, their heights, resistances, and distance 
apart. While it is beyond the scope of this book to derive them, 
they are given without proof to aid the student in gaining an 
idea of the magnitude of the effects to be expected at various 
di'Stances and with different types of antennas. In the for- 
mulas which follow h stands for the height of an antenna or 
coil, I for current, X for wave length, d for the distance apart of 
the two antennas or coil aerials, while the subscripts s and r 
refer to the sending and receiving ends, respectively. R stands 
for the resistance of the receiving circuit. All lengths are sup- 
nosed to be in meters. 

If the waves are sent out by a simple flat top antenna and re- 
ceived on a similar one, we have 

'iSShghj.Ig ,„„> 


If the waves* are sent out by a simple antenna and received on 
a coil, we have 

^'~ RX'd ^^^^ 

where h is the length of the receiving coil and Nr the number 
of turns of wire with which it is wound. 

If the waves are sent out by a coil and received on a simple 
antenna, we have 

. l\Mh±KNJ. 



where h is the length of the sending coil and Na the number of 
turns of wire with which it is wound. 

If the waves are sent out by a coil and received on a similar 
one, we have 

The above formulas are for transmission through free space, 
and do not take into consideration the diminution of the wave 
intensity by absorption of the radiated energy in the surface 
over which the wave travels. The absorption effect can be taken 
into account by multiplying the values of received current 
obtained from any of the above formulas by the factor 

^-0.000047 _A^ 

where d is the distance in meters, \ is in meters, and e 
is equal to 2.718. This correction factor as computed from this 
formula is intended to apply to daytime transmission over sea 
w^ater. It can be neglected in short-distance work. Thus, 
at wave lengths of about 1000 meters this correction can be 
neglected at distances less than 100 miles, but at considerable 
distances becomes much more important. For transmission 
over land the value of this correction factor will be modified 
according to the nature of the land. If it is night in all or part 
of the territory over which the waves travel the received current 
is somewhat greater. 

These formulas were developed by J. H. Bellinger and first 
published in Radio Transmission Formulas, a confidential 
paper of July, 1917. They are given in Bureau of Standards 


Scientific Paper No. 354, Principles of Radio Transmission and 
Reception with Antenna and Coil Aerials, by J. H. Bellinger, 
June 18, 1919. 

The formula (83) given above for transmission from a simple 
flat-top antenna to a similar antenna is the theoretical formula 
for a Hertzian oscillator having its length the actual height, /is, 
of the antenna above ground. For an antenna over a good con- 
ducting surface there is probably a considerable image effect, 
tending to increase the value of /is, but there are other factors 
which tend to reduce it ; hence the formula is a practical approx- 
imation to ordinary conditions. Austin's formula, which has 
been much used, assumes the existence of a perfectly conducting 
surface but defines hs not as the actual height, but as the 
" effective height " of the antenna. If the ground is assumed 
to be a perfect conductor, the antenna and its image can be 
considered to form a hypothetical oscillator of a length equal 
to twice the height of the antenna to its center of capacity. 
It is found in many cases that the effective height is about 
half the total height, and seldom approaches the full value. 
The effective height depends on how good a conducting sur- 
face there is under the antenna, and is greater for a good 
conducting surface. Dr. Austin has also published formulas 
for the other three cases, in which coil antennas are used, 
which yield values of received current twice the values which 
are obtained from equations (83), (84), (85), (86). given 
above. Dr. Austin has published his formulas, together with 
experimentally observed values, in the " Proceedings of the 
Institute of Radio Engineers," vol. 8, pages 416-420, October, 
1920. Transmission formulas are also discussed by G. W. O. 
Howe, Radio Review, vol. 1, page 598, September. 1920. 

135. Examples of Use. — To illustrate the use of the formulas 
suppose it is desired to know how much current must be put 
into a plain antenna 20 meters high sending a 300-meter wave, 
in order that the current in a similar antenna 50 km. away 
shall be detectable easily with a crystal detector (that is, shall 
be about tjj.ttf? amp. ) , the resistance of the receiving antenna 
being 10 ohms. 

Solving the first equation for Is, we have : 

J. RXdl, 10x300X50,OOOXtwo7 1 • * , 

^^-iSSKhr 188X20X20 ^J^^V- approximately. 


As another example, suppose that the receiving antenna, in 
the first example, is replaced by a square coil of 2 ohms resis- 
tance, having sides 2 meters long and wound with 10 turns of 
wire. If the sending current is i amp. as before, what will be 
the current in the receiving coil? Using the second formula 

1184 K K h ^r J3 _ 1184X20X2X2X10X^ _2.1 ^mneres 
'~ R\^d 2X300X300X50,000 lo^ ^ 

For a current of this size it would be best to use a simple elec- 
tron tube receiver instead of a crystal detector. 

As a third example, suppose the sending aerial to consist of 
a single square turn of wire 10 meters on a side, in which the 
current is i amp. at X=1000 meters. With how many turns 
should a square coil 2 meters on a side and having a resis- 
tance of 5 ohms be wound to receive at a distance of 50 km., if 

an electron tube which can detect a current of j^ ampere is 

used ? Solving the fourth equation for Nj. we have 
RX^dl, _ 5X10^X5X10^X1/10^ _ 

136. General Deductions. — From the formulas certain general 
conclusions can be drawn. Thus since \ appears in the de- 
nominator, it follows that, for given heights of antenna, send- 
ing current, receiver resistance, and distance apart, there will 
be more current in the receiver, the shorter the wave length 
used. On the other hand, there is more absorption of short 
waves than long ones, as was stated when we were considering 
the modifications that free waves undergo (Sec. 129). This 
effect is taken account of in the correction factor to be used 
for large distances. In this factor, X enters in such a way as 
to make the received current less when the wave length is 
short than when it is long. Hence, in general, we conclude 
that to get the greatest possible received current, we should use 
short waves for short distances and long waves for long dis- 

It may be seen from the formulas that, for simple antennas, the 
received current (for a given wave length, sending current, re- 
ceiver resistance, and distance apart) is greater, the greater 
the heights of the antennas. In the case of coil aerials under the 
same conditions, the received current is greater the larger the 
areas and the number of turns of the coils. For the dimensions 
actually used, antennas are much more effective radiators and 



receivers than closed coils. In order to secure the same radia- 
tion or received current with a closed coil as with an antenna, 
other conditions being the same, its dimensions must be made 
nearly as great as the antenna height. However, it is often pos- 

FlO. KiS 

PlQ. IC'-A 

> ' . '. \ : / 

■Sim Isle -^orm of dPiTennA 

Umbrelld. tyt^e of Antenna 

V. Ant«rinA 

sible to put more current into a transmitting coil than into the 
corresponding antenna, and also the resistance of a receiving 
coil is usually smaller than that of the corresponding receiving 
antenna. Hence the coil can be a smaller structure than the 

53904° — 22 20 


The coil has some other advantages. For a given power input 
in the transmitter, the coil aerial is not at quite such a disad- 
vantage with the ordinary antenna as the formulas show, be- 
cause a larger fraction of the radiation is sent out in the direc- 
tion desired. As a receiver, the coil has the very great 
advantage that the direction of the waves it receives can be 
determined. These points are discussed further in Sections 151- 

E. Devices for Radiating and Receiving Waves. 

137. Description of the Antenna. — In radio communication it 
is necessary to have a device to radiate electric waves and a 
device to receive electric waves. Devices used for this purpose 
are called antennas. Often the same antenna is used both to 
radiate and receive. 

There are two general classes of antennas, those which act 
primarily as electrical condensers and those which act pri- 
marily as electrical inductances. The first type is usually 
referred to simply as an " antenna." The second type is 
usually referred to as a " coil antenna," " coil aerial," " loop," or, 
when used for a particular purpose, as a " direction finder." We 
will first consider antennas of the first type. Coil antennas are 
discussed in Sections 151-152. 

A simple antenna of the condenser type would consist simply 
of two parallel metal plates, separated, as shown in Fig. 157. 
The energy radiated or absorbed by an antenna of the con- 
denser type depends on its capacity, and to form an antenna of 
large capacity two metal plates would have to be so large as to 
be very expensive and cumbersome. 

Instead of using two parallel metal plates, it would be pos- 
sible to form a condenser consisting of one metal plate sus- 
pended over and parallel to the ground, providing the surface 
of the ground is appreciably conducting. Such an antenna is 
shown in Fig. 163. The plate P is supported above the earth 
and insulated from it, except for the connection through the 
wire W, called the " lead-in wire," or " lead-in." The plate and 
the conducting surface of the earth form the two plates of a 
condenser, the air between them furnishing the dielectric. The 
apparatus used for receiving is introduced into the lead-in, 
between the plate and the ground. When radio waves reach 


an antenna they set up an alternating emf. between the wires 
and the ground. When an alternating emf. is introduced into 
the wire, charging currents flow into and out of P and the 
earth, the dielectric being strained first in one direction and 
then in the other. As has been explained in the previous chap- 
ter, these strains are equivalent to displacement currents of 
electricity through the dielectric, which serves to complete the 
circuit. A region in which the dielectric is undergoing alternat- 
ing strains is the starting point of electric waves. The larger 
the plate and the higher it is raised from the earth, the greater 
the amount of space in which this strained condition exists, 
and the more powerful the waves which are radiated. 

However, in order to construct with a given amount of metal 
an antenna having the greatest possible capacity, the metal 
should not be used in the form of a single plate. A much more 
efficient form consists of a number of parallel wires. The 
antennas found in practice usually consist of arrangements of 
wires. A single vertical wire is, for its size, the best radiator, 
but it has to be made extremely long in order to get sufficient 
capacity for long wave or long distance work (see Sec. 141). 
Antennas consisting of horizontal or inclined wires are, how- 
ever, also very satisfactory. Any arrangement of wires which 
will constitute one plate of a condenser may be used, although 
some arrangements will radiate and receive much better than 

An investigation has been made at the Bureau of Standards 
of the use for reception of a condenser antenna consisting of 
two parallel pieces of metal screen a few feet apart.^ The 
amount of energy absorbed by such an antenna is necessarily 
small, but for some purposes, when used with sensitive receiv- 
ing equipment, it has advantages. 

A satisfactory antenna can also be constructed, using a suit- 
able arrangement of wires for the upper plate of the condenser 
and using for the lower plate a number of parallel wires ele- 
vated a few feet from the earth and insulated from the earth. 
No connection is then made to the earth itself. The wires 
forming the lower plate of the condenser are then called a 

" counterpoise antenna " or simply a " counterpoise." 

, — 

^ See Wireless Age, 8, pp. 11-14, April, 1921. 



In reception electric waves reaching an antenna set up an 
alternating emf . between the wires forming the upper plate of the 
condenser, and the ground or other lower plate of the condenser. 
The longer and higher the wires forming the antenna the 
greater the emf. produced. As a result of this emf. an alter- 
nating current will flow in the antenna wires. The energy of 
the current is absorbed from the passing wave, just as some of 
the energy of a water wave is used up in causing vibrations in 
a slender reed which stands in its way. 


138. Different Types. — An antenna consisting of horizontal 
parallel wires supported between two masts and insulated 
therefrom is common. This is a standard form for ship sta- 
tions. If the lead-in wires are attached at the end of the hori- 
zontal wires (Fig. 166) the antenna is said to be of the in- 
verted L type. If the lead-in wires are attached at the center 
of the horizontal wires, the antenna is said to be of the T 
type. Both of these types are found at many land stations, 
including amateur stations. The wires are kept apart by 
" spreaders," which may be of wood. These two types are often 
referred tc as " flat-top " antennas. 

The V type of antenna (Fig. 167) consists of two sets of hori- 
zontal or slightly inclined wires supported by three masts, so 



that the horizontal portions form an angle. The V type is used to 
some extent in militai^ work, but is not much used elsewhere. 

The " fan " or " harp " antenna consists of a number of wires 
radiating upwards from a common terminal to various points 
on a supporting wire to which they are connected. ( Fig. 167-A. ) 
The supporting wire is insulated at each end from the tower 
or other support. Practical advantages of the fan type are 
that there are only two in- 
sulators, so that leakage is 
small, and that the me- 
chanical strain to be car- 
ried by the supports is com- 
paratively small. 

The " cage " type of an- 
tenna IS used to a consider- 
able extent, particularly on 
ships. (Fig. 167-B.) A 
number of parallel wires, 
often six or eight, are sup- 
ported from a single point 
and are kept apart by star- 
shaped separators which 
may be of wood, or by 
hoops. One advantage of 
the cage type for military 
purposes is that if one or 
two wires are shot away 
the antenna can still be 

For transmission over short distances a very simple antenna' 
may be used, such as, for example, a single wire supported be- 
tween two stakes at a height of only a few feet from the 
ground. In some cases a long insulated wire may be laid upon 
the ground or in a shallow trench, forming a " ground antenna." 
(See Sec. 150a.) For receiving stations equipped with good 
electron tube amplifiers (see Chapter 6) very simple antennas 
may be employed, even for long-distance work, such as a single 
suspended wire, a ground antenna, or a coil antenna. (See 
Sec. 151.) 

The umbrella type of antenna, Fig. 164, consists of a number 
of wires which diverge from the top of a mast, and are attached 

FIG. 167-B 



to anchors in the ground through insulators, A, as shown in the 
figure. Lead-in wires L are brought down from the junction of 
the wires B to the apparatus. 

For high-power stations a type called the " multiple-tuned 
antenna " is sometimes used ; this is described briefly in Sec- 
tion 143. 

139. Current and Voltage Distribution in an Antenna. — When 
an emf. is introduced into an antenna, a charging current flows 
in the wires as was described in the ideal case of Fig. 163. If 
we attempt to form a picture of this process in the wire antenna, 
we must remember that every inch of the wire forms a little 
condenser, with the earth acting as the other plate. The an- 
tenna is said to have a distributed capacity. 

As the electricity flows from the bottom of the antenna, some 
of it accumulates on each portion A of the wire, causing a dis- 
placement current through the dielectric to earth, as shown in 


DisjsldcemenT cyrrenTs 
from An antenrvA 


FlQ no A'^l.'=>AiY of AnttnnA A 
V lb r<iti 1^ .strlni, . E.ff ect 
^ ofeArfKin^. ^ " 

,'**v )io raoTioOjUrAe force 
^; ;Liir^ motion, sm<il I fortjE 

'y' tJo nrxoTi'on.lAr^e force 

DisTribotion o|' current 

drid Voltage alon^An 

i4o current 

Larift current 
SrrSTl volTa^e 


LAr>e correnT 

ijo current 

AB (Fig. 168). The current in the wire accordingly diminishes 
as the free end F of the antenna is approached, and becomes zero 
at that end. The current is evidently different at different parts 
of the antenna, being zero at the free end and a maximum 
where the antenna is connected to the ground (Fig. 169). This 
is in marked, contrast to the case of a direct current, which 
always has the same value at every point of the circuit. The 
difference here is brought about by the very high frequency 
of the currents. 

The voltage of the antenna, on the contrary, is zero at the 
grounded end and has a maximum value at the free end. In 
fact, the latter is the point where the most intense sparks 
can be drawn off ; therefore the insulation of the antenna from 



near-by objects and the earth must be particuhirly good at this 
point. ( In Fig. 169 the voltage and current are supposed to be 
measured by the liorizontal distance from the solid vertical 

A large capacity to earth, concentrated at any point of the 
antenna, causes a large change in the current at that part of the 
antenna. If this bunched capacity is located at the top of the 
antenna, such as is the case with a flat-topped antenna of long 
wires, with only a few vertical lead-in wires, the average cur- 
rent in the flat top portion will be large, and it increases slightly 
in strength as the charges pass down through the lead-in wire 
(picking up the charges there), hence giving a large current 
through the receiving apparatus. It is a distinct advantage to 
have as large a part of the total capacity of the antenna as 
possible at the top. 

The action of antennas is discussed in Bureau of Standards 
Circular No. 74 and in Bureau of Standards Scientific Paper 
No. 326, " Electrical Oscillations in Antennas and Inductance 
Coils," by John M. Miller. 

140. Action of the Ground — Counterpoises. — The electric oscil- 
lations in an antenna may be regarded as somewhat analogous 
to the vibrations of a string stretched between two points A 
and B and plucked at the middle, C, in Fig. 170. The stretch- 
ing forces on the string are greatest at the points A and B. 
while the portion C is under very small force. The motion of 
the string is most considerable at C, while the points A and B 
do not "move. If we regard current as similar to motion and 
voltage to force, we can see (according to statement in the 
preceding section) that the top of the antenna resembles in its 
behavior the end A {or B) of the string, while the bottom of the 
antenna corresponds to the point C of the string. 

The part played by the earth may now be understood. If we 
suppose for a moment that the antenna is disconnected from the 
ground and insulated, then the lower free end would become a 
point where the current w^ould be zero and where the variations 
of voltage would be large (corresponding to point B, Fig. 170). 
The portion where the current would be a maximum would lie 
at some elevated point. To set a string in vibration requires 
the smallest force when it is plucked at the middle. Right at 
the ends it is almost impossible to set it in vibration. Just so 
the antenna, if disconnected from earth, would be almost impos- 



sible to set in vibration if tlie emf. were applied at the bottom 
end. For successful working, the exciting apparatus would 
have to be joined to inaccessible ix)ints of the wire higher up. 
It is necessary, then, to make sure that the lower end of the 
antenna is a region where a current is large, and with a good 
ground this condition is satisfied. 

In places where the ground has poor conductivity (dry, rocky 
soil, with ground water at some considerable depth) it becomes 
difficult to satisfy the above condition. In such cases a " coun- 
terpoise antenna " or " earth capacity " must be used. The 
counterpoise is another antenna of suitable type, supported a 
few feet above the ground, and. insulated from it. The station 
apparatus is connected to the regular antenna and the counter- 



rrincif)le oy the. 

FlCj |-T2^ 




Wave length 


Fig n3 



Aii Ub 

V^Pidtron of the Illoatratin^ Method 

Lffect('ve ^esiatdnee ^^ triAr^uldtion 

ofdn AntenrvA 

poise, instead of to the regular antenna and earth. The use 
of a properly designed counterpoise is often advantageous even 
where the earth has fairly good conductivity. As far as the 
antenna is concerned, the counterpoise takes the place of the 
ground. To some extent the action of a counterpoise can be 
considered as that of two condensers in series ; one antenna 
consisting of the regular antenna and the counterpoise, and the 
other consisting of the counterpoise and the more moist layers 
of the earth (TF, Fig. 171) deep below the surface. The coun- 
terpoise is usually simply a number of wires supported a few 
feet from the ground, but may be a metal screen or netting. 
The wires may be distributed radially from the foot of the an- 
tenna. The area covered by the counterpoise should preferably 
be several times as large as the area of the antenna itself, but 
in any event should be as large as the area of the antenna. 


On aircraft, a counterpoise must necessarily be used. The 
counterpoise is furnished by the metal wires of the frame- 
work, the engine, stay wires, metalized wings, etc. The an- 
tenna may consist of a long wire which trails behind the 
plane when in flight, has a weight attached to its end. and 
is wound up on a reel before landing.* With such an antenna 
the antenna is below the counterpoise, but the action is not 
different from the ordinary antenna and counterpoise systems. 
The trailing wire antenna is inconvenient in some respects. 
In many cases it is found more convenient on aircraft to use a 
coil antenna, which may be wound on the wings of a plane, or 
may be wound on a small frame and installed aft in the plane 
(see Sec. 152). 

F. Antenna Characteristics. 

The behavior of an antenna depends upon its capacity, in- 
ductance, and effective resistance, just as is the case with any 
oscillating circuit. The capacity and inductance determine the 
length of the radiated waves (see Sec. 116); the resistance 
determines the damping. 

141. Capacity. — The energy which can be given to a condenser, 
when it is charged to a voltage E, is equal to one-half the 
capacity C, multiplied by the square of the voltage. The 
energy which is supplied to an antenna each second when it 
receives .A' charges per second is, therefore (as given in Sec. 

p=^ CE-N. 

We may. evidently, increase the supply of power to an antenna 
by increasing the number of charges per second, or by raising 
the voltage. 

It is not practicable to raise 'the rate of charging beyond 
about 1,000 to 1,500 sparks per second. The voltage on the 
antenna can not be made greater than about 50,000 volts with- 
out loss of power through leakage and brush discharges. The 
only remaining factor which can be varied is C in the above 
formula ; therefore, a high power sending antenna must have a 

^ See .T. M. Cork. Airplane Antenna Constants, Bureau of Standards 
Scientific Paper No. .341 ; 1919. 


large capacity. Large capacity means many wires of great 
length ; that is, a large and costly structure. 

The capacity of a single wire parallel to the ground can be 
calculated approximately, as also the capacity of certain simple 
arrangements of parallel wires (see Circular 74, pp. 237-242). 
Even in the simplest cases, however, the presence of houses, 
trees, and other neighboring objects, and the difficulty of allow- 
ing for the lead-in wire, makes any precise calculation impos- 
sible. It should be noted, however, that the capacity of a wire 
is proportional to its length. The capacity of two wires near 
together is less than the sum of their capacities, and, in general, 
although each added wire adds something to the capacity, it 
adds much less than the capacity it would have alone in the 
same position. As an indication of what values of antenna ca- 
pacity may be expected, the following values may be cited : 

Airplane and small amateur antennas, 0.0002 to 0.0005 micro- 

Ship antennas, 0.0007 to 0.0015 microfarad. 
Large laud station antennas, 0.005 to 0.015 microfarad. 
That is, in spite of their size and extent, antennas do not 
possess greater capacity than is found in ordinary variable air 
condensers (see Sec. 32 and Sec. 184). 

The following formula has been found to give fairly accurate 
values for the capacity of a flat-top antenna under conditions 
met in practice: 
Taking C=capacity of antenna, micromicrofarads 

.4= Area of flat top of antenna in square meters (tl^e 
triangular, or quadrilateral area, or area of other 
shape, inclosed by the bounding wires of the 
antenna ) 
7i= average value of actual height of antenna above 
ground, in meters (for horizontal top, /i=actual 
height above surface of ground) 
the formula may be written 

C=40V3+8.85 ^- 

For a very long antenna, having a length I more than eight 
times the breadth of b, the above formula must be multiplied 
by an elongation factor 



For values of capacity computed by this formula the height 
is not so important as it is for values of capacity computed ac- 
cording to some other formulas which have been suggested. 
Values of capacity computed according to the formula just 
given have been found to agree fairly well with measurements 
made on actual antennas. 

This formula was published by L. W. Austin, Journal Wash- 
ington Academy Sciences, volume 9, page 393, August 19, 1919; 
Proceedings Institute Radio Engineers, volume 8, page 164, 
April, 1920; and has been discussed by G. W. O. Howe, Radio 
Review, volume 1, page 710, November, 1920. 

142. Inductance. — Although principal stress has been laid upon 
the conception of the antenna as a condenser, the inductance 
which its wires necessarily possess is of equal importance in 
determining the wave length of the radiated waves. The 
antenna is, in fact, an oscillating circuit, and as such the 
wave length or frequency of free oscillation depends upon the 
product of the inductance and capacity. See formula (79), 
Section 116. 

The inductance in general is not large — 50 to 100 microhenries 
is a common range of values — but larger capacity is necessarily 
associated with larger inductance, so that high-power antennas 
are naturally long- wave antennas. Methods for measuring in- 
ductance and capacity of antennas are described in Section 171, 
page 392, and in Circular 74 of the Bureau of Standards, pages 
79 to 86, and 98. The relations between the wave length of an 
antenna, and its capacity and inductance, are discussed in Cir- 
cular 74, page 79. 

148. Resistance. — The wires of an antenna offer resistance to 
the current, which is greater for the high-frequency antenna 
current than it would be for a steady current, on account of the 
skin effect (see Sec. 117). In addition to this, the radiation of 
energy in waves causes a further increase in the apparent 
resistance of the antenna. The "effective resistance of the 
antenna " is defined as the quotient of the power given to the 
antenna by the square of the antenna current. That is, if R is 
the effective resistance, the total power put into the antenna is 
RP, where / is measured at the base of the antenna. The 
effective resistance is different for different frequencies, as is 
shown below. 


The total power is dissipated in the following ways: (1) As 
heat in the antenna wires and earth connection, (2) brush dis- 
charge, (3) leakage over or through insulators, (4) heat in the 
dielectric surrounding the antenna, and in any condensers that 
are in the antenna circuit, and (5) radiated waves. Part of 
(5) will also be turned into useless heat by Inducing eddy cur- 
rents in near-by conductors, such as guy wires or metal masts. 
If R'P represents all the power except that radiated, and 
R"P represents the power radiated as waves, then it is evident 
that R'P+R"P=R I\ or R'-\-R"=R, the effective resistance. 
R" is called the " radiation resistance." It might be defined as 
that resistance which, if placed at the base of the antenna, 
would cause as great a dissipation of energy as the energj^ radi- 
ated in waves. It will be different at different frequencies. It 
gives an idea of the radiating power of the antenna for each 
ampere of antenna current. 

When the effective resistance of an antenna is measured at a 
number of frequencies and the results are plotted, a curve is ob- 
tained like curve 4, Fig. 172, page 310. The shaps of the curve is 
explained by considering the laws according to which the differ- 
ent kinds of resistance in the antenna vary with the wave length. 
The radiation resistance decreases as the wave length increases, 
the relation being that the radiation resistance is inversely pro- 
portional to the square of the wave length. Such a variation is 
represented by curve 1, Fig. 172, page 310. The resistance of 
the conductors and earth connection is nearly constant with 
different wave lengths, curve 2. The dielectric resistance in- 
creases nearly as the wave length, curve 3. Curve 4 is the sum 
of curves 1, 2, 3. If the losses in the dielectric are very small, 
the curve does not have a minimum, as at A, but becomes hori- 
zontal at the right end. If these are negligible, the curve merely 
falls toward a limiting value. 

To reduce the dielectric losses, no portion of the antenna 
should be near buildings or trees. To reduce eddy current 
losses, care should be taken to have the antenna a reasonable 
distance from guy wires, and especially large masses of metiil. 
Guy wires may be cut up and insulated in sections. On ship- 
board, induced currents are produced in iron stacks and guy 
wires near the antenna, and in cases where the frequency of 
the waves agrees with the natural frequency of oscillation of 



these metal objects, considerable power losses may result. These 
show themselves, when they are present, as hiunps on the ex- 
perimental curve 4, Fig. 172, page 310. at the frequencies in 
question. Reference may also be made to Bureau of Standards 
Scientific Paper No. 269, '* Effect of Imperfect Dielectrics in the 
Field of a Radiotelegraphic Antenna," by John M. Miller. 

The effective resistance of an antenna is often as high as 20 
to 30 ohms at the fundamental wave length. The minimum 
value may be 5 to 10 ohms for a land station and as low as 2 
ohms for a ship station. 










1 1 1 1 ' 

, FiqJ72-A. Graphical JYlethod 
of Determininq the Funda 
mental Wave Length of an . 







■ ■ j 


y- ■< 

! £ 

>■■ ■ 7 

d 1 

1 I 


Turns of Ir)ductance Coil 

Methods for the measurement of the capacity, inductance, and 
resistance of an antenna are described in Section 171, page 392. 

At high-power stations employing high-frequency alternators 
an antenna of comparatively small effective resistance has 
been secured by the use of a " multiple-tuned antenna." At 
such stations the antenna may be a mile or more in length and 
may constitute a considerable part of the total cost of the 
station equipment. The multiple-tuned antenna is a long an- 
tenna which is grounded at several points along its length 
through loading inductances, by means of which the individual 
sections are tuned to the wave length which it is desired to 
radiate. (See Fig. 173-A.) A high-frequency alternator or 
other transmitting apparatus may be inserted, as shown at A. 



This is equivalent to connecting several antennas in parallel; 
the radiation resistance remains the same as for the antenna 
connected in the ordinary way, but the actual resistance of the 
ground connections of the whole antennn is the resistance of a 
single ground connection divided by the number of ground 
connections. The antenna at the high-frequency alternator sta- 
tion at New Brunswick, N. J., is about 1 mile long, and has 
been grounded at five intermediate equidistant points. The 
antenna so connected is equivalent to six independent radi- 
ators, and the total resistance of the antenna has dropped from 
3.8 ohms with the ordinarj^ system of grounding to 0.5 ohm 
with the multiple ground at a wave length of 13,600 meters. 
The ground resistance has been reduced from about 2 ohms to 


0.33 ohm. Antennas of this type have so far been used only 
for high-power work, and a detailed description will not be 
given here. The multiple-tuned antenna is well adapted for use 
with the high-frequency alternator, because in this case the 
radiated wave length of a given alternator dei>ends only on its 
speed and not on the antenna. The multiple-tuned antenna does 
not, however, seem to be so well adapted to tube and arc trans- 
mitters and not at all to spark transmitters, because in such 
transmitters the radiated wave length depends on the antenna. 
For further information the reader may consult papers by 
E, F. W, Alexanderson, General Electric Review, volume 23, 
page 794, and E. E. Bucher, General Electric Review, volume 
23, page 813, October, 1920. 

144. Wave Length and its Measurement. — The wave length of 
tlie waves emitted by an antenna, when no added inductance or 
capacity is inserted in. the antenna circuit, is known as its 
" fundamental wave length." By putting inductance coils 


("loading coils") in the antenna circuit, longer waves may be 
radiated, while on the contrary, condensers put in series with 
the antenna enable it to produce shorter waves than the funda- 
mental. The use of a series condenser is avoided where possible, 
since it has the effect of decreasing the total capacity of the 
antenna circuit (Condensers in Series, Sec. 35) and thereby 
diminishing the amount of power which can be given to the 
antenna. The addition of some inductance has a beneficial 
effect, since the decrement of the antenna is thereby lessened 
and a sharper wave results. It is not advisable to load the 
antenna with a very great inductance, however, as it is not 
an efficient radiator of waves. The waves emitted are very 
nmch longer than the fundamental wave length. As a general 
rule small sending stations, for short ranges, work best on short 
waves, and long-distance stations on long waves. Long waves 
have the advantage for long-distance work that they are not 
absorbed in traveling long distances to the extent that short 
waves are. 

The United States radio laws at present provide that every 
commercial radio station shall be required to designate a cer- 
tain definite wave length as its normal transmitting and receiv- 
ing wave length, and that this wave length must not exceed 
600 meters or must be longer than 1,600 meters. Ship stations 
must be equipped to transmit on either 3(X) or 600 meters. 
Amateur stations must not transmit on a wave length exceeding 
200 meters. It is probable that the radio laws will be revised 
in the immediate future. For authoritative information re- 
garding current radio laws and regulations inquiry should be 
made of the Bureau of Navigation, Department of Commerce, 
Washington, D. C. See also Appendix 6. 

Communication with ships is usually carried on with a wave 
length of about 600 meters. Radio compass stations on shore 
operate on 800 meters, and radio beacon stations on shore, 
which transmit to ships to enable the navigator on the ship to 
determine its position, usually operate on 1.000 meters. 
Most high-power stations, such as those for transatlantic work, 
operate on a wave length of at least 2,500 meters, usually con- 
siderably more. The Annapolis station, for instance, operates 
on about 16,900 meters and the New Brunswick station on about 
13,600 meters. 


Measurement of Antenna Ware Length. — For a simple vertical 
wire grounded antenna the fundamental wave length is slightly 
greater than four times the length of the wire. The constant 
is often used as 4.2, and applies approximately also to flat top 
antennas (L or T types) with vertical lead-in wire, the total 
length being measured from the transmitting apparatus up the 
lead-in wire and over to the end of the flat top. It is usually 
easier, and certainly more accurate, to measure the wave length 
radiated from an antenna directly by the use of a wavemeter 
(Sec. 112). The wavemeter coil needs merely to be brought 
somewhere near the antenna or lead-in wire and the condenser 
of the wavemeter adjusted to give maximum current in the 
wavemeter indicator. The wave length corresponding to the 
wavemeter setting is then the length of the waves radiated by 
the antenna. The " fundamental " wave length of the antenna 
may be determined by gradually decreasing the number of turns 
in the loading coil, measuring the wave length for each setting 
of the loading coil, and plotting a curve showing the wave length 
corresponding to the various numbers of turns of the loading 
coil, as shown in Fig. 172-A. The " fundamental " is the wave 
length corresponding to zero turns, and corresponds to the point 
where the extension of the curve cuts the wave length axis. 

The amateur is required by law to transmit on a wave length 
not exceeding 200 meters and is interested to know the kind of 
antenna to use. It is impossible to give an exact rule for con- 
structing an antenna for a particular wave length, because 
many local conditions peculiar to each case must receive con- 
sideration. An approximate rule which will be found con- 
venient in constructing an antenna which is to transmit on a 
ware length not exceeding 200 meters is that the over-all 
length of the circuit from the ground connection through the 
entire path which the current follows to the end of the antenna 
must not exceed 120 feet. This distance, 120 feet, includes the 
distance from ground up the ground lead to the antenna switch, 
from the antenna switch to the oscillation transformer and back 
to the antenna switch, through the antenna lead-in to the 
antenna top, and along the antenna top to its end. This ap- 
proximate rule applies to the various types of antennas ordi- 
narily found at amateur stations, including inverted L, T. and 
fans. In the case of an antenna for which the lead-in is taken 


off the antenna top at an intermediate point, as in a T antenna, 
the distance along the antenna top should be measured to the 
most distant end of the top, if the lead-in is not connected at 
the middle of the top. If an antenna is constructed in which 
the distance measured as described does not exceed 120 feet, it 
is probable that with suitable transmitting apparatus and no 
loading it will be possible to transmit on less than 200 meters, 
but if loading inductances are used or equivalent changes made 
in the transmitting apparatus the emitted wave length may, of 
course, considerably exceed 200 meters. 

145. Harmonics of Wave Length. — A simple radio circuit has a 
reactance equal to zero at a single frequency, namely, the reso- 
nance frequency, and the maximum current possible with the 
given emf. will then flow. This result is strictly true only when 
the capacity and inductance are concentrated at definite points 
of the circuit. In an antenna, however, the inductance and 
capacity are distributed, and it is found that a maximum of cur- 
rent is obtained for a whole series of different frequencies or 
wave lengths. 

What is called the " fundamental frequency " is the lowest 
frequency for which the current attains a maximum when not 
loaded with either capacity or inductance. Denoting this by f, 
there are in the same antenna other reasonance frequencies 3/", 
5/, If, etc., called the " harmonic frequencies " of the antenna^ 
With the usual methods of producing current in an antenna it 
radiates principally waves of its fundamental frequency alone ; 
free oscillations of the harmonic wave lengths are almost en- 
tirely lacking. However, when emfs. having the harmonic fre- 
quencies are applied, vigorous oscillations of those frequencies 
may be set up. (See also Bureau of Standards Scientific Paper 
No. 326.) 

146. Directional Effect. — It is a familiar fact that devices for 
transmitting or receiving wave motion of any kind, which are 
not symmetrical with respect to a line perpendicular to the 
plane in which the wave travels, will transmit and receive bet- 
ter in one direction than in another. Thus a resonator for 
receiving sound from a distance should be turned perpendicular 
to the direction of the source of the sound, to give the maximum 

53904° — 22 21 



A single vertical wire (Fig. 173-B) forms an antenna which 
IS entirely symmetrical for radio waves traveling horizontally, 
and such a wire has no directional effect. If for a given 
antenna fixed in a given position we plot a curve showing the 
strength of the received current received from transmitting sta- 
tions located in different directions, we will find this curve a 
very useful means of describing the directional characteristics 

of the antenna. For the single vertical 
wire the directional characteristic is 
simply a circle drawn with the foot of 
the wire as center. The electrical and 
magnetic fields radiated in transmitting 
from a vertical wire antenna are shown 
in Fig. 159, page 297. Most of the other 
types of antennas ordinarily used have 
directional properties, at least to some ex- 
tent. The inverted L antenna has a con- 
siderable directional effect. An inverted 
L antenna with a long, low top (Fig. 
]73-C), such as are often found at large 
stations, has a marked directional effect, 
as shown by the directional characteristic 
in Fig. 173-C. The length of the line 
drawn from the central point A in any 
direction indicates the strength of the 
current received from a transmitting sta- 
tion located in that direction. It will be 
noted that the inverted L transmits and 
receives best in the direction opposite to 
that in which the antenna top points. 
The multiple-tuned antenna, as shown in 
Fig. 173-A, has a considerable directional effect. Ground an- 
tennas (see Sec. 150-a) have marked directional characteristics. 
The most important type of directional antenna is, however, the 
coil antenna, described in Sections 151-152. Particular kinds of 
directional effects can be secured by combining different kinds 
of directional antennas. 

The directional properties are most often made use of for 
receiving, but are also used for transmitting. 

In transmitting, a considerable part of the energy may be 
concentrated in a particular direction by the use of a direc- 



tional antenna, and the range of a transmitting station thus 
increased and interference decreased. Directive transmission 
may also be very helpful to a ship or airplane in aiding it to 
determine its location. 

In receiving, an antenna having a marked directional char- 
acteristic, such as a coil antenna, will receive strong signals 
from a particular direction, and weaker signals from other 
directions. This is valuable in reducing interference from sta- 
tions which it is not desired to receive, since in general the 
interfering station is not likely to lie in the same direction as 
the station which it is desired to receive. 

A further and very important application of antennas with 
directional characteristics is the possibility of triangulation. If 



C, Fig. 173. page 310, is a transmitting station, and the waves 
come in to station A from a direction which makes an angle x 
with the north, while at station B waves from C arrive from 
the direction BC, which makes an angle y with the north, then 
the positions of the stations A, B, C can be calculated, provided 
only that the distance AB and the angles x and y are known. 
If C is an enemy station, it may be located by measurements of 
its direction, as observed from receiving stations A and B, 
whose positions are known. Or if C is supposed to be a light- 
house station which is radiating signals, a vessel can deter- 
mine its unknown position A, even in a fog, by observing the 
direction of C and then after sailing a known distance AB 
making similar radio observations of the direction of C from its 
new position B. The positions A and B and the ship's course 
can be worked out. Even in clear weather it is often desirable 


to have a means of checking up astronomical observations of 
the ship's position, since a small error of observation may- 
have serious consequences when a vessel is near the coast. 
For further information regarding direction finding see Sections 

G. Antenna Construction. 

147. Towers and Supports. — For land stations wooden masts 
have been much employed. For portable antennas these are made 
in sections, which fit together like a fishing rod. For liigher- 
power stations latticed metal masts are common and in some 
cases tubular metal masts in telescoping sections. Except in spe- 
cial instances, guy ropes or wires are necessary, and in some 
cases the support is sustained entirely by these. It has been 
quite generally regarded as a structural advantage to allow a 
small freedom of movement to the mast, so that it may rock 
slightly in the wind. A simple one-wire antenna may be held by 
any support that is available. When a tree is used to support 
either end, a rope should run out for some distance from the 
tree and the wire be attached to this by an insulator, so that the 
antenna wire itself may not be in or near the tree. The stand- 
ard flat-top ship antenna makes use of the ship's masts for sup- 
ports. The antenna wires are stretched between two booms or 
spreaders, from which halyards run to the masts. 

148. Insulators. — The insulation of an antenna is a matter re- 
quiring careful attention. If an insulator is defective or dirty 
or wet, the energy radiated from the antenna will be consider- 
ably reduced. Defects of insulators may be caused by breakage 
after installation or faulty manufacture, such as small cracks 
or other openings through which the insulator may absorb 
water, or nonuniformity of the material of the insulator. Dirty 
insulators are likely to be found near industrial plants, and on 
ships wet or salt-covered insulators may cause trouble. In Fig. 
174 is shown an antenna of a type often found on ships and at 
the smaller land stations, with its insulators. Porcelain is one 
of the most satisfactory materials for use in constructing in- 
sulators because of the large voltages which it will stand with- 
out failure, but it is not suitable for use under severe me- 
chanical vibration. Antenna insulators are often made of com- 
positions, such as the material called " electrose," which is made 



with a shellac binder. These insulators are made in various 
shapes, including rods, and usually have eyebolts or other metal 
pieces molded in. Insulators are also made with ribs or petti- 
coats which may extend farther than the ribs shown in Fig. 
176 ; the purpose of the ribs is to lengthen the leakage path 
which the current must follow between eyebolts and to secure 



Itiverfgd "L" Antenna , Showtnc^ In&ul&tors 

F(c5 ns 

F(Q nG 

ji'li^iiijiggal Insulator for 

C4,rryir\^ Le^d-irN Wire^ 

Etog Ti^pe StrAin Insulator. 

ThroOjR^ A Wdkll 

better insulation when the insulator is wet by collecting the 
water on the lowest points of the ribs. In the case of antennas 
for land stations, wire guys are interrupted by " strain " in- 
sulators to prevent the guy from having a natural wave length 
approximately the same as the wave length of the antenna. A 
form of nearly spherical porcelain insulator, so grooved as to 
carry the two wires lirmly without their coming in contact, is 


shown in Fig. 175. In the event of this insulator breaking, the 
wires do not part. 

Where the lead-in wires from the antenna pass through the 
walls of the house in which the sending and receiving apparatus 
is installed, special care needs to be taken to ensure good in- 
sulation. A form much used for this purpose is shown in Fig^ 
176. In the case of some large aerials, the supporting mast itself 
has to be insulated from the ground at its base. The design 
of an insulator which combines sufficient mechanical strength 
with good dielectric properties is a difficult matter. 

149. Antenna Switch. Conductors. — An antenna switch is a. 
necessity in all permanent installations. This has the function 
of disconnecting the receiving apparatus from the antenna com- 
pletely when a message is to be sent, and vice versa. The action 
of such a switch is made such that it is impossible for the 
operator to make a mistake and impress the large sending volt- 
age upon the delicate receiving apparatus. 

Every radio station should be provided with a lightning switch 
on the outside of the building by means of which the antenna 
should be grounded at all times when not in use to avoid possible 
damage from lightning. Information regarding the requirements 
made by insurance companies for lightning protection may be 
secured from the National Board of Fire Underwriters, New 
York, and from local insurance agents. See also Appendix 9, 
page 578. 

Antenna ivire. — Desirable qualities in a metal to be used for 
antenna wire are that it shall not be brittle, that it shall be 
durable when exposed to weather and other conditions met in 
service, that its weight shall not be excessive, that its cost shall 
be reasonable, and that its ohmic resistance shall be low. It is 
also sometimes important that a metal used for antenna wire 
shall possess high tensile strength ; this is obviously most im- 
portant for large antennas of long span. 

It has been pointed out in Section 117, page 263, that at high 
frequencies the flow of current in a conductor takes place 
largely near its circumference. This results in the resistance of 
a wire at radio frequencies being higher than its resistance to 
direct current or to alternating current of low frequencies, such 
as 60 cycles, and is called the " skin effect." The skin effect is 
considerably greater for wires of iron or steel or other magnetic 
material. For this reason ordinary iron or steel wires are not 
suitable for use as antenna wire. 


Hard-drawn copper wire is often used, but has the disad- 
vantage that it is brittle and kinks easily. Tinned copper wire 
is sometimes used. Soft-drawn copper wire may also be used, 
depending on the tensile strength required for the distance to 
be covered. Aluminum wire is also used, and is satisfactory if 
careful attention is given to the connections and joints, to avoid 
corrosion. An important advantage of aluminum wire is that it 
is light. This is particularly important in large antennas, which 
cover long distances. 

Iron or steel wire which has been heavily galvanized is also 
used. Since the current flows largely in the zinc coating, the 
resistance is much less than that of an ungalvanized steel wire. 
Steel wire to which a thick coating of copper has been perma- 
nently welded, is sometimes used. Information regarding the 
resistance of coated wires of this kind is given in Bureau of 
Standards Scientific Paper No. 252, " Effective Resistance and 
Inductance of Iron and Bimetallic Wires," by John M. Miller. 
The resistance losses in the coated steel wires are about the 
same as in solid copper wire, provided that the coated steel 
conductors are not too close together. 

Bare, uninsulated wires are in general use. In some cases 
the antenna wire is covered with a thin coating of enamel, whose 
purpose is to eliminate corrosion of the wire by exposure to the 
weather, smoke, or acid or other fumes. 

Solid copper or other conductor, in sizes such as No. 14, is 
often used. Stranded conductor, however, has advantages, in- 
cluding flexibility, and lower resistance at high frequencies than 
solid conductor, because of the skin effect. In the stranded 
conductor for a given weight of copper there is much more 
cross-sectional area available for carrying the current than there 
is in the solid conductor. The individual strands should, how- 
ever, always be enameled in stranded wire used for radio- 
frequency currents, or the stranded conductor may have a higher 
resistance than solid conductor of the same Aveight. 

An antenna conductor composed of seven or more strands of 
carefully enameled No. 22 copper wire is usually found to give 
good satisfaction. Antennas of unenameled solid conductor, 
which are very satisfactory on the day they are installed, after 
exposure for even a week to the weather, often show a very 
considerable increase of resistance. Phosphor-bronze stranded 
wire of seven or more strands is sometimes used, has a high 


tensile strength, but is open to tlie objections that it is rela- 
tively very expensive, and has a comparatively high ohmic 
resistance. Phosphor-bronze wire corrodes easily when exposed 
to weather, and when corroded is very likely to have higher 
resistance than a solid conductor. A silicon bronze wire is now 
being used to some extent, which does not corrode easily, has 
comparatively low ohmic resistance, high tensile strength, and 
has been found very satisfactory. For many ordinary antennas, 
hard-drawn solid copper wire, carefully enameled, will be found 
most convenient, and will give good satisfaction. 

150. Grounds and Counterpoises. — To obtain a good conducting 
ground connection is a comparatively easy matter for a ship 
station. In a steel ship a wire is attaclied to the hull of the 
ship and the good conductivity of the sea water assures an inti- 
mate connection with the ground. A usual method of grounding 
on a wooden ship propelled by steam is to connect the ground 
lead to the thrust box and depend on the propeller to make 
contact with the water. The hulls of some wooden ships are 
protected by being covered with copper sheathing, and a good, 
ground connection may be made to this sheathing. In some 
cases a ground for a wooden ship may be made by means of a 
large metal plate attached to the outside of the ship, under 

The ground connections for a land station should be designed 
with the idea of constructing one plate of a condenser of which 
the antenna is the upper plate. The area covered by the ground 
connections should be several times the area of the antenna, and 
should be laid out fairly symmetrically with respect to the an- 
tenna. The effort should be made to obtain a considerable num- 
ber of points of contact with the earth, having paths of low re- 
sistance. Metal plates buried in the earth are often used. A 
good ground system may be constructed by burying metal plates 
of the same area, symmetrically arranged around the circum- 
ference of a circle having the station as the center, and con- 
nected to the station by wires suspended a short distance above 
the earth. A good general principle to follow is that the same 
current should be carried per unit area by each buried plate. If 
this principle is not observed, as in a ground system laid out at 
random consisting of a number of ground connections of differ- 
ent impedances located at varying distances from the station, it 


may be found that the over-all resistance of the system will be 
considerably greater than the resistance of the best one of the 
ground connections used alone. A considerable number of cop- 
per wires run radially from the foot of the antenna to a distance 
considerably greater than the length of the antenna will make 
a good ground if the earth is moist. When radial wires are 
used it is often found advantageous to run the wires for a short 
distance suspended above the ground before burying them. In 
dry localities a ground connection is sometimes made to a well ; 
this may be found useful for receiving, but in general is not 
very satisfactory. In cities a ground connection may be made 
to water pipes or gas pipes. Connections to steam pipes and 
sometimes to gas pipes may be unsatisfactory because they may 
make poor contact with the ground. Connections to gas pipes 
should always be made between the meter and the street. 

Counterpoises have been briefly discussed in Section 140. The 
counterpoise should be designed with the idea of constructing 
the lower plate of a condenser of which the antenna is the upper 
plate, and should cover an area at least as great as that of the 
antenna, and preferal^ly somewhat greater. The counterpoise 
may consist of an arrangement of parallel or of radial wires, 
supported 3 or 4 feet above the surface of the ground and insu- 
lated from the ground. Metal screen may also be used, A coun- 
terpoise should be supported at as few points as possible to keep 
its resistance low. To construct an antenna system of low 
resistance it is necessary to take all precautions to keep low 
the resistance of the condenser constituting the antenna. Only 
those insulating materials should be allowed in the field of the 
counterpoise which have little dielectric power loss. Wooden 
stakes should be kept out of the field of the counterpoise, be- 
cause wood usually has a considerable power loss. Porcelain 
insulators are usually satisfactory. The counterpoise should 
be carefully insulated from any wooden stakes which support 
it by suitable insulators. If used for transmission with con- 
tinuous waves, a counterpoise should be rigidly supported so 
that it will not sway with the wind in order to prevent varia- 
tions in the transmitted wave length. 

150a. Ground Antennas. — It has been found by Kiebitz and 
many other observers that signals can be effectively received 
on an antenna consisting of a single long wire on or a short 


distance under the surface of the ground. This is called a 
ground antenna. It operates more effectively when the soil is 
wet rather than dry, and with an insulated rather than a bare 
wire. It can also be used under the surface of either fresh or 
salt water. In salt watei- it should be submerged only a short 
distance below the surface. The best results are usually ob- 
tained with wires well insulated with moisture-proof material. 

It seems on first consideration contrary to the usual explana- 
tions of radio reception that an antenna extended in a hori- 
zontal direction and on or under the ground should be acted 
upon by a radio wave. The explanation is, first, the wave front 
of an advancing radio wave is tilted, the amount of this tilt 
probably being greater just at the surface of the ground than 
at higher points ; and, second, the waves penetrate the ground 
to some extent, the amount of penetration depending upon the 
wave length and character of the ground. 

The amount of power received by a ground antenna is consid- 
erably less than that received by the usual elevated antenna. 
It is usually necessary to use amplifiers (see chapter 6) to get 
satisfactory signals. The ground antenna, however, has a num- 
ber of compensating advantages, so that for some kinds of work 
its use is desirable. It is a directional receiving device, the 
strongest signals being received when the wire extends along the 
line of direction of propagation of the waves. It is stated that 
the ground antenna does not exhibit the usual troubles during 
local thunderstorms which make an elevated antenna dangerous 
to the operator. The ground antenna also, as sometimes em- 
ployed, has a somewhat greater ratio of signal strength to strays 
than the usual elevated antenna. The use of the ground antenna 
in combination with a coil antenna has been found to be of con- 
siderable assistance in the elemination of interference and 
strays, since under proper conditions this combination forms a 
unidirectional receiving system. 

Ground antennas have been used in some experiments for 
transmitting, but there is apparently no advantage in their use 
for this purpose. 

The length of the wire which should be used as the ground 
antenna depends on the wave length of the signals to be re- 
ceived. Thus for long wave lengths longer wires should be used 
than for short wave lengths. The length of the ground antenna 


or underwater antenna which should be used for the reception of 
a particular wave length depends on the diameter of the conduc- 
tor itself and also on the nature of the dielectric material adja- 
cent to the conductor. That is, the best working wave length of 
a given wire depends on the kind of insulation used on the wire, 
whether the wire is in earth or in water, and if in earth whether 
the earth is dry or moist. It has been stated that the best work- 
ing wave length of a ground antenna is inversely proportional 
to the capacity of the wire to ground per unit length of the 
wire. That is, with a given size of wire, the thicker the insu- 
lation the longer the most effective wave length, and with a 
given thickness of insulation, the larger the wires the shorter 
the most effective working wave length. 

If it is desired that a wire buried in the ground should re- 
main in effective operation for more than a few months it is 
usually necessary to use wire insulated with at least one-fourth 
inch of good live rubber. Such construction is, of course, ex- 
pensive. For temporary work an insulated wire is sometimes 
simply laid out on the surface of the ground. 

In earth of the average range of moisture content a ground 
antenna 75 feet long may be expected to give satisfactory re- 
ception from about 150 to 500 meters. For the reception of 
long waves, as 6,000 meters to 15,000 meters, it may be neces- 
sary to use a ground antenna 1.000 or 1,500 feet long. Under 
average conditions it will be found suitable to use stranded or 
solid copper conductor, about No. 14 B. & S., with good rubber 
insulation, buried in a shallow trench from 6 to 12 inches be- 
low the surface of the ground. Under some conditions it may 
be advisable to bury a wire as deep as 24 inches. 

It has been found advantageous to place wires in fairly wet 
soil or in water, because louder signals will be usually ob- 
tained and because the best working wave length of a given wire 
will remain more nearly constant. 

With an underwater wire the signal falls off rapidly with the 
depth in salt water, but in fresh water wires have been sub- 
merged as deep as 60 feet without appreciable decrease of 

It should be noted that a gi-ound antenna can not be expected 
to give good ' results when used with a crystal detector alone 
or with a single detector tube, and that for good signals it is 


usually necessary to use several stages of amplification. (See 
Sec. 196, p. 479.) At a small receiving station with usual equip- 
ment it will usually be found more satisfactory to use the ordi- 
nary elevated antenna with good ground connection in prefer- 
ence to a gi-ound antenna. 

For further information regarding ground antenna the reader 
should consult the following papers in the Proceedings of the 
Institute of Radio Engineers : A. H. Taylor, volume 7. page 337, 
August, 1919 ; A. H. Taylor, volume 7, page 559. December, 1919 ; 
A. H. Taylor, volume 8. page 171, June, 1920; R. A. Weagant, 
volume 7, page 207, June, 1919; L. W. Austin, volume 9, page 
41, February, 1921. 

H. Coil Antennas. 

151. Coil Antennas — Directional Characteristics. — It has been 
pointed out in Section 137 that the ordinary elevated antenna 
acts primarily as an electrical condenser, while the coil antenna 
can be considered to act primarily as an electrical inductance. 
A coil antenna consists essentially of one or more turns of wire, 
forming a simple inductance coil. 

In both types of antennas, an approaching radio wave in- 
duces an emf. in a wire or arrangement of wires. In the ordi- 
nary elevated antenna the induced emf. causes a current to 
flow in a circuit which includes a condenser consisting of the 
antenna and ground, or antenna and counterpoise. In the coil 
antenna the induced emf. causes a current to flow in a circuit 
connected to the detecting apparatus which is completely 

It is a common experience in radio stations to be able to 
hear signals on a sensitive receiving set when the antenna is 
entirely disconnected from the set. This is largely due to the 
action of the wiring of the set as a coil antenna. 

A common type of coil antenna consists of four turns of cop- 
per wire wound on a square wooden frame about 4 feet on a 
side. The amount of energy received on such a coil antenna is 
far less than that received on any of the ordinary elevated types 
of antennas as practically used. 

It can not be emphasized too strongly that satisfactory re- 
sults can not be expected in reception using coil antennas 
unless very good electron tube amplifiers are used to amplify 


many times the feeble current received in the coil. Usually a 
six-stage amplifier (see Chapter 6) is used for satisfactory re- 
sults, but even with two stages of audio-frequency amplification, 
some signals can be received from nearby stations. 

The practical development of the coil antenna and its present 
widespread applications are due entirely to the development of 
the electron tube amplifier to a high state of perfection. 

Coil antennas may be used for either transmission or recep- 
tion, but their use for transmission is rather limited, while 
their use for reception is extensive and constantly increasing. 

A coil antenna may be used with satisfactory results inside 
an ordinary building. With suitable amplification a compara- 
tively small coil can be used for receiving transatlantic stations. 

Coil antennas are particularly used when a compact, portable, 
type of antenna is desired, or when an antenna having a marked 
directional characteristic is desired. 

The action of the coil antenna can be considered from differ- 
ent points of view. We can imagine two vertical wires of the 
same length, say 300 meters apart, supported b yand insulated 
from any convenient supports, with their lower ends also insu- 
lated. Then any radio wave approaching the two wires will 
induce an emf. in each wire. If the wave approaches from a 
direction perpendicular to the plane of the two wires, the crest 
of the wave will reach each of the wires at the same instant 
and the two induced emf.'s will be exactly in phase. If the 
wave approaches from any other direction, the induced emf.'s 
will in general be out of phase, and for a given wave length 
the difference of phase will l)e greatest for a wave approach- 
ing in the direction of the plane of the two wires. If we 
assume a wave approaching from the direction of the plane of 
the two wires and having a wave length of 600 meters, the 
emf.'s induced in the two wires will be 180° out of phase, be- 
cause the time required for the wave to travel the distance of 
300 meters between the two wires will be one one-miUionth of a 
second, or one-half the time required for the wave to pass a 
given point. Hence the emf. at the lower end of one wire will 
have a positive maximum when the emf. at the lower end of 
the other wire has a negative maximum. If now the upper 
ends of the two wires are connected and receiving apparatus 
is connected across the lower ends of the two vertical wires, a 


current will flow in the rectangular circuit so formed and can 
be detected in the usual manner. The horizontal wires con- 
tribute nothing to the effective emf. in the coil circuit. 

However, for a wave approaching from a direction per- 
pendicular to the plane of the two coils the emrf.'s induced in 
the two vertical wires will be exactly in phase, and the emf. 
at the lower end of one vertical wire will reach a maximum 
at the same instant as the emf. at the lower end of the 
other vertical wire, and no current will flow in the rectangular 

A similar explanation will obtain for a wave length other 
than twice the distance between the two vertical wires. For a 
given wave length the maximum instantaneous potential differ- 
ence will exist across the lower ends of the two wires for a 
wave approaching in the direction of the plane of the two wires, 
and no potential difference will exist for a wave approaching 
perpendicular to this direction. 

The rectangular circuit, consisting of the two vertical wires 
and the two horizontal cross connections, of course constitutes 
a coil antenna. Coils consisting of two or more turns of wire 
can be regarded as equivalent to vertical antennas of two or 
more times the height of the side of the coil. 

Another way of regarding the action of the coil antenna is 
to consider it as an inductance coil which is threaded by the 
magnetic field of varying intensity which is associated with a 
radio wave. As pointed out in Section 128, this varying mag- 
netic field is at right angles to the direction of travel of the 
wave, and it is horizontal. When the wave is traveling in the 
plane of the coil, the maximum number of lines of magnetic 
force are linked with the coil. When the wave is traveling in a 
direction perpendicular to the plane of the coil, no lines of 
magnetic force are linked with the coil and no emf. is induced 
in the coil. 

It is obvious that if the coil is mounted on a frame which can 
be rotated about a vertical axis, then for a wave approaching 
from a given direction the position of the coil can be adjusted 
BO that zero signal will be obtained in receiving apparatus con- 
nected in the coil circuit. The adjustment of the position of 
a coil for zero signal is analogous to the adjustment of the 
arms of a Wheatstone bridge (Sec. 27) to obtain zero current 



in the galvanometer or other detecting apparatus used with 
the bridge. 

Constants and Design of Coil Antennas. — The turns of a coil 
antenna possess a distributed capacity of their own, and the 
coil has a natural or fundamental wave length of its own. 
The fundamental wave length of a coil antenna is the wave 
length which is radiated by the coil when oscillating freely by 
itself without being loaded with any other capacity or induc- 
tance (Sees. 114, 144, 145). As a guiding rule, it may be stated 
that a coil antenna should not be used to receive waves which 
are shorter than about two or three times its fundamental wave 
length. However, when not used for direction-finder purposes, 
very satisfactory results can be obtained by using a coil near 

Fio- ni 

Fia. 116 


D'lPecTiona! charac+eriitic 
of clo&ed Coil aerial 

FUt 5{jiral Aeridt 


^c|uare fansm aertat 

its natural wave length. That is, to receive short waves a 
coil of small inductance and small distributed capacity should 
be used. Such a coil must have few turns. To receive longer 
waves, coils of a larger number of turns may be used. Expe- 
rience shows that best results are obtained with one or two 
turns embracing a large area for use wdth short waves, and for 
long waves coils with 20 to 30 turns, or even 100 turns, not so 
large in area. 

It is. of course, desirable to make the received current as 
large as possible. It is found that in a coil antenna turned in 
the direction of the approaching waves the received current is 
greater, the larger the number of turns of wire on the coil, the 
greater the area of the coil and the greater its inductance. The 
current varies directly as the area, directly as the number of 
turns, inversely as the resistance, and inversely as the wave 
length of the wave which is being received. 



It would seem at first sight that the increase in resistance 
clue to increasing the number of turns and their area would be 
offset by the rapid increase of the inductance with the number 
of turns and the area of the coil. The resistance to high- 
frequency currents is, however, dependent on the wave length 
and increases rapidly as the latter approaches the value of the 

fundamental wave length of 
the coil. 

Information of interest in 
connection with the design of 
coil antennas is given in Bu- 
reau of Standards Scientific 
Paper No. 354 and in a paper 
by A. S. Blatterman. Journal 
Franklin Institute, volume 188, 
page 289, September, 1919. 
Some information regarding 
the design of coils for short 
wave lengths is given in the 
book " AVireless Experimenter's 
Manual," by E. E. Bucher. 

For convenience of construc- 
tion square coils are found to 

^ be the most suitable. 

The wire may be 
wound in a flat 
spiral (Fig. 178) or 
on the surface of a 
square frame ( Fig. 
179) . With flat 
spirals only a few 
turns are used, since 
the inner turns rapidly become less useful as the area dimin- 
ishes. The spiral type of coil is comparatively little used in the 
United States. 

The usual type of coil antenna consists of one or more turns 
of wire wound on a square or rectangular frame. One or two 
turns of copper wire wound on a simple wooden frame 3 or 4 
feet square will make a simple coil which will be suitable for 
some purposes. For indoor use for all ordinary purposes the 



FIG.) 79 -A 




wire used for a coil antenna may be No. 20 or No. 22 ordinary 
insulated copper wire, with solid conductor. 

The spacing of the turns of a coil depends on the allowable 
capacity of the coil. Spacings of one-half inch and 1 inch are 
common ; a spacing of one-quarter inch is also used sometimes. 

The capacity of a coil of given dimensions increases with the 
number of turns, at first rapidly, and then more slowly. With 
the wires close together, the capacity is a maximum and grows 
rapidly less when the wires are separated, until a certain criti- 
cal spacing is reached, beyond which the capacity changes very 

For a square coil 8 feet on a side the wires should be placed 
at least 0.35 inch apart ; for one 4 feet square, 0.2 inch ; and for 
a 2-foot coil, one-eighth inch. Increasing the distance between 
the wires decreases the inductance of the coil ; at the same time 
it reduces the capacity. However, it is found that, for a given 
length of wire, properly spaced as just indicated, the funda- 
mental wave length of the coil is about the same with different 
dimensions. This fact is illustrated in the following table, 
where 96 feet of wire are used in each case. 

Characteristics of coil antennas. 


of a side 

of the 



















These coils should be used with a condenser of sufficient ca- 
pacity to bring them into resonance at 500 to 600 meters. The 
first coil would be most suitable for these wave lengths on ac- 
count of its small high-frequency resistance and greater effective 

The following observations, taken on actual coils, show the 

effective wave-length ranges of different types of construction 

for a given capacity of tuning condenser, connected directly 

across the coil terminals, as shown in the circuit of Fig. 17^A. 

53904° — 22 22 



Coil, 5 feet square, spacing of turns in each case, one-half 
inch. Using variable condenser having maximum capacity 
0.00065 microfarad, minimum capacity 0.00004 microfarad. 

With 4 turns \=200 to 400 meters. 

With 8 turns X=350 to 700 meters. 

With 16 turns X=500 to 1,000 meters. 

Coil, 5 feet square. Spacing of turns, one-half inch. Using 
variable condenser having maximum capacity 0.00140 micro- 
farad, minimum 0.000045 microfarad. 

W^ith 4 turns X=380 to 650 meters. 

With 8 turns X=400 to 950 meters. 

With 16 turns X=675 to 2,300 meters. 

Coil, 4 feet square. Four turns, spaced 1 inch. Using vari- 
able condenser having maximum capacity 0.00140 microfarad, 
minimum 0.000045 microfarad, X=180 to 500 meters. 

Coil, 4 feet square. Four turns, spaced 1 inch. Using vari- 
able condenser having maximum capacity 0.00060 microfarad, 
minimum 0.00004 microfarad, X=150 to 350 meters. 

Additional data on 4-foot coils is given in the following table : 

[Wave-length range in meters for various values of capacity across 
coil terminals, using circuit of Fig. 179— A. Coil four feet square, wound 
with No. 20 double cotton-covered copper wire, turns spaced one-half 
inch. Above 24 turns the winding is sectioned and is wound with 2, 3, 
5, or 10 conductors in each of 24 slots, as stated, the entire winding 
consisting of 24 groups of turns connected in series, the wire composing 
each group being continuous.] 


Condenser capacity (microfarads) 

ber of 




























' 1,250 

















24 slots, 2 turns per slot. 








24 slots, 3 turns per slot. 



4, 500 



14, 700 

17, 700 

24 slots, 5 turns per slot. 








24 slots, 10 turns per slot. 

Note. — Condensers having maximum capacities from 0.0005 to 0.003 
microfarad may be expected to have a minimum capacity of about 
0.00005 microfarad. Hence, from the table, with a condenser of maxi- 
mum capacity of 0.001 microfarad, and three turns on the 4-foot coil, 
the wave-length range will be from 130 to 400 meters. 


The distance over which coil antennas can be used for the 
reception of field transmitting sets is. of course, short. When 
used to receive high-power stations, however, very good results 
may be obtained. With good amplification the high-power Euro- 
pean stations can be heard in Washington, using coil antennas 
such as have been described. An instance is on record where 
all the great European stations were received in France on a 
coil only 18 centimeters square, having 200 turns. On a coil 
10 inches in diameter signals have been received in Paris from 
the arc station at Annapolis. 

Very compact, self-contained, receiving sets can be made 
using coil antennas. A successful receiving set has been made at 
the Bureau of Standards in a small suit case only 7 by 11 
by 18 inches, containing a coil antenna and six electron tubes, 
type N (see Sec. 193). Good signals from near-by stations can 
be received with this set. 

The name " resonance wave coil " has been applied to a coil 
antenna consisting of a large number of turns of very fine wire 
wound on a tube a few inches in diameter. When one ter- 
minal of such a coil is connected to ground and the other end 
left free, and a turn or two of wire coupled to the coil and con- 
nected to the input of a good amplifier, signals can be received 
from a considerable distance. Such a device, however, does not 
act entirely as a coil antenna. 

It is not necessary that a coil antenna be entirely insulated 
from ground, although this is desirable. Signals can be re- 
ceived with a single-turn coil having the lower cross connection 
completed through the ground. Thus, in a large building having 
two perpendicular pipes, perhaps 30 feet or more long and a 
similar distance apart, running direct from the ground up 
above the roof, a workable single-turn coil antenna can be con- 
structed by simply connecting the upper ends of the pipes by a 
wire and inserting the receiving apparatus in the middle of the 
wire. The current flows from the top of one pipe down that 
pipe, through the ground, up the other pipe, and across the 
connecting wire through the receiving apparatus to the top of 
the first pipe. Good results have been obtained with such a 
single turn coil, and it has been found to have well-marked 
directional properties. Since it is always grounded, it is at all 
times protected against lightning. If it is not convenient to lo- 




cate the receiving apparatus on the top floor of the building, a 
pair of wires may be tapped in on the upper connecting wire 
and run down to a lower floor. On account of the large size of 
a loop of this kind it is not well adapted for the reception of 

waves less than about 1,000 
meters in length, the effective 
working wave length range of 
a particular loop depending of 
course on its dimensions. 

A single-turn coil antenna has 
also been developed for use on 
board submarine boats, in which 
the coil circuit is completed 
through the hull of the sub- 
marine. This type of coil has 
been developed by J. A. Wil- 
loughby and P. D. Lowell, of 
the Bureau of Standards, for 
use on submarines of the United 
States Navy. A submarine 
equipped with this type of coil 
is shown in Fig. 179-C. Two 
insulated wires are run from 
the conning tower of the sub- 
marine through in- 
sulated supports, 
and one wire is fas- 
tened to each end 
of the hull, to whicli 
it is electrically con- 
nected. Tests have 
shown that a sub- 
marine equipped 
with such a single- 
turn loop may both 
transmit and receive when completely submerged, and it is 
therefore possible for a submerged submarine to remain in com- 
munication with ship and shore stations and other submarines. 
Good sig-nals have been received from European long-wave sta- 
tions on submarines off the New England coast when the top of 






the loop was submerged 8 feet below the surface. Signals have 
been successfully transmitted from a submarine to a distance of 
3 miles, with the top of the loop submerged 9 feet below the sur- 
face, using a 1-kilowatt transmitting set. 

152. Direction Finders, — In Section 146 the directional effect 
of several types of antenna has been discussed. The coil antenna 
is much more markedly directional than any of the other types 
ordinarily used. The directional characteristic of a coil antenna 


is shown in Fig. 177, and consists of two equal circles, tangent. 
As has been stated, in reception the strongest signal is received 
when the transmitting station being received is located in the 
plane of the coil. In Fig. 177 the coil antenna can be considered 
to be fixed in position with its plane in the direction BOA and 
its vertical axis passing through the point 0. The maximum 
signal will then be received from a transmitting station located 
in the direction OA, or in the direction OB, and the current re- 
ceived from a station located in the direction OA is indicated by 
the length of the line OA. 

The strength of the current received from a transmitting sta- 
tion located in another direction, such as ON, is indicated by 
the length of the line ON. From a station located in a direc- 
tion perpendicular to the line OA, no signal at all will be 

It is evident that with the curve of Fig. 177 the characteristic 
is symmetrical with reference to a plane through O perpen- 
dicular to the line BA, and that the current received from any 
direction, such as ON, is the same as the current received from 
the opposite direction, differing by 180 degrees, such as OM. 

If a coil antenna is mounted on a vertical axis so that it can 
be rotated freely, and a curve is plotted showing for a wave 
approaching from a particular direction the variations in the 
strength of the received current as the coil is rotated, there will 
be obtained the same kind of a curve as the one shown in Fig. 
177. A coil so mounted is called a direction finder, or 7'adio 

By rotating the coil while receiving from a particular station 
it is therefore possible to locate the line of direction of the sta- 
tion. The coil may be for maximum signal and the trans- 
mitting station then lies in the plane of the coil. Or the coil 
may be set for minimum signal and the transmitting station 
then lies in a direction perpendicular to the plane of the coil. It 
will be noted by reference to Fig. 177, however, that for a varia- 
tion of, say, 3 degrees, a nmch greater change in received current 
is caused when the coil is at the minimum than when at the max- 
imum. Therefore a much sharper determination of direction is 
possible by setting on the minimum position, and the minimum 
method is the one usually used for direction-finder work. One 


difficulty with tlie minimum method is that the minimum sig- 
nal may be obscured by transmission frojii another station. 
The maximum method is not subject to this objection. 

It should be noted that with this simple apparatus it is pos- 
sible to determine only the line of direction of the transmitting 
station, but not its sense. That is. if the line of direction 
determined is east and west, it is not known whether the 
transmitting station is located on the east or on the west. 
Methods for determining the sense of the direction will be dis- 
cussed later. 

A simple coil antenna circuit is shown in Fig. 179-A. The 
coil is tuned to the wave length of the incoming wave by means 
of a variable condenser connected across its terminals. These 
terminals are also directly connected to the input of the elec- 
tron tube amplifier. 

A direction finder is provided with a horizontal graduated 
circle to identify the position of the plane of the coil. To make 
a determination of direction, the coil is rotated on its vertical 
axis until the signals disappear. There will usually be a cer- 
tain range of angular positions of the coil, perhaps between 1 
and 5 degrees, for which no response will be obtained in the 
detector. For a given coil and a given transmitting station 
this range depends on the sensitivity of the receiving apparatus 
and the sensitivity of the ear of the receiving operator. The 
action can be understood by again referring to Fig. 177. If 
the radius of the circle, drawn with as a center, represents 
the smallest received current which causes a just audible signal 
in the detecting circuit, then it is evident that for positions of 
the coil lying within the angles COD and EOF no signal can 
be received. 

To determine the line of direction of the waves the positions 
C and D may be noted on the graduated scale, for which 
the signals just disappear and just become audible, respectively, 
and then the coil is turned about 180° and the two similar 
positions E and F are sought. By taking the average of the 
circle readings at C and D and E and F that position of the 
coil may be determined which lies at right angles with the de- 
siretl direction. The instrument is set up at the start, so that 
the scale reading will give directly the direction of the waves 


in degrees from the north and south line. This method is, how- 
ever, not ordinarily necessary when a direction finder has been 
calibrated, as described below. 

The characteristic shown in Fig. 177, consisting of two equal 
tangent circles, is an ideal characteristic, and fails to take into 
account several conditions found in practice. 

As has been stated, a coil antenna can be considered to act 
primarily as an inductance. It is, however, an arrangement of 
wires elevated above the ground, and with the ground forms a 
condenser. The coil antenna will act as an ordinary condenser 
antenna to an extent depending on what kind of a condenser it 
forms with tlie ground. In considering this condenser we should 
take into account not simply the capacity of the coil alone to 
ground but also the capacity of all the receiving apparatus asso- 
ciated with the coil. 

Let us return to the consideration of the coil antenna as two 
ungrounded simple vertical wire antennas having tlie same 
length as the height of the coil. The emf. induced by an ap- 
proaching wave in each wire will tend to cause a current to 
flow between each vertical wire and the ground, through the 
capacity of each vertical wire to ground. If the coil system is 
symmetrical about its vertical axis, and the receiving apparatus 
associated with the coil is symmetrical with respect to this 
axis, so that the capacity to ground of each lateral half of the 
coil and coil circuit is the same, this effect is not important and 
will not destroy the symmetry of the directional characteristic. 

In the circuit shown in Fig. 179-A it will be noted that the 
filament battery and other apparatus is connected to the left 
coil terminal, while the right coil terminal is connected only to 
the grid of the first tube. The filament battery of course has 
an appreciable capacity of its own to ground, and therefore the 
system consisting of the coil and its associated apparatus has a 
greater capacity to ground on the side to which the filament 
connection is made than on the other side. Other parts of the 
circuit and the operator's body may also contribute to unsym- 
metrical capacities to ground. The emf.'s induced in the two 
vertical sides of the coil will cause a current to flow through 
the unsymmetrical ground capacities, and this current will flow 
even when the coil is perpendicular to the direction in which 
the wave is traveling. The effect is that the directional char- 


acteristic of a coil system with unsymmetrical capacities to 
ground is not the two equal tangent circles shown in Fig. 177, 
but is a figure shaped like an hourglass, the width of the neck 
depending on the extent to which the capacities are unsymmet- 
rical. There is an appreciable signal when the coil is at right 
angles to the direction of the approaching wave, and if the 
effort is being made to rotate the coil, to determine this direc- 
tion it is much more difficult to determine the position of mini- 
mum signal. This troublesome effect can be reduced by placing 
the batteries as far above the ground as is practicable. 

This undesirable effect can be eliminated by use of a " bal- 
ancing condenser," as shown in Fig. 179-B. This is simply a 
variable condenser with two sets of fixed plates and one set of 
moving plates, connected as shown, the moving set of plates 
being connected to ground. The condenser is adjusted until the 
capacity to ground on the side of the coil connected to the grid 
is equal to the capacity to ground on the side connected to the 
filament. This restores the sharpness of the position of mini- 
mum signal. The ground connection of the compensating con- 
denser should be symmetrically placed so that the compensating 
adjustment of the condenser will be independent of the station 
being received. Compensation is not particularly important 
when, a coil antenna is being used simply for reception, but is 
very Important when it is being used for direction-finding work. 

Coil antennas can be used satisfactorily for the reception of 
wave lengths of 200 meters, but when used for direction-finding 
work the simple coil circuit should not be used at wave lengths 
of less than 300 meters and preferably not less than 450 meters. 
If the effort is made to use an ordinary coil antenna as a 
direction finder at a wave length of 200 meters, the effect of 
the capacity to ground of even a pair of leads 3 feet long may 
be greater than the effect of the coil antenna proper. If it is 
desired to use a direction finder for such short wave lengths, 
a balancing condenser should be used, the batteries, amplifier, 
and other receiving apparatus should be mounted symmetrically 
inside of the coil itself and all wiring made symmetrically. 

For operating coil antennas on comparatively short wave 
lengths the method described in Section 205 of reducing the 
high radio frequency of the input voltage to the amplifier 
by a beat method to a lower radio frequency may be used to 


advantage. The use of such a method of beat reception for 
this purpose is described in Q. S. T., volume 5, page 24, August, 

In Section 130 reference was made to " strays," or atmos- 
plierie disturbances, which often cause serious interference in 
radio reception. Strays of some kinds come from particular 
directions, and can be minimized by directional reception; that 
is, the ratio of signal to strays is increased by directional re- 
ception. Coil antennas are often used for this purpose. The 
combination of a coil antenna and a ground antenna has been 
found particularly good for eliminating strays.® Such directional 
reception can also be used for eliminating signals from stations 
which it is not desired to receive. For long-distance reception 
in commercial and Government communication, either coil an- 
tennas or ground antennas or a combination of both are largely 
used now. The coil antennas used may, however, be out of 
doors and of dimensions comparable to those of an ordinary 
antenna of medium size. 

When with a direction finder equipped with an amplifier giv- 
ing high amplification the signal entirely disappears when the 
coil is at right angles to the direction of the approaching wave, 
the direction finder is said to have a " perfect minimum." This 
can be obtained only with very good balancing. It is evidently 
very desirable to have a very sharp minimum, both to obtain 
precise settings and to obtain speed in taking bearings. In 
order to get a sharp minimum, it is necessary to have a fairly 
strong signal and a good amplifier, usually a 6-stage amplifier. 
Under such conditions an experienced operator can often make 
a very accurate setting with only two swings of the coil. 

A coil antenna can be used with a circuit of the type shown 
in Fig. 239-A, page 427. The part of Fig. 239-A to the left of 
points A and B should be deleted, and the terminals of the coil 
antenna connected directly to points A and B. This circuit is 
particularly advantageous on short wave lengths. 

^ See tho following papers in the Proceedings of the Institute of 
Radio Engineers : A. H. Taylor, vol. 7, p. 337, August, 1919 ; A. H. 
Taylor, vol. 7, p. .^).59, December, 1919 ; A. H. Taylor, vol. 8, p. 171, 
J-une, 1920 : R. A. Weagant, vol. 7, p. 207, .Tune, 1919 ; G. W. Pickard, 
vol. 8, p. 358, October, 1920 ; L. W. Austin, vol. 9, p. 41, February, 


The type of coil for direction finding work described above 
consists of simply one rectangular inductance coil of one or 
more turns. Direction finders have been developed in which 
two similar coils are used, crossed at right angles to each other. 
Such a direction finder has a directional characteristic which is 
the resultant of the directional characteristics of the two coils 
alone, and has advantages for particular purposes. For infor- 
mation regarding this " double-coil " or " crossed-coil " direction 
finder the reader may refer to any standard treatise on radio 
comnmnication or to the paper by H. J, Round mentioned at the 
close of this section. 

A direction finder has also been developed in which the cir- 
cuit is open at the top — that is, tliere are two vertical sides 
and one lower horizontal connection. Sometimes the two ver- 
tical sides are bent toward each other, but they do not touch. 
This is one of the early types developed by Bellini and Tosi. 
This direction finder does not act as a coil antenna, but is a 
particular kind of a directional antenna. The later form of the 
Bellini-Tosi direction finder employs two triangular antennas, 
open at the top, and crossed at right angles. These crossed 
triangular antennas are used with auxiliary apparatus, as de- 
scribed in books listed at the end of this Section. 

Unidirectional Direction Finders. — It has been pointed out 
above that the simple coil antenna having a symmetrical direc- 
tional characteristic will give the line of direction of a trans- 
mitting station, but will not tell on which side the transmitting 
station lies. It is evident that if we have an antenna having 
an unsymmetrical directional characteristic, such as that of 
the inverted L antenna, as shown in Fig. 173-C. it will be pos- 
sible also to tell on which side the transmitting station lies. 
In general, it is found that the line of direction can be deter- 
mined most accurately by using a coil antenna alone with 
proper balancing, and then afterwards to determine on which 
side the transmitting station is located by a " unilateral " 
method, which does not alone give the line of direction so 

To get a direction finder suitable for determining on which 
side the transmitting station is located, we have only to destroy 
the symmetry of the coil's directional characteristic in some 
way. One way to do this is by throwing the balancing condenser 



out of balance and inserting in the ground lead of the balancing 
condenser an inductance and capacity in parallel, hy which 
the coil is tuned as a vertical antenna to the incoming wave 

Another way is to use an antenna of the condenser type 
coupled to the coil antenna. The antenna used is ordinarily a 
short vertical wire erected along the axis of the coil, and is 









coupled to the coil antenna circuit in the usual way with a 
variable coupler. This coupling is adjusted until the strength 
of the signal from the antenna alone is the same as the 
strength of the signal from the coil alone, when the coil is in 
the position for maximum signal. Under these conditions the 
directional characteristic of the combined system is as shown 
in Fig. 179-D. In this figure the small dotted circles are the 
symmetrical directional characteristics of the coil alone. The 
coil is shown as a heavy line at Lo. The large dotted circle is 


tlie directional characteristic of the vertical antenna alone. 
The resultant characteristic is the curve shown in full line 
passing through B. It is evident that for a wave approaching 
from B a good signal will be received, while for a wave ap- 
proaching from A practically no signal will be heard. 

It is often not necessary to use a unilateral connection to de- 
termine on which side a station lies. Thus in the case of a 
direction-finder station located on the coast which is receiving 
signals from a ship it is definitely known that the ship can be 
on one side only. When a direction finder is used on a ship 
which wishes to determine the bearing of another ship, however, 
the unilateral method is desirable in general. 

With a coil antenna properly adjusted for unidirectional re- 
ception it is possible in Washington to receive signals from San 
Diego, Calif., while the station at New Brunswick, N. J., is 
transmitting, although the directions of San Diego and New 
Brunswick from Washington are nearly in the same straight 

Distortion of Wave. — When possible a coil antenna used as a 
direction finder should be used in a location well removed from 
buildings, trees, and, as far as possible, from any metal of any 
kind. Such objects distort the wave front and an erroneous 
determination of direction may be made. Neighboring masses 
of metal having a natural frequency of oscillation approximately 
the same as that of the wave being received are likely to cause 
particularly bad errors in determinations of direction. The 
Bureau of Standards has used direction finders in the imme- 
diate neighborhood of the Washington Monument and has in- 
vestigated the distortion of the wave front in that locality for 
different wave lengths. At a wave length of 800 meters the 
maximum error occurred in the reading given by the direction 
finder, showing that the natural wave length of the JNIonument 
is about 800 meters. When a direction finder is used on board 
ship, it is of course not possible to get away from all sources 
of distortion, but the effort should be made to get as far away 
as possible from such objects, and to have such distorting ob- 
jects as are present arranged as symmetrically as possible with 
respect to the center line of the ship from bow to stern. By 
calibrating a direction finder, as described below, the errors 
caused by such distortion can be corrected. 


When a coil antenna is used in a closely built-up city block 
it will seldom give accurate bearings because the wave tends to 
follow the electric wires in the street and other metal masses 
which run largely in the length of the block. 

Undamped waves of long wave length are particularly likely 
to have their wave front considerably distorted, even when well 
removed from metal and other objects. Such distortion is 
especially marked at sunrise and sunset. (See A. H. Taylor, 
Bureau of Standards Scientific Paper No. 353; 1919.) 

Calibration. — After a direction finder is installed in as favor- 
able a location as possible it should be calihrated, as is usually 
done with measuring instruments of all kinds. The direction 
finder receives signals from a station whose direction is known 
by other methods, and the dilference between the observed bear- 
ing and the true bearing is noted. This is done for as many 
different directions as convenient, and a curve is plotted show- 
ing the corrections which must be made to get the true bearing. 
Points for the calibration curve should be taken at least every 
10 degrees. When a direction finder on board ship is to be 
calibrated, the ship may be navigated in a circular course in 
sight of a transmitting radio station, and simultaneous visual 
and radio bearings taken. Information regarding the calibra- 
tion of direc-tion finders will be found in the paper by Kolster 
and Dunmore, mentioned at the close of this section. 

Apijlicationa of Direction Finders. — One of the most important 
applications of the radio direction finder is in navigation. A 
ship lost in thick fog can determine its position and set a course 
if it is equipped with a radio direction finder. By communicat- 
ing by radio with direction-finder stations on the shore it can 
also determine its position. This application is of great prac- 
tical importance, since many lives and much property may be 
saved if a ship can be navigated correctly in dangerous waters 
in tliick weather. In thick weather the beam of light from 
lighthouses does not penetrate far, and the observed direction 
of sound signals sent out from lighthouses may vary a great 
deal from the true direction. 

The Bureau of Standards has developed a system of radio 
direction finding for use on ships which is very simple and 
accurate. Two or more radio transmitting stations are erected 


at points in the neighborhood of a harbor and automatically 
transmit characteristic signals during a fog, each station having 
a different characteristic. Thus one station may transmit dots 
in groups of three, a second may transmit dots in groups of 
two, and a third may transmit dots in groups of twenty or more. 
The navigator takes successive bearings on each of the trans- 
mitting stations. The position of the ship is then easily deter- 
mined by plotting the bearings on a map. 

In cooperation with the Bureau of Lighthouses, the Bureau of 
Standards has installed transmitting equipment for this purpose 
at three light stations at the approaches to New York Harbor — 
Fire Island Lightship, Ambrose Channel Lightship, and the 
light station at Sea Girt, N. J. Radio transmitting stations 
intended for this service are called " radio beacons." These 
three radio beacons are now regularly in commission, and any 
ship approaching New York which is equipped with a radio 
compass can get bearings. The Bureau of Standards has also 
designed a coil for use on shipboard and has installed such a 
coil direction finder on the lighthouse tender Tulip. This direc- 
tion finder is shown in Fig. 179-E. Accurate determinations 
of direction can be rapidly made by the navigator of the ship ; 
it is not necessary that radio bearings be taken by an expe- 
rienced radio operator. This system has proved to be very 
satisfactory, and plans are being made to establish other radio 
beacons at other light stations in the United States. For fur- 
ther information regarding this system see the paper by Kolster 
and Dunmore mentioned at the close of this section. 

San Francisco Light Vessel has recently been equipped and 
placed in commission as a radio beacon. 

There is another system of applying the radio direction finder 
to navigation in which a ship desiring to learn its position is 
not equipped with a direction finder but simply with radio 
transmitting apparatus. On shore there is a group of. direction- 
finder stations connected by a land wire. The ship sends out a 
request for its position, which is received by the several stations 
on shore, and each shore station takes a bearing and transmits 
the observed bearing to a central control station, which plots 
the bearings and determines the ship's position, which is trans- 
mitted to the ship by radio. In this method considerable time 
may elapse between the request for position and the return of 
this information from the central control station, and the delay 


Fig. 179-E. — Bureau of Standards type of direction finder 
installed on lighthouse tender Tulip. 


is necessarily greatest in the thickest weather, when every ship 
wants radio bearings, and the interference caused by various 
ships transmitting simultaneously may be serious. 

The radio direction finder is also very useful on airplanes. A 
number of turns of wire may be wound on the wings of an air- 
plane and used as a coil antenna, and as a direction finder. 
When it is desired to do direction-finding work on a large air- 
plane it is usual to mount a small rotatable coil aft in the fuse- 
lage. The direction finder will permit flying at night or in thick 
weather, when flying would otherwise not be possible. The use 
of direction finders on airplanes is in itself an important prob- 
lem on which a great deal of work has been done and a consid- 
erable number of papers have been published. 

On airplanes considerable interference may be caused in re- 
ceiving signals by the ignition system of the engines. This 
may be considerably reduced by very careful shielding of all the 
wiring of the ignition system. 

The direction finder has found important uses in military 
operations, and can be used for determining the positions of 
enemy stations of various kinds. 

Coil Transmitters. — Coil antennas can be used for transmit- 
ting as well as for receiving, although at the present time their 
use as transmitters is much less important. Coils are used 
for fransmitting, in most cases, when a transmitted wave having 
a marked directional characteristic is desired. It has been 
found that two similar coils mounted on the same axis perpendi- 
cular to each other give a directional characteristic which is very 
useful for some purposes. Coil transmitters have been employed 
to aid a ship or an airplane to determine its direction from a 
fixed transmitting station. If desired, a course can be set for 
the transmitting station. As has been mentioned, the single 
turn loop installed on a submarine has been used for trans- 

The use of a coil antenna may be particularly advantageous-- 
on small boats when conditions prohibit elevated structures of 
any kind. Thus on a lifeboat, it is not possible to have any 
elevated wires sti-ung over the boat, because they would inter- 
fere with the throwing of lines. The Bureau of Standards, ini 
cooperation with the U. S. Coast Guard, has recently developed 
a single-turn coil antenna for use on lifeboats of the Coast 
53904°— 22 23 


Guard. A 36-foot motor-driven lifeboat with heavy metal keel 
has been equipped with a single-turn coil antenna of which the 
metal keel formed a part. Two-way radiotelephone conversa- 
tions have been maintained between the boat and the short, 
using transmitting apparatus of low power. 

For further information regarding coil antennas and direc- 
tion finders, the reader may refer to : 

J. H. Bellinger. Principles of Radio Transmission and Re- 
ception with Antennas and Coil Aerials. Bureau of Standards 
Scientific Paper No. 354: 1919. 

F. A. KoLSTER and vF. W. Ditnmore. The Radio Direction 
Finder and Its Application to Navigation. Bureau of Standards 
Scientific Paper No. 428: 1922. 

F. A. KoLSTER. Blindfold Navigation — By Radio. Shipping, 
vol. 13, p. 13, Feb. 25, 1921. 

G. W. PicKARD. Proceedings Institute Radio Engineers, vol. 
8, p. 358, October, 1920. 

S. Ballantine. Year Book of Wireless Telegraphy, 1921. 
Page 1131. 

H. J. Round. Direction and Position Finding. Journal In- 
stitution Electrical Engineers (London), vol. 58, p. 224, March, 
1920. Science Abstracts B No. 428, April, 1920. 

J. Robinson. Method of Direction Finding by Wireless 
Waves. Radio Review, vol. 1, p. 213, February, 1920, and vol. 
1, p. 265, March, 1920. Science Abstracts B No. 429, April, 1920. 


(Exclusive of Electron Tubes.) 

A. Apparatus for Damped Wave Transmission. 

158. Function of Transmitting Apparatus. — Electric waves, by 
means of which radio communication is carried on, are produced 
by the transmitting apparatus. Power must be supplied by some 
kind of electric generator; this must be converted into high- 
f)-equency currents which flow in tlie transmitting aerial and 
cause electric waves which travel out through space. The 
M'aves may be undamped or damped. Damped waves consist of 
groups or trains of oscillations repeated at regular intervals, 
the amplitude of the oscillati(!ns in each train decreasing con- 
tinuously. The number of these trains of waves per second 
is some audible frequency. When such waves strike a receiving 
apparatus (described later), they cause a sound in the tele- 
phone receiver. Signals are produced by means of a sending 
key. which lets the trains of waves go on for a short length of 
time (pr('ducing a dot) or a longer time (producing a dash). 

Tlie principles of damped and of undamped waves are the 
same in many respects, so that much of what is told regarding 
apparatus for damped waves applies to apparatus for undamped 
waves as well. Particular attention is first given to damped 
waves, since the apparatus is simple and easily adjusted, and is 
suitable for portable sets and for short-distance communication. 

The most importam; type of apparatus used for generating 
damped waves is the spark gap, including the rotary gap and 
the quenched gap. For field use, for emergencies, and for ama- 
teur comnninication. where low power is sufficient, the induc- 
tion coil is sometimes used. For generating undamped waves 
the important sources are the high-frequency alternator, the 
arc converter, and electron tubes. The timed spark gap gives 
waves which are jiractically undamped. When an undamped 
wave is interrupted at the transmitting station at an audible 
frequency by a '' chopper." the wave radiated affects receiving 
apparatus in some ways as if it were a damped wave. 




154. Simple Spark Discharge Apparatus. — Damped oscilla- 
tions are produced when a condenser discharges in a circuit 
containing inductance. The condenser is discharged by plac- 
ing it in series with a spark gap and applying a voltage to it 
high enough to break down or spark across the gap. As ex- 
plained in Section 115, the oscillations produced when the con- 
denser discharges in such a circuit are damped and soon die 
out. Methods of producing a regular succession of such con- 
denser discharges are explained in the following. A high 
voltage must be applied to the condenser at regular inten-als. 
This is done by the use of a transformer. Through the primary 
of the transformer is passed either an alternating current or a 

CJnoove— » 

Fta 183 .^rJMm, 

Fjq IfiO 

simple ^fjarK cJi'achar^e a^^ratua 

Qu«,nehed S^nC Dischai^p 

current regularly interrupted by a vibrator operated by the 
transformer (induction coil). For the use of the induction coil, 
as in radio trench sets, see Section 157. The principle is best 
studied first in the alternating-current method. 

In Fig. 180, P and *S are the primary and secondary of a 
step-up transformer (Section 58), which receives power from 
an a.c. generator. The primary may be wound for 110 volts, 
and the secondary for 5,000 to 20,000 volts. By means of the 
transformer the condenser C is charged to a high voltage, and 
stores up energj\ When the voltage becomes great enough it 
breaks down the spark gap and the discharge takes place as an 
oscillatory current in the inductance coil h and its leads. See 
Section 115. The main discharge does not take place through 
the turns of /S on account of its relatively high impedance. The 



transformer is sometimes still further protected from the con- 
denser discharge by inserting choke coils (not shown in Fig. 
ISO) in the leads between the transformer and condenser. These 
obstruct the high-frequency current, but do not hinder the pas- 
sage of the low-frequency charging current into the condenser. 
Fig. 181 shows a transformer used in radio sets. 

The standard generator frequency is 500 cycles per second. 
This causes the condenser to discharge 1000 times a second, once 
for each positive and each negative maximum if the spark gap 

Pig. 181. — Step-up transformer for charging condenser. 

is of such length as to break down at the maximum voltage given 
by the transformer. The number of sparks per second is called 
the " spark frequency." With the standard spark frequency of 
1000 per second the amount of power the set sends out is con- 
siderably greater than it would be at a low frequency like 60 
cycles per second, because the transmitted radio waves are more 
nearly continuous, as will be shown later. The radiated wave 
trains strike a receiving antenna more frequently and their am- 
plitude does not need to be so great to produce the same effect 
as stronger waves received at longer intervals of time. The 


higher frequency produces a tone in the receiving telephone 
that is more easily heard, because the ear is most sensitive to 
sound waves of about 1000 per second and also the tone is more 
easily heard through atmospheric disturbances. A 60-cycle sup- 
ply may be used if the number of sparks per second is increased 
by using a rotary spark gap giving several sparks per cycle. See 
Section 156. 

Each condenser discharge produces a train of oscillations in 
the circuit, and each train of oscillations consists of alternations 
of current which grow less and less in amplitude. This is illus- 
trated in Fig. 192, and the comparative lengths of the trains of 
oscillations and the lapse of time between their occurrence are 
discussed in Section 160. 

155. Transmitting Condensers. — Before discussing the means 
of getting the oscillations into an antenna (Section 160), the 
apparatus used in generating the oscillations will be described 
in detail. 

The most common types of condensers used in radio trans- 
mitting circuits have mica or glass as the dielectric, with tin- 
foil or thin copper as the conducting coatings. Condensers hav- 
ing air or oil as dielectric are sometimes used, but are bulky. 
For very high voltages the condenser plates are immersed in oil 
to prevent brush discharge. For moderate voltages a coating of 
paraffin over glass jars, especially at the edges of the metal 
foil, will satisfactorily reduce brush discharge. For calculation 
of the size of transmitting condenser needed see Section 170. 

156. Spark Gaps. — When the gap is broken down by the high 
voltage it becomes a conductor, and readily allows the oscilla- 
tions of the condenser discharge to pass. During the interval 
between discharges the gap cools off and quickly becomes non- 
conducting again. (See Section 160.) If the gap did not re- 
sume its non-conducting condition, the condenser would not 
charge again, since it would be short circuited by the gap, and 
further oscillations could not be produced. The restoration of 
the non-conducting state is called " quenching." A device called 
the " quenched gap " for very rapid quenching of the spark is 
described below in this section. Additional appliances for the 
prevention of arcing are discussed in Section 167. 

Plain Gap. — A plain spark gap usually consists of two metal 
rods so arranged that their distance apart is closely adjustable. 



(See Fig. 182.) It is important that the gap be kept cool or it 
will arc : for that reason the sparking surfaces should be ample. 
Often the electrodes have fins for radiating away the heat. An 
air blast across the gap will greatly aid the recharging by re- 
moving the ionized air, to which the conducting power of the 
gap is due. At the sparking surfaces an oxide slowly forms 
which, being easily removed in the case of zinc or magnesium, 
is not very troublesome. With other metals in general the 
oxidation is serious and is rapid enough to make operation 
unstable and inconvenient. 

With a given condenser, the quantity of electricity stored on 
the plates at each charging is proportional to the voltage im- 
pressed (Sec. 30), and this can be regulated by lengthening or 
shortening the spark gap to obtain a higher or lower voltage at 
the beginning of the discharge. The length of the gap which 
can be employed is limited by the voltage that the transformer 
is capable of producing, the ability of the condenser dielectric 
to withstand the voltage, and the fact that for readable signals 
the spark discharge must be regular. If the gap is too long, 
sparks will not pass, or only at irregular intervals. The con- 
denser is endangered also. If the gap is too short it may arc 
and burn the electrodes. Arcing causes a short circuit of the 


transformer, and the heavy current that flows interferes with 
the high-frequency oscillations. An arc gives a yellowish color 
and is easily distinguished from the bluish white, snappy sparks 
of normal operation. Even if no arc takes place, the voltage 
is reduced by using too short a gap, and this results in reduced 
power and range. The length for smooth operation can usually 
be determined by trial. 

Quenched Gap. — It is found that a short spark between cool 
electrodes is quenched very quickly, the air becoming non- 
conducting almost immediately after the spark is broken down, 
or as soon as the current falls to a low value. This action is 
also improved if the sparking chamber is air tight. The stand- 
ard form of quenched gap consists of a number of flat copper 
or silver discs of large surface, say 7 cm. to 10 cm. in diameter 
at the sparking surface, with their faces separated by about 0.2 
mm. To provide the necessary total length of gap for high- 
voltage charging, a number of these small gaps are put in series, 
so that the spark must jump them all, one after the other. The 
discs are separated by rings of mica or paper, see Fig. 183, p. 
354. Fig. 184, p. 359, shows a commercial type of quenched gap. 
The motor-driven blower attached serves to keep the discs cool. 
They are usually made with projecting firs for radiating the 
heat, and in one design air spaces are provided between the 
pairs of discs which form the successive gaps. The number of 
gaps is determined by the voltage, allowing about 1200 volts for 
each gap. Eight or ten gaps are usually sufficient. (See also 
Section 123, page 279.) 

Until comparatively recently the quenched gap has not been 
in use on a supply frequency as low as 60 cycles per second. It 
has recently been found possible to use quenched gaps with 60- 
cycle supply and still get smooth tones and excellent communi- 
cation by the use of a variable series resistance in the primary 
circuit of the transformer, and also by employing a transformer 
of the resonance type with an unusually high secondary voltage. 
By altering the series resistance, the spark rate may be changed 
as desired, as to 60, 120, or 240 per second. This adjustment is 
somewhat critical and difficult to maintain exactly under condi- 
tions where line voltage variations are encountered. Such 
variations of line voltage result in a roughening of the tone, 
which does not, however, seem to seriously affect communica- 

Fig 1S4 — Radio telegraph transmitting and receiving set witla queucbed 
gap. Signal Corps Type SCR-49. (Pack set.) 

1. Quenched gap. 8. Loading inductance. 

2. Transmitting condenser. 9. Primary inductance. 

3 Safety ^^ap l'^- Secondary inductance. 

4 Transfol-nier 11- Common terminal of primary 
5'. Receiving set. «iid secondary. 

6 Kev 12. Antenna switch. 

7 Tool box 13. Ammeter in counterpoise lead. 




One advantage of the quepched gap is its quietness of opera- 
tion, in comparison witli the noisy discharge of tlie ordinary 
types of rotary gap. This is because of the very short gaps, 
and the inclosure of the spark. 

When 500-cycle supply is used with a quenched gap. it is 

customary to so adjust the voltage and the number of gaps that 

there is one discharge per half cycle, or 1.000 sparks per second. 

( See Fig. 185. ) 
Unless the antenna resistance is very high, there will usually 

be found with any quenched gap critical values of coupling 
between the primary and secondary of the oscillation trans- 
former. The antenna current will be found to decrease when 
the coupling is either tightened or loosened from one of these 
critical coupling adjustments. There may be as many as three 

Pig. 185 

One SjaarK (ae-p 
half cycle with 
Quenched ^ab 



of these critical values of coupling. When the coupling is not 
adjusted at one of the critical values, the tone usually becomes 
rough and the wave becomes broad, or even shows two well- 
marked peaks on its resonance curve. By not properly adjust- 
ing quenched gap circuits it is quite possible to produce a very 
broad wave comparable to the waves of worst interfering quali- 
ties produced by other types of sets. Some of these broad-wave 
adjustments may result in large antenna currents which may 
eeem desirable to the operator, although resulting in far less 
effective communication than a sharper wave with less antenna 
current and a clear tone. The desirable qualities of a pure 
wave are discussed in section 165, page 377. 

The adjustment of the generator voltage is also critical and 
determines to a large extent the purity of both the tone and the 

The quenched gap will continue to operate fairly satisfac- 
torily under close coupling, while the usual type of rotary gap 


would begin to produce coupling waves under the snme condi- 
tions. Tlie operation and adjustment of quenched gap sets are 
further discussed on page 378. 

For further information regarding the quenclied gap, the 
reader may refer to " Wireless Telegraphy, with Special Refer- 
ence to the Quenched Spark System," by Bernard Leggett. 

Rotanj Gaps. — A rotary gap consists of a motor-driven wheel 
with projecting teeth. There are usually two fixed electrodes 
so placed that when a moving tooth on the wheel comes oppo- 
site one fixed electrode, another moving tooth is opposite the 
other fixed electrode. A recent type of rotaiy gap is shown in 
figure 186. When two teeth are respectively opposite the two 
fixed electrodes the current jumps from the one fixed electrode 
to the wheel, flows across the wheel, and jumps to the other 
fixed electrode. There are thus two sparks in series. In this 
way a spark occurs each time that a tooth passes a fixed elec- 
trode. Arcing is prevented by interruptions produced by the 
rotating wheel. 

The principal advantages of a rotary gap are : 

(1) It serves as an automatic switch and discharges the con- 
denser at regular intervals, thus producing a steady tone. 

(2) The fanning action of the wheel keeps the gap cool. 

(3) The spark takes place in the compressed air driven ahead 
of the teeth, and hence the spark is better quenched. 

When the rotary gap is mounted on the shaft of the alternator 
supplying the alternating current of 500 cycles or other fre- 
quency, or is driven by a synchronous motor from the same 
line which supplies the transformer, it is known as a synchro- 
nous gap. Such gaps are usually equipped with as many teeth 
as there are poles on the generator ; hence one spark occurs per 
half cycle, giving the same pitch but a better quality tone than 
a fixed gap. The fixed electrodes are mounted on an adjust- 
able member which is rotated until the spark takes place at the 
instant that the alternating voltage on the condenser reaches 
its maximum values, positive and negative. This means that 
the teeth must be closest to the fixed electrodes a little after 
the condenser would reach full charge, since the spark will 
jump to the moving tooth a little before the tooth is opposite the 
fixed electrode. Synchronous gaps are also constructed with 
twice as many teeth as there are generator poles, giving two 
sparks per half cycle. These sparks are spaced the same dis- 



tance on both sides of the peak of the condenser voltage wave. 
Thus all sparks are still exactly alike and the synchronous qual- 
ity of the tone is retained, but the pitch is raised an octave. 

Fig. 186, — Nonsynchronous rotary gap. 

This is sometimes regarded as desirable on 60-cycle supply 
frequency, and such gaps have been used to a considerable 



More than two sparks per half cycle can not be produced 
without having some of them occur at different voltages. 

If it is desired to secure a higher pitch than the double-fre- 
quency note mentioned above, or if it is not convenient to mount 
the gap on the generator shaft, it is customary to use a sepa- 
rate motor which runs without any special regard to the gen- 
erator speed. Such a gap is called a nonsynchronous gap and 
is usually operated at speeds giving from two to four sparks 
per half cycle. Better communication is secured with the lower 
rates of discharge, even though they involve the use of a less. 
desirable tone. 

A modified form of rotary gap is shown in Fig. 187. 

riQ. 187 




Rbtiry €^arK ^f) with two 
rotaitin^ electrodes 

' 4mm 

f iq. 188 

Circuits of an mdootion coil 

Muffled rotary gaps. — Rotary gaps are frequently muffled to- 
diminish the noise of the discharge. The muffling drum of 
metal or wood carries insulating bushing through which the 
fixed electrodes pass. In the case of a synchronous gap the 
drum is made adjustable so that it can be rotated. Muffled 
gaps have the incidental advantage that after a portion of the 
oxygen in the air has been combined with other gases present, 
a little better operation is obtained. Sometimes a hydrocarbon 
gas is introduced into the muffling drum. Hydrogen may be 
drawn from a cylinder, or illuminating gas may be used. Some- 
times alcohol is allowed to drop into the muffling drum ; the 
heat of the discharge decomposes the alcohol, producing hydro- 
gen. The presence of the hydrogen in the drum accelerates, 
deionization and results in better quenching, for reasons whichi 


are explained in connection with the arc converter in Section 
177, page 413. 

Special types of rotary gaps have also been constructed which 
have in series a number of very short gaps with large surface, 
one gap being provided for approximately each 1,100 volts. 
Such gaps are known as rotary quenched gaps, and are usually 
muffled, or equipped with a discharge chamber which can be 
filled with a gas, but sometimes operate in the open air. This 
type of gap produces a note that has the qualities of the note 
of a 500-cycle quenched gap, but operates on commercial supply 

When large powers are used, the problem of removing the 
heat generated in a rotary gap becomes quite serious, since it 
is difficult to provide a method of ventilation without destroy- 
ing the effectiveness of the muffler. For medium powers, cool- 
ing vanes exposed to an air blast are used. 

The plain spark gap is not now used except in small sets; 
quenched or rotary gaps are the rule. The plain gap can not be 
properly deionized to allow the condenser to recharge, and it 
is very difficult, or impossible, to prevent arcing when large 
power is used, especially with a large number of sparks per 
second, as in modern practice. 

When a rotary gap is used on an airplane, it may be driven 
by a small fan. The speed of the fan is usually regulated by a 
self-governing mechanism, so that the speed of the gap does not 
vary seriously when the speed or direction of the airplane 
changes. Electron tube transmitters are used considerably for 
transmitting from airplanes. (See Chapter 6.) 

Timed Spark. — ^A form of rotary gap called the " timed 
spark " has been developed, which gives substantially continu- 
ous or undamped waves. The essential feature of the timed 
spark transmitter is a series of synchronous rotary gaps 
mounted on the same shaft, each gap having the same number 
of electrodes and the electrodes of successive gaps being stag- 
gered, .so that each gap discharges at a different time. Several 
forms of circuit have been used. In one circuit each gap is 
connected in a separate primary circuit and all the primary cir- 
cuits are coupled to the same antenna circuit. The times of 
discharge of the various gaps are so arranged that the resultant 


wave in the antenna circuit is substantially smooth and con- 
tinuous. Stations of this type have given very satisfactory 
service. The stations at Marion, Mass., and Stavanger, Nor- 
way, use timed spark transmitters. For further information, 
the reader may consult A. N, Goldsmith, Radio Telephony, page 
73, and E. E. Bucher, Practical Wireless Telegraphy, page 274. 
The use of timed spark transmitters is decreasing, because of 
improvements in other generators of undamped waves, particu- 
larly the high-frequency alternator and the arc transmitter. 

157. Simple Induction Coil Set. — For short distance communi- 
cation in trenches, and in general for power below f kw., it is 
common to use an induction coil or a power buzzer instead of 
an alternator and transformer, to charge the condenser. The 
wiring of an induction coil is shown in Fig. 188. P is the pri- 
mary (Oil of a few turns (heavy lines) : (S is the secondary of 
many turns of fine wire; / is a laminated soft-iron core mag- 
netized by the primary current ; and ^ is a piece of soft iron 
at the end of a spring forming a sort of vibrating hammer ; R 
is an adjusting screw for the vibrator ; C is a condenser of a 
few microfarads shunted around the vibrator points to prevent 
their burning. The vibrator points may be replaced when 
necessary by drilling a hole and driving in a piece of silver. 
T' shows the vibrator points where the primary current is made 
and broken in rapid succession as long as the key K is closted. 
When current flows, H is first attracted by the iron core, 
breaking the current at V after which the spring causes it to 
return to its first positicm, remaking the current. The action 
is then repeated. The frequency of operation depends upon 
the mass of the hammer H and the stiffness and length of the 
spring. It is similar in that respect to an electric bell. This 
piece of apparatus is really an open core transformer, the 
changes of current being produced by the automatic interrupter 
or vibrator, which is operated by the magnetism of the core. 
The source of power is usually a storage battery of 8 to 20 
volts. Owing to the changes of primary current, rapid changes 
of magnetic flux occur and produce a high voltage in the large 
number of turns of the secondary coil. 

Referring again to Fig. 180, consider the induction coil put 
in place of the a.c. transformer. When the coil is put into 



operation, with its secondary terminals connected to the con- 
denser and discharge circuit, a continuous stream of sparks will 
pass across the spark gap as long as the key is pressed. 

158. Operation of Induction Coils from Power Lines, — Fairly 
large power induction coil sets are used as emergency trans- 
mitters on ships. These employ batteries, so as to be inde- 
pendent of the ship's generator. On land, however, when a 
battery is not available, it is possible to operate an induction 
coil from a d.c. 110-volt power line by inserting a rheostat in 
series. In this case, it is absolutely necessary to shunt the 
transmitting key with a condenser similar to the vibrator con- 
denser, or else a serious arc at the key will take place at the 


lo ohm? I I % oKr 

FiQ. m 

Induction coil on ^ 

d c. jaowcr line 
(Secondary circyit 
no1" •shown) 




Fia, HO 


rower bu'jT^r circoil" __ __ 

first attempt to signal, and the current will not be broken when 
the key is released. Of course, the method of inserting a rheo- 
stat is very wasteful, since the RP loss in the rheostat is large, 
much greater in fact, than the power actually used in the radio 

A scheme to avoid a voltage as high as the 110 volts across 
the break at the key is to use a voltage divider (see Sec. 15) 
consisting of two rheostats in series, as in Fig. 189. Suppose 
the spark coil has 2 ohms resistance in the primary, and re- 
quires 10 volts to operate it. If one rheostat is set at 10 
ohms and the other at 2 ohms, with the induction coil and key 
in a shunt around the 2-ohm coil, then the voltage applied to 
the induction coil will be 10 volts with the key closed. Note 
that the voltage across the key when open is 18.3 volts. 

With a.c. supply the methods are different. One method of 
operating an induction coil from 110 volts a.c. is to use a small. 


Step-down transformer to reduce the voltage to an equivalent 
battery voltage. This requires no series resistance or reactance, 
and is a fairly efficient method. Induction coils are sometimes 
operated on 110-volt a.c. power lines by insertion of a series 
reactance. The vibrator in the primary circuit is not necessary 
if the supply is 500-cycle, and it is preferable to clamp it per- 
manently in the closed position. The set then becomes similar 
to Fig. 180. Induction coils may have the primary wound for 
110 volts, in which case there is no need for any step-down 
transformer series reactance, or resistance. 

159. Portable Transmitting Sets. — For portable sets, or for 
Army field use the simplest apparatus for short distance is a 
small induction coil set, operated from a storage battery. A 
plain spark gap may be used, for simplicity, but the use of a 
quenched gap will usually improve the operation. When fairly 
long distances are to be covered it is advisable to replace the 
induction coil by a small step-up transformer. A source of 
alternating current then takes the place of the battery. For a 
small set this source may be a generator which is driven by 
hand through gearing. For larger power the generator may be 
driven by the engine of a motor-cycle or some other gasoline 

For short-distance work the condenser may be charged and 
radio oscillations produced, without an induction coil, by the 
use of a power buzzer and a storage battery or a few dry cells. 
See Fig. 190. The buzzer is shown at Z. The more voltage 
applied to it the gi'eater is the charge given to the condenser (7. 
When the vibrator arm is at the right in the diagram, the con- 
denser discharges through the inductance L. This forms the 
closed oscillating circuit. The condenser should be compara- 
tively small ; the apparatus is limited to short wave lengths. 

160. Simple Connections for the Production of Electric 
Waves. — Up to this point have been shown the means by which 
an oscillating discharge is produced in a condenser circuit. It is 
necessary now to learn how the oscillations can be gotten into 
an antenna so they may be sent out as radio waves. The wiring 
connections for the different methods are given in this and the 
following sections, showing first the simplest transmitting con- 
nections and then leading up to standard sets. 

53904°— 22 24 


Tiie simplest possible wave transmitter is a straight wire cut 
in the middle by a small spark gap. See Fig. 191. If the wire 
were not cut. and if oscillations could be produced in it, the 
charges would travel rapidly back and forth owning to the 
capacity and inductance of the wire and waves would move 
out into space as explained in Chapter 4. The oscillations 
taking place in the wire are of the same nature as those in the 
circuit CL of Fig. 180. The student should learn to think of 
the wire as uncut, for the gap becomes a conductor when the 
spark is passing. Oscillations are produced by the same means 
described in Section 154, using a high voltage to start a 
discharge across the spark gap. This is done by connecting a 
transformer or an induction coil to the gap. The use of an 
induction coil is shown in Fig. 191. The two halves of the 
wire charge up as a condenser until the potential difference 
rises so high that the insulating property of the gap is broken 
down. There is then a discharge across the gaps and oscilla- 
tions pass freely until the energy is spent. The gap then be- 
comes nonconducting again, as has been explained, and permits 
a renewed charging. The process is repeated as many times a 
second as the vibrator works. 

The interval from one break at the vibrator to the next may 
be about 0.01 second, while it will take only in the neighborhood 
of 0.00001 second for the discharge to be completely accom- 
plished (basis of illustration is a wave length of 150 meters, 20 
waves to a train). Thus it is seen that there is a comparatively 
large time interval between successive wave trains, in which the 
gap may cool and be restored. A sketch of the discharge cur- 
rent is shown in Fig. 192, but the wave trains are not shown 
nearly far enough apart for the case of a damped oscillator such 
as that of Fig. 191. To show how relatively large the time inter- 
val between successive wave trains is, it might be staled that 
in this illustration the length of the wave train itself compares 
with the length of the idle interval between wave trains about 
in the same ratio as one day compares with three years. 

The next theoretical step toward a standard radio transmit- 
ting set is to add large metal plates to the outer ends of the 
straight wires. See Fig. 193. This increases the capacity of the 
oscillator and causes larger charges to accumulate for the same 



potential difference, thus giving a larger flow of current back 
and forth in the wire and sending out more electric and magnetic 
lines of force. The strength of signals and the range are thus 

It is shown in Section 132 that the lower half of the oscillat- 
ing system, Figs. 191 or 193, may be replaced by the ground, the 
action of the upper half remaining as before. Also, it is 
customary to replace the upper capacity plate of Fig. 193 by 

Simple trArNSfTMltir^ 
Set(i/sir\g irvdoctiorv 




Fio. 1^2 -;; 

f lO. )^3 

E,Ad ^UteS ■for 


ooool Sec 



OOI ^^r. J 

PdrrNJaed WAve trckifNS ( »!oT to •scdltf) 

one or more wires, horizontal or nearly so. See Fig. 194. A 
relatively large capacity can thus be added, and the construc- 
tional difficulties and arrangements of support are simplified. 
This assemblage of wires forms the " antenna." A variable 
inductance coil inserted in the antenna wire will permit tuning 
to different frequencies or wave lengths. Thus a simple trans- 
mitting outfit is built up. 

The arrangement shown in Fig. 194 is sometimes called a 
" plain antenna connection " to distinguish it from the in- 
ductively coupled set explained below. It is a good radiating 
system, but the waves emitted are of such high decrement that 
they can not be readily tuned out in receiving apparatus wlien 



one does not desire to receive them. See Section 116. Hence 
this system is not permissible in general practice.^ Its advan- 
tages besides simplicity are, however, its effectiveness in 
cases where the sending operator wants all possible sta- 
tions to hear him, as, for instance, when a ship needs help, 
and secondly its military use in purposely drowning out or 
" jamming " other signals which an enemy is trying to re- 
ceive. The connection is very quickly made by inserting the 
spark gap directly between the antenna and ground wires and 

tndcictively cqylslecJ tr*ns- 
tnitlirA Af)par«4TOs with 

3|>a(i(^^acnas» frAnsforn>er 

Fio. 1^5 

Inductively cou^lsci 

TrdnsmiTtirtg Aff>*'"<i1'Lid 

connecting the current source across the gap. Arcing in the gap 
must be guarded against, and care should be taken not to open 
the gap too wide, or the antenna insulation may break down. 

161. Inductively Coupled Transmitting Set. — Instead of con- 
necting the spark gap directly in series with the antenna it 
may be placed in a separate oscillating circuit like that of Fig. 
180 and this circuit then coupled with the antenna. In the most 

1 The radiation of a wave having a decrement per complete oscilla- 
tion exceeding 0.2 is forbidden by law. except for the transmission of 
distress signals. See the pamphlet Radio Communication Laws of the 
United States^ for sale by the Superintendent of Documents, Wash- 
ington, D. C. 


common method the coil of the oscillating circuit (called the 
" closed " circuit to distinguish it from the open or antenna 
circuit) is coupled inductively to the inductance coil in series 
with the antenna. The circuits thus become Fig. 195. One of 
the advantages of this method is that the condenser in the 
closed circuit may have much greater capacity than the an- 
tenna and thus may store more energj^ for each alternation of 
the supply voltage ; this energy is handed over to the antenna^ 
which thus becomes a more powerful radiator. Other features^ 
of the method are given in Section 163 below. 

As before, either an induction coil or a transformer with, 
a.c. supply voltage may be used. In Fig. 195 the latter is shown, 
T is an iron core transformer, somewhat similar in construc- 
tion to the ordinary transformer used in electric light systems. 
The two inductance coils P and /Sf constitute what is sometimes 
called an " oscillation transformer." A hot-wire ammeter is in 
series with the antenna. The positions of the spark gap and 
condenser are sometimes interchanged, bringing the spark gap 
across the transformer. See Fig. 196. There is no practical 
difference in the operation. 

The condenser discharge can not take place through the 
transformer T on account of its very great impedance, but 
passes across the spark gap and through the few turns of the 
primary coil P, producing a rapidly changing magnetic flux 
within the coil. The secondary coil S is placed near or inside 
of coil P, so that part of the alternating magnetic flux of P 
passes through /S. There are three principal styles of oscilla- 
tion transformer, the double helix, hinged coil, and flat spiral 
types. See Figs. 197, 198, 199. In order to have a low resist- 
ance the conductor is usually a copper ribbon of large surface, 
or edgewise-wound copper strip. The amount of coupling, or 
the mutual inductance, between them is varied by moving one 
or both of the pair. Connections are made to such coils by 
movable clips, so that any desired amount of self-inductance 
may be used. 

The hot-wire ammeter is used for measuring the current in 
the antenna circuit. For merely tuning to resonance a low- 
resistance lamp such as a small flashlight lamp may be used in 
place of the hot-wire ammeter, the maximum current being indi- 
cated by the maximum brightness of the lamp filament. If the 




current is too great for the lamp, it should be shunted by a 
sliort length of wire. The ammeter or lamp may be short cir- 

FiG. 197. — Double helix oscillation transformpr ; coils separated axially. 

cuited except when actually needed in order to keep the resist- 
ance of the antenna circuit low. 



162. Direct Coupled Transmitting Set, — Direct instead of in- 
ductive coupling- may he used between the closed circuit and 
the antenna circuit, as in Fig. 200. (Direct coupling was ex- 
plained in Sec. 119.) One inductance coil is all that is needed. 
By the contacts shown, as much or as little of the inductance as 
desired can be used in either circuit. In order to tune to some 
wave leii.uths it may be necessary to have an additional coil in 

Fig. 198. — Hinged coil oscillation transformer. 

series in the closed circuit. By making the part of the in- 
ductance that is common to both circuits a small part of the 
total inductances in the circuits the coupling can be made as 
loose as desired. Since direct and inductive coupling are 
strictly equivalent, the discussion of one applies to both. 

163. Comparison of Coupled and Plain Antenna Sets. — In the 
plain antenna set of Fig. 194 the spark gap is in series with the 
antenna. Thus the resistance of the gap is present and helps to 



make the decrement of the radiated waves high. While high 
decrement is an advantage in special cases, as explained in 
Section 160, it is usually not desirable. When the spark gap 
is in a separate circuit, coupled either inductively or directly 
to the antenna, as in Figs. 195 or 200, the resistance of the 
spark gap does not enter into the antenna resistance. The 
resistance of the gap is high, and can not be changed much 
under practical operating conditions, and therefore in a set with 
plain antenna connectioji the decrement of the emitted wave is 
only to a small extent subject to control. If a set with a plain 
antenna connection is worked at a wave length several times 

the fundamental of the an- 
tenna, a smaller decrement 
man be obtained, but the 
power radiated will be con- 
siderably reduced. 

In a coupled circuit the re- 
sistance of the antenna and 
the resistance of the ground 
connection are important fac- 
tors in determining the decre- 
ment of the radiated wave. 
Hence in a coupled circuit, 
for a given gap adjustment, 
the decrement of the radiated 
wave can to a considerable 
extent be controlled by varying the resistances of the antenna 
and the ground connection and by varying the coupling. The 
varying of the coupling will affect the decrement as well as the 
•' purity " of the radiated wave. In a coupled circuit, with the 
resistance fixed, increasing the capacity of the primary circuit 
and decreasing its inductance will decrease the decrement of 
the radiated wave. 

One important advantage of the coupled connection is that 
the maximum power which can be radiated from a given 
antenna is considerably greater with a coupled connection than 
with a plain antenna connection. 

Radiation of a sharp wave is especially important in military 
work. There may be several hundred stations transmitting in 
the area occupied by an Army corps, and the wave emitted by 

Tig. m 

Tiat 5piraf Type 
Oscillation Transformer. 



even the best spark transmitter may not be satisfactory. Tlie 
use of the electron tube transmitter (see Chap. 6) is being 
greatly extended for such work, and spark sets are used only 
under special conditions. 

When a quenched gap is used it would make the decrement 
much worse if used in the antenna circuit. When used in the 
closed circuit, however, the oscillations in the closed circuit 
have such a high decrement that they stop almost immediately 
and simply start the antenna circuit oscillating, which there- 
after oscillates with its natural decrement, which may be 
small. This is the condition which exists when the proper 


Direct cou^lsd 

critical coupling is used. Many operators, however, fail to 
operate quenched gap sets properly adjusted for critical cou- 
pling. When a quenched gap is not properly adjusted, the wave 
may be very broad and the tone may be very poor. (See also 
page 360.) 

On account of the small decrement of the oscillations in the 
antenna circuit the instantaneous voltages do not reach as high 
values, with a given current and power output, as they do when 
the oscillations are strongly damped. Thus the voltages in the 
antenna are not as great when the coupled circuit is used and 
the antenna insulators are not as likely to fail. 

164. Tuning and Resonance, — A very pronounced maximum of 
current is obtained in the antenna circuit when its natural 
period of oscillation is the same as that of the primary circuit. 
This occurs when LgCg=LpCp. (See Chap. 3, Sec. 116.) L^ is 


the inductance of the antenna circuit, including the antenna 
itself, lead-in wire, and the secondary coil of the air-core trans- 
former. Cg is the capacity of the same circuit. L^ is the in- 
<luctance of the primary circuit, and since the wiring is short 
the inductance is nearly all in the coil L. Likewise, since C has 
i\ large capacity, Op is practically the capacity of this condenser. 
It is not necessary in operation to measure any of these quan- 
tities. The hot-wire ammeter will show by trials when the prod- 
ucts are equal, or a wavemeter will enable the operator to 
adjust each circuit P and S' to the same frequency, or to any 
desired wave length. The principal case where the inductances 
and capacities need to be known is in the design of a set which 
differs from previous sets so much that the proper size of ap- 
paratus is not known. To adjust the apparatus to send out long 
waves, a large inductance may be used in series with the an- 
tenna. It is preferable, however, to use a large antenna, thus 
obtaining large capacity, which stores up large charges and 
allows a large radiating current. 

165. Coupling. — When the antenna and closed circuits are 
adjusted independently to the same frequency or wave length, 
and then closely coupled together, waves of two frequencies ap- 
pear in each circuit. See Section 120. For showing the double 
wave in radio apparatus, a wavemeter (see Section 112) placed 
near either of these coupled radio circuits will be found to 
indicate a maximum response at two different wave lengths. If 
then the coupling between the two circuits is diminished, the 
two wave lengths approach each other and the wave length for 
which the circuits were set, and at a very loose coupling only 
one wave length will be discernible. Figs. 201 to 204 show 
resonance curves for the case where the primary and secondary 
are adjusted separately to 600 meters, and then are coupled by 
bringing the secondary and primary coils near together (when 
the coupling is inductive). When the coupling is direct it is 
made closer by making a larger part of the inductance of each 
circuit common to both circuits. These effects are more pro- 
nounced when a plain or rotary rather than a quenched gap is 

Fig. 201 might allow of fairly sharp tuning on one of the 
Avave lengths, but only the energy of one wave could be utilized 
by a receiving apparatus. Figs. 202 an4 203 would be the 



equivalent of a single wave of very broad shape or high decre- 
ment, such that the strength of the signals is nearly the same 
over a wide range of wave lengths. In Fig. 204 the signals are 
strong ;it or near only one wave length, and diminish rapidly if 
any of the apparatus adjustments are changed. This is said to 
be a "pure" wave/ It is desirable to have as sharp a reso- 
nance curve as possible, and hence loose coupling is the rule 
when a plain gap is used. The advantage is that all the power 
sent out is concentrated into a narrow range of wave lengths, 
and that receiving stations can tune to the one wave length 


Fia. Z03 

>1 C !ter 5 

Resondince corve.Ooils .3e^r<»l«A 


Ft q. 204 


l?esoriAPic« curv«, Coils 3e(>4rdi1ee( -further Resorvance curve, very loos« cou^lir^ 

emitted by the transmitting station which they desire to receive 
and exclude all other wave lengths from other transmitting 

Action of the Quenched Gap; Relation to Coupling. — Refer 
again to the inductively coupled apparatus of Fig. 195 and to the 
waves of Fig. 154 in Chapter 3. Also refer to the description 

' The United States radio law requires that if a transmitting station 
emits more than one wave length, the energy in no one of the lesser 
waves shall exceed one-tenth of the energy in the principal wave. See 
the pamphlet, " Radio Communication Laws of the United States." is- 
sued by the Bureau of Navigation, Department of Commerce. Copies 
may be secured from the Superintendent of Documents, Government 
Printing Office, Washington, for 15 cents each. 


of the quenched g:ap in Section 156. The action of the quenched 
gap is to open the primary circuit, by suppression of the spark 
at the end of its first train of waves (point D in Fig, 154). 
This prevents the secondary from inducing oscillations in the 
primary again ; that is, from giving energy back to the primary. 
The secondary or antenna oscillations are not thereafter inter- 
fered with by the primary and the antenna goes on oscillating 
until the energy is all dissipated as waves or heat (see Fig. 
155). The length of the train will depend only upon the decre- 
ment of the antenna circuit. By reducing the resistance, the 
dielectric losses, the brush discharges and leakage, the antenna 
current may be made to oscillate for a comparatively long time, 
at the frequency for which the set was adjusted. This quench- 
ing of the primary avoids the double waves of Figs. 201, 202, 
and 203, even with close coupling. In fact, the coupling should 
be close for good operation with the quenched gap. Some care 
has to be taken in the adjustment of the coupling, but when ad- 
justed properly this gap gives a high pitched, clear note. The 
wavemeter will readily show when a single sharp wave is 
obtained (see Section 1G8), and the sound in the telephone 
receiver will indicate the proper adjustment for good tone. The 
quenched gap is very efficient, because the close coupling pro- 
duces a large current in the antenna. 

It is well to note that the principles of operation of the 
quenched gap and plain gap are exactly opposite. The former 
aims to stop the primary oscillations quickly, after the second- 
ary has been brought to full activity. The latter aims to keep 
the primary oscillations going as long as possible, all the time 
giving energy to the secondary as it is radiated away ; the 
coupling is loose and the primary decrement is kept low. The 
rapid decrease of the oscillations in a quenched gap circuit is 
assisted by having a large ratio of capacity to inductance. This 
has the incidental advantage that the voltages across the con- 
denser and coil are thus kept low. 

166. Damping and Decrement. — If the energj^ in the antenna 
circuit is dissipated at too rapid a rate, owing either to radiated 
waves or heat losses, the oscillations die out rapidly and not 
enough waves exist in a received train to set up oscillations of 
a well-defined period in a receiving antenna. Such waves are 
strongly damped and have a large decrement. They produce 


received currents of about the same value for a considerable 
range of wave lengths. Thus selective tuning is not possible.^ 
To increase the number of waves sent out in each wave train 
from the open circuit (that is, to make the oscillations last 
longer) the resistance of the circuits must be kept low. When 
using a plain spark gap the coupling between closed and antenna 
circuits must be small enough not to take energy too fast from 
the closed oscillating circuits. At each condenser discharge the 
primary has a train of oscillations which at best die out long 
before another train starts (see Fig. 192) ; these oscillations 
are stopped more quickly, however, if the energy is drawn 
rapidly out of the circuit by the antenna. Close coupling is 
permissible only when a quenched gap is used (see remarks at 
the end of the preceding section). With any other kind of gap 
the secondary is kept oscillating by energy continually received 
from the primary. 

A great many factors contribute to the resistance of the an- 
tenna circuit, and this must be kept as low as possible. The 
antenna must have a good low-resistance ground, must use 
wires of fairly low resistance, and must not be directly over 
trees or other poor dielectrics. The resistance of the closed 
circuit particularly must be very low. Heavier currents flow 
here than in the antenna wires. For this reason the closed cir- 
cuit wires should be short and of large surface, preferably 
stranded wires or copper tubing. The condenser should be a 
good one, free from power loss. 

167. Additional Appliances. — A number of additional appli- 
ances are necessary or desirable for the operation of a damped 
wave generating set. The operation is improved by having a 
variable reactance (iron core inductor) in series with the 
alternator, to tune the alternator circuit to the alternator fre- 
quency. See Bureau of Standards Circular 74, p. 230. 

Changes of Wave Lenf/th. — In many sets of apparatus it is 
customary to have connections arranged by means of which 
different chosen wave lengths, say 300 or 600 meters, can be 
transmitted without the necessity of a readjustment of the 
apparatus after each change. An antenna alone without any 
inductance coil has a natural wave length of its own, dependent 

3 Sep also section 116. The United States radio laws require that 
no station shall transmit a wave having a decrement exceeding 0.2. 



upon its inductance and capacity. See Sections 116 and 145. The 
antenna is usually so designed that its natural wave length is 
shorter than the wave length to be used, and the wave length 
is brought up by adding inductance in series or merely bj^ the 
added inductance of the secondary of the oscillation trans- 
former. In the case of a small antenna, such as that on a small 
sliip. it is necessary to use a large inductance. Since it is de- 
sirable to have the coupling loose, a part of the secondary in- 
ductance can be in a separate coil called the antenna " loading 
coil." Tliis loading coil is not coupled to the primary. Fig. 205 
shows this arrangement. For a quick change of wave length 
a single switch is often provided, which, by a mechanism of 

Fjo. Z05 




-• •- 





Tories - ^railel 

Conr\ectior\ crf'"foor 

ConcJ Aniens 

le\ers, changes simultaneously the adjustments on all three 
coils. From these coils are taken out taps over which three 
switch blades pass, adjusting all the inductances to approxi- 
mately the values needed for the particular wave length desired, 
keei>ing the circuits in resonance and at the proper coupling. 
Foi- tine adjustments an additional variable inductor may be 
provided in the primary and in the secondary. 

Fig. 205 also shows an arrangement whereby the operator can 
obtain wave lengths shorter than the natural wave length of 
the antenna by inserting a condenser in series (see Sec. 35) in 
the antenna circuit. In this case the loading coil will be set at 
zero turn.s to diminish the wave length. The condenser in- 
serted nmst be capable of withstanding high voltages similar to 
those in the main transmitting condenser. By using a small 
capacity the wave length can be reduced to approach one-half 


of the natural wave length. It should not be reduced that much, 
however, for the radiation is inefficient if the condenser is too 
small. A zero capacity (an open circuit cutting off the antenna 
entirely from the ground) would be necessary to produce half- 
wave length exactly. 

Choke coils. — Fig. 205 shows also choke coils to prevent the 
high-frequenc.\' condenser discharge from getting into the trans- 
former and puncturing the insulation. The coils choke down 
the radio-frequency current but do not obstruct the low-fre- 
quency charging current from the transformer. They must be 
specially designed so that they do not have capacity enough to 
allovv' the radio-frequency current to pass. They can often be 
dispensed with. See also Appendix 9, page 578. 

168. Adjustment of a Typical Set for Sharp Wave and Radia- 
tion. — The set is assumed to be an inductively coupled set. ar- 
ranged as in Fig. 205. The first step in adjusting it to work 
properly is to tune the closed circuit to the wave length which 
is to l>e used. This is usually done by varying the primary in- 
ductance, which includes the primary of the oscillation trans- 
former. The primary capacity is usually fixed in value and 
not readily changed. Manufacturers usually mark on the pri- 
mary variable inductance the wave lengths corresponding to 
various settings. If this has not been done, it will be neces- 
sary to determine the wave lengtli by the aid of a wavemeter 
having in its circuit a sensitive hot-wire ammeter. The wave- 
meter is placed at a distance of one or more meters from the coil 
of the closed circuit, and with the set in operation but the an- 
tenna circuit opened, the wavemeter coil is so turned that a small 
current is observed in the wavemeter ammeter. With the wave- 
meter set at the chosen w^ave length the closed circuit induc- 
tance is varied until resonance is obtained. If no resonance 
point is found, it is probable that the closed circuit inductance 
or capacity is either too large or too small. This inductance 
should be varied and a resonance point will be located after a 
few trials. It may also be necessary to increase or decrease 
the number of condensers used. 

The next i:)rocess is to adjust the secondary inductance and 
the coupling to obtain a pure, sharp wave; that is, to get as 
nmch as possible of the power into the wave length that is to 
be used. Both primary and secondary circuits are closed and 


coupled together, using at first a fairly loose coupling unless 
the spark gap is a quenched gap. The secondary of the oscilla- 
tion transformer or the antenna loading coil is varied until 
resonance is obtained, as shown by a maximum reading of the 
hot-wire ammeter in series with the antenna. This adjustment 
may be checked with a wavemeter. The wave length at which 
maximum current is obtained should be the same as the wave 
length for which the primary was adjusted. The wavemeter 
should not be coupled to the secondary of the oscillation trans- 
former, but to a loading coil or other coil at a distance, or to 
the ground connection. The coupling is then made closer until 
two points of resonance appear. It is desirable to have a pure 
wave ; that is, have only one resonance point. Therefore the 
coupling is loosened until it is certain that there is just one 
sharp point of resonance. If the set has a quenched gap, the 
coupling is kept close, and varied only enough to insure a single, 
sharp, wave. The radiation of maximum current at the de- 
sired wave length will not occur when the coupling is tightest, 
nor will it necessarily occur when the reading of the antenna 
ammeter is greatest. The condition for efficient transmission 
is that maximum energy radiation should be secured at the wave 
length to which the set is adjusted. 

It is next necessary to adjust the generator voltage and the 
length of the spark gap to get maximum current in the an- 
tenna at the desired wave length, and a good clear spark tone. 
The field current of the alternator and the length of the spark 
gap are adjusted until maximum current and best tone are ob- 
tained, the wave length and coupling adjustments being kept 
fixed. It is often desirable to vary the coupling a little and 
then repeat this adjustment, since in some cases a small in- 
crease of coupling may make it possible to obtain increased 
antenna current without seriously affecting the sharpness of 
the radiated wave. For a quenched gap, the coupling adjust- 
ment required for maximum antenna current and best tone is 
very critical. 

The first two adjustments mentioned are made for the pur- 
pose of obtaining in the circuits resonance to the radio fre- 
quency which it is desired to radiate. It is, however, also im- 
portant to obtain proper tuning with respect to the low audio 
frequency (perhaps 60 to 1,000 cycles) generated by the alter- 


nator. The audio frequency to which the circuit should be 
tuned to get the best tone and most satisfactory operation is 
not the frequency supplied by the alternator, but is some 10 
per cent to 20 per cent lower than the alternator frequency. 
The reactances of the transformer and of the rotor of the 
alternator are very important in determining the audio-frequency 
tuning characteristics, and for a given transmitting set the 
transformer and alternator are usually so designed that their 
reactances will be of the proper magnitudes at the operating 
frequency. If the transformer and alternator do not have the 
proper reactance, it may be necessary to supply an inductance 
in series with the alternator field. If such a series inductance 
is used', its setting to a proper value constitutes a fourth ad- 
justment of a spark set. For a further discussion of tuning 
to the audio frequency, see Bureau of Standards Circular 74, 
p. 230, and H. E. Hallborg, Proceedings Institute Radio Engi- 
neers, vol. C, p. 107, June, 1915. 

169. Efficiency of the Set. — To maintain good efficiency, all re- 
sistances in the circuits must be kept as low as possible. A 
number of suggestions for keeping resistances low were given 
in Section 166. It is also necessary to avoid brush discharges 
and arcs, to keep all connections tight, condenser plates and 
other parts of circuits free from dust and moisture, and antenna 
well Insulated. Brush discharges may be reduced by eliminat- 
ing sharp points or edges on conductors, or by coating the edges 
of metal plates with paraffin. The guy wires of the antenna 
should be divided into short lengths with insulators between 
them to reduce the flow of current in them. The inductance 
coils and the spark gap must be properly designed. 

The efficiency may be defined as the ratio of the power ra- 
diated away as electric waves from the antenna to the power 
input in the transformer. The power input P in the transformer 
may be measured by an ordinary wattmeter. The power radi- 
ated from the antenna can be expressed in the form RP where 
I is the current in the ammeter at the base of the antenna and 
R is the radiation resistance. The efficiency is then RP divided 
by P. As explained in Section 143, the radiation resistance can 
not be measured directly, but can be found from the total effec- 
tive antenna resistance by subtracting those resistances which 
give rise to heat losses. 
53904°— 22 25 


Representative values for the efficiency of the entire set are 2 
per cent to 15 per cent. The transformer efficiency may be 
rouglily 85 per cent to 95 per cent. The closed oscillation cir- 
cuit losses are very large in proportion to the power transferred, 
a fair value of efficiency being about 25 per cent (by careful 
design and adjustment using the quenched gap this may some- 
times be increased to 50 per cent). The efficiency of the antenna 
circuit (radiated power divided by power given to the antenna) 
may be between 20 per cent and 2 per cent or lower, or may be 
made as high as 50 per cent if special pains are taken. The 
product of the three separate percentages gives the over-all effi- 
ciency. For an interesting table of comparative values of 
efficiencies see J. A. Fleming's *' Wireless Telegraphist's Pocket 
Book." pp. 221 and 223. 

170. Calculations Required in Design. — This section gives methods for 
determining the values of condensers and coils to be used in transmit- 
ting apparatus, and enables one to calculate the capacity or induc- 
tance of such condensers and coils as are commonly employed. The 
most important design formula is the one for wave length, 


where C is in microfarads and L in microhenries and X in meters. 

Transmitting Condensers. — The amount of capacity needed in the 
condenser in the closed transmitting circuit may be determined from 
the formula 

where C is the capacity in microfarads, P is the power in watts, 2V is 
the number of condenser charges per second, and E(, is the maximum 
emf. in volts. It may be seen from this that if a low voltage E^ is used 
the capacity needed for a given power will be large and if a high volt- 
age is used the capacity may be smaller. There is a large reduction of 
capacity with a small increase of voltage, because the voltage term is 
squared, therefore to avoid using unduly large condensers it is well to 
use as high a voltage as possible without brush discharge taking place. 
For instance, if the voltage were doubled, a condenser only one-fourth 
as large could be used for the same power. As an illustration, if it is 
desired to use I kw. at 12,000 volts, with 1,000 sparks per second, 

2X106X500 „ _ . , . 
5=0.00/ microfarad. 



Knowing the total capacity required, the number of sheets of dielec- 
tric required to make up the condenser is obtained from the formula, 

1 nS 

C=0.0885Xj^X.^y (88) 



where K is the dielectric constant of the insulating material, n is the 
number of sheets of dielectric, S is the area of each shei't in square 
centimeters, t is the thickness in centimeters, and C is the capacity 
in microfarads. Supposing that mica is not available, it may be re- 
quired to find the number of sheets of glass required to make up the 
condenser of 0.007 microfarad required above. Suppose the sheets are 
15 by 20 cm., 0.25 cm. thick, and the dielectric constant is 7. Substi- 
tuting in the formula just given, 

0.25X0. 007 XlQfi 
**" .0885 X 7 X 15 X 20" ^ 

Thus nine sheets of this dielectric are needed. 

Fia. 207 


rtelix^ round wir« 


"SceC^ionAl view of-fUtsljnak 
Woynd <jf mat»t ripborv 

rtcliA, fldt condocTor 


Side view df flats^ir*t 

It should be noted that the higher the spark frequency N the smaller 
may be the condenser used to give the same power. For this rear^on, 
as well as the others previously given, it is a distinct advantage to 
use a high spark frequency. 

When the voltage at which it is desired to operate the spark gap is 
so high that it will break down the particular insulation used in the 
condensers or cause brush discharge, the connection of four con- 
densers, each of capacity C, as shown in Fig. 206, p. 380, will give a 
resultant capacity C, while subjecting each condenser to only half the 
full voltage. 



Inductance Coils. — The principal inductance coils in a radio set are 
the primary and secondary of the oscillation transformer and the an- 
tenna loading coil, and the three corresponding coils of the receiving 
set. The three coils, oscillation primary and secondary and loading 
coil, are very similar. In actual practice few operators know even 
approximate values of the inductances ; a standard form is used, depend- 
ing somewhat on the size of the set, and adjustments by clips or taps 
enable the proper values to be used. In order to design a set the in- 
ductances of the coils are calculated and an allowance made for the 
small inductance in the leads and other parts of the circuit. The form 
usually used for coils in transmitting circuits is either the helix (single 
layer spaced coil) of round wire or edgewise wound strip, Figs. 207 and 
208, or the flat spiral or pancake of bare metal ribbon. Figs. 209 and 

Fid. 211 

Fi<3. 2'2 

oi form for 

Cr»5> Section of MulhUyier cei 

Fio. 213 


Cross ■Section of <"ir\8le Uyercoi/ 

210. For wavemeters a multilayer coil is used, having wires insulated 
and close together. Figs. 211 and 212. For receiving coils the common 
form is a single layer of insulated wires, Fig. 213. The coils are sup- 
ported or held together by some insulating material, and no iron is 
used in them. 

Helix of Round Wire. — The inductance of the helical single-layer coil 
or solenoid of Fig. 207 is given in microhenries by 




where a and h are shown in Fig. 213, o being the mean radius of the 
solenoid and 6 the total length of the solenoid ; n is the number of turns 
of wire in the single layer ; d is the diameter of the bare wire ; and K 
is a shape factor depending upon the relative dimensions, all lengths 
being expressed in centimeters. A brief table of values of K is given 
below. In the figure, D is the pitch of the winding or the distance 



between centers of adjacent wires ; c is the radial thickness of the 

As an example, find the inductance of a solenoid having 15 turns of 
bare wire of diameter 0.4 cm., pitch of winding 1.1 cm., diameter of 
core 24 cm. In the formula d^O.4 cm., D=l.l cm., n=15, 6=»iZ)=16.5 

2a 24 4 
cm., a=12+.2=12.2 cm. Then with -r^=T-^. = lA8, K is found as 0.598. From the 
' lu.5 

above formula the inductance in microhenries is given by 

Zr = TTT-? XO. 598=48.0 


If it is desired to compute the inductance more closely than a few 
per cent, more accurate formulas should be used as given on page 253 of 
Bureau of Standards Circular No. 74 and in Bureau of Standards 
Scientific Paper No. 169. 

(Shape Factor of HeUcal Inductance Coils.) 













0. 761 : 






.735 1 






.711 ; 




.939 ; 








. 638 

































Helix of Edgewise Wound Strip. — Refer to Fig. 208. For this case 
the formula is 

L = 

0. 0395 a^n^K 0. 0126 n'^ac 


microhenries, where K is given in the table above. 

As an illustration of use of the formula, a helix of 30 turns is 

wound with metal strip 0.635 cm. wide by 0.159 cm. thick with a 

^winding pitch of 0.635 cm., to form a solenoid of mean diameter 25.4 

cm. Here Z>=0.635 cm., «=12,7 cm., c=0.635 cm., b=nD= 

30X0.635=19.05 cm. For ^ =1.333, A'=0.623. 
Then from the above formula 

jr _ 0. 0395X12. 72X900X0. 623 0. 0126X900X12. 7X0- 635 
19. 05 19. 05 

L=182.5 microhenries. 


Flat Spiral. — See Figs. 209 and 210. The inductance is given by 

i=0.01257an^x[2.303(l+3g,+^)log4«-y,+^y3] (gj, 

whose o =01 + ^(71—1)2); d= V^2 + C2,- and yi and ys are shape factors 
given in the following table. See example below. 

Shape Factors for Flat Spiral Inductance. 













0. 677 





























































Illustration. — A flat spiral of 38 turns is wound with copper ribbon 
whose cross sectional dimensions are 0.953 cm. (3/8 in.) by 0.793 
cm. (1/32 in.), the inner diameter being 10.3 cm., and the measured 
pitch 0.4 cm. Here w=38, 5=0.953, D=0.4, c=nD=38 X 0.4=15.2 

cm.; 2ai=10.3 therefore a=5.15+^X0.4=12.55 cm.; d= Vo.9532+15.22=15.23 cm.; 



= 0.0002; 

x= 0.0152 


r-^„=0.09i; —=0.0627. Then from the table, 

d=^-^^^' 3-2^2="-"^^' 9& i6a2- - c 

yi=0.5604 and 1/3=0.599. From the above formula, 

I,=0. 01257X12. 55X382Xf2.303X1.015XlOgio6,592-0.5604+0.09lX0.599] 

i=323.3 microhenries. 

This is correct to J of 1 per cent. 

Multi-Layer Coil. — The coil is made of insulated wire closely wound 
as in Fig. 211. Such coils are used in wavemeters. The insulating 
frame on which the coil is wound has the cross section shown iu 
Fig. 212. The inductance is given by 


0.0395 o2n2X" 0.0126 TC2ac 

6 6 

where E is given by the following table 











0. 289 






































As an illustration, a coil has 15 layers of insulated wire, with 15 
turns to a layer, the mean radius being 5 cm. The coil is 1.5 cm. deep 
and 1.5 cm. in axial length. Here a=5, n=225, 6=c=1.5. From the 
tables K is 0.267 and E is zero. Then the formula gives 

^^0.03948X25X225^ ^ ^ ,^^_ 0.01257X225^X5X1.5 ^ ^ ^^^ 


L=6682 microhenries. 

Single Layer Coil. — Refer to Fig. 213. The inductance is computed 

by the formula (89). As an illustration, a coil has 400 turns of wire 

in a single layer, pitch of winding 0.1 cm., radius of coil out to center 

of wire 10 cm. Here a=10, n=400, Z>=0.1, b=nD=40. With 

2(1 20 

■r- =77^=0.5, K is found as 0.818. 

0.03948 X 100 X 400=^ y 0.818=12920 microhenries. 
For any other inductance calculations see Bureau of Standards Cir- 
cular 74, Sections 66 to 73, and Bureau of Standards Scientific Paper 
No. 169. 

171. Simple Field Measurements. — On high power radio trans- 
mitting sets it is desirable to have instruments reading the cur- 
rent taken from the generator, the voltage of the same, the 
power so taken, and the frequency of the current. The four 
instruments, ammeter, voltmeter, wattmeter, and frequency 
meter, are permanently mounted on the switchboard. The 
measurements of the various radio quantities are explained 

Voltage. — A simple method of measuring a voltage, either 
direct current or alternating current at high or low frequen- 
cies, is to determine the length of the air gap between two elec- 
trodes across which the given voltage will just cause a spark 
to pass. The sparking voltage depends to some extent on the 
humidity, the temperature and the pressure of the air, and the 
time of application of the spark. In the case of alternating 
current this method measures the maximum value of the volt- 
age wave during a cycle. For approximate measurements this 
method can be considered to give results not depending on the 
wave form or frequency. For sine-wave alternating current 
the effective value of the voltage (the value indicated by an 
ordinary voltmeter) is, of course, the maximum value divided 
by 1.414. The observer should be cautioned not to attempt to 
change the length of the gap while the spark is passing. 



For approximate measurements at voltages under 30,000, a 
needle gap is fairly satisfactory. The needle gap is somewhat 
inconvenient because results depend to some extent on the 
diameter and the sharpness of the needles and because the 
needles must be replaced after each discharge. Fig. 214 shows 
the maximum values of sparking voltages corresponding to vari- 
ous lengths of needle gaps in air at atmospheric pressure, No. 12 
sharp needles being used." More reliable results can be ob- 
tained with a gap having brass spheres as terminals.' Fig. 214 

Length of Spark Gap - centimeters 

also shows for air at atmospheric pressure the maximum 
values of sparking voltages corresponding to various lengths of 
gap with terminals consisting of spheres one inch (2.54 cm.) in 
diameter. The results used in plotting both curves were ob- 
tained with alternating current, but will also apply to the meas- 
urement of d.c. voltages. 

* See H. W. Fisher. Trans. Int. El. Congress, 1904, vol. 2, p. 297; 
N. Campl>ell, Phil. Mag., 38, 214, August, 1919. 

^See E. A. Watson, Journal Inst. El. Eng. (London) 43, 120 (1909) ; 
J. de Kowalski, Phil. Mag., 18, 699 (1909) ; J. A. Fleming, Wireless 
Telegraphists' Pocket Book, p. 110 (London, 1915) ; F. W. Peek. 
Dielectric Phenomena in High Voltage Engineering, 2d ed., p. 88 
(New York, 1920). 


Current. — The principal cii?rent measurement in practice is 
that of the current in the antenna. A hot-wire ammeter is in- 
.serted in the lead-in or ground wire. If its reading is lower 
than normal, it indicates trouble in the adjustment of the 
apparatus, or in the grounding, and means decreased distance of 
transmission. In order to avoid undue interference with other 
stations, the ammeter current should be kept as small as will 
give the needed range. As has been stated before, a low re- 
sistance lamp can be used in place of the ammeter. When the 
closed circuit and antenna are not iu resonance, the lamp burns 
feebly or not at all. Current measurements are also necessary 
in connection with some of the various measurements. 

Wave Lengths. — The theory and use of the wavemeter have 
been discussed in Sections 112 and 168. A wavemeter placed in 
inductive coupling with a coil or antenna carrying radio cur- 
rent will show pronounced increase of current in its own coil 
and condenser whan it is tuned to resonance with the source. 
The wave length is read directly from the wavemeter setting for 
resonance, or from a calibration curve. A receiving set can be 
used to measure the wave lengths of received waves if it is 
first standardized in terms of wave lengths. This standardiza- 
tion is done by the arrangement of apparatus shown in Fig. 215, 
where Z is a buzzer, LC a wavemeter, and A the inductance 
coil of the receiving circuit. 

The operator listens in the telephone of the receiving set (not 
shown in the figure). As the wavemeter condenser knob is 
turned the loudest sound is heard when the wavemeter circuit 
is tuned to the same wave length as that for which the receiving 
set is adjusted. The wave length is then read from the wave- 
meter scale or calibration curve. Continuing in this manner, 
the receiving circuit can be calibrated as a wavemeter, by set- 
ting it at many different adjustments and reading vhe wave 
lengths at resonance each time. The wavemeter need never be 
used, after that for received waves, and the operator always 
knows where to tune for any wave length. 

Inductance. — To find the unknown inductance Z/x of a coil, a 
tuned source, which need not be a wavemeter, is excited by a 
buzzer, shown at Z in Fig. 216. A wavemeter with a coil of 
known inductance L is brought near, and its variable condenser 
adjusted to resonance at a setting C by the use of a detector 


and telephone connected as shown in Fig. 216. L is then re- 
placed by Lx and a new value of capacity C" is found for reso- 

nance. Then LC=L^C^ , and X^ is found as L*^. If the wave- 
meter reads directly in wave lengths, and \ is the wave length 
corresponding to resonance for the circuit containing L, and X' 

corresponds to resonance L^, then Lx is found as L ( r-7 j . The 

value thus measured is the apparent inductance, which depends 
somewhat on the frequency of the oscillation (see Sec. 114). 
Values of Lx can be obtained at different frequencies of the 

A second way of measuring inductance is by the use of a 
standard condenser instead of a standard coil (see Fig. 216). 
Li is connected to the standard condenser Ci, and that circuit 
is set in oscillation by the buzzer Z. The wave length is meas- 
ured by a wavemeter, and Li is computed from the relation 
X=1884VCL, where C is in microfarads, L is in microhenries, 
and X is the wave length in meters. 

A better way of connecting the detector and telephones in a 
wavemeter circuit is what is known as the " unipolar connec- 
tion," shown in Fig. 217. This method has the advantage that 
the decrement of the wavemeter circuit is kept low, permitting 
sharp tuning to resonance, and the further advantage that the 
wave length of the circuit can be accurately calculated from 
the value of L and C, which is not the case with the connection 
shown in Fig. 216. (See Circular 74 of the Bureau of Stand- 
ards, p. 105.) 

Inductance of Antennas. — The inductance of an antenna can 
be measured by the use of two loading coils whose inductance 
is known. The coils are successively connected into the antenna 
circuit, and the wave lengths for which the antenna is in reso- 
nance are determined. If the inductances of the coils are, re- 
spectively Lx and Z2, and the corresponding wave len gths are Xi a nd 
X2, then since Xi=1884 ■^{Li-\-L,)C^ and X2=1884 V(^2+-^a)Ca we 
have the relation 

L2\^ — Li\ 

-^a — ^2 > 2 
^2 ~^1 


c4^ I 

Wave Ltncfth Calibration 
of a Recti vino Set 





, § 

^r 1 

t(U) '"^ 


Fi(] Z16 


c. ul 


1 »l 1 

S 4 

Uf Lq0J 


F,<^ 21 T 


■c l: 

Ft<j 213 



#c. L 

Fiiy ^/^ 





F/y ^^^ 



Capacity of Condensers. — The simplest method to measure 
the capacity of condensers is that of comparison with a stand- 
ard variable condenser. A tuned circuit LC is excited by a 
buzzer. Z in Fig. 218. The unknown condenser Cx is placed in 
series with an inductance coil Li and the buzzer circuit adjusted 
to resonance, using the detector and telephone of the circuit 
under test. The unknown condenser Ox is then replaced by the 
standard condenser Cs, which is now^ adjusted to resonance 
with the buzzer circuit. The capacity of the unknown con- 
denser is then the same as that read on the standard. 

If a standard condenser is not obtainable, the capacity of the 
unknown variable condenser can be found by connecting it to 
an inductance of known value L and exciting the circuit by a 
buzzer. The wave length is read on a wavemeter (Fig. 219). 
Cj is found from the relation Xjji=1884VCxL. 

Accurate results are easily obtained by the first method de- 
scribed, that of comparison ; but the second method is open to 
error because of the distributed capacity of the lead wires and 
the coil, and the inductance of the leads. The effect is slight 
if the capacities employed are large. 

Capacity of Antennas. — The capacity of an antenna may be 
determined by either of the two methods just described for de- 
termining the capacity of condensers. The antenna and the 
ground form the two plates of the unknown condenser. If the 
inductance of the antenna has been determined by the method 
described above, the capacity can be calculated by substituting 
the value of La in either of the wave length equations. 



Resistance and Decrement. — Three simple methods are avail- 
able for the measurement of high-frequency resistance, (1) 
resistance substitution, (2) resistance variation, and (3) re- 
actance variation. These same methods can be used for the 
measurement of decrement, since the resistance and decrement 
are connected by the simple relation S=19.7 RfC, where R is 
the resistance in ohms, f is the frequency, and C is the capacity 
in farads at resonance which is known from the condenser 


setting. Of the three methods, the first is best if a variable 
high-frequency resistance standard is available ; the second is a 
good all around method, requiring resistance standards, but 
these need not be variable ; the third requires no resistance 
standard, and is especially suited to measuring the decrement 
of a vrave. In all three methods, the best results are obtained 
if the exciting source gives continuous or only slightly damped 
oscillations. In the resistance-substitution method, the re- 
sistance R to be measured is inserted in a tuned circuit with a 
variable condenser JC and an inductance coil L coupled loosely 
to the source, as sho\ATi in Fig. 220. A hot-wire anuneter is 
inserted at A. The circuit is tuned to the source and the 
reading of A is noted. The resistance R is then replaced by a 
variable resistance standard which is adjusted until the am- 
meter reading is the same as it was before. The known amount 
of resistance inserted is the same as R. 

In the resistance-variation method, the current is first read 
in the circuit tuned to the source, and then a known resistance 
is inserted in the circuit and the current is again read. If / 
is the current in the circuit alone, and /i is the current ob- 
served after adding the resistance Rs, then 

R.= ^' 


This method is particularly adaptable to the measurement of 
antenna resistance. 

Resistance standards for radio work must be of fine wire to 
avoid skin effect, and must be short and straight in order to 
have very little inductance. 

For additional information on measurements the reader may 
consult Circular 74 of the Bureau of Standards, and also a 
paper by J. H. Bellinger, The Measurement of Radio-Frequency 
Resistance, Phase Difference, and Decrement, published in 
the Proceedings of the Institute of Radio Engineers, vol. 7, 
pp. 27-60, February, 1919. Information regarding the measure- 
ment of antenna constants is given in Bureau of Standards 
Scientific papers Nos. 326 and 341. See also The Wireless Ex- 
perimenter's Manual, by E. E. Bucher. 


B. Apparatus for Undamped Wave Transmission. 

172. Advantages of Undamped Oscillations. — Undamped oscil- 
lations are not broken np into ^oups like damped oscillations. 
Exactly similar current cycles follow one another continuously, 
except as they are interrupted by the sending key or subjected 
to variations in amplitude. The principal sources of undamped 
oscillations are the high-frequency alternator, the arc con- 
verter, and electron tubes. The timed spark transmitter emits 
weaves which are only very slightly damped. (See Sec. 156.) 
This chapter does not take up electron tubes and their uses, 
these being treated in the following chapter. 

For transmission over long distances, as between the United 
States and France, it has been found that much better results 
are usually obtained by the use of undamped waves. Damped 
waves are, however, still used for some long-distance work. 
Desirable characteristics in transmitting apparatus for use in 
long-distance work are that it should generate a " pure wave " — 
that is, a fundamental wave in which practically no har- 
monics are present — that it should provide reliable service 
economically, that it can be manufactured in units of large size, 
that it be adapted to high-speed signaling, and that it will 
efficiently generate a wave of considerable length. For long- 
distance work it is in fact essential that long wave lengths be 
used. (See Sec. 134.) Thus the usual wave length used by the 
Annapolis 500-kw. arc station is about 17,100 meters, and the 
usual wave length used by the New Brunswick 200-kw. high- 
frequency alternator station is 13,600 meters. 

Principal advantages obtained by the use of undamped waves 
are the following: (1) Radiotelephony is made possible if a 
pure wave can be obtained. (2) Extremely sharp tuning is ob- 
tained, and it is possible for two near-by stations to work on 
wave lengths which are very close together without interfering 
with each other. The tuning is, in fact, so sharp that a slight 
change of adjustment throws a receiving set out of tune and 
the operator may pass over the correct tuning point by too 
rapid a movement of the adjusting knobs, particularly on the 
shorter wave lengths. (3) Since the oscillations go on con- 
tinuously instead of only a small fraction of the time, as in the 
case of damped waves, their amplitudes need not be so great, 


and hence the voltages applied to the transmitting condenser 
and antenna are lower. (See Sees. 116, 160.) The antenna is 
often the most expensive part of the transmitting station, and 
since the radiating power of an antenna is limited by the maxi- 
mum voltage during one impulse the radiating power of a given 
antenna is much greater with a generator of continuous waves 
than with a spark transmitter. (4) Very sensitive methods of 
reception can be used, particularly beat reception (see Sec. 205, 
p. 501), which increases the range to which an undamped wave 
station can work. (5) With damped waves, the pitch or tone 
of received signals depends wholly upon the number of sparks 
per second at the transmitter. When the beat method is 
used for receiving undamped waves the receiving operator con- 
trols the tone of the received signals, and this can be varied 
and made as high as desired to distinguish it from strays and 
to suit the sensitiveness of the ear and the telephone. These 
advantages — freedom from interference from other stations 
through selective tuning, the use of high tones, and the greater 
freedom from strays — combine to permit a higher speed of teleg- 
raphy than could otherwise be obtained. 

173. High- Frequency Alternators. — In Section 95 there has been 
briefly described the construction of several types of high- 
frequency alternators. In the United States the Alexanderson 
typQ of high-frequency alternator is the only one of practical 
importance, and this is the only type which we will consider 
In this section. As has been pointed out in Section 95, the 
Alexanderson alternator generates the frequency desired 
directly, and the frequency generated is directly proportional 
to the speed of the alternator. It is therefore necessary to have 
very constant speed in order to have a constant wave length, and 
with the regulators used with these machines a speed regulation 
of one-tenth of 1 per cent has been obtained, which is sufficient 
for practical pui-poses. The high-frequency alternator is adapted 
primarily to wave lengths longer than 10,000 meters — that is, to 
frequencies less than 30,000 cycles per second — and is therefore 
primarily of use for long-distance work. Frequencies as high as 
200,000 cycles have been obtained, however, in small units. The 
station at New Brunswick is equipped with a 200-kw. Alex- 
anderson alternator, which delivers 600 amperes to the antenna 
when working at full power. 



The inductance and capacity of tlie antenna used with a 
high-frequency alternator sliould be of such values as to give 
the circuit the same natural frequency as the frequency gen- 
erated by the alternator at the speed at which it is to be run. 
This tuning of the antenna circuit is accomplished by adjusting 
the antenna loading coil until maximum antenna current is 
obtained. At high-power stations equipped with alternators 
the multiple tuned antenna is often used. (See Sec. 143.) 

Fig. 221 shows completely assembled, with the induction motor 
which drives it, a 200-kw. Alexanderson alternator of the type 

Fig. -:21. — 20U kw. Alexaudersou alternator. 

used at New Brunswick, X, J., Tuckerton, N. J., and Marion, 
Mass. This type of machine is built to operate at wave lengths 
from 11,500 to 20,000 meters. At New Brunswick the normal 
operating wave length is 13,600 meters, which corresponds to a 
frequency of about 22,100 cycles per second. The New Bruns- 
wick station is operated by remote control, using a land wire 
from an office in New York City, about thirty miles away. 
Plans have been completed for the construction of a very large 
station of this type at Port Jefferson, Long Island, about GO 
miles from New York. This station when complete will have 
six separate alternators and six antennas. One alternator 
rated at about 200 kw, w^as placed in service in November, 


1921. The use of the alternator secures the advantages of un- 
damped waves, which are considered in the preceding section. 
The alternator has several advantages over the arc converter, 
chief of which is the freedom of the alternator from harmonics. 
The operating characteristics of large arcs make their use for 
radio telephony not practicable in their present state of de- 
velopment. The first cost of the alternator, however, is much 
higher than an arc of the same power. The arc has the 
advantage that it is more rugged, more simple, and when out of 
order can usually be quickly repaired by the regular station 
force, while if a high-frequency alternator is seriously disabled 
it is usually necessary to secure a skilled man from the factory 
to make repairs. It is possible to use the high-frequency alter- 
nator with the simplest possible kind of a circuit, simply con- 
necting one side of the alternator to ground and the other side 
to the antenna through a variable inductance. In actual prac- 
tice, however, the circuits are more complicated. Because of 
the large currents necessary for high-power stations, it is de- 
sirable to have the signaling controlled by a method which does 
not make it necessary to break the full current. This is accom- 
plished by the use of a device called a "magnetic amplifier," 
which is a variable impedance connected in shunt with the ex- 
ternal circuit of the alternator, but physically is of the nature 
of an oil-cooled transformer. The magnetic amplifier has been 
described by Alexanderson in a paper published in the Proceed- 
ings of the Institute of Radio p]nghieers, April, 1916, vol. 4, 
p. 101, and in A. N. Goldsmith, Radio Telephony, p. 192. 
The iron core is made of thin laminations and is so designed 
that the magnetic permeability of the iron core can be varied by 
causing magnetic saturation by an auxiliary-control circuit. 
This auxiliary circuit may be actuated by the signaling key in 
the case of radiotelegraphy, or by the output of a microphone 
in the case of radlotelephony. With the circuit now used the 
controlling current is in an entirely separate circuit from the 
radio-frequency current, and a control current of a few amperes 
will control an antenna current of several hundred amperes. 
When the sending key is open the magnetic amplifier short cir- 
cuits the alternator through circuits including condensers and 
detunes the antenna, thereby reducing the antenna current to a 
negligible value. When the sending key is closed the output of 
53904° — 22 26 


the alternator is delivered to the antenna at the working wave 
length. The magnetic amplifier has been successfully used ex- 
perimentally for transmitting at speeds of 500 words per minute. 
When the alternator is used for radiotelephony the magnetic 
amplifier is used for varying the alternator output in accord- 
ance with the wave form of the speech which is being trans- 
mitted. The use of small magnetic modulators for controlling 
currents of five amperes or less in electron tube radiotelephone 
sets is mentioned in Section 207, page 518. It is not possible 
in this book to describe the operation of the Alexanderson 
alternator in detail, and for further information the reader 
is referred to the papers by E. F. W. Alexanderson, Pro- 
ceedings American Institute Electrical Engineers, vol. 38, 
p. 1077, October, 1919 ; Proceedings Institute Radio Engi- 
neers, vol. 8, p. 263, August, 1920; General Electric Review, 
vol. 23, p. 794, October, 1920 ; and to a paper by E. E. Bucher. 
General Electric Review, vol. 23, p. 813, October, 1920. 

174. Arc Converters. — Introduction. — At the present time the 
arc is the most widely used type of transmitting apparatus for 
high-power, long-distance work. It is estimated that the arc is 
now responsible for upward of 80 per cent of all the energy 
actually radiated into space for radio purposes during a given 
time, leaving amateur stations out of consideration. The ad- 
vantages of undamped waves for transmission over long dis- 
tances have been pointed out in Section 172. and the arc is a 
source of such undamped oscillations. Its chief advantages over 
the high-frequency alternator described in Section 173 are that 
its initial cost is much lower for a given power, that it is a 
much more rugged device than the high-frequency alternator 
and does not require the extreme accuracy in machine work re- 
quired for the alternator, and that it is not so critically sensi- 
tive to small changes in operating conditions as the alternator. 
The speed of the high-frequency alternator must be maintained 
almost exactly constant to secure satisfactory operation and a 
constant wave length. Electron tube transmitting sets have 
usually been constructed to cover only comparatively short dis- 
tances and have been rated at a few kilowatts. Recently, how- 
ever, tube transmitting sets of higher power have been con- 
structed. A tube transmitter at Clifden, Ireland, is in use 
for transatlantic work, and is capable of putting over 200 am- 


peres into the antenna. Experimental investigations of arc 
transmitters are usually conducted only at stations where such 
sets are installed and not at all electrical laboratories, because 
of the comparatively high initial cost of the arc compared with 
usual laboratory equipment. For this reason the arc has been 
studied by a much smaller number of investigators than some 
other radio devices, such as the tube, which are at present really 
of less importance than the arc in high-power, long-distance 

The new radio station at Bordeaux, France, constructed by 
the United States Navy and at the present time the most power- 
ful radio station in the world, is equipped with a 1000-kw. arc. 
The most powerful radio station in the United States — the Naval 
Radio Station at Annapolis — is equipped with a 500-kw\ arc. 
Duplicate arcs are installed at both of these stations to provide 
for continuous operation in case of breakdown. All the 
capital battleships and many other ships of the United States 
Navy and all important shore stations controlled by the United 
States Navy are equipped with arc transmitters as primary 
equipment. The arc equipment of naval shore stations varies 
in power from 2 kw. for small stations to 500 kw. for Annapolis. 
The Signal Corps is operating a considerable number of arc 
stations at various points in the United States and its posses- 
sions and is installing additional arc equipment. A large num- 
ber of ships owned by the United States Shipping Board are 
being equipped with arc transmitters. Arc transmitters are 
also extensively used abroad. Small arcs, in sizes as low as 
2 kw., are in commercial use. For arc converters of medium 
power the initial cost can be very roughly stated to be some- 
thing like $1,000 per kilowatt. About six years ago the largest 
arc in use was rated at about 30 kw., and much of the develop- 
ment of the arc to its present state, when 1000-kw. arcs are con- 
sti-ucted, has occurred during the past four years. At the 
present time arcs are not used commercially in radiotelephony, 
as has been stated above, but improvements may make this 
possible in the future. It is customary to rate arc trans- 
mitting according to their d.c. power input. One operating 
difficulty with the arc transmitter is that it often generates, 
in addition to the fundamental wave, harmonics, that is, 
waves having frequencies which are multiples of the funda- 


mental frequency. Besides the harmonics, arc transmitters 
also often generate irregular intermediate frequencies, called 
** mush," the strongest of which frequencies fringe the funda- 
mental and harmonics. The harmonics and the " mush " often 
cause interference on shorter wave lengths, particularly at 
near-by stations. 

175. The Characteristics of the Direct-Current Electric Arc. — 
If between two pieces of conducting material, such as two car- 
bon rods, separated in air by a vshort distance, there is applied 
a considerable d.c. voltage, an arc will be formed between the 
carbon electrodes and will continue if a sufficient voltage is 
maintained. The voltage required to maintain the arc will be 
much less than that required to start the arc cold, and, in fact, 
an arc is not usually started with the electrodes separated. 
If we study the behavior of such an arc and measure the cur- 
rent corresponding to various d.c. voltages maintained at the 
terminals of an arc already formed, we will obtain a curve for 
voltage plotted against current like that shown in Fig. 223. 
This curve shows that as the applied voltage is increased the 
current through the arc decreases. The corresponding charac- 
teristic curve of an ordinary ohmic resistance would be a 
straight line sloping upward to the right from the origin. This 
behavior of the arc, exactly opposite to what occurs when the 
voltage applied to an ordinary conductor is increased, is de- 
scribed by saying that the arc has a " falling characteristic," 
or that it is a variable resistance, which increases as the ap- 
plied voltage increases. It is this " falling characteristic " of 
the arc that makes possible its use as a generator of undamped 

When the arc is used to generate undamped oscillations the 
current which flows at any instant between the arc electrodes 
is the resultant of the steady current supplied by the d.c. 
generator and the current in the condenser shunt circuit, as de- 
scribed in the next section. In the first two cases described in 
the next section, which can properly be considered to be arc 
discharges, the current between the electrodes always flows in 
the same direction, but may vary in magnitude. 

The statement is sometimes made that an arc is a " negative 
resistance " ; this statement can not be considered correct. The 
current in an arc passes from the electrode of higher voltage to 



the electrode of lower voltage, and the resistance of the arc 
should therefore be considered to be positive, since in this 
respect it behaves as any ordinary resistance. If for some 
reason the current through the arc falls to zero, the voltage 
will rise only to the value required to start the arc again, which 
is called the '* ignition voltage." If, while an arc exists the 
voltage is raised sufficiently, the current will decrease until the 
arc is extinguished ; this value of the voltage is called the 
" extinction voltage," and is less than ths ignition voltage. If 






^JJrc Chamber 



F'lg ZZZ. Production of Undamped Oscil/atiorys 
bij the D. C. /Jrc. 

a pulsating d.c. voltage is applied to the arc, the a.c. compo- 
nent of the current will be 180° out of phase with the a.c. com- 
ponent of voltage. 

In practice, an arc is usually originally started by striking the 
two electrodes together and then immediately separating them, 
instead of applying an initial voltage high enough to start the 
arc in the cold gap. Arcs usually operate on voltages of about 
500 to 600, The spark occurring when the contact between the 
electrodes is broken volatilizes the electrode and it becomes 
incandescent. In passing between the arc terminals the current 
is carried by " ions." These ions are molecules of air or other 


gas which may be present in the arc gap which have acquired an 
electric charge because of the intense electric field existing 
between the arc terminals (See Electrons, Sec. 6). Particles of 
the electrode may also break off in the intense heat and assist 
in carrying the current across the gap. If the applied voltage 
is reduced to zero, the current will cease and the ions will lose 
their electric charge. When the arc is first started, the full 
current is not immediately established; there is a delay of a 
small fractional part of a second during which time ions are 
being formed in the gap in sufficient numbers to carry the full 
current. If the arc has been previously extinguished only a 
short time before, there will still be present in the gap a 
number of ions which have not yet lost their charges, and 
therefore a shorter time will be required to build up the full 
current. If it is desired to make the arc sensitive to changes 
in applied voltage, it is important to make provision for rapidly 
" deionizing " the arc gap. Methods for accomplishing this 
deionization are described below. 

In general, the conduction of electricity through any gas is 
by means of ionization, and, in general, gaseous conductors have 
a " falling characteristic." 

An arc chamber should never be opened after the arc has been 
in operation until ample time has been allowed for the carbon to 
cool. If air is admitted it may form an explosive mixture with 
the hydrogen which is used in the chamber, which will be 
ignited by the hot carbon. 

176. Production of Continuous Oscillations by the Arc. — In 
about 1900 it was discovered by Duddell that, if across the ter- 
minals of a d.c. arc there were connected in series an induct- 
ance and a capacity of suitable values, the arc would emit a 
musical note, due to continuous variations in the current 
through the arc. The connections for such an arc are shown in 
Fig. 222. 

In discussing the oscillations in arc circuits it is convenient 
to recognize three cases, depending on the relative values of the 
current in the condenser shunt circuit (io, Fig. 222), and the 
steady current supplied from the d.c. generator (ii, Fig. 222). 

(o) The maximum instantaneous value of the oscillatory cur- 
rent io in the condenser circuit may be so much less than the 
steady d.c. current U, that the arc is not extinguished at any 


moment, but burns continuously. This is the case of the musical 
arc first described by Duddell, and is of no practical importance 
in present types of arc transmitters for radio communication. 
The oscillations generated are undamped but feeble. 

(&) The discharge current /o from the condenser may be large 
enough to extinguish the arc at an instant when io is near its 
maximum value but not large enough to start an arc again in 
the direction opposite to that in which the supply direct current 
Is flowing. This is the case of the Poulsen arc, and is the case 
usually met in practice with arc transmitters. The oscillations 
generated are undamped and under proper conditions have large 
energy content. 

(c) The oscillating current io, after extinguishing the arc, 
may start an arc in the direction opposite to the direction of the 
steady current ii. In such a case it is said that reignition 
is present. Such oscillations are produced by the quenched 
spark gap, with the ordinary spark gap, described in Section 
154 as an extreme case. The oscillations of type (c) are 

In the case of an oscillatory discharge in a circuit including 
an ionized gap, the distinction between the terms " arc " and 
" spark " is not altogether clearly drawn. In the case of oscil- 
lations of types (a) and (5) just mentioned, the term "arc" is 
applied. In the case of type (c) oscillations, there may be a 
question as to the characteristics which require the use of the 
term " spark." If the periods during which the current flows 
through the gap are separated by comparatively long intervals 
when no current flows, it is usual to call the discharge a spark. 
If for some purpose it is desired to know just what are the char- 
acteristics of the discharge in a given circuit, the wave forms of 
the current and voltage of the gap should be obtained with a 
high-frequency oscillograph. It is usually said that the conduc- 
tion in an arc is mostly by ionization. 

While the theoretical distinction between an arc discharge 
and a spark discharge requires precise consideration, the prac- 
tical forms of spark apparatus and arc apparatus are usually 
quite different, and the two systems of communication require 
the separate consideration which has been given to them in this 
book. As has been stated in Section 156, in discussing the 
operation of a spark gap, when a spark gap is operating nor- 



mally there is a bluish-white snap which is easily distinguished 
from the yellowish color and comparatively quiet operation of 
an arc discharge. 

For the production of high-frequency undamped waves for 
use in radio communication, the type (b) oscillations are the 



-Ignition ydta^e 
Extinction Yolta^e 

Fig.ZZ^.Carrent- Voltage 
Characteristic of the DC Fi^.ZZ4. Current and 

flfC. Voltage Waves of the 


Os CI II at in CI /frc. 


Carbon Copper (v 




Copper (<^) 

Fi^.ZZS JTction of the Jfla^netic Field 
on the ffrc Flame. 

only ones of importance, and we shall omit further reference 
to types (a) and (c). 

Let us consider the operation of an arc transmitter when the 
circuit is so arranged that the oscillations of type (&) are 
generated. To the terminals of the arc there is applied a d.C. 


voltage, which is often about 500 volts, but may vary from 200 
to 1200 volts according to the size of the arc. (Fig. 222.) 
First, suppose that the arc is burning steadily with the shunt 
circuit disconnected which includes the condenser and in- 
ductance. The large inductances in the generator supply line 
will tend to maintain constant the current supplied by the gen- 
erator, even if the instantaneous voltage across the arc termi- 
nals varies. These inductances should have low resistance and 
low distributed capacity. If now the shunt circuit is connected, 
the condenser C begins charging with the lower plate of the 
condenser as shown in Fig. 222 positive, and draws current 
away from the arc, since the current supplied by the generator 
can not increase suddenly. As the current through the arc 
decreases, the potential difference of the arc increases because 
of the falling characteristic (Fig. 223) and helps the charging. 
The charging continues until the counter emf. of the condenser 
equals that applied from the d.c. source. As the charging nears 
its end, the charging current becomes gradually less, and the 
current through the arc increases to its normal value, with a 
corresponding drop in the voltage. The lowering of the voltage 
across the terminals of the arc permits the condenser to dis- 
charge, and the effect of the inductance in the circuit tends ta 
keep the current flowing, and charges are accumulated on the 
condenser plates having signs opposite to those which first 
existed, so that the upper plate of C in Fig. 222 has a positive 
charge. As this charge with opposite signs now nears its 
end, the charging current to the right through the arc to the 
negative side becomes gradually less, and the arc current 
decreases, causing the voltage to rise. From Fig. 222 it is 
seen that the rise of d.c. voltage is such as to attempt to 
charge the lower plate of C positively, and that the posi- 
tive charge on the upper plate begins at once to come back, 
going to the left through the arc and decreasing the current. 
There is a consequent further rise of voltage (Fig. 223), which 
is in a direction to assist first the condenser discharge, and 
then the recharge in the opposite direction. The action now 
begins all over again, and thus continuous oscillations take 
place through the circuit. 

The original development of practical forms of arc for the 
generation of oscillations of type ( & ) is largely due to Poulsen, 
and we shall consider the Poulsen arcs as now in use. 


177. Construction of Arc Converters. — The apparatus generally 
used for the generation and transmission of radio signals by- 
means of the arc consists of : 

A source of direct current of suitable voltage. 

An arc converter, often called simply an arc. 

An inductance for loading the antenna. 

An antenna and ground system. 

A signaling device. 

Auxiliary and control apparatus. 

The arc "converter" is so called because it converts the 
power supplied by the d.c. generator into high-frequency un- 
damped alternating current. 

The Poulsen arc converter, as manufactured by the Federal 
Telegraph Co., consists of one rotating carbon electrode and 
one copper electrode burning in an atmosphere of hydrogen or 
a gas containing hydrogen in the presence of a strong magnetic 
field. The copper electrode, or anode, is connected to the posi- 
tive side of the d.c. supply and is of hollow construction, so 
that it may be cooled by water circulation. The electrodes are 
contained in a chamber usually made of bronze. This chamber 
is called the " arc chamber," and is often cooled by water cir- 

Fig. 226 shows a 100-kw. arc converter of the open magnetic 
circuit type, with the case removed, and with the various parts 
marked. Fig. 227 shows the interior of a 2-kw. arc of one 
type used on the ships of the United States Shipping Board, 
with the upper portion tilted back. 

Both the copper anode and the carbon cathode require re- 
newal from time to time. The anode may not require renewal 
for a considerable length of time; its life is greatly lengthened 
by proper cooling and the use of pure water in the circulating 
system. The carbon cathode will usually serve for about 24 
hours' continuous burning. The sizes of the carbons for a 
few arcs are, for a 2-kw. arc, diameter | inch, length 8 inches; 
for a 5-kw. and other medium-sized arcs, diameter f inch, length 
10 inches; for arcs larger than 100 kw., diameter If inches, 
length 12 inches. The rate of consumption of the carbon de- 
pends on the chemical composition of the gas in the arc chamber. 

The carbon electrode is so mounted that it can be screwed in 
and out for the purpose of striking and adjusting the arc. The 



length of the arc flame is adjusted by moving the carbon elec- 
trode to secure maximum antenna current. 

Practical Operating Characteristics. — When an arc trans- 
mitter is properly adjusted for operation, the antenna current 

Counterpoise . 

Upper Field. 

JCerojene Cu.p. 

MeeL. ■ 

lotrer Field 
Win din if . 


Fig. 226. — 100-k\v. Federal arc converter, with casing removed. 

is 0.707 of the d.c. current supplied to the arc. Under these 
conditions, it is not necessary to place an ammeter in the an- 
tenna circuit to determine the antenna current. It has been 
found that for arcs rated from 15 kw. to 100 kw. the antenna 
current is, very closely, one ampere per kilowatt of rating when 
the arc is properly adjusted for operation. The efficiency of an 



arc in converting d.c. power into high-frequency oscillations 
seldom exceeds 50 per cent; the remainder of the power sup- 
plied is largely dissipated in the arc chamber in the form 
of heat, and provision must be made for conducting the heat 
away and for preventing excessive temperatures in the arc 

If an arc could be adjusted so that the voltage wave and the 
current wave were sine waves, the effective value of the alter- 




WAref*: iM^_eT - . 





CMfi.l>'BE« DOOR 

Fig. 227. — Interior of 2-kw. Federal arc converter. 

nating current generated by the arc would be 0.707 of the direct 
current supplied, and the effective value of the a. c. voltage 
generated by the arc would be 0.707 of the d. c. voltage sup- 
plied. Hence, under these conditions, the a. c. power output 
of the arc would be 50 per cent of the d. c. power supplied to 
the arc proper. In considering the power supplied to the arc 
proper, the power supplied to the magnet windings and other 


accessory apparatus should not be included. In practice, how- 
ever, the wave forms of the arc are not sine waves, but are 
distorted, and the efficiency of conversion may differ from 50 
per cent. With some kinds of distortion it might be possible 
to have the efficiency of conversion exceed 50 per cent, but the 
existence of such distortion is not a desirable operating con- 

It has been observed at many arc transmitting stations that 
the maximum antenna current is obtained when transmitting 
at a wave length which is, roughly, about three times the 
natural wave length of the antenna alone. Up to this wave 
length an increase of wave length brought about by increasing 
the loading inductance will, in general, result in an increased 
antenna current. 

It has already been pointed out (Sec. 175) that it is important 
to provide means for rapidly deionizing the gap. Some of the 
means for securing this result are : the use of a strong mag- 
netic field, or " magnetic blow-out," which removes ions from 
the immediate vicinity of the arc gap ; the use of an anode made 
of copper, containing a channel through which water circulates ; 
the use in the arc chamber of hydrogen or hydrocarbon gas 
having similar properties. 

Magnetic Field. — Two powerful electromagnets are usually 
connected in series and placed in a position such that the mag- 
netic field set up between them is transverse (i. e., at right 
angles) to the flow of the ions across the arc. A stream of ions 
flowing in a straight line corresponds to the flow of a current 
in a straight conductor, and, as has been pointed out in Sec- 
tions 4 and 97, such a conductor in a magnetic field is acted 
upon by a force which tends to move it from the stronger field 
to the w^eaker field. (Fig. 225a.) By the action of the mag- 
netic field, therefore, the arc flame is quickly blown to one side 
of the gap so far that most of the discharge takes place on the 
side rather than the tips of the electrodes, and under the further 
action of the field the flame path reaches such a length that the 
arc is extinguished. The path of the flame on ignition is simply 
from tip to tip of electrode, as shown at /, Fig. 225c, instead of 
the longer path marked E in Fig. 225c, which is the flame path 
at the moment of extinction. This difference in length of flame 
path is the reason for the fact that in commercial arc equip- 


ment the ignition voltage is not very much greater than the 
extinction voltage. Any ions which may be emitted by the in- 
candescent electrodes during the intervals when no arc is 
passing will also be removed by the magnetic blow-out. The 
magnets used in high-power arcs are very large ; the magnets of 
a 500-kw. arc weigh about 65 tons. The strength of the mag- 
netic field which must be supplied to have a given arc operate 
properly depends on the wave length and the magnitude of the 
radio-frequency current, the rate at which ions are formed, and 
what other means are provided for deionization. In an ordi- 
nary type of 100-kw. arc, designed for operation over a wide 
range of wave lengths, it is necessary to supply a magnetic field 
having a flux density from 2,000 to 10,000 lines per square centi- 
meter. In some arc converters fiux densities as high as 15,000 
lines per square centimeter may be used. In general there is a 
best flux density for each wave length. If an arc is to operate 
on only one wave length, instead of over a considerable range 
of wave lengths, a more efficient design can be made. Arc con- 
verters designed to supply short wave lengths, such as 1,000 
meters, require the most powerful magnetic fields. At wave 
lengths of less than 1,000 meters the proper deionization of the 
gap requires a magnetic field so strong as not to be practicable. 
With the usual type of signaling apparatus, clear tones are not 
obtained with arcs operated below 1,000 meters, but if a chopper 
is used to break up the arc oscillations into groups of audible 
frequencies the tone on short wave lengths will be much 

The 500 kw. arc converters at Annapolis are suitable for 
operation at wave lengths from 6,000 to 20,000 meters at the 
full-load radio-frequency current of 350 amperes. 

Electrodes. — The advantage of the use of copper as the 
material for the positive electrode arises from the fact that 
copper has a very high heat conductivity, and, consequently, 
conducts heat away from the gap rapidly which aids in reducing 
the number of ions present in the gap. The cooling of the 
copper anode by a water-circulation system has the same pur- 
IX)se — to reduce the temperature of the gap. Practical con- 
siderations require that the cooling water should be very pure. 
The use of salt water will short-circuit the arc, since the water 
practically always flows through pipes which are connected to 


the ground, and current will flow directly from the copper 
anode through the salt water to the ground, instead of across 
the arc to the carbon cathode which is connected to the ground. 
In order to improve the regularity of the operation of the arc 
the carbon electrode is rotated about its axis about once a min- 
ute. A recent improvement in arc design consists in the addi- 
tion of a copper ring around each electrode. The eddy cur- 
rents induced in the copper rings so modify the magnetic field 
as to keep the flame from creeping back to the pole pieces of 
the magnets and injuring them. These rings permit the use of 
a shorter air gap between the pole pieces. 

Use of Hydrogen in Arc Chamber. — The presence of hydrogen 
in the arc chamber assists in rapid deionization, because 
hydrogen is a very light gas and diffuses very rapidly into the 
space outside the gap proper, carrying ions with it. The 
denser the gas used in the arc chamber the greater is the 
strength of magnetic field required for proper deionization. 
Further, hydrogen itself has a high heat conductivity and aids 
in conducting heat away from the gap. Other advantages in 
the use of hydrogen are that the presence of hydrogen mini- 
mizes the oxidation of the metal parts of the arc chamber and 
that an arc will start for a given distance between electrodes at 
a lower voltage in hydrogen than in air. This latter property 
makes it possible, as the electrodes are consumed, to obtain 
greater constancy in the wave length and the intensity of the 
oscillations of an arc by the use of hydrogen, since a longer 
gap can be used. 

The hydrogen may be supplied as a gas from cylinders. It 
is common practice, however, especially aboard ships, to slowly 
drop into the arc chamber alcohol or kerosene, which are 
volatilized by the heat of the arc, yielding hydrogen. A disad- 
vantage is that considerable soot is deposited throughout the 
arc chamber. At shore stations illuminating gas is sometimes 
used, since this has a considerable hydrogen content, but this 
also results in the deposit of considerable soot. 

Arc Transmitter Circuits. — It is general practice in the United 
States at present to connect the copper anode directly to the 
antenna through a loading coil ; this practice is largely due to 
commercial reasons involving patent rights. This circuit gives 
best results with antennas of large capacity using large in- 

r -""c=7* ^fJrc Chamber 

-h, ' — .-^i" I , - ■ 

Fig. ^^8 Circuit for ffrc Transmitter 
with Direct fJntennoL Connection and 
Signaling Circuit for Compensation Method. 


Flj.ZZ^ Circuit for ffrc Transmitter 
with Coupfed J-fntenna Circuit. 



ductances in series with the antenna. The connections of a 
typical arc transmitter of American manufacture are sliown in 
Fig. 228. In some types of arcs of European manufacture the 
antenna circuit is coupled as shown in Fig. 229. The antenna 
loading coils are usually wound with stranded high-frequency 
conductor to minimize the high-frequency resistance. ( See Sec. 

Small arc transmitters are often provided with a " chopper " 
to interrupt the radio-frequency oscillations at an audio fre- 
quency. The use of the chopper permits simple detector recep- 
tion, and on short wave lengths where the arc operates some- 
what irregularly this improves the tone of the received signal. 
There are several methods for connecting the chopper. In small 
arcs the chopper may be connected directly in the antenna cir- 
cuit and shunted by a condenser of suitable capacity. Another 
method is to connect the chopper to a few turns coupled to 
the antenna circuit, which causes a slight variation in the 
emitted wave lengths when the chopper contact is closed. The 
use of the chopper is discussed in connection with electron tube 
transmitting sets in Section 211, page 529. 

178. Signaling Methods. — For the purpose of controlling the 
output of an arc transmitter, the key can not be placed directly 
in the primary circuit, as can be done in spark systems, be- 
cause if the primary circuit were broken by the key for an 
appreciable length of time the arc would be extinguished and 
would not reignite until the electrodes were again brought into 
contact and separated. Signaling has usually been accom- 
plished by wave-length variation, the closing of the signaling 
key changing the constants of the transmitter circuit to an 
extent sufficient to cause a small change of the emitted wave 
length. Other methods of signaling are described below. 

Compensation-Wave Method. — In the conipensation-icave 
method of signaling two wave lengths are emitted. The re- 
ceiving station to which the arc is transmitting tunes to the 
wave length emitted by the arc when the key is closed, which 
wave is called the " working wave." When the key is open 
the arc emits a wave length from about 1 to 5 per cent greater 
or from 1 to 5 per cent less than the " working w^ave." The 
wave emitted when the key is open is called the " compensa- 
tion wave," or " back wave." If a receiving station is tuned 
53904° — 22 27 


to the compensation wave it will receive only the intervals 
between the dots and dashes. If the compensation wave is 
too close to the working wave confusion will result. In arcs 
up to about 70 kw. the compensation method is usually used 
by short-circuiting by the signaling key a few turns of the 
inductance in series with the antenna ; the arc emits a shorter 
wave length when the key is closed. (Fig. 228.) In larger 
arcs an inductance of a few turns is coupled to the induc- 
tance in series with the antenna, and the closing of the key 
short-circuits this coupled inductance. "When the key is closed 
the effective inductance in series with the antenna is re- 
duced (see transformers, Sec. 58, page 131), and hence the 
working wave is shorter than the compensation wave. It is, 
of course, possible to so adjust the connections of the key that 
the coupled inductance will be short-circuited only when the key 
is up, which will result in interchanging the working wave and 
the compensation wave, and the latter will be shorter. The 
compensation wave is sometimes called the " spacing wave." 

The compensation-wave method of signaling has the serious 
objection that two waves are radiated, somewhat separated in 
length, and that therefore an arc station which has a com- 
pensation wave interferes over a much wider band of wave 
lengths than a station which radiates a single wave. One of 
the principal objects of using undamped waves for communica- 
tion is to restrict each station to a narrow band of wave lengths, 
and this the compensation method fails to accomplish. It is 
probable that the use of the compensation wave will be dis- 
continued within a few years. 

Uniivave Methods. — Recently there has been developed a 
method of signaling called the " uniwave " method, or "one- 
wave " or " single-wave " method. This method involves the 
radiation of a single wave from the antenna. There are two 
principal ways of accomplishing this result — the " ignition '* 
method in which the arc is extinguished and reignited with 
each dot and dash, and the absorption method, in which two 
waves are generated, but the " back " wave is absorbed in an 
auxiliary circuit. 

Ignition Method. — One form of the ignition method uses an 
" ignition key." The ignition key consists of a solid metal rod 
introduced inside of the arc chamber. This rod is usually called 
the " striker." One end of this rod is caused to make or break 


contact with an electrode connected to the positive side of the 
arc. The rod is connected through a suitable resistance to the 
negative side of the d.c. generator supplying power to the arc. 
The in-and-out radial motion of the striker is controlled by an 
electromagnet. When the signaling key is up, the striker makes 
contact w^ith the positive electrode, thus shgrt-circuiting the 
usual current path between the electrodes through the incan- 
descent arc. In this position of the striker the d.c. current from 
the generator goes to the positive electrode of the arc, then 
across the striker through the striker series resistance, and 
back to the negative side of the generator. When the striker 
magnet is energized by closing the signaling key in the magnet 
circuit, the striker is withdrawn from contact with the anode, 
producing a small arc between the striker and the anode. This 
small arc reignites the regular arc between the anode and the 
cathode. The striker will successfully operate in this manner 
only when the arc is hot. To start the arc when cold, it is 
necessary to start oscillations in the usual manner. Other 
" ignition " methods have been described for extinguishing the 
arc without the use of the striker Inside the arc chamber by 
short-circuiting the arc through an external circuit containing 
resistance, or aluminum electrolytic cells, and employing auxili- 
ary circuits to expedite reignition. 

The ignition key will give fairly satisfactory results on small 
arcs, such as 2 kw. or 5 kw. It is not as yet satisfactory for 
larger arcs because the heavy currents required rapidly con- 
sume the striker. 

Absorption Method. — In both the compensation- wave method 
and the absorption method of signaling the radio-frequency out- 
put of the arc converter is maintained practically constant from 
instant to instant. In the compensation-wave method the com- 
pensation wave is radiated from the antenna. In the absorption 
method or " back-shunt " method the compensation wave does 
not reach the antenna, but is absorbed in an additional oscil- 
lating circuit, and only a single wave length is radiated by 
the antenna. The auxiliary absorption circuit, or " tank '" 
circuit, comprises inductance, capacity, and resistance. (See 
Fig. 229-A.) The relay key used for signaling has a front 
and back contact — that is, it is a single-pole double-throw 
switch. One side of the absorption circuit is permanently 
connected to the negative electrode of the arc, which is 



grounded, and the other side of the absoi'ption circuit is con- 
nected to the back contact of the relay key. The middle con- 
tact of the signaling key is connected direct to the positive 
electrode of the arc, and the front contact of the key is con- 
nected to the antenna. When the key is depressed the arc 
circuit is connected to the antenna, and radiation occurs. 
When the key is up and the back contact of the key is closed, 
the positive electrode of the arc is connected to the absorp- 
tion circuit to which the entire output of the arc is delivered, 
so that no wave is radiated by the antenna. The signaling key 
is so designed that the back contact is not broken until after 
the front contact is closed, so that during signaling there are 



instants when the arc is connected both to the antenna and to 
the absorption circuit. Tlie arc would be extinguished if en- 
tirely disconnected from both circuits. 

The capacity, resistance and inductance of the absorption cir- 
cuit are adjusted until the same current is delivered by the arc 
when it is connected to the absorption circuit as when the arc 
is connected to the antenna. The adjustment of the capacity, 
resistance, and inductance of the absorption circuit for satis- 
factory operation is not at all critical. The wave length gen- 
erated when the arc is connected to the absorption circuit may 
be only one-half the wave length generated when the are is 
connected to the antenna. When applied to medium and 
high power arcs the flow of the current to antenna or absorp- 
tion circuit is controlled by impedance variations without 


breaking the antenna current at the relay. The absorption 
method of signaling is in very successful operation at a number 
of semi-high-power arc stations, and is being developed for use 
at the larger stations. One disadvantage of the absorption 
method is that when the signaling key is up and the arc is con- 
nected to the absorption circuit sufficient powder is radiated 
by the absorption circuit to affect the receiving apparatus in 
the same station, so that it is not possible to receive signals 
while the arc is causing oscillations in the absorption circuit. 
The ignition key method does not possess this defect, since the 
arc is not generating oscillations when the signaling key is up. 
Detailed information regarding the absorption method is given 
in a paper by W. A. Eaton, Electric Journal, vol. 18, p. 114, 
April, 1921. 

For further information concerning the arc converter, the 
reader may consult the following: E. W. Stone, Elements of 
Radiotelegraphy ; W. H. Eccles, Wireless Telegraphy and Tele- 
phony ; J. A. Fleming, Principles of Electric Wave Telegraphy ; 
Manual of Federal Arc Radio Transriiitters, published by the 
Federal Telegraph Co. (describes 2-kw. and 5-kw. converters) ; 
P. O. Pedersen, Proceedings of the Institute of Radio Engineers, 
vol. 5, p. 255, August, 1917; L. F. Fuller, Proceedings of the 
Institute of Radio Engineers, vol. 7, p. 449, October, 1919; The 
Elwell Arc Generator, Electrician, vol. 85, p. 648, Dec. 3, 1920 ; 
P. O. Pedersen, Proceedings Institute Radio Engineers, vol. 9, 
p. 434, October, 1921; J. H. Morecroft, "Principles of Radio 

C. Apparatus for Reception of Waves. 

179. General Principles. — Receiving sets are divided into two 
general classes, those suitable for the reception of damped 
waves and undamped Avaves modulated at an audible fre- 
quency and those suitable for the reception of unmodulated 
undamped waves. The former involve the simpler construc- 
tion, and will be discussed first. With a few modifications, a 
set for receiving damped waves can be adapted to receive un- 
modulated undamped waves. Damped weaves may be received 
In a simple circuit containing a crystal detector or simple elec- 
tron tube detector (see Sees. 182, 194) and a telephone receiver. 
The tone heard in the telephone receiver is that corresponding 



to the frequency of the groups of damped waves. Undamped 
waves are ordinarily received by an electron tube method 
which produces beats (see autodyne method, p. 503.) These 
will be made clear in the diagrams which follow, where, for 
the purpose of explaining principles, the simplest possible sets 
will be shown first, even though not now used in military work. 
The fundamental principle of reception of signals is that of 
resonance. If the receiving circuits are tuned to oscillate at the 


Fig Z50. 

Simplest apparatus 
for reception of radio 

Fig 231 
/Jctior) oT rectifier on recei^ea 
wat^e trains 


Siiriplest apparatus 
for reception of radio- 
tetegrophic signals. 






FiQ. Zi2> 
Simple tuned 
receiving apparatus 


same natural frequency as the incoming waves, then these 
waves, though extremely feeble, will after a few impulses build 
up comparatively big oscillations in the circuits. In reality, 
then, for reception of signals all that is needed is an antenna 
circuit tuned to the same wave lengths as that of the transmit- 
ting station and an instrument capable of evidencing the cur- 
rent which flows in the antenna-connecting wire. This is shown 
in Fig. 230. This is the simplest possible arrangement for re- 
ception and will operate on either damped or undamped waves. 
A current-indicating instrument is shown at A. In practice the 
current is too feeble for any hot-wire ammeter. An ammeter is 
more suitable for quantitative measurements than for receiving 


telegraphic signals, since the dots and dashes are not readily 
distinguished unless made so slowly as to be impracticable for 
transmitting messages. 

Use of the Telephone. — A telephone receiver having magnet 
windings consisting of a large number of turns of fine wire is 
a much more sensitive receiving device. The action of the tele- 
phone receiver has been discussed in Section 60-b, p. 148. The 
diaphragm can follow the audio-frequency variations of current 
occurring in ordinary speech, but can not follow the very rapid 
radio-frequency variations. The effect is as if the diaphragm 
tried to go both ways at once, with the result that no ob- 
servable motion takes place. For this reason a telephone re- 
ceiver alone can not be used to receive radio waves. To remove 
this difficulty a crystal detector (see Sec. 182, p. 433) is put 
into the circuit, which permits current to flow in one direction 
but not in the other ; or, more exactly, the current in the reverse 
direction is negligibly small compared with the current in the 
principal direction. See Fig. 232. Referring to the reception 
of damped waves, it is well to remember that the waves are in 
widely separated groups. The action of a crystal detector upon 
damped oscillations is shown in Fig. 231 ; the lower halves of 
the waves are drawn dotted to indicate the portion of the cur- 
rent that is cut off by the crystal detector. 

It is found that the cumulative effect of one group or train of 
waves — for instance, that due to one condenser discharge at the 
transmitter — pulls the telephone diaphragm away from its neu- 
tral position. The number of such pulls per second is equal to 
the number of wave trains per second. With a 300-meter wave 
having 1000 wave trains per second the radio frequency is 
1,000,000 and the audio frequency is 1000, or one is a thousand 
times as high as the other. The upper limit of audio frequency 
for the human ear is 16,000 to 20,000 sound waves per second, so 
that even if the telephone diaphragm could, without a rectifier, 
follow the radio frequency, the ear would not hear the signals. 
In telegraphic signaling either a dot or a dash lasts long enough 
to contain many wave groups, and in the telephone, where the 
pitch corresponds to the spark frequency, a tone is heard during 
the length of the dot or dash. 

Simple Receiving Sets. — In Fig. 232 is shown the simplest 
connection for reception with a telephone receiver. It is suit- 


able only for damped waves. At D is shown the rectifier, com- 
monly called a " detector," although it detects nothing ; it alters 
the waves so that the telephone can detect them. The apparatus 
shown receives strongest signals from a station transmitting 
waves of the same length, or nearly the same length, as the wave 
length of the receiving circuit. The fact that the current from 
the antenna to ground must pass through either the telephone or 
the detector, both of which have a high resistance, renders this 
circuit not very selective, so tliat it will respond to a wide range 
of wave lengths. The circuit may be tuned by inserting a vari- 
able inductor in series between the antenna and the detector, 
the inductance being varied to change the wave length. This 
connection is similar to the so-called " plain antenna connec- 
tion " of Fig. 194, page 370, with the spark gap, the apparatus 
which supplies energy to the antenna, being replaced by the de- 
tector and telephone, the apparatus which uses the energy re- 
ceived by the antenna. 

A simple variation of this circuit which allows fairly sharp 
tuning is shown in Fig. 233, in which the detector and telephone 
are connected at the ends of the tuning inductance. It will be 
seen that this circuit is analogous to the wave meter circuit 
shown in Fig. 216, page 393, the antenna acting as the capacity G 
and the coil L as the inductance, with the detector and tele- 
phone shunted across the inductance. It is well to notice how 
simple is the apparatus actually needed for reception, contrary 
to what the uninitiated person supposes. Three pieces of ap- 
paratus — telephone receiver, rectifier, and tuning coil — with a 
suitable antenna, are all that are necessary to receive effectively 
from stations transmitting damped waves. 

ISO. Typical Circuits for Reception of Damped Waves. — A fur- 
ther improvement is the circuit shown in Fig. 234, in which the 
tuning coil has two adjustable connections. In the circuit 
shown in Fig. 233 the coupling between the antenna circuit and 
the detector circuit can be varied only by varying the wave 
length, but in the circuit shown in Fig. 234 the coupling can be 
varied, while the wave length is not changed. 

Direct Coupled Receiving Set. — A further improvement, as 
regards selectivity, is shown in Fig. 235, where a variable con- 
denser C2 has been added. This is called the direct coupled 
connection. Let Li be the inductance in the antenna circuit, Ci 



the capacity between the antenna and groimd, and I/2 and Oa 
the corresponding constants of the closed circuit, shown by 
heavy lines. The antenna circuit is called the primary, since 
the energy enters the set there. The circuit containing Lo and 
C2 is called the secondary and is the closed oscillating circuit. 
In the same manner in which the transmitting antenna circuit 
is a good radiator of powder, so the receiving antenna circuit is a 
good absorber. It is tuned to resonance with the incoming 
waves by adjustment of -Li. The power is given over magneti- 
cally to the secondary, which is tuned to resonance by adjust- 
ments of Lo and C2. Comparatively large oscillations result in 
the secondary, producing voltages across the condenser which 

Fia. 234 




Fia. 235 



" === Direct cou^teij recoi'viryk Set 

are detected by the crystal and telephone, and which are not irt 
either oscillating circuit. The oscillations are not damped 
thereby, and sharp tuning is obtained. 

Attention is invited to the analogy of Fig. 235 with the 
coupled transmitting set of Fig. 200 in Section 162, page 373. 
The open absorber of one corresponds to the open radiator of 
the other; the closed oscillating circuits correspond, each hav- 
ing its L and C; shunted around the condenser in one case 
(Fig. 235) is the apparatus where the used energy is taken out, 
namely, the detector and telephone, and in the other case the 
apparatus where the energy is put in, namely, the power trans- 
former with its generator. 

Inductively Coupled Receiving Set. — In Fig. 236 is shown 
the inductively coupled receiving set. This may be taken as 
the standard upon which all later changes are based. A fixed 



condenser ot about 0.005 microfarad is shunted around the tele- 
phone and this increases the strength of tlie signals. Its action 
is explained as follows : Suppose the principal current flows 
downward through the detector and telephone. While this 
current flows the fixed condenser is charged with top plate 
positive. When the reversal of the radio oscillation comes the 
current through D and T ceases. Then the condenser dis- 
charges down through T and tends to maintain the current till 
the next oscillation downward through the instruments. In this 
Avay the gaps between the successive pulsations of rectified cur- 

FjO. 237 



Receiving ciVcuit* "for v«ry 

■aEs- lon^ or yary shorT v>A»vea 

rent are filled in, and the cumulative effect of a wave group is 
strengthened. In practice the telephone cord, containing as it 
does two conductors separated by dielectric, forms a condenser 
which in some cases is sufficient so that an added fixed con- 
denser gives no improvement. 

The connection in Fig. 236 is similar in its action to the 
direct coupled arrangement of Fig. 235. In either case, on 
account of the coupling between the primary and secondary 
coils, there are reactions of each coil upon the other, with con- 
sequent double oscillations when the coils are near together. 
See Section 165. If the coupling is tight and the resistance 
high, sharp tuning becomes impossible. It is found, however, 
that if the coupling is not too tight and the resistance of the cir- 


cuits is low, extremely sharp tuning is obtained. The antenna 
is tuned to the incoming waves by changes of the inductance Li. 
Sometimes if very sharp primary tuning is desired, a variable 
condenser is shunted around Li, and fine adjustments are made 
therewith. The secondary is tuned to the primary, the opera- 
tions of tuning being done alternately until the telephone gives 
the best response. In the secondary the coarser tuning is done 
by changes of the inductance L2, and the fine tuning with the 
variable condenser Cz. 

Comparing Figs. 195 and 236 it will be found that the circuits 
are the same. One finds in both places the antenna circuit 
(radiator or absorber), the closed oscillating circuit, the cou- 
pling coils, and the power inserted or detected in shunt connec- 
tions to the condenser. The main difference of apparatus is 
that instead of a high voltage condenser as in Fig. 195, C2 is a 
small variable air condenser, and instead of spaced-turn coils 
of large wire, the coils of the receiving apparatus have many 
turns of insulated wire closely wound. 

For receiving a longer wave in the primary circuit than is 
possible by using all of the inductance I/2, a series inductance 
I/3, called a loading coil, is added. See Fig. 237. Also a variable 
condenser may be connected as shown at Cs to increase the wave 
length and afford fine tuning. It is better practice, however, to 
have the series inductance L3 continuously variable or variable 
by small steps, so that it can be used for fine tuning. The sec- 
ondary may also be provided with an extra inductance in series 
with Z/2 if needed. It is possible to receive short waves on a 
large antenna by inserting a series condenser d in the ground 
connection. It is short circuited when not in use. It should 
be noted, however, that a set used for the reception of short 
waves should be designed for that purpose and that best results 
will not be attained using a set intended for long waves and 
inserting capacity in series. 

In the typical set of Fig. 236, a crystal rectifier (Section 179) 
is used as the detector. The principal disadvantage of this type 
of detector is that it can not be depended upon to stay in adjust- 
ment. A good deal of time is usually required for the frequent 
readjustments. (See Sec. 182.) 

Fig. 238 shows exactly the same connection, but with the crys- 
tal detector replaced by a two-electrode electron tube, or " Flem- 



ing valve," V. This is a glass bulb containing two electrodes 
and having the air exhausted. One electrode in the vacuum 
is a lamp filament which is heated by current from a storage 
battery A. The other electrode is a metal plate. The heated 
filament gives off a stream of electrons (Sec. 187) toward the 
plate. Chrrent from incoming electric waves can pass through 
the vacuum in only one direction determined by the flow of the 
electrons, the current in the opposite direction being suppressed. 
In this way the tube acts as a rectifier. It is a very stable detec- 
tor, but not very sensitive as ordinarily used some years ago. 

Fia. 238 

Fiq. 239 


Fleming valve or tv\/o elec- 
trode electron tube circuit. 

Three electrode electron 
tube receiving circuit. 

The two-electrode electron tube is now practically obsolete as a 
detector. Present practice is to use a three-electrode tube. 

A receiving circuit using a three-electrode tube is shown in 
Fig. 239. It is seen here that the circuits joined to the filament 
and the nearer electrode are exactly the same as in Fig. 238. 
The telephone, however, is in a circuit with a battery B. and 
the signals received thereby are much louder than in the case 
of Fig. 238. For the theory and operation of the three-electrode 
electron tube as a detector see the next chapter. Section 194. 

An inductively coupled circuit is shown in Fig. 239-a, which 
has been found to be particularly adapted to wave lengths 
shorter than 400 meters and also to give good results on longer 
wave lengths. In this circuit it is essential that the variable 



inductances Li and Lz shall be continuously variable. The 
name " variometer " is sometimes applied to a form of con- 
tinuously variable inductance often used with this circuit. 
Variable inductance Li may be of the usual type, variable by 
steps. Condenser C2 may be variable by steps, and is not neces- 
sarily continuously variable. Ci and Li are adjusted to approxi- 
mately the wave length of the incoming signal, but it is not 
essential that the primary be accurately tuned. It is, however, 
essential that the secondary be very accurately tuned, and in- 
ductance 1/2 must be very carefully adjusted. The inductance 
Lz in the regenerative circuit (see Sec. 199, p. 487) should also be 

Fig. 239-a. — Tuned plate regenerative tuning circuit, using continu- 
ously variable inductances. 

carefully adjusted until maximum response is secured in the 
telephone receivers. 

This same circuit can be used for receiving continuous waves 
by the " autodyne " method (see Section 205, p. 503) by adjust- 
ing Lz so that the tube is in the oscillating condition. For 
continuous waves the best signal will usually be received when 
Lz is adjusted just above the point when the tube is in the 
oscillating condition. For spark reception, this circuit will 
usually give best results when Lz is adjusted just below the 
point where the tube is in the oscillating condition. 

This same type of circuit can also be used for reception with 
a coil antenna. (See Section 151.) In this case the antenna 
and receiving transformer shown in Fig. 239-a are not present ; 
that is, in Fig. 239-a the part of the figure to the left of points 



A and B is deleted. The terminals of the coil antenna are con- 
nected directly to points A and B. 

Capacitively Coupled Receiving Set. — A method of coupling 
receiving apparatus to the antenna circuit which affords com- 
pactness is shown in Fig. 240. By fixing the primary and 
secondary coils Li and Lj, permanently at right angles to each 
other, inductive coupling between the two is prevented. In- 
stead the coupling between the two circuits is effected through 
the condensers C, Ci, which are referred to as " coupling con- 
densers." Such an arrangement is called " electrostatic " or 
"capacitive" coupling. The condensers are arranged so that 



Fia. 240 








PiQ. 241 




=■ Ca^Ac'&w/e or electre>«t»tic cou^ir^ -^ <::A^»acit^ve scf-for 

by turning one handle both are varied together. One of the 
condensers, Ci, the one connected to earth, may be omitted, but 
better results are usually obtained with two. The advantages 
of capacitive coupling are as follows: (1) The coils are of com- 
pact form. They are wound as rings with rectangular or square 
winding section, thus giving large inductances in small space. 
This is a great saving of room compared \^ith sets using vari- 
able inductive coupling where the coils must be so constructed 
that one of them can move with respect to the other, and where 
they are usually wound on long tubes in order to get suitable 
variation of coupling. (2) The coils are fixed. In the induc- 
tive type they must sometimes be separated many centimeters 


for very loose coupling. (3) The coupling is quickly and easily 

Capacitive coupling, however, is not found to give as sharp 
tuning as inductive coupling. 

Sets for Quick Tuning. — When simplicity of tuning is the prin- 
cipal requirement, and it is desired to reduce the tuning opera- 
tions to a minimum number, even at the expense of a certain 
amount of selectivity, the following methods are used : 

In Fig. 241 is shown a moditication of the capacitive connec- 
tion of Fig. 243 ; in practice the change from one to another is 
accomplished by one switch. The secondary is removed, and the 
telephone is put in shunt with the detector instead of with the 
fixed condenser FC. If a medium value of coupling is used it 
Is not usually necessary to alter it; therefore the only tuning 
adjustment is that of the primary inductance. 

Another device for quick tuning is shown in Fig. 242. This 
employs an inductive coupling. The primary is tuned sharply 
to the incoming waves, while the secondary is untuned. With 
the connections as shown, the secondary will respond in prac- 
tically the same manner to a wide range of wave lengths, owing 
to the high resistance of the detector. Then the only adjustment 
the operator has to make is that of the primary inductance. 
Sometimes additional provision is made for adjustment of the 
coupling by separating the coils; this gives variation in the 
sharpness of tuning and in the signal strength. 

*' Stand-By'' Circuits. — These are also called "pick-up" cir- 
cuits. When listening for possible calls from a number of sta- 
tions it is convenient to have apparatus which will respond to 
a wide variety of wave lengths. The circuit of Fig. 241 will 
do this to a limited extent if the coupling is close. This is also 
true of Fig. 242. Probably the most broadly tuned of all the 
receiving sets is the so-called " plain antenna connection " 
already shown in Fig. 232 or Fig. 233. It is, however, too 
broadly tuned to be used if many stations are transmitting. 

A fairly good pick-up circuit is the ordinary inductive set of 
Fig. 236 when used with a tight coupling. The decrement is 
then high and the tuning broad. A switch may be provided, 
if desired, to put the receiving instruments over into the an- 
tenna circuit. 


181. Typical Circuits for Reception of Undamped Waves. — 
While damped waves are transmitted as detached groups or 
trains, undamped waves are usually not separated into groups. 
Undamped waves, even if rectified, will not be detected in a tele- 
phone receiver unless the waves are broken up into groups in 
some way. This is because the telephone diaphragm and the 
ear can not respond to so high a frequency as that of the radio 
oscillations. Hence it is necessary to interrupt the undamped 
wave dot or dash into many groups by rapid interruptions of 
the current. It is arranged in practice to have, for example, 
1000 interruptions a second, and as long as a signal continues 
a note of pitch 1000 is heard. These interruptions may be made 
to take place either at the transmitter or at the receiving sta- 
tion. A method for producing them at the transmitting sta- 
tion is to insert a rapidly operating circuit breaker called a 
" chopper " in the antenna wire ; or if it is inconvenient to 
break the current, the chopper may be used to short circuit 
some of the turns of the antenna inductance coil to throw the 
circuits out of resonance periodically. (See Sec. 211, p. 529). 
This divides up the v\'aves into groups to which the receiving 
telephone can respond, A rather more convenient method is 
to have the chopping done at the receiving station, for then 
the receiving operator can control the pitch of the received 
signals. There are at least five ways of modifying the waves at 
a receiving station to obtain an audible frequency : ( 1 ) A 
chopper in series with the detector and telephone; (2) a vari- 
able condenser with rapidly rotating plates; (3) a " tikker " 
used instead of a detector; (4) a ''heterodyne" in a separate 
circuit; (5) an " autodyne " or electron tube device arranged 
so that the detecting tube also produces the heterodyne action. 
The last method is explained in Section 205, page 501. 

Chopper. — This may be any device for rapidly making and 
breaking the current. It is inserted in the circuit of the de- 
tector and telephone as in the ordinary damped wave set of 
Fig. 236. It consists of a rotating toothed wheel with a sta- 
tionary contact touching the successive teeth or a break con- 
trolled by an electrically operated tuning fork, or it is some- 
times a light high speed vibrator similar to that of an electric 



Rotating Plate Condenser. — If the movable platesi of the 
tuning condenser C2 in Fig. 236 are rotated rapidly the appa- 
ratus will be in tune once for each revolution. Each of these 
revolutions will produce an impulse of the telephone diaphragm. 
The speed can be adjusted so that the impulses will cause sounds 
while waves are being received. In practice it is found best to 
keep part of the capacity of the condenser C2 constant, and vary 
only a part of it. If the main plates were rotated the appara- 
tus would give sounds at only a small sector of each revolution, 

method for 
receiving con- 
tinuous waves. 

near the resonance adjustment. To accomplish a more pro- 
longed train of impulses during one revolution the adjustment 
can be held near resonance for a larger proportion of the time 
if the rotating condenser is made very small, and is put in 
parallel with C2. The latter does not then rotate except for 
ordinary hand tuning. The capacity of Cz plus the maximum 
capacity of the rotating condenser is adjusted to give reso- 
nance. The circuit is not far from this condition when the 
moving plates are farthest apart, so that the signals affect the 
receiver during a considerable portion of the revolution. 

Tikker. — See Fig. 243. The tikker is usually a stationary fine 
wire of steel or gold with its end running in the groove of a 
53904°— 22 28 


smooth, rotating brass wheel.. It is a slipping contact device. 
The wire does not remain in perfect contact with the wheel, 
but owing to the sliglit irregularities there are variations of 
contact, which in effect keep making and brealving the circuit. 
With tlie tikker contact open, suppose the secondary inductance 
and condenser Cz to be tuned to resonance with the incoming 
waves. If now the tikker is closed when Cz has any stated 
value of charge, some of the charge will be given to the con- 
denser C and furthermore the radio oscillations cease because 
the addition of C throws the apparatus out of tune. When the 
tikker is opened the condenser C discharges through the tele- 
phone, and in the meantime the secondary oscillations build up 
again, ready to give a charge over to C when the contact is 
closed. In this manner the current impulses through the tele- 
phone are of the same frequency as the operation of the tikker, 
and this can be controlled by the speed of the wheel. The 
capacity of C should be about 1 microfarad. No separate rec- 
tifier is needed. The tone obtained is not musical, since C2 is 
charged to different potential differences at the different times 
w^hen the tikker closes, and the action depends also upon some- 
what irregular contact. 

Heterodyne. — In this method an apparatus is arranged to 
produce undamped electric oscillations in the receiving circuit, 
of nearly the same frequency as that of the waves which are 
being received, and their combined action is made to affect the 
receiving telephone. Beats are produced having a frequency 
equal to the difference of the frequencies of the two waves. 
The connections are shown diagramatically in Fig 244. Any 
source of undamped or slightly damped oscillations is con- 
nected at A. In the antenna circuit at 5 is a single turn or 
loop, coupled inductively to A. The antenna circuit thus gets 
the effect of the oscillations from A as well as from the incom- 
ing waves. Suppose those received have a frequency of 100.000, 
and the heterodyne A is adjusted to give a frequency of 99,000. 
As long as both act, the telephone will respond to a pitch of 
1,000 vibrations per second, which is of course audible. When 
the incoming waves cease the heterodyne continues to act alone 
at 99,000 cycles, but is inaudible. Therefore signals are heard 
only during the time when the incoming radio waves are re- 


ceived. Further information regarding lieteroayne reception is 
given in Section 205, page 501. 

Receiving from a Radio Telephone Transmitter. — In radio 
telephony, speech is transmitted by means of continuous waves, 
tlie amplitude of which is varied in accordance with the wave 
form of tlie sound which is being transmitted, and these varia- 
tions occur at tlie speech frequency, which is, of course, an audio 
frequency. The speech can tlierefore be received with a crystal 
detector or a simple electron-tube detector, just as damped 
waves, or continuous waves interrupted by a " chopper " at the 
transmitting station would be received. Any type of apparatus 
suitable for the reception of damped waves may, in general, be 
used for reception in radio telephony. If the received signal is 
feeble, it may be necessary to use amplifiers, as in the case of 
any feeble signal. In some cases better results may be secured 
by adjusting the circuits or the diaphragm of the telephone re- 
ceiver for a particular audio frequency. A " chopper," or 
" tikker " can not be used at the receiving station for receiving 
in radio telephony, and if the effort is made to do so, the speech 
is altogether unintelligible. The transmitting equipment and 
the wave forms used in radio telephony are described in Sections 
206-210. In Fig. 294, page 528, there is shown the circuit used 
in a Signal Corps set for the reception of radio telephone mes- 
sages. The uninitiated person often assumes that particular 
forms of elaborate apparatus are required for reception in radio 
telephony, but this is not the case. 

182. Contact Detectors. — A very simple and convenient kind of 
detector is obtained by placing in contact two dissimilar 
solid substances properly chosen. Many different substances 
have been found suitable for use in such detectors. This tjT)e 
of detector is easily portable, but the most sensitive forms 
require frequent adjustment. The electron tube, when properly 
connected, is a far more sensitive detector, but is subject to 
breakage in field work. For field sets, where a compact and 
easily portable form of detector is required, the contact de- 
tector is very convenient. The use of contact detectors is 
largely confined to such work now, and even in the portable 
military sets the contact detector is being largely replaced by 
the electron-tube detector. 


Crystals. — A contact detector may be formed by tlie contact 
of two dissimilar metals. Thus, a contact of a steel point on 
a piece of metallic silicon forms a good detector. Detectors 
can also be made by a contact of carbon with steel and tellu- 
rium with aluminum. The fused metallic silicon commonly 
used is a product of the electric furnace. 

The most important class of contact detectors consists of 
selected specimens of crystals, either native minerals or artifi- 
cial, in contact with a metallic point. Examples of minerals 
which can be so used are galena, iron pyrites, molybdenite, 
bornite, chalcopyrite, and zincite. Carborundum, which is 
crystalline silicon carbide formed in the electric furnace, can 
also be used. Galena is lead sulphide, crystallizes in cubes, and 
is blue-gray, usually with a metallic luster. Iron pyrites is a 
sulphide of iron, crystallizes in cubes, and is bright yellow, 
usually with a metallic luster. Molybdenite is a sulphide of 
molybdenum, is blue-gray, and can usually be separated into 
thin sheets somewhat like mica. Bornite and chalcopyrite are 
combinations of the sulphides of copper and iron. Zincite is 
a natural red oxide of zinc. 

Sensitive iron pyrites detectors are often sold under the trade 
name " Ferron." The detector sold under the name of " Peri- 
kon " consists of a bornite point in contact with a mass of 
zincite. The name " Lenzite " has been applied to an impure 
galena found in some localities, which is sometimes sensitive. 

Crystal detectors, particularly galena, may have their sensi- 
tivity entirely destroyed by the application of even moderate 
heat. They are usually mounted in an alloy having a low melt- 
ing point, such as Wood's metal, which will melt in hot water. 
The alloy is usually contained in a small metal cup a little 
larger than the crystal. A sensitive galena crystal may become 
almost worthless if mounted in ordinary solder. 

Different kinds of detectors require different kinds of con- 
tacts. With galena satisfactory results are obtained only with a 
light contact made by a fine wire, perhaps No. 30 or smaller, 
which makes contact with only a very small surface. Iron 
pyrites and molybdenite usually give best results with a fine- 
wire contact, but can be used with larger points. Silicon can be 
used with a fine-wire contact, but will also give good results in 
contact with the end of a small machine screw under consider- 


able pressure. The screw is usually taperetl to a blunt point. 
Iron pyrites is sometimes used in contact with the tapered point 
of a screw, under pressure. Carborundum gives best results 
with a contact of appreciable area under considerable pressure, 
providing the contact is made with the most sensitive spots, 
which may be deep in the mass of crystals in a specimen. 

For service in the field or on shipboard, where it is necessary 
to have rugged instruments which require very little adjust- 
ment, silicon or carborundum, in contact under considerable 
pressure with the blunt point of a screw, are therefore most 
desirable. With silicon and carborundum the same contact may 
be used for a considerable time. For permanent land stations, 
where new crystals are easily available and new adjustments 
can be easily made, the more sensitive galena crystals are 

It is usually necessary to examine a considerable number of 
specimens of any of these minerals before a crystal is found 
which is sensitive as a detector. The three most widely used 
contact detectors are probably galena, iron pyrites, and silicon. 
Pieces of metallic silicon are usually sensitive. Sensitive speci- 
mens of galena are obtained only by careful selection, and 
sensitive iron pyrites is still harder to find. Good specimens 
of galena and iron pyrites are usually the most sensitive crystal 
detectors. Sensitive specimens of molybdenite are much more 
easily found, but molybdenite is usually much less sensitive 
than galena or iron pyrites. Crystals should be kept in a 
closed box when not in use for any considerable period of time, 
and when picked up should be handled carefully with tweezers 
or a cloth, so that they will not come into contact with the 
fingers. Repeated contact with the fingers may almost entirely 
destroy the sensitivity of a good specimen of galena. A galena 
detector will become much less sensitive after a few months' 
exposure to the air, whether in service or not. Iron pyrites 
will usually retain its sensitivity much longer when exposed 
to the air than galena. Carborundum and silicon are also not 
so seriously affected by exposure. 

On the surface of a given sensitive crystal of most kinds 
different points will vary greatly in sensitivity. This is par- 
ticularly true of galena and iron pyrites, and to some extent 



of carborundum. Good specimens of fused metallic silicon 
usually have sensitive spots all over their surface, which vary 
comparatively little in sensitivity. A sensitive spot on a 
galena crystal may entirely lose its sensitivity if acted upon 
by an unusually strong signal, caused, for instance, by strong 
static. When this occurs it is necessary to move the fine-wire 
contact around until a new sensitive spot is found. The most 
sensitive spots on carborundum are often found deep in the 
spaces between the faces of the crystals which form the usual 

Via. 245. — One method of mounting crystal detectors. 

For some purposes it is desirable to have a permanent con- 
tact detector which will not require any readjustment of the 
contact at all. There are several ways in which such de- 
tectors may be constructed, but in general they are found to 
be nmch less sensitive than the same crystal used with the 
appropriate form of adjustal)]e contact. One form of perma- 
nent contact detector has a fine wire soldered to a small piece 
of molybdenite, but this detector will give a much weaker sig- 
nal than the same piece of molybdenite with a fine-wire ad- 
justable contact. If the sensitive spot of a permanent contact 
detector is destroyed by too strong a signal, the detector is, 


of course, no longer useful, since a new sensitive spot can not 
be used. 

Fig:. 245 shows a typical crystal detector which is formed 
by a contact of silicon and antimony. 

Properties. — In order to act as a detector for radio signals, 
a contact detector should either (1) allow considerably more 
current to flow when a given voltage is applied in one direc- 
tion than when it is applied in the opposite direction or (2) its 
conductivity should vary as different voltages in the same direc- 
tion are applied. Practically all detectors formed by the con- 
tact of two dissimilar substances possess both of these proper- 
ties, at least to a slight extent. The first property is sometimes 
referred to as the property of " unilateral conductivity," or 
simply the property of " rectification," and is the property made 
use of in most contact detectors. 

To make use of the second property, an auxiliary battery 
is required in series with the crystals, as explained below. Such 
a battery is seldom useil with any crystal except carborundum. 
Some crystals, such as galena, silicon, and iron pyrites give 
about as good results as simple rectifiers as when the auxiliary 
battery is used. They are ordinarily used without the battery, 
to simplify the apparatus. 

Figs. 246 and 247 show a current-voltage characteristic curve 
for carborundum in contact with a metal. Such curves are ob- 
tained by applying known voltages to the crystal and measuring 
the current which flows. The curves show that the current 
flows much more readily in one direction than in the other 
under equal but opposite voltages. For exailiple (Fig. 246). 
under a constant impressed emf. of 10 volts in one direction a 
current of 100 microamperes is obtained, while with the voltage 
reversed the current is only 1 microampere. This illustrates 
the property of " unilateral conductivity." or rectification. The 
second property is shown in both Figs. 246 and 247. When the 
voltage is applied in the direction giving the larger current, 
the conductivity (the ratio of current to voltage) increases as 
the voltage increases. This is sliown in the right-hand portion 
of Fig. 246. The conductivity of an ordinary metallic con- 
ductor would remain constant with varying voltages, and its 
characteristic curve would be a straight line. 



The question whether a given crystal detector can be used 
without an auxiliary battery depends entirely on its current- 
voltage characteristic curve. If the characteristic curve is 
practically zero to the left of the point representing zero voltage 
and rises rapidly immediately to the right of the point repre- 
senting zero voltage, good results may be obtained without an 
auxiliary battery. The rise will, of course, be most marked if 





1 600 

^ 400 

20 10 






10 ZO 1 

FiQZ46 Curve showing the 
carborundum detector to conduct 
in one direction better than the other 














I 5 "5 4 volts 

Fig.Z47. Curve shoyving Current- 
Yoltaqe Characteristic of Carbo- 
rundum Detector. 

. ^^V^V^V .^W^V%^. f\j^^^K 


/\j\f\r\ r\j^Kj^^""' p^f\j^Kj\ 

FigZ"^ JJdion of crystal detector with booster batter ij. 

the characteristic curve is concave downward. Galena, iron 
pyrites, silicon, and various other substances are so used 
without a battery. The incoming voltage oscillations vary 
from a small positive voltage to a small negative voltage of 
the same value. When positive voltages exist the crystal allows 
a current to flow whose value is determined by the character- 
istic curve, but does not allow any current to flow when negative 
voltages exist. If the curve slopes rapidly upward to the right 
from the point corresponding to zero voltage, as is the case with 


the crystals just mentioned, the current flowing when positive 
voltages exist will be of appreciable magnitude, and in a circuit 
containing only resistance will be a direct current pulsating 
between zero and a maximum value. If the incoming voltage 
oscillations are trains of damped waves having an audible train 
frequency, or undamped waves broken up into groups of an 
audible frequency, the pulsations of the rectified current will 
produce a note in a telephone receiver connected in the circuit 
corresponding to the train or group frequency. The addition of 
the inductance of the windings of the telephone receiver to the 
circuit smooths out the pulsations of the rectified current, so 
that the pulsations do not drop to zero with each radio-fre- 
quency cycle. 

Booster Battery. — In order to make use of the second prop- 
erty — namely, the curvature of the current-voltage character- 
istic — a local or " booster " auxiliary battery is inserted in 
series with the crystal. The voltage of the booster battery is 
adjusted so that the crystal .operates at the sharpest bend of 
the characteristic curve, so that a slight increase of voltage in 
one direction will produce a fairly large increase of current 
while an equal decrease of the voltage on the crystal will pro- 
duce a relatively smaller decrease of current. 

The action of the booster battery can be understood by refer- 
ence to Figs. 247 and 248. Suppose the carborundum crystal is 
used with, a booster battery which is adjusted to supply two 
volts to the receiving circuit in which the crystal is used. 
Consider this circuit to be subjected to incoming radio waves 
which cause the voltage in the receiving circuit to vary from 
— 0.5 volt to -|-0.5 volt, these variations occurring at the radio 
frequency. In Fig. 248, curve d represents the voltage in- 
duced in the circuit by the incoming waves. The resultant 
voltage wave acting on the crystal is at each instant two volts 
greater than the value of the induced voltage, and is represented 
by curve 6. Under the minimum instantaneous applied voltage 
of 1.5 volts, shown at point p in curve 6, the ciystal will allow a 
current of 2 microamperes to flow, as shown by curve c in 
Fig. 248. For the maximum instantaneous applied voltage of 
2.5 volts, a current of 8 microamperes will flow. These two in- 
stantaneous values of the current are determined bj^ the char- 
acteristic curve of Fig. 247. Curve c represents the condition 


which would exist in a circuit containing no inductance nor 
capacity. Fig. 248 shows undamped waves, whicli are broken 
up into groups as by a " cliopper." In actual reception, both 
inductance and capacity are present, and the actual current 
wave through the telephone receivers, as smoothed out by the 
inductance of the telephone receiver windings and the other 
inductance in the circuit, is shown in curve d. During the time 
that the incoming voltage oscillations are acting the average 
value of the current d is somewhat greater than four micro- 
amperes. Between wave trains, when no incoming voltage os- 
cillations are acting, the current d drops to just four micro- 
amperes, corresponding to an applied voltage of two volts. The 
current d in the telephone receivers thus comes in pulses having 
the same frequency as the frequency of the groups into which 
the incoming oscillations are broken up, and the note heard in 
the telephone receiver will correspond to this frequency. If 
damped waves are being received, the note will, of course, cor- 
respond to the train frequency of the damped waves. 

When a contact detector is used under ordinary operating 
conditions, it is approximately true that the rectified current 
is proportional to the square of the amplitude of the incoming 
voltage oscillations. This is a relation which holds for any 
kind of simple detector which operates by virtue of the curva- 
ture of the current-voltage characteristic curve, as long as the 
incoming oscillations are of only moderate intensity. A con- 
tact detector used without a booster battery really operates by 
virtue of a sharp cur\'ature of its characteristic curve at zero 
voltage, and both classes of contact detectors mentioned above 
operate by virtue of the curvature of this characteristic curve. 

183. Telephone Receivers. — The construction of a telephone re- 
ceiver of the watchcase type has been described in Section 60b, 
page 148. This is the type of receiver commonly used in radio 
work. The distinctive features of telephone receivers for radio 
work are lightness of the moving parts and the employment of 
a great many turns of wire around the magnet poles. The light- 
ness of the moving parts enables them to follow and respond to 
rapid pulsations of current. The large number of turns of wire 
causes a relatively large magnetic field to be produced by a 
feeble current. The combined effect is to give a device which 
will respond to very feeble currents. Since the size of wire used 


varies very little (usually B. & S. No. 40 copper), the amount 
of wire, and therefore the number of turns, is usually specified 
indirectly by stating the number of ohms of resistance in the 
windings. The resistance of the windings of each of a pair 
of receivers for radio work is seldom less than 500 ohms, and 
may be as high as 4000 ohms, the values of resistance being 
measured with direct current. For radio work the windings of 
the two receivers constituting a pair are almost always con- 
nected in series. 

The diaphragm of the ordinary watchcase receiver has one 
frequency to which it will respond most strongly ; this is the 
" resonant frequency " of that receiver. For some purposes it 
is desirable to vary this frequency, but for the ordinary type of 
receiver the resonant frequency can not be varied except with 
much inconvenience. Special types of receivers have been de- 
vised in which the resonant frequency can be easily varied ; 
these are sometimes called tuned telephone receivers. In one 
type of tuned receiver made by S. G. Brown, of London, the vari- 
ations of the magnetic field operate a vibrating reed which is 
attached to a non-magnetic diaphragm. The position of the 
vibrating reed can be adjusted by a set screw and the resonant 
frequency of the receiver thus varied. 

Another type of receiver sometimes used is the mica- 
diaphragm receiver. The regular diaphragm is made of mica 
and is placed in the usual place in the receiver, but of course 
is not acted upon directly by the magnets. Between the magnet 
poles a soft-iron armature is pivoted inside a solenoidal winding. 
It is arranged so that as it moves in response to changes in the 
magnetic field a small stitf wire transmits the motion to the 
mica diaphragm. The armature is so mounted that there is 
no pull upon it except when pulsations of current are passing 
through the coil. This is different from the ordinary magnetic 
telephone receiver, in which the magnet is always exerting a 
pull on the diaphragm. Since there is no strain in the dia- 
phragm between pulsations, the vibratory movements caused by 
incoming signals are greater than if a strain were already ex- 
isting in the diaphragm or armature. 

A similar constru(?tion is employed in the " loud-speaking 
reproducer," which is often used at large public gatherings for 
transmitting the voice of the speaker to a considerable dis- 



tance. The loud-speaking reproducer is a telephone receiver 
with large magnets having windings of low resistance. In one 
type of American loud-speaking reproducer the windings of the 
large magnet have a resistance of about two or three ohms. In 
this same type the armature is a small coil of fine wire in the 
shape of a ring, which moves up and down in the ring air gap 
of a cylindrical electromagnet. The armature is attached by a 

















small rod to the center of the metal diaphragm, which may be 
aluminum. These reproducers are commonly used in connec- 
tion with electron tube amplifiers of special design. (See 
Chap. 6.) One type of loud-speaking reproducer is shown in 
Fig. 248-A. The construction of one type of loud-speaking re- 
producer is described in United States Patents Nos. 1266988 
and 1329928. 


Impedance. — The impedance of telephone receivers depends 
upon tlie frequency of applied voltage. Around the range of 
audio frequencies the receivers act as an inductive reactance 
in series with a resistance, both increasing fairly regularly with 
frequency, except for a drop in both at the natural or resonant 
frequency of the diaphragm, where considerable energy is ab- 
sorbed because of the motion of the diaphragm. For radio fre- 
quencies the capacity between the leads to the receiver is im- 
portant. Here the receiver set (the two receivers with the 
leads) acts as a capacity reactance in series with a resistance. 
The resistance of a set for fairly high frequencies, such as 
600,000 cycles, is usually lower than the resistance measured with 
direct current. A considerable part of the current is shunted 
by this capacity and does not pass through the telephone re- 
ceiver windings. The capacity is not, however, ordinarily suf- 
ficiently large to constitute a path of negligible impedance for 
the radio-frequency current, and to take the place of a regular 
by-pass condenser of proper capacity in cases in which a by-pass 
condenser is required. 

It is the practice of some manufacturers to mark telephone 
receivers for radio use as having a certain number of ohms 
"A. G. Resistance," the quantity so marked being the im- 
pedance measured at a certain frequency which varies with 
different manufacturers. In the case of one American manu- 
facturer *'A. C. Resistance " means the impedance at 800 cycles ; 
in the case of another it means the impedance at 1000 cycles. 

^ When using a receiving set, both the radio-frequency and the 
audio-frequency impedances will be of importance. Practically 
none of the radio-frequency current passes through the receiver 
itself, but practically all of the audio-frequency current passes 
through the receiver windings and is effective on the dia- 

184. Receiving Coils and Condensers. — The coils used in re- 
ceiving apparatus are very simple in construction. They are 
usually wound in a single layer on an insulating tube, which 
may be pasteboard, wood, fiber, one of the materials called 
"bakelite," or some other material. The wire is covered with 
an insulation of silk or cotton and is sometimes stranded. A 
common type of receiving transformer is shown in Ifig. 249. 
This is often called a " loose cpupler." The points of the 


switches are connected by tap wires to the turns of the wire in 
the coils. On the primary one switch usually takes care of 
single turns, and the other switch makes contact to groups of 
perhaps 10 turns each. To cover 100 turns of coil, for example, 
one switch used for coarse adjustment would have 9 points of 
10 turns each and a zero point, making 10 points in all, and the 
units switch w^ould also have 9 points and a zero point. Then 
any number of primary turns from to 100 turns could be 
used. If the primary had 400 turns, the first switch in groups 
of 20 turns could have 20 points, including zero, and the unit 
switch could also have 20 points for 19 unit turns and zero. 

Fig. 249. — Receiving transformer. 

Other arrangements can be used. In the receiving transformer 
shown in Fig. 249 one primary switch has 34 turns between 
points, and the other switch has 2 turns between points. The 
secondary switch adjusts by groups of turns; fine tuning is 
accomplished by a variable condenser. The coupling between 
the primary and the secondary is loosened by pulling the sec- 
ondary out of the primary. The switches of the transformer 
are adjusted until the approximate wave length range of the 
station which it is desired to receive is reached. The secondary 
circuit is then tuned by a variable condenser to the station 
which it is desired to receive. 

Some coils used in radio receiving sets have more than one 
layer. Fig. 250 shows a coupling coil with a type of winding 



which resembles a lattice. This type of coil is variously called 
" lattice wound," " cellular," " basket wound," " honeycomb." 
A slightly modified form, in which the wires in successive layers 
are slightly staggered with reference to each other, is called a 
" duo-lateral " coil. Advantages of this type of winding are 
that a winding of given inductance occupies a smaller space 

Fig. 250. — Lattice-wound variable coupling coil. 

than if a single-layer winding were used and that the dis- 
tributed capacity of the winding is small. The mechanical 
construction of this type of coil does not readily permit of 
coupling at short wave lengths. They have not been found to 
give very satisfactory results on wave lengths less than 2.500 

For use in receiving, a type of inductance coil has recently 
been developed which is called " stagger-wound," " spider-web," 



or " basket woven." The frame of this type of coil consists of 
radiating arms arranged like the spokes of a wheel. The wire 
is wound in successive turns in and out around the arms. The 
wire starts from the center and is wound until it reaches the 
extremities of the arms. In most cases an odd number of arms 
is used, and therefore adjacent turns are on opposite sides of 
and separated by an arm. With this type of construction, very 
compact coils may be nmde. An important advantage of this 

Fig. 251. — Rotary variable air condenser. 

kind of coil is that the construction results in low distributed 
capacity of the winding, which is particularly important in 
receiving short wave lengths. The construction of a coil of 
this type is described by George Adams, Radio News, volume 3, 
page 293, October, 1921. 

When the inductance of the receiving transformer is not 
large enough to be tuned to the wave length to be received, 
additional inductance coils or "loading coils" may be used. 
Loading coils are not at present used as extensively as they 



have been in the past; present practice is to have more than 
one receiving set, if necessary, to cover the wave-length ranges 
at which it is desired to work. The inductance of any par- 

FiG. 252. — Simple receiving set (Signal Corps Type SCR-54-A), port- 
able cabinet type. 

1. Primary inductance switch. 5. Secondary condenser. 

2. Secondary inductance switch. 6. Crystal detector. 

3. Coupling adjustment. 7. Test buzzer. 

4. Antenna series condenser. 

ticular inductance coil can be calculated by reference to Sec- 
tion 170. 

Fig, 251 shows a type of variable condenser with air dielec- 
tric, which is in general use. The maximum capacity is about 

53904° — 22 29 


0.0005 microfarad, adjustable to a minimum of nearly zero. 
A set of semicircular metal plates is rotated between a corre- 
sponding set of fixed plates, forming alternate layers of air 
dielectric with adjacent conductors of opposite polarity. In 
receiving sets employing electron tubes, it is particularly true 
that most of the tuning is done with variable condensers. For 
the reception of continuous waves very sharp tuning is required ; 
for this purpose a variable series condenser may be used in the 
primary circuit, and a small variable condenser, called a 
" vernier " condenser, connected in parallel with it. 

Fig. 252 shows, with the various parts marked, a typical 
simple receiving set in cabinet form, with the tap switches and 
variable condensers, and a knob for changing the coupling be- 
tween the primary and secondary coils. A considerable number 
of different kinds of receiving sets are on the market. Much 
care is required to design a receiving set which will be satis- 
factory under the varying conditions met in practice, 

185, Measurement of Received Current. — The current received 
by a radio receiving set can be measured with suitable appa- 
ratus. One simple method of doing this is by the use of a 
crystal detector and galvanometer; by this method currents as 
small as 10 microamperes can be measured. This experiment 
requires careful manipulation ; information regarding it is given 
on pages 167 to 170 of Circular 74 of the Bureau of Standards. 
The measurement of the received current is of interest in com- 
paring the intensities of the signals received from different 
stations, with the same receiving apparatus. Rough compari- 
sons of signal intensity are often recorded in the log kept by 
radio operators, and it is sometimes desirable to make more 
accurate comparisons. 

The careful comparison of two signals is a measurement 
requiring apparatus which is usually available only in large 
laboratories. A simple method of obtaining approximate re- 
sults for purposes of rough comparison is the " shunted tele- 
phone method." A resistance is placed in parallel with the 
telephone receiver and the resistance is reduced until the limit 
of audibility in the telephone is reached — that is, until the 
sound in the telephone becomes so weak that the operator can 
just barely distinguish between dots and dashes. If t is the 
impedance in ohms of the telephone for the frequency of the 


current pulses through it. s the impedance of the shunt, It the 
least current in the telephone which gives an audible sound, and 
/ the total current flowing in the combination of the telephone 
and shunt, 

I^ s-\-t 

It 5 

This ratio, s-\-t to s, is called the " audibility " of the signal. 
It can be expressed in units of current if proper calibration is 
made. This measurement is, of course, affected by the sensitive- 
ness of the ear of the operator. A set consisting of a pair of 
telephones and a variable resistance used as a shunt, which has 
been calibrated, is sometimes called an " audibility meter." 

There are a number of other methods of measuring signal 
intensity which are more accurate; in some cases the signal 
to be measured is compared with a locally generated signal of 
known intensity. The more accurate measurements require 
apparatus not available in the ordinary station. 

An idea of the relative sensitiveness of detectors may be ob- 
tained from the following comparison, in which the current 
values given are the lower limiting values of antenna currents 
which will give satisfactory reception with the type of detector 
mentioned, when used with a good telephone receiver. The 
values here given should be considered as only approximate, 
since actual receiving apparatus and conditions are subject to 
considerable variations — for an ordinary crystal detector, a 
current of 50 microamperes; for an exceptionally sensitive 
crystal, 10 microamperes; for the ordinary electron tube with 
simple detector circuit, 10 microamperes. For specially good 
detector tubes containing gas or for the ordinary tube con- 
nected in a circuit for regenerative amplification, 1 microam- 
pere; for an oscillating tube operating in a good circuit under 
satisfactory conditions, 0.01 microampere. 


186. The Development of the Electron Tube. — During the past 
few years there has been added to the apparatus emploj-ed in 
radio communication a new device, called the " electron tube," 
which has made possible many important advances in the art. 
A small electron tube of a simple type resembles closely in gen- 
eral appearance an ordinary 10-watt incandescent electric lamp. 
Since these tubes may be used for a variety of purposes — to 
generate, to amplify, and to modulate radio oscillations, as 
well as to detect them — they now are used in most types of 
radio apparatus. New applications have come rapidly, and 
there is every reason to believe that further developments may 
be expected. The electron tube is of primary importance in 
radio communication, but it has many important applications 
in other fields of electrical engineering, particularly in ordi- 
nary telephony with wires, where its use makes possible con- 
versation between points separated by a distance of 3000 miles. 
One fact of importance is that such tubes make possible the use 
of apparatus that is easily portable — a primary consideration in 
military communication, and of importance also in various com- 
mercial applications. The principles which underlie the opera- 
tion of electron tubes and their action under the widely differ- 
ent conditions met in actual practice therefore deserve careful 

A. The Electron Flow in Electron Tubes. 

187. The Electron and the Two-Electrode Tube. — The name 
" electron tube " is derived from the fact that the action of the 
tube is due to very small particles of matter called " electrons." 
An electron is much smaller than an atom, and is the building 
block of which atoms are constructed. An idea of the ex- 
tremely small size of the electron may be obtained from the 
estimate that in a very tiny spherical globule of copper hav- 
ing a diameter of one one-hundred-thousandth of an inch, 
there are about 20 billion electrons. The atom was for- 



merly regarded as the smallest particle of matter which 
conld exist ; something like 25,000 hydrogen atoms would have 
to be placed in contact in a row to make up a length of one ten- 
thousandth of an inch. The weight of an electron is only 
about one two-thousandth of the weight of a hydrogen atom. 
An electron carries a charge of negative electricity whose value 
can be measured. Since the comparatively recent general recog- 
nition by scientific men of the existence of the electron, many 
ideas formerly held as the explanations of various physical 
phenomena have been considerably modified. The fact that 
the electron carries a charge of negative electricity makes pos- 
sible the use of the electron tube in radio communication. For 
further information regarding the electron the reader may con- 
sult a book by R. A. Millikan, The Electron. 

If two wires are connected to a battery, one to each terminal, 
the other two ends of the wires may be brought very close to- 
gether in air, yet so long as they do not touch no current flows 
between them. The two ends may be inclosed in a bulb like 
that of an incandescent electric lamp and the air pumped out, 
and still so long as the ends are separated no current will flow. 
Thus, when the filament in an incandescent electric lamp breaks, 
the current stops and the light goes out. 

About 1884 Edison discovered that if inside an exhausted 
incandescent electric lamp of the ordinary type, containing a 
filament whose two ends were connected to two wires insulated 
from each other, there was introduced a third wire insulated 
from the filament connections and maintained at a voltage 
positive with respect to the filament, then a current would flow 
across the vacuum inside the tube from the third wire to the 
filament as long as the filament was incandescent, but that the 
current ceased as soon as the filament became cold. This 
phenomenon is generally called the " Edison effect." It is 
due to the fact that the incandescent filament shoots off electrons 
at high velocity, each carrying its charge of negative electricity, 
and that the electrons are attracted to the positively charged 
third wire. The passage to the third wire of the negative 
charges of the electrons is equivalent to the flow of a current 
between the fllament and third wire. In order that a cur- 
rent of one-billionth of an ampere should flow between the 


filament and the plate, it is necessary that more than six billion 
electrons should pass each second from the filament to the 
plate. It should be particularly noted that while the electrons 
move from the heated filament to the cold third wire, the current 
passes from the third wire to the filament, according to the 
usual idea that the direction of an electric current is from the 
positive (higher) to the negative (lower) voltage. This dis- 
tinction between the direction of electron flow and the direction 
of current floio should be carefully noted. 

As each electron leaves the filament, the filament acquires 
a charge of positive electricity equal in amount to the nega- 
tive charge carried by the electron. If no voltage is applied 
to the third wire, electrons will still be emitted by the incan- 
descent filament, but will travel only a very short distance 
before being attracted back to the filament by the positive 
charge acquired by the filament. The voltage applied to the 
third wire must be sufficient to overcome this attraction of the 
filament. No current will flow if the negative terminal of the 
battery is connected to the third wire, because the electrons 
will not be attracted by the negatively charged third wire, and, 
in fact, will be repelled back into the filament. 

A tube containing a filament and one additional wire or 
other piece of metal, is called a two-electrode tube, the filament 
being considered as one electrode, and the additional piece of 
metal the second electrode. Fig. 253 shows the essential ele- 
ments and connections of a two-electrode tube. The additional 
piece of metal inside of the tube is here a small plate of metal. 
The current which flows between the filament and plate is often 
called the "plate current." 

188. Ionization in Electron Tubes. — The above explanation of 
the mechanism of the flow of current between the filament and 
plate in an electron tube applies to a tube having a very per- 
fect vacuum. If there is more than the merest trace of gas 
remaining in the tube, the operation is more complicated, and a 
larger current will usually flow with the same applied voltage. 
This happens in the following manner. 

In a rarefied gas some of the electrons present are constituent 
parts of atoms and some are free. These free electrons move 
about with great velocity, and if one of them strikes an atom 



it may dislodge another electron from the atom. Under the 
action of the emf. between plate and filament the newly freed 
electron will acquire velocity in one direction — the direction in 
which the colliding electron is moving — and the positively 
charged remainder of the atom, called an " ion," will move in 

Fia ^&5 

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F.Q 255 

characteristic curves of a two- 
electrode tube -for two different 

the opposite direction. Thus both of the parts of the disrupted 
atom become carriers of electricity and contribute to the flow 
of current through the gas. This action of a colliding electron 
upon an atom is called " ionization by collision," and, on account 
of it, relatively large plate currents are obtained in electron 
tubes having a poor vacuum. The earlier tubes were of this 


sort, but at the present time most tubes are made with a better 
vacuum than formerly, so that ionization by collision is respon- 
sible for but a small part of the current flow. 

At first it would seem to be an advantage to have ionization 
by collision, because a larger plate current can be obtained, but 
there are two difficulties which have proved so great that tubes 
are now usually so made as to have only the pure electron fiow. 
The first of these difficulties is a rapid deterioration of the 
filament when there is flowing a large plate current which is 
caused by ionization by collision. The positively charged parts 
of the atoms are driven violently against the negatively charged 
filament, and since they are much more massive than electrons 
(an oxygen or nitrogen ion has about 25,000 times the mass of 
an electron), this bombardment actually seems to tear away 
the surface of the filament. A second disadvantage of tubes 
with poor vacuum is that too large a battery voltage may cause 
a " blue-glov/ " discharge ; the difficulties connected with the 
presence of this visible kind of current flow are mentioned in 
Section 194. 

Two similar tubes with poor vacuum seldom, if ever, contain 
just the same quantity of gas, and therefore their electrical 
characteristics may be considerably different. For this reason 
it is not ordinarily practicable to connect in parallel two tubes 
having poor vacuum. Tubes with high vacuum, on the other 
hand, can be constructed very uniformly, so that a number can 
be connected in parallel. It is often advantageous to be able to 
connect several tubes in parallel in generating sets. 

Tubes containing a little gas, i. e., having a poor vacuum, are 
often called " gas tubes," or " soft tubes." Tubes with high 
vacuum are often called " hard tubes." " Soft " tubes are 
particularly useful as detectors, and if properly selected and 
used may be much more satisfactory as detectors than " hard " 
tubes of similar construction. 

Let us consider what happens in a two-electrode tube having 
a good vacuum, when there is a variation in either the tem- 
perature of the filament or the voltage of the battery connected 
between the plate and filament. 

189. Characteristics of Two-Electrode Tubes. — Effect of Plate 
Voltage, — Suppose first that the filament temperature is kept 


constant. Then a definite number of electrons will be sent out 
per second/ The number of electrons that travel across the 
tube and reach the plate per second determines the magnitude 
of the current through the plate circuit. The number of elec- 
trons that reaches the plate increases with an increase of the 
battery connected between the plate and filament {B, Fig. 253). 
If this voltage is continuously increased, a value will be reached 
at which all the electrons sent out from the filament arrive at 
the plate. No further increase of current is possible by in- 
creasing thjB voltage, and this value of current is called the 
saturation current. This is illustrated in Fig. 254 (full line 
curve), which shows that when the voltage applied to the plate 
is small (horizontal distance) the current flowing between fila- 
ment and plate, which, as has been stated, is called the plate 
current (vertical distance), is also small, but if the voltage 
applied is made larger the plate current increases more rapidly 
than the voltage up to a certain value. The bend in the curve 
shows that when the voltage has been made large enough there 
is little further gain in current. 

If now the temperature of the filament is raised to a higher 
constant value by means of the filament-heating battery and the 
same voltage steps again applied, the plate current curve will 
coincide with that obtained before, until the bend is reached; 
then it will rise higher, as shown by the dotted portion of the 
curve in Fig. 254. The explanation of this is that the number 
of electrons sent out by the filament increases with the tempera- 
ture approximately as the square of the excess of the filament 
temperature above red heat, and thus more electrons are avail- 
able to be drawn over to the plate. Thus a higher value of 
plate current will be obtained before reaching the limiting con- 
dition when all the electrons emitted arrive at the plate. When 
this finally happens, the curve, as before, bends over until 
nearly horizontal. 

^ The law giving the number of electrons emitted per second as it 
depends upon the temperature of the filament was first given by O. W. 
Richardson, whose book, The Emission of Electricity from Hot Bodies 
(1916), describes his experiments in detail. See, also, I. Langmuir, 
Physical Review, vol. 2. p. 450, 1913 ; and S. Dushman, General Elec- 
tric Review, vol. 18, p. 156, 1915 ; and W. H. Bccles, Continuous-Wave 
Wireless Telegraphy (1921). 


Effect of Filament Temperature. — Suppose now that the volt- 
age of the plate battery {B, Fig. 253) is kept at a constant value 
T\ and the filament temperature is gradually raised by in- 
creasing the current from the filament-heating battery. The 
number of electrons sent out will continue to increase as the 
temperature rises. The electric field intensity (Sec. 33) due to 
the presence of the negative electroiis in the space between 
filament and plate may at last equal and neutralize that due 
to the positive potential of the plate, so that there is no force 
acting on the electrons near the filament. This effect of the 
electrons in the space is called the " space charge effect." It 
must not be supposed that the space charge effect is caused by 
the same electrons all the time. Electrons near the plate are 
constantly entering it, but new electrons emitted by the fila- 
ment are entering the space, so that the total number between 
filament and plate remains constant at a given temperature. 
After the temperature of the filament has reached a point where 
the effect of the electrons present in the space between fila- 
ment and plate neutralizes the effect of the plate voltage, any 
further increase of the filament temperature is unable to cause 
an increase of the current. The tendency of the filament to 
emit more electrons per second, because of the increased tem- 
perature, is offset by the increase in space charge effect which 
would result if electrons were emitted more rapidly, or. more 
exactly, for any extra electrons emitted, an equal number of 
those in the space are repelled back into the filament. If now 
the plate voltage is increased to a new value, Fa, the plate- 
current curve will rise higher before bending over as shown by 
the dotted portion of the curve in Fig. 255, because it takes 
a larger space charge to offset the effect of the plate at the 
higher voltage. 

190. The Three-Electrode Electron Tube. — Between the filament 
and plate of a tube we may insert another piece of metal. This 
third electrode inteiT>osed in the stream of electrons between 
filament and grid is usually in the form of a metallic gauze or 
a grid of fine wires, and is generally called the " grid." A 
tube which contains a filament, plate, and grid is called a 
three-electrode tube and is capable of many more uses than the 
two-electrode tube. Fig. 256 shows the construction of a 





Fig. 256. — Construction of the three-electrode electron tube. 



three-electrode tube of American manufacture. The addition 
of the third electrode makes it possible to increase or decrease 
the current between plate and filament through wide limits. If 
a voltage is impressed upon the grid by means of a third battery 
connected between the filament and grid, shown at C in Fig, 
257, the space charge effect will be modified. The electrons 
traveling from filament to plate pass between the wires forming 
the grid. If the grid is given a potential which is negative 
with respect to the filament the grid will repel the electrons, but 

many of them will still pass through, and reach the plate, be- 
cause of their high velocity, because the positive plate potential 
still affects them to some extent. If the grid potential is made 
still more negative the plate current will diminish until finally it 
may be stopped entirely. 

Suppose, however, that the grid is given a positive potential 
instead of negative. Electrons are now attracted to the grid as 
well as to the plate, and more electrons are now drawn toward 
the plate than would otherwise pass, so that the plate current 
increases. The charge of the grid partially neutralizes the 
effect of the space charge. As in the two-electrode tube, a limit 


to the magnitude of the plate current will finally be reached, 
Avhen the space charge caused by the large number of negative 
electrons in the tube fully counteracts the influence of the 
positive charges on grid and plate. The attainment of the 
limiting or saturation value of the plate current is assisted 
by the absorption of more electrons into the grid if its positive 
potential is increased. This absorption gives rise to a relatively 
small current in the circuit FGCF (Fig. 257), which is called 
the grid current. The total electron flow is the sum of the 
plate current and the grid current. As the potential of the 
grid is made more and more positive, more and more electrons 
will be absorbed by the grid. The action of the three-electrode 
tube in its various applications is discussed in detail in the 
following sections. 

For an extensive treatise on the electron tube the reader is 
referred to a book by Dr. H. J. van der Bijl, The Thermionic 
Vacuum Tube and Its Applications. Another excellent book, 
which gives somewhat more attention to the practical applica- 
tions of the electron tube, is volume 2 of a Text Book on 
Wireless Telegraphy, by Rupert Stanley. A treatise of some 
theoretical aspects of electron tubes is found in a book by W. H. 
Eccles, Continuous-Wave Wireless Telegraphy.. A recent com- 
prehensive treatise of electron tubes and electron-tube apparatus 
is " Thermionic Tubes in Radio Telegraphy," by John Scott- 

191. Characteristic Curves. — In applying electron tubes for 
different purposes in radio communication the performance is 
studied in terms of characteristic curves. In simple electrical 
devices, as an ordinary ohmic resistance, what will happen when 
the device is used with other equipment can be determined, if 
at all, from knowledge of only the one property of the device — 
its ohmic resistance. With electron tubes it is necessary to use 
diagrams from which all possible combinations of voltages and 
currents that will occur in practice may be determined. 

These diagrams, known as characteristic curves, are easily 
obtained experimentally by keeping the filament-heating current 
constant and applying various known voltages between the plate 
and the filament and between the grid and the filament and 
reading the resulting currents that flow to the plate and grid. 
Fig. 258 shows how the characteristics may be determined 



with direct-current instruments. Potential dividers Pi and Pa 
may be used to adjust tlie values of plate voltage bp and grid 
voltage eg to desired values. The currents are then read by 
the milliammeters ip and ie. Correction for the resistance of 
the milliammeters may be made to determine the true voltage 
between the cold electrodes and filament if a high order of 
accuracy is desired, but this correction is usually negligible. 

Two diagrams are required to express the relations on a plane 
sheet. One shows how the plate current depends upon the plate 
and grid voltages and the other how the grid current depends 
upon the plate and grid voltages. Fig. 259 shows plate char- 

Circuit ^or DetermiTvirto Characteristic 

^ Curves of Elect roTL Tubes 

_ F/G. 2 5a 

acteristics for a tube used in receiving equipment, this being 
obtained (see Fig. 258) by setting the plate voltage at 20, 40, 
60 volts in turn and finding how the plate current changes 
as the grid voltage is changed. Fig. 260 shows the grid current 
determined under the same conditions. An alternate method of 
expressing characteristics is shown in Figs. 261 and 262. 

Amplification Coefficient. — These curves may be used to illus- 
trate the phenomena mentioned above in regard to tube action. 
For example, a change of grid voltage by one or two units 
causes as great change of plate current as would a change of 
plate voltage by five or ten units. The amplification coefficient 
of a tube expresses the relative effects of grid voltage and 
plate voltage in influencing the plate current. It may be de- 



termined roughly by the use of the equipment shown in Fig. 
258, using the following procedure. By means of the potential 
dividers, adjust e? and eg to the point for which the amplifica- 
tion coefficient is desired, as, for example, ep=40 volts, eg=0, 
and read the plate current, say ip==3.00 milliamperes. Now 
increase es by 0.2 volt, for example, and decrease the plate 









'^Utit Curi/e3 of i 




Current t 





1 1 J 
















































































+ 4- 

+ 6 

voltage ep until the plate current is the same as before. Sup- 
pose the new setting gives a plate voltage ep=38 volts. Then 
the amplification coefficient of the tube is the change of plate 
voltage divided by the change of grid voltage, the plate cur- 
rent being held fixed. For this example, the amplification co- 
efficient At=10 — that is, the grid voltage exerts 10 times as 
much influence upon the plate current as does the plate voltage 
itself, at this particular point on the characteristic. 


Internal Resistance. — Another coefficient of importance is the 
internal resistance of the tube, wliicli is measured by the effect 
in changing the phite current of the plate voltage alone. Thus, 
in the above experiment, let the grid voltage eg be fixed at 
zero. Change the plate voltage by a small amount, five volts, 
for example, and read the change in plate current, say 0.5 
milliampere. Then the ratio of voltage change to current 
change, keeping the grid voltage fixed, is the internal output 
resistance of the tube. In this experiment the value is 10,000 

These two coefficients determine how the apparatus connected 
in the plate or output side of the tube will behave when the grid 
voltage is changed. Other coefficients are necessary to deter- 
mine how much power is required for producing the grid voltage 
changes, so that a knowledge may be had of how the tube reacts 
upon the apparatus to which the input or grid side is connected. 

Power Amplification Coefficient. — By operating the grid at a 
low or negative voltage, the input power required to produce 
the changes in grid voltage may be made exceedingly small 
compared with the output power of the tube. The output power 
is obtained from the plate battery. The ratio of plate output 
power to the grid input power is known as the power amplifi- 
cation coefficient of the device, and may be as high as 10,000. 
This ratio can not be infinite because grid current always exists, 
even at highly negative grid voltages, and the ratio of plate 
output power to grid input power could become infinite only if 
the grid current should be zero. 

The Tube as a Variable Resistance. — An alternate method of 
expressing characteristics is by plotting the volt-ampere rela- 
tions of each electrode by itself — that is, in Fig. 258, to obtain 
the volt-ampere characteristics of the plate circuit, fix the grid 
voltage at a given value, and determine all possible relations 
between plate volts and plate current. These relations for a 
tube used in transmitting equipment are shown in Fig. 261, 
using grid voltages from — 40 to +50 by steps of 10. From these 
diagrams it is seen that a three-electrode tube may be thought 
of as a variable resistance, the setting of which depends upon 
the grid voltage. The higher the grid voltage, the less is the 
resistance, and vice versa. For low grid voltages on this dia- 
gram the resistance changes mth plate current in a manner 



similar to a carbon lamp, the resistance of which goes down as 
the lamp heats up. At high grid voltages it changes as does 
a metallic filament lamp, the resistance of which increases with 

-^ -I.O 0.6 0.6 Off- O.Z -O-^ OZ 0.4- 0.6 0.3 /.o. 

increasing current. This conception of a tube is very helpful 

in studying its operation, especially in transmitting equipment. 

The resistance of the tube can not be clianged without the 

dissipation of power in the grid-filament circuit. The amount 

53904°— 22 30 


of input power which is thus dissipated and must be supplied 
is always very much less than the power output which is liber- 
ated by the change in resistance. This small input power which 
is required to control the resistance can be calculated from the 
characteristic curve showing the relations between the current 
and the voltage in the input circuit, or grid-filament circuit. 
These characteristics, which are shown in Fig. 262, are ob- 
tained in a manner similar to that employed for obtaining the 
characteristics of the plate circuit, by keeping the other cold 
electrode, in this case the plate, at a fixed voltage, and deter- 
mining the relations between the grid current and the grid 

The grid characteristics are usually plotted to a larger scale 
than the plate characteristics, because grid voltages and cur- 
rents are small compared with plate voltages and currents. In 
a transformer, if the secondary or output voltage is higher than 
the primary voltage, then the secondary current is lower than 
the primary current (Sec. 58, page 128). An electron tube 
differs from a transformer in that the output currents and 
voltages are both larger than the input currents and voltages. 
It must be remembered that the law of conservation of energy 
is not violated, since the output power is derived from the plate 
battery, which is a part of the output circuit, and is not derived 
from the grid input power. 

Another lack of symmetry between the action of the plate and 
grid electrodes is that while increasing grid voltage tends to 
increase the plate current, an increasing plate voltage tends to 
decrease the relatively small grid current. 

192. Operating Characteristics. — While the characteristic curves 
determine what relations can possibly exist between voltages 
and currents, the values which do exist between them when 
the tube is operating in any of its applications is determined by 
the characteristics of the apparatus used with the tube as 
■well as by the characteristics of the tube itself. For example, 
if in Figure 263 a resistance R is inserted in the plate lead, in 
series with the plate battery Eh, then the only values of ev and 
h which can exist when the tube is operating are given by the 
equation ep^Eb — Rip, where ^b and R express the character- 
istics of the equipment used in connection with the plate or 
output side of the tube. On the plate diagram the dotted line 



shows what values of plate current and voltage can exist with 
a resistance of 5000 ohms and a plate battery of 300 volts 

,0, . «o ^ «0 *« • <l 

■vdJadarwijiiu ut yuajjno ^^^Irf 

externally placed between the filament and plate of the tube. 
If the grid voltage, for example, is — 10, then the plate voltage 
will be 220 volts and the plate current 16 milliamperes, as de- 



termined in Fig. 2<51 by the intersection of the dotted line and 
the curve marked " Grid voltage= — 10." In other words, 
these values are both consistent with the tube characteristics, 
and the characteristics of the external plate battery and re- 
sistance. The grid voltage and plate voltage also determine 
the grid current, so that if the Instantaneous grid voltage is 

FicyZeZ Qrid Voltage - yolts 

known, then all the other quantities are determined by the tube 

Thus, if the grid voltage at any instant can be found from 
the equation eg= — 10+60 sinw/ — that is, if a sine wave voltage 
is impressed upon the grid, between limits of —70 and +50 
volts — then the wave forms of plate voltage and plate current 
and grid current for the particular output circuit of Fig. 263 
are readily determined to be as shown in Fig. 264. The dotted 



line between the terminal points A and B (Fig. 261) corre- 
sponding to tlie maximum and minimum grid voltages is known 
as the oscillation cliaracteristic. 

It will be noted in the tube operation that when any external 
impedance is present in the plate circuit the plate voltage is 
low when the other quantities — the plate current, grid voltage, 
and grid current — are high. This relation holds whenever the 


■^- E, 

Electron Tuhe Circuit With /Resistance 
Load in. Piute Circuit 

tube is used for producing a magnified output, whether the tube 
is used as a detector, amplifier, generator, or modulator. In 
receiving tubes the variations of tube quantities are small com- 
pared with average values, but in transmitting tubes they are 

The case shown with a pure resistance load in the plate 
branch is the simplest possible case. If there are condensers, 
inductances, or antennas connected in the output side of the 
tube, the volt-ampere characteristic of the load is usually a 
very complicated relation, and the tube operation can not be 
accurately computed by simple methods. The line of operation 
or oscillation characteristic will not be a straight line and the 
wave forms of the plate voltage and plate current will not be 



of similar appearance. However, the general relation that the 
plate voltage will be low when the plate current and grid volt- 
age are high will hold whenever the tube is producing alter- 
nating power in the output side. 




















Vate c 















"jr/d c 






xrid V 





— > 







Fig.ZG^ Wave Forms of Grid Current, Plate 
Current and Plate Yoltaqe for a Sine Wave 
Voltaqe Impressed on the Grid. 

In power applications of tubes the oscillation characteristic 
is restricted to certain regions. The plate current drawn from 
the plate battery by a tube is given by the average tube cur- 
rent, and the plate battery voltage is approximately the average 


plate voltage. Too high plate voltages and currents can not be 
used, because the plates of the tube will become very hot and 
may be destroyed. Tubes used as generators automatically 
limit themselves to certain regions of the characteristic on 
account of the high grid current drawn when the plate voltage 
becomes low. 

193. Practical Forms of Three-Electrode Tubes. — In Figs. 265 
and 266 are shown a number of American and foreign tubes. 
In Fig. 265 the tubes numbered 1 to 5 are some of the smaller 
types of American transmitting tubes. Tube No. 1 is made 
by the Western Electric Co. and designated by the Signal Corps 
as Type VT-2 ; it has a filament coated with oxides, such as 
those of barium, calcium, or thorium, for the purpose of in- 
creasing the electron emission from the filament, and is rated at 
about 5-watts output. Tubes Nos. 2, 3, 4 are made by the Gen- 
eral Electric Co., have pure (uncoated) tungsten filaments, and 
are rated at about 5-watts output; No. 2 is designated as Type 
VT-14, and Nos. 3 and 4 are two different forms of Type VT-16, 
Tube No. 5 is a more powerful General Electric tube designated 
as Type VT-18 or Type U, and is rated at about 50-watts 

The tubes numbered 8 to 15 are American receiving tubes, 
which are also used for amplifying. Tubes Nos. 8 and 9 are 
made by the Western Electric Co., have coated filaments, and 
are designated, respectively. Type VT-1 and Type VT-3. Nos. 
10 and 11 are made by the General Electric Co., have uncoated 
tungsten filaments, and are designated, respectively, as Type 
VT-11 and TyY)e VT-13. Tube No. 12 is made by the De Forest 
Radio Telephone and Telegraph Co. and is designated as Type 
VT-21. Tube No. 13 is made by the Moorehead Laboratories 
and is extensively used. Tube No. 14 is made by the Connect- 
icut Telephone and Electric Co. and has a plate outside of the 
glass tube in which the filament and grid are contained, the 
electron flow to the plate occurring through the glass. Tube 
No. 15 is a very small tube made by the Western Electric Co. 
and is designated as Type VT-5, or Type N. 

Tubes Nos. 16, 17, 18, 19 are French tubes. Tubes Nos. 16, 
17, 18 are intended primarily for receiving, but are also used 
to some extent for transmitting. Tube No. 16, which has two 
projections at the top, is designed primarily for apparatus in- 

8 9 10 II 12 13 14 15 

Fig. 265. — Practical forms of three-electrode electron tubes. 



tended to operate on short wave lengths, the idea of the con- 
struction being to keep the connections to the grid and plate 

Fig. 266. — Large transmitting tubes. 

as widely separated as possible to minimize the capacity be- 
tween them. In all these French tubes the filament is straight, 
the grid is a spiral wire surrounding the filament, and the plate 


is a cylinder surrounding both. Tubes Nos. 17 and 18 are re- 
ceiving and amplifying tubes for general service and are made 
by different manufacturers. Tube No, 19 is designed primarily 
for transmitting and has an output of about 40 watts. Tube 
jS^o. 20 is a " Telefunken " German receiving tube, which is 
similar to the French receiving tubes. 

In Fig. 266 tubes Nos. 21, 22, 23 are larger transmitting 
tubes. No. 21 is an American tube made by the De Forest 
Radio Telephone and Telegraph Co., and is called by that com- 
pany an " oscillion " ; it has a power output of about 100 watts. 
Tube No. 22 is an American tube made by the General Elec- 
tric Co. and called by them a " Type P Pliotron " ; it has a 
rated output of 250 watts. In Tube No. 22 the plates as well as 
the filament are made of tungsten and the plates are stamped 
with concentric rings to prevent buckling under extreme heat. 
A modified form of this tube, called the " UY-204," having a 
thicker filament and operating at a lower filament voltage, has 
recently been placed on the market. Tube No. 23 is a British 
transmitting tube made by the Edison-Swan Electric Co. and 
designated as Type ES-9 ; it has an output of about 250 
watts. This tube is equipped with an Edison screw base, 
through which the filament connections are made. 

The over-all length unmounted of tube No. 1 is about 4 
inches ; tube No. 5, 7 inches ; tube No. 13, 4 inches ; tube No. 
15, 2 inches ; tube No. 18, 4 inches ; tube No. 22, 14 inches. 

The present tendency is to make receiving tubes somewhat 
smaller than heretofore. This is illustrated in tube No. 15, 
having an over-all length of only 2 inches and very small ele- 

B. The Electron Tube as a Detector. 

194. Detector Action. — There are two methods of using an 
electron tube as a detector : First, the use of the properties of 
the tube when worked at the curved portion of the curve show- 
ing the relations of grid voltage and plate current (Fig. 259), 
and, second, the use of the properties of the tube when worked 
at the curved portion of the curve showing the relations of grid 
voltage and grid current (Fig. 260). 

In the first method the detector tube is connected directly 
across the condenser in the receiving circuit (Fig. 267). Suppose 


the receiving antenna picks up a signal. Then oscillations in 
the tuned circuit LC are set up and the radio-frequency alter- 
nating voltage across the condenser Ci is impressed between the 
grid and filament, bringing about changes in the plate current. 
If the plate current is normally at a point on the bend of the 
characteristic curve — say in the region a to c, Fig. 259 — the in- 
crease of plate current when the grid voltage is positive is 
greater than the decrease of plate current when the grid voltage 
is negative. Thus, on the average, the plate current is in- 
creased while the oscillations due to the signal last. In Fig. 
268 are shown, roughly, the form of (1) the high-frequency 
oscillations impressed upon the grid. (2) the high-frequency 
variations in plate current, (3) the audio-frequency fluctuations 
of telephone current. The frequency with which these telephone 
fluctuations occur in the frequency of the incoming wave trains 
and in order to be heard must be within the range of audible 
sound. The radio-frequency fluctuations wiiich occur in the 
plate current shown in (2) do not pass through the windings of 
the telephone receivers, because the inductance of the coils in 
the telephone receiver is so great that the radio-frequency vari- 
ations in the plate current can not flow througli them, but flow 
througli the capacity existing between the leads and windings 
and across the by-pass condenser. Thus these radio-frequency 
variations are by-passed by this effective capacity of the leads 
of the telephone receiver and only the average current flows 
through the inductance of the telephone receiver windings (3). 
When using this method of detection, no current flows in the 
grid circuit because the average value of the grid voltage is 
maintained negative with respect to the filament in order to 
operate on the curved portion of the curve showing the relation 
between plate current and grid voltage. 

With simple detector action of the kind here described, when 
signals of ordinary intensity are being received, the mean 
value of the change of the plate current, for a given operating 
point on the grid voltage-plate current curve, is very nearly 
proportional to the square of the amplitude of the voltage 
oscillations impressed on the grid. For very strong signals, 
however, this relation does not hold. This is a relation which 
holds for any detector which operates by virtue of the curva- 



ture of tlie curve showing the current which it delivers for 
various impressed voltages. 

In some cases it is necessary to use an additional battery, 
called a "C" battery, between points f and g (Fig. 267) in 
order to bring the plate current to the bend of the characteristic 
curve (Fig. 259). This, however, does not change the action; 
the variations of the plate current are brought about by the 
alternating emf. between the terminals of the coil L just 
as when the battery C Is absent. It is interesting to note 
here that we are employing resonance in the circuit LGx to ob- 
tain as large an emf. as possible between the terminals of the 
coil and condenser with a given signal. (See Sec. 109.) 


Connections for usina electron 
tube as a simple detector 

Fig. 266 
I Voltage oscillations impressed en the grid, 
i Resulting variations in plate current. 
3 Corresponding fluctuathns of telephone 


/Action of electron tube as detector 

If the grid battery voltage is adjusted so that the plate cur- 
rent has a value near the upper bend of the curve showing 
plate current plotted against grid voltage, instead of near the 
lower bend, the action will be essentially the same, but the 
effect of the arrival of a wave train will be to decrease mo- 
mentarily the plate current instead of to increase it. As be- 
fore, there will be fluctuations of the plate current keeping 
time with the arrival Qf wave trains, and there will be a sound 
in the telephone of a pitch corresponding to the number of wave 
trains per second. 

Care must be taken in the use of receiving tubes that the 
plate battery voltage is never high enough to cause the visible 
" blue glow " referred to in Section 188. The tube becomes very 



erratic in behavior \\-lieii in this condition and is very uncer- 
tain and is not sensitive as a receiver. This is because the 
plate current becomes so large tliat it is unaffected by varia- 
tions of the grid voltage. Characteristic curves will not repeat 
themselves if the tube shows the blue glow, and sharp breaks 
may appear in any or all of the curves. Furthermore, the 
electrodes are heated and may be damaged by the blue-glow 

Condenser in Grid Lead. — With many tubes louder signals are 
obtained if the grid is made positive with respect to the nega- 






wv ^== 


-^Piate Current 

-=^ Fi^.Z60. J^eceivmg Circuit us/ng f^lectron 
Tube as Detector of Dampec/ Oscillations. 
Condenser m Gr/d Lead. 

five end of the filament, so that current flows in the grid cir- 
cuit. Instead of operating on the curved portion of the grid- 
voltage, plate-current curve the tube operates upon the curved 
portion of the grid-voltage, grid-current curve and the straight 
portion of the grid-voltage, plate-current curve (see Fig. 272). 
When using the curvature of the grid-current characteristic 
in this fashion, a condenser is connected in series with the 
detector tube and with the receiving circuit from which the 
signal voltage is obtained (C in Fig. 269). Now suppose that 
a series of wave trains falls upon the antenna of Fig. 269, as 
shown in (1) of Fig. 272. If the circuit LC is tuned to the 
same wave length as the antenna circuit, oscillations will be 



set up in it and similar voltage oscillations will be communi- 
cated to the grid by means of the condenser C. As shown in 
(2), Fig. 272, each time the grid becomes positive the electron 
current which flows at the voltage eo will be increased more 
than it is decreased when the grid voltage goes below eo. Thus 
during each wave train the grid will continue gaining negative 
charge and its voltage will, on the average, be mostly nega- 
tive, as shown in (3), Fig. 272. This negative charge on the 

,> Radio -fre<iuer)Cj Signal voltage 

Fm 270. Effect of Mpplijing Signal 
to fjectron Tube Detector 

u y w 
Grid voltage 

FigZV Voft-/fmpere 
Characteristic of an Electron 
Tube Shotviog Operation as 
an Ffmplifier 

grid opposes the flow of electrons from filament to plate and 
produces a much magnified decrease in the plate current 
throughout the train of oscillations, as shown in (4), Fig. 272. 
A.t the end of each wave train this charge leaks off either 
through the condenser or through the walls of the tube, or 
both, and the plate current becomes steady again at its normal 
value (4), Fig. 272. This should happen before the next 
wave train comes along, and in order to insure this a resistance 
of about a megohm (a million ohms) is shunted across the 
condenser. Such a resistance is called a "grid leak." As has 
been stated above, the inductance of the coils in the telephone 


receivers is so great that the radio-frequency variations in the 
plate current can not flow througli them, but flow through the 
capacity existing between the leads and windings and across the 
by-pass condenser. The current which actually flows through 
the windings and operates the telephone receivers, if drawn, will 
look something like the dotted line in (4) and the heavy line in 
(5). Thus, as in the case of the circuit of Fig. 267, the note 
heard in the telephone corresponds in pitch to the frequency of 
the wave trains. If the waves falling upon the antenna are un- 
damped waves, they may be detected using either of these 
circuits if they are first divided off into audio-frequency 
groups. (For methods see Sec. 181, p. 430, and Sec. 211, p. 529.) 
To receive undamped waves which are not divided into groups 
of audible frequency, electron tubes may be used in special ways 
called the heterodyne and the autodyne methods. (See Sec. 
205, p. 501.) 

195. Experimental Data on Detectors. — The decrease in plate 
current in a detector tube with grid condenser and grid leak 
which takes place when a radio wave train is applied to 
the grid can be shown experimentally. In Fig. 270 is shown 
the average plate current in microamperes as it varies with 
increasing radio-frequency voltage applied to the grid con- 
denser in a circuit such as that of Fig. 269. The tube used 
here is a receiving tube, Signal Corps Type VT-1. At zero, 
or no incoming signal voltage, the plate current is 500 micro- 
amperes, corresponding to the point P in Fig. 272. As the 
amplitude of the oscillations in grid voltage is increased to 0.5 
volts, the plate current decreases to 480 microamperes, then to 
420 microamperes at 1.0 volt, etc. This curve was taken with a 
condenser (C in Fig. 269) of 250 micromicrofarads and a leak 
resistance of 2 megohms. The operating point, or steady grid 
voltage, about which the potential of the grid was caused to os- 
cillate by the incoming signal, was +0.8 volts, corresponding to 
the point eo in Fig. 272. 

The tubes generally supplied to the Signal Corps for receiving 
(types VT-1, VT-11, VT-21) operate best with a leak resistance 
of 2 megohms and with the return connection made from the 
grid condenser through the receiving circuit to the positive side 
of the filament. Owing to the flow of the steady grid current 



through the high leak resistance, this fixes the steady voltage of 
the grid at about 0.5 to 0.8 volts positive with respect to the 
negative end of the filament 

'^. Plate current oscillations 

J. Grid voltage 

/. Oscillations of 
Voltage of incoming 

Fig.27Z.JTction of Detector Tube in deception 
Usina Grid Condenser. 

In order to get a readable signal from a good tube detector, it 
is usually necessary to apply to the grid a voltage of two 
millivolts effective value, which would correspond approxi- 


mately to an alternating current of about 0.01 microampere in 
the grid circuit. These values apply to a completely modulated 
wave — that is, a wave whose oscillations reach a zero value at 
regular intervals which correspond to the audio frequency of the 
wave trains. 

C. The Electron Tube as an Amplifier. 

196. General Principle of Amplification. — It was shown in Sec- 
tion 194 that an electron tube acts as a detector or rectifier 
because an alternating voltage applied to the grid circuit can 
be made to produce unsymmetrical oscillations in the plate cir- 
cuit. While the tube is thus acting as a detector it is also, as 
a matter of fact, acting as an amplifier — that is, oscillations of 
greater power are produced in the plate circuit for a given 
alternating voltage in the grid circuit than would be produced 
by the same voltage directly in the plate circuit. This explains 
why the electron tube may be a more sensitive detector than the 
crystal detector, which acts as a rectifier only. 

It is sometimes desired to amplify an alternating current 
without any rectifying or detecting action. This is done by 
keeping a voltage on the grid of such value that the symmetry 
of the oscillations in the plate circuit is not altered. Thus, if 
there is a steady voltage applied on the grid of such value that 
the plate current is on the part of the characteristic curve that 
is nearly straight (as point P in Fig, 271), then a small change 
in grid voltage in either direction causes the plate current to 
increase or decrease the same amount. For instance, if the grid 
voltage is increased from v to iv (Fig, 271) or decreased by an 
equal amount from v to ii, the current will, in the first case, 
increase from a to c and in the second case fall off by an equal 
amount, from a to b. In other words, the wave form of the 
grid voltage variation will be repeated in the fluctuating plate 
current. The latter will now be equivalent to an alternating 
current superimposed upon the steady plate current from the 
plate battery. The magnitude of the alternating-current part 
of the plate current will be greater, the steeper the slope of the 
curve at the point P. 

For the same voltage acting' in the two circuits the power 
expended in maintaining the oscillations of the grid current is 
53904°— -22 31 


far less than that involved in the corresponding variations in 
the plate current. For example, referring to the electron tube 
whose characteristic curves are given in Fig. 260, if the plate 
voltage is maintained constant at 60 volts and the grid voltage 
oscillates, so that the plate current varies between the values 
b and d, the grid current will change from about 0.57 to 4.85 
microamperes, and the average voltage on the grid is 0.7 volt. 
The corresponding change in plate current is from 862 to 1000 
microamperes. Since the power in watts in any circuit is the 
product of the amperes by the volts effective in the circuit, we 
have in the grid circuit a power expenditure of (4.85— 0.57) X 
0.7=3.00 microwatts, and in the plate circuit a corresponding 
power change of (1000—862) X 60=8280 microwatts. This mag- 
nified power is drawn from the energy delivered by the plate 
battery. The signals may be thought of as exerting a sort of 
relay action on the plate circuit, causing magnified power to be 
drawn from the plate battery. The tube is said in this case to 
act as an " amplifier." The variations of current in the grid 
circuit have been compared to the slide valve of an engine, since 
they admit energy from the battery into the plate circuit much 
as the slide valve admits energy into the cylinder of the engine. 
The oscillations impressed on the grid circuit may be of high 
radio frequency or of an audible frequency of perhaps 300 to 
3000 cycles per second. 

To utilize the amplified alternating current in the plate cir- 
cuit, the primary of a transformer T (Fig. 273) may be placed 
In the plate circuit. From the secondary of this transformer the 
alternating current (see Sec. 58) is delivered to a detector, 
which may be an electron tube operating as a rectifier or a 
crystal detector. If further amplification is desirable, the alter- 
nating current from the secondary of the transformer may be 
delivered to the grid circuit of a second amplifying tube, as 
shown in Fig, 273. From this second tube it then goes to a 
detector tube or to a crystal detector. This method of suc- 
cessively using two or more tubes for amplification is called 
cascade amplification. The last tube in such an amplifier of 
radio-frequency waves is called the detector tube, and the other 
tubes are called amplifier tubes. An amplifier consisting of 
one detector tube and two amplifier tubes is said to have two 
stages of amplification. 


Instead of transferring the amplified energy by means of a 
transformer coupling, the coupling may be simply a resistance, or 
may be a condenser. A circuit using resistance coupling is 
shown in Fig. 274, in which the radio-frequency power is ampli- 
fied by two tubes coupled together through resistances, and then 
detected. After passing through the detector, the currents of 
audio-frequency can be further amplified by one or more audio- 
frequency stages. An amplifier in which the signal is amplified 
before reaching the detector is called a radio-frequency ampli- 
fier. An amplifier in which the signal is amplified after passing 
through the detector is called an audio-frequency amplifier. Re- 
sistance couplings in radio-frequency amplifiers have been exten- 
sively used in France, but not to so great an extent in the 
United States. The advantage of a resistance-coupled amplifier 
is that while the amplification per tube may not be so great as 
with transformer couplings, the amount of amplification is prac- 
tically independent of the wave length for long wave lengths. 
Resistance-coupled amplifiers seldom give full amplification at 
wave lengths below 1,000 meters. In order to get the greatest 
power output, and hence the greatest power amplification, from 
a tube, a resistance should be used in the plate circuit of a value 
equal to the average internal resistance of the tube between 
plate and filament. In this respect the tube is similar to any 
other electrical machine and to a battery, as described in Section 
24. Usually, however, such small currents flow into the detector 
used with radio-frequency amplifier that the detector may be 
considered a voltage-operated device, in which case the maxi- 
mum voltage output and not the maximum power output is de- 
sired from the amplifier tubes. This is realized by making the 
coupling resistances larger than the internal resistance of the 
tube between plate and filament, in some cases two or three 
times as large. These high resistances require higher plate 
voltages than are required for transfonner coupling, perhaps 
voltages two or three times as great as for transformer coup- 
ling. In some cases, as in some military applications, this may 
be a real disadvantage. An interesting discussion of resistance- 
coupled amplifiers is given in the British Admiralty Handbook 
of Wireless Telegraphy. 

For audio-frequency amplification, iron core transformers are 
used. For transformer-coupled radio-frequency amplification 


the small transformers used generally have air cores — that is, 
no iron is used. There have recently been developed radio- 
frequency transformers with iron cores, very thin laminations 
being used. 

197. Elementary Theory of Amplification. — The characteristic 
curves of an electron tube show that an increase in the grid 
voltage makes a much greater increase in the plate current than 
the same increase in the plate voltage itself would do. Consider, 
for instance, the two upper curves of Fig. 259. page 461. From 
the curve corresponding to a plate voltage of 40 volts we see 
that the plate current increases from 430 to 530 microamperes 
when the grid voltage is increased from 0.4 to 1.0 volts, or 167 
microamperes per volt change. If, on the other hand, the grid 
voltage is left unchanged at 0.4 volts, and the plate voltage 
increased to 60 volts, the upper curve shows that the plate cur- 
rent increases to 862 microamperes, a change of 21.6 micro- 
amperes i>er volt. In other words, a volt added to the grid 
voltage makes eight times as much change in the plate current 
as a volt added to the plate voltage would make. This number, 
which represents the relative effects of grid voltage and plate 
voltage upon plate current, is called the " amplification co- 
efficient " of the tube.^ The greater the value of this amplifica- 
tion coefficient is for a given value of internal plate-circuit 
resistance of the tube, the more efficient is the tube as an ampli- 
fier of weak signals. The amplification coefficient may be 
defined as the ratio of the change in plate current per volt 
change on the grid, to the change in plate current per volt 
change on the plate. 

The two principal constants of a tube are the amplification 
coefficient just defined and the internal output resistance or 
internal plate-circuit resistance, and these have been discussed 
in Section 191. The internal plate-circuit resistance is the 
resistance to small alternating currents which exists between 
the plate and the filament in the tube, and, since it is the re- 

^The theory of amplification has been presented in detail by Lang- 
muir. Proc. Inst. Radio Engineers, 3, 261, 1915 ; Latour. Electrician, 
78, 280, 1916 ; van der Bijl, Phys. Rev. 12, 171, 1918 ; van der BijI, Proc. 
Inst. Radio Eng., 7, 97, April, 1919 ; van der Bijl, The Thermionic 
"Vacuum Tube and its Applications. 



sistance of the output circuit of tlie tube, is often called 
the internal output resistance. These two constants may be 


FiQ.Z75.ConnecCions for Cascade /Amplification 
Transformer Coup/in^. 



^wv) *> 1|- 

R, Detector 

Fig. 274. Resistance Coupled JJmplifier. 


Fig.275, Regenerative Circuit for 
simultaneous amplififing and rectifying. 

calculated from the characteristic curves of the tube or may be 
measured by a simple method like a bridge measurement or may 
be calculated approximately from the structural dimensions of 


the tube.^ The voltage amplification given by an amplifying 
circuit may be calculated from these two constants of the 
electron tube. 

The voltage amplification may be defined as the ratio of the 
voltage change produced in the output apparatus in the plate 
circuit to the change in the voltage impressed on the grid. 
Thus, ill the resistance-coupled amplifier of Fig. 274, it is the 
ratio of the voltage between a' and h' at the terminals of R 
to the voltage applied between a and &. Calling the amplifica- 
tion coefficient A' and the internal output resistance i^o it can be 
shown that the voltage amplification for such a combination is 


198. Audio-Frequency Amplification. — In the preceding discus- 
sion of amplification it was pointed out that after a radio- 
frequency current is amplified it is passed through a rectifying 
device, often a detector tube, and the term " audio-frequency 
amplifier " was defined. If an audio-frequency current is to be 
amplified, it is not necessary to pass tlie amplified current 
through a detector, since the amplified current is audible if 
received with a telephone receiver placed in the plate circuit 
of the amplifier. It is sometimes desired to amplify the audio- 
frequency current produced in a radio rectifying device, in 
which case the amplifier is an audio-frequency amplifier. In 
this case the radio current consisting of groups of radio- 
frequency oscillations is first impressed upon the detector and 
the pulses of current having the group frequency are passed on 
into the amplifier. The amplifying process may be carried on 
through several steps, as in the cascade amplification shown in 
Fig. 273. An amplifier consisting of two Type VT-1 tubes in 
cascade may give a power amplification of 20,000 times. 

In some amplifiers as many as six tubes may be used. In such 
cases it is general practice to use perhaps three tubes as radio- 
frequency amplifiers, then the detector tube, and then perhaps 
two tubes as audio-frequency amplifiers. One reason for using 
the radio-frequency amplification is because under proper oper- 
ating conditions with signals of moderate intensity the output 

8 See Miller, Proc. Inst. Radio Engineers, 6, 141, 1918 ; Miller, Proc. 
Inst. Radio Engineers, 8. 64, February, 1920 ; van der Bijl, Phys. Rev., 
12, 171, 1918 ; R. W. King, Phys. Rev., 15, 256, April, 1920. 


of a detector tube is approximately proportional to the square 
of the input voltage, and hence the output of the detector tube 
increases rapidly as the input voltage is increased. If more 
than three stages of radio-frequency amplification are used, 
troublesome regenerative effects are very likely to occur in the 
output circuit of the amplifier. Regenerative effects are also 
likely to occur if more than two stages of audio-frequency am- 
plification are used, causing "howling" noises in the output 
circuit. If, therefore, we wish to use as many as six tubes in 
an amplifier, it is necessary to use both radio-frequency and 
audio-frequency amplification. These troublesome effects can 
be reduced by properly shielding the various circuits of the 
amplifier, as by inclosing in metal. If very feeble incoming 
oscillations are impressed on the input of such a six-tube am- 
plifier of a tjT)e now in extensive use, the over-all voltage 
amplification of the amplifier may be several million. It is 
only by the use of amplifiers of this type that it has been possi- 
ble to use the coil antennas, which may be 4 feet square or 
even smaller, as receiving devices and as radio compasses. 

Amplifiers with a large number of tubes have been used, 
especially for very short waves, such as 50 meters. The use of 
even six tubes requires very careful design to prevent difficul- 
ties due to regenerative effects. With a greater number of 
tubes and greater amplification every disturbance is magnified, 
and even greater care in design is essential and shielding is par- 
ticularly important. The use of more than six tubes in a com- 
pact, portable, unit, is especially difficult. A six-tube amplifier, 
properly designed, will usually give all the amplification neces- 
sary for ordinary purposes. 

The use of radio-frequency amplification for short wave 
lengths, particularly for less than 300 meters, is attended with 
many difficulties caused by the low-impedance paths which 
the capacities between the leads and between the elements of 
the tubes offer at high frequencies. For short waves the high 
frequency may be changed before amplification by the beat 
method. (See Sec. 205, page 506.) 

If an amplifier with transformer coupling or capacitive coup- 
ling is to be used on one particular wave length a much more 
effective amplifier can be designed than if it is required that 
the amplifier operate over a considerable range of wave lengths. 


The performance of a resistance-coupleil amplifier, however, 
when used on long wave lengths depends very little on the wave 
length. Resistance-coupled amplifiers seldom give full amplifi- 
cation at wave lengths below 1,000 meters. 

Adjustment of grid potential. — In discussing contact detectors 
in Section 182, page 439, the effect of using a " booster " bat- 
tery for causing the detector to operate on the most desirable 
•part of the characteristic curve was described. A somewhat 
similar method may be used w^ith tube detectors and amplifiers, 
although the phenomena involved are by no means as simple as 
in the case of the contact detector. The grid of a tube may be 
maintained at a definite voltage above the negative terminal of 
the filament, so that the tube operates at a particular point on 
the characteristic curve showing the relation between grid volt- 
age and plate current. For a detector it is desirable to have 
the operating point at the sharpest bend in the characteristic 
curve, as has been explained above. For an audio-frequency 
amplifier it is usually desirable to have the operating point at 
about the center of the steepest part of the characteristic curve. 
The d. c. voltage so used is often called a " biasing potential." 
The use of a " C " battery for obtaining this biasing voltage has 
been described in Section 194, page 474. A method of obtain- 
ing this biasing potential, which is extensively employed, is by 
the use of a voltage divider arrangement, which consists of a 
resistance of perhaps 200 or 300 ohms connected across the 
filament battery terminals and an adjustable contact, which is 
connected to the grid. 

StahUl::€r. — In receiving damped waves or interrupted con- 
tinuous waves with an amplifier it is necessary to prevent the 
various tubes in the amplifier from oscillating. This may be 
done by applying a positive voltage of the proper magnitude to 
tlie grid. The voltage divider arrangement just mentioned may 
be used for this purpose, and when so applied to amplifier tubes 
is called a " stabilizer." The stabilizer is usually so adjusted 
that the circuit of the tube for which it is used is just below 
the oscillating condition. In an amplifier of several stages, 
such as the six-tube amplifier mentioned above, having both 
radio-frequency stages and audio-frequency stages, it is desir- 
able to have one separate stabilizer for the radio-frequency 


Stages and one stabilizer for the audio-frequency stages. A sep- 
arate voltage divider should also be used for adjusting the grid 
potential of the detector tube. The use of the stabilizer makes 
the grid sufficiently positive so that the grid circuit will absorb 
an appreciable amount of power. Stabilizers may be used with 
amplifiers having either inductive, capacitive, or resistance cou- 
pling. Stabilizers may greatly increase the sensitivity and use- 
fulness of an amplifier and are now found on many radio-fre- 
quency amplifiers of recent design. 

199. Regenerative Amplification. — The sensitiveness of an elec- 
tron tube as a detector may be enormously increased by a 
method which multiplies its amplifying action. The connec- 
tions are shown in Fig. 275. The explanation of the amplifying 
action is as follows. Oscillations in the circuit LLiC applied to 
the grid through the condenser Ci produce corresponding varia- 
tions in the continuous plate current, the energy of which is 
supplied by the plate battery {B, Fig. 275). This plate current 
flows through Ls, and by means of the mutual inductance M 
some of the energy of the plate oscillations is transferred back 
to the grid circuit, and the current in the circuit LLoC is thus 
increased. This produces amplified grid oscillations which, by 
means of the grid, produce larger variations in the plate cur- 
rent, thus still further reinforcing the oscillations of the sys- 
tem. Simultaneously with this amplification the regular de- 
tecting action goes on ; the condenser Ci is charged in the usual 
way, but accumulates a charge which is proportional not to 
the original signal strength but to the final amplitude of the 
oscillations in the grid circuit. The result is a current in the 
telephone much greater than would have been obtained from 
the original oscillations in the circuit. 

To obtain maxinmm voltage on the grid, the circuit LL^C 
should have large inductance and small capacity. The con- 
nections between Z2 and 7.3 must be so made that their mutual 
inductance is of proper sign to produce an emf, which will aid 
the oscillations instead of opposing them. Various modifica- 
tions of this method are used. The condenser C may be across 
L3, so that the tuned oscillatory circuit is in series with the 
plate instead of the grid; or C may be connected across all 
of the inductance in series, the oscillation circuit then including 
L, Lj, and I/3. 



Combination Radio and Audio Regenerative Amplification. — 
A single electron tube can be used to amplify and detect radio- 
frequency current and simultaneously to amplify tbe telephone 
pulses of audio frequency. The circuits are shown in Fig. 276, 
Here M2 represents the coupling for the radio frequency, and 
the coils are of relatively small inductance. Mz is the coupling 
for the audio frequency, and the transformer is made up of 
coils having an inductance of a henry or more. The variable 
condensers Ca and d have the double purpose of tuning lU to 



C3 '-s 

Fiq 276 


Combination radio and audio 
irequency amp/iucation 


Tin -277 

Comhmation of Electron 
tube amplifier and crystal detector 

the audio frequency and of by -passing the radio frequencies. 
The radio-frequency variations in the plate current flow through 
the circuit PFLzdC^L^ and at the same time the audio-frequency 
variations flow through the circuit PFL^LeTBLi. The audibility 
of weak signals received by this method is about 100 times the 
audibility obtained with a single tube connected in a simple 
detector circuit. On stronger signals the amplification is 

200. Electron Tube Amplifier with Crystal Detector. — ^The char- 
acteristic curves of an electron tube show that the best value 
of grid voltage for amplification is not the same as for best 


detecting action, which is an argument for using separate tubes 
for these two pui*poses. This adds somewhat to the complexity 
of the apparatus, and in apparatus in which for some reason 
it is desired to use only one tube the combination of an electron 
tube for amplifying and a crystal detector for detecting may 
be used.* Such a circuit is shown in Fig. 277. 

The oscillating circuit LC is coupled to the antenna and is 
tuned to the frequency of the latter, which is the frequency of 
the incoming waves. The alternations of voltage between the 
terminals of the coil L are applied between the filament F 
and the grid G through the battery &, which has been previously 
adjusted in voltage so that the plate current has a value cor- 
responding to a point on the straight part of its characteristic. 

The amplified oscillations in the plate circuit are communi- 
cated to the oscillating circuit LiCi, which is coupled to the 
plate circuit through the coil M. The circuit LiCi is tuned to 
the frequency of the received waves like the other two circuits. 
The alternations of voltage between the terminals of the coil 
Zi are rectified in the crystal detector D in the usual way and 
cause an audio-frequency current to flow through the telephone 

For further information regarding the amplifying action of 
the electron tube and various types of amplifiers, the reader 
may refer to : H. J. van der Bijl. " The Thermionic Vacuum 
Tube and Its Applications ;" J. H. Morecroft, " Principles of 
Radio Communication;" John Scott-Taggart, "Thermionic 
Tubes in Radio Telegraphy ;" and the "Admiralty Manual of 
Wireless Telegraphy." 

D. The Electron Tube as a Generator. 

201. Conditions for Oscillation. — The electron tube can be 
made to generate high-frequency currents and thus act as a 
source of radio current for the transmission of signals and 
other purposes. Any regenerative circuit, such as that shown 
in Fig. 275, can be made to generate spontaneous oscillations, 

* G. Martinez, L'Elettrotecnica, 4, 278, May 25, 1917 : Science Ab- 
stracts B, No. 481. 1917. Other receiving circuits using crystal de- 
tector with electron tube amplifier are shown in the books, W. H. 
Eccles. Wireless Telegraphy (2nd ed.), PP. 302-304, and E. E. Bucher, 
Vacuum Tubes in Wireless Communication, pp. 73-75. 



if it be so arranged that any change in grid voltage makes a 
change in plate current of such magnitude that there is induced 
in the grid circuit a larger voltage than that originally acting. 
It has already been pointed out that in any electron tube much 
more power is produced by variations in the current to the 
plate than must be expended in changing the grid voltage to 
produce these variations. Thus there are a great variety of 


Ip Iriaie CurrenU 


Grid .-Vo^ io (Grid Current) 

1 { 


(. Grid Voltage 
C^ Oscillations 

Grid yo/taq 


Time — 

iiqZJQ Duildinq up of Oscillations 
in a Qenerahnq Tube 

circuits in which the plate circuit is coupled back to the grid 
circuit in such a manner as to supply this small power to the 
grid and make the surplus power available for use in an ex- 
ternal circuit in the form of continuous or undamped oscilla- 
tions of any frequency from even less than one per second to 
10,000,000 or more per second. 

This " feed-back " action can be obtained by the use of direct 
coupling from the plate back to the grid circuit, by inductive 


coupling, or by electrostatic coupling. The only requirement 
for continuous oscillations is that the voltage induced in the 
grid circuit must vary the plate current through an amplitude 
which supplies to the external or coupling circuits power suffi- 
cient or more than sufficient to maintain this voltage in the grid 
circuit. Thus in the circuit shown in Fig. 275 if the mutual in- 
ductance M be increased beyond a certain point the pulsating 
plate current flowing through the coil L^ will supply enough 
power through the coupling between Lz and La to maintain an 
oscillating current through the condenser circuit LL^C, which, in 
turn, varies the grid voltage to produce the changes or oscilla- 
tions in the plate current. The frequency with which the oscil- 
lations of current and voltage occur throughout the whole 
system is approximately the natural frequency of the LL2C 

202. Circuits Used for Generating Oscillations. — The circuit 
shown in Fig. 279 is one which is used quite extensively for 
transmitting purposes. The capacity and resistance C and R 
can be replaced by an antenna and ground connection. It is of 
the inductively coupled type. Any slight disturbance, such as 
the closing of the plate battery switch, sets up minute oscilla- 
tions in the closed inductance-capacity circuit. An alternating 
voltage is induced on the grid by virtue of the mutual induct- 
ance Mg. This causes alternations in the plate current of suf- 
ficient magnitude to supply through the mutual inductance Mp 
an emf. in the condenser circuit greater than that already pres- 
ent. Thus the voltage and current oscillations build up, as 
shown in Fig. 278, until a further increase in grid voltage no 
longer increases the pulsating plate current owing to the fact 
that the plate current can neither pass below the zero line nor 
increase above saturation value. The oscillations are then 
maintained at constant amplitude, when the power supplied to 
the oscillatory circuit through the coupling J/p by the pulsating 
plate current h (Fig. 278) is just equal to the power dissipated 
by the current I2 (Fig. 279) flowing through the resistance R 
plus the power expended in the grid circuit by the grid current 
le (Fig. 278). The current h flowing through the output circuit 
is built up to an amplitude many times greater than that in the 
plate circuit of the tube. 


AVheii this steady state of oscillation is readied the current h 
can have an amplitude many times greater than that in the 
plate circuit of the tube. The reason for this follows imme- 
diately from the preceding statement regarding the equality of 
power supplied in the plate circuit and power expended in the 
output circuit. The power supplied in the plate circuit may be 
regarded as the ijroduct of the square of the plate current Ji 
and the effective resistance of the tube between plate and fila- 
ment during the oscillation, which is negative in sense (since 
the plate voltage decreases as the plate current increases) and 
is of the order of magnitude of several thousand ohms. The 
power dissipated in the output circuit is the product of the 
square of the output current /- and the resistance R, which is 
usually only a few ohms, possibly ten. Hence when these two 
values of power balance each other in the steady oscillation 
the output current I- nuist be considerably larger than the plate 
current /i. 

In Fig. 280 is sliown a direct-coupled circuit in which the 
mutual inductance Jfp is replaced by the coil Lv and the mutual 
inductance J/g, by the coil Lg. In Fig. 281 is shown a circuit 
in which the tube supplies power to the oscillatory circuit by 
means of the voltage across a condenser Cp and power is ex- 
tracted by the grid circuit by the voltage across C%. With this 
type of circuit the direct-current power furnished by the plate 
battery or generator is connected in series with a radio-fre- 
quency choke coil directly from plate to filament. This is called 
a " parallel-type " circuit, since the source of direct-current 
power, the output circuit, and the tube are all in parallel. If 
it is desired to use this circuit for transmitting, the condenser 
Cp can be replaced by antenna and ground, the ground being 
connected to the key side of Cp. 

203. Practical Considerations in Using Electron Tubes as Gen- 
erators. — The useful power output from an oscillating tube is 
the power expended by the oscillating current 1 2 (Fig. 280) in 
the resistance of the output circuit. The power input to the 
tube, exclusive of that used in heating the filament, is the 
product of the plate supply voltage and the average plate cur- 
rent during an oscillation. Thus, with the Type VT-2 tube used 
by the Signal Corps, which may be operated with a plate voltage 




CO r-^ 


Fig Z73. Electron Tube Generating Circuit 
Inductive- Couplinq 




Fig.ZdO. Electron Tube Qenerating Circuit 
Direct Inductive Coupling 




Fiq-jiSI. Electron Tube Generating Circuit 
Direct Capacitive Coupling 


of 300, a direct-current ammeter connected in the plate circuit 
may read 0.05 amperes wliile the system oscillates. The power 
taken by the tube from the plate battery or generator is thus 
15 watts. The current I^ may reach a value of 0.5 ampere 
effective, through a resistance j?=16 ohms. Thus the useful 
power output is 4 watts and the efficiency of conversion of the 
direct-current power into alternating-current power is 26 per 
cent. The remainder of the 15 watts is expended in the grid 
circuit and in heating the plate. Maximum efficiency is seldom 
obtained in a circuit adjusted for maximum output. It may be 
advisable to include a battery in the grid circuit to make the 
average value of the grid voltage negative with respect to the 
filament, thus reducing the grid current, and hence the power 
dissipated by the grid. The type VT-2 tube normally operates 
with a grid voltage of — ^20. 

In place of a grid battery it is often more convenient to insert 
in the grid lead a resistance shunted by a condenser. Since 
grid currents flow through the resistance, during oscillation 
the grid voltage becomes negative : the amount of the nega- 
tive voltage is the product of the resistance in ohms by the 
current in amperes. A third method of obtaining a nega- 
tive voltage on the grid is to insert a resistance in the lead 
from the negative side of the plate battery to the filament and 
to connect the grid at the battery side of the resistance. The 
negative voltage is determined by the product of the battery 
current by the inserted resistance. This third method is much 
less efficient than either of the other two. 

In tubes of the coated-filament type in which the filament 
emission is high the plates may become dangerously hot, even 
at the rated plate voltage and filament temperature. This at 
once leads to the inquiry as to why the efficiency of an electron 
tube generator is so low, leaving a relatively large fraction of 
the power input for dissipation in heat. The answer is indi- 
cated by the fact that the average value of the plate current 
while the tube is oscillating must always be greater than zero 
(Fig. 278). Since the plate current always flows in the same 
direction, its instantaneous peak value reached during an oscil- 
lation can never be much greater than its average value dur- 
ing the oscillation, even if the pulsations are not in the fonn 


of sine waves. Assuming that the current supplied to the tube 
has pulsations in the form of sine waves, if the average value 
of the current to the tube, as indicated by a direct-current in- 
strument is 0.05 ampere, then during an oscillation the maxi- 
mum variation from the average value can not be greater than 
0.05 ampere. This maximum variation corresponds to an effec- 

0. 05 
tive value of the alternating part of the current of —p^ or 0.03o 

ampere effective current. Hence the plate can never become 
negative with respect to the filament, and the greatest possible 
peak value for the plate voltage to assume at any instant dur- 
ing an oscillation is that of the plate battery, say 300 volts, 

which corresponds to an effective value of —j^ volts. Thus, 

unless there be a marked distortion of the plate current wave, 
causing the effective value of current to be greater than the 
peak value divided by V2, the alternating-current power in the 
plate circuit, which must supply both the grid and the output 

300, 0.05 
circuit, can not exceed ~7^^~7o"' ^^ J^®^ ^^^^ ^^^ power 

supplied by the plate battery or generator. The remaining 50 
per cent of the input power is wasted in heat and may cause 
the plates to become incandescent. It is consequently desirable 
always to operate the tube with the circuit adjusted for maxi- 
mum output and at the lowest value of filament heating current 
and plate voltage which will just supply this output. 

No general rules can be given for adjusting a circuit to 
maximum output. If the resistance and capacity are fixed, as 
is frequently the case where an electron tube is used to excite 
an antenna, it is desirable to have means for varying inde- 
pendently the coupling between the plate circuit and the 
antenna circuit, the coupling between the antenna circuit and 
the grid circuit, and also the absolute value of inductance in 
the antenna circuit. In general, for a given inductance, the 
higher the resistance of the output circuit the lower the value 
of capacity at which maximum output is obtained. 

The electron tube is far superior to the buzzer as a source of 
oscillations for measurement purposes. To secure constancy 
in both amplitude and frequency, it is desirable when several 

53904°— 22 32 


tubes are used in the same circuit to have separate batteries 
for each tube. With care in this regard, constancy in botli 
amplitude and frequency may be secured to one-tenth of 1 per 

The filaments of electron tubes used for generating may be 
supplied with direct current from a source which will maintain 
a constant voltage, as described above. For many purposes 
satisfactory results can, however, be obtained by supplying the 
filament with alternating current of the proper low voltage. A 
convenient source is a small transformer connected to a 110- 
volt lighting circuit. The transformer should have a tap from 
the mid-point of the low voltage secondary winding, to which 
the negative side of the plate battery may be connected. The 
voltage applied to the filament should be regulated by adjusting 
the primary circuit. A condenser of fairly large capacity should 
be connected from the mid-tap to each terminal of the secondary 

A fuse or other protective device should be inserted in the 
plate lead of the larger generating tubes, such as those supply- 
ing more than 10 watts. Since the currents involved are 
small, perhaps 0.3 ampere, the ordinary types of fuses will not 
answer. A simple homemade fuse can be made by fastening a 
small rectangular piece of tin foil to a piece of cardboard and 
connecting the tin fgil into the circuit so that the current will 
pass along the longest dimension of the piece of tin foil. The 
width of a piece of tin foil of a given thickness required to 
construct a fuse which will open the circuit when a certain 
current is reached can be determined by starting w^ith a wide 
piece and successively removing strips of tin foil until the cir- 
cuit through the remaining strip is opened. 

A by-pass condenser of fairly large capacity is usually con- 
nected across the terminals of the d.c. generator, so that the 
radio-frequency currents do not pass through the armature of 
the generator. (Figs. 279 and 280.) This reduces the im- 
pedance of the radio-frequency circuit and protects the gen- 
erator against injury due to excessive currents which might be 
caused by high-frequency surges flowing through the generator 
windings. The condenser also serves to reduce the " commu- 
tator ripple," i. e., the slight drop in generator voltage occurring 


when brushes do not touch any commutator segment. This 
commutator ripple may be found troublesome in communication. 
See also Appendix 9. p. 578. 

Instead of the condenser, aluminum electrolytic cells may be 
connected across the line. One type of such an electrolytic cell 
can be constructed in a simple manner by placing a strip of 
aluminum and a strip of lead in a glass jar containing a satu- 
rated solution of borax. The voltage which an aluminum elec- 
trolytic cell can safely be called upon to handle depends upon 
the solution used ; a cell containing the saturated solution of 
borax just mentioned should not be expected to withstand more 
than 100 volts.' 

The aluminum electrolytic cell can also be used for rectifying 
alternating currents, although there are various practical in- 
conveniences incidental to its use for this purpose.® 

Tubes Suitable for Developing Considerable Poicer. — It has 
been explained that the two factors which determine the power 
put into a tube are the plate voltage and the filament emission 
and that the efficiency with which this power is converted into 
oscillating current depends for values of efficiency below 50 
per cent only upon the adjustment of the external circuits. 
Thus the possible output of a tube can be increasetl either by 
increasing the surface area, and hence the emission of the 
filament, or by increasing the degree of vacuum, in order to 
allow a higher plate voltage to be used. The large " pliotrons " 
(see Fig. 266) are capable of developing as high as 500 watts 
output because they are so highly exhausted that several thou- 
sand volts may be applied to the plate and because they can 
carry a plate current as high as 0.4 ampere. Since at least 
half the power put into the tube can not be used in producing 
oscillations, means must be provided to dissipate this waste 
heat. In certain pliotrons an average plate current of 0.15 
ampere flows when a plate battery of 4000 volts is used, 600 

^ For further information regarding the use of the aluminum electro- 
lytic cell as a protective device the reader may refer to : E. E. F. 
Creighton, General Electric Review, vol. 16, p. 248, April, 1913 ; C. P. 
Steinmetz, General Electric Review, vol. 21, p. 590, September, 1918 ; 
Williams and Cork, Electrical World, vol. 74, p. 937, Nov. 15, 1919 ; 
Rhoads, Journal A. I. E. E., vol. 40, p. 318, April, 1921. 

^ The construction of the aluminum electrolytic cell and its operation 
as a rectifier for use with tube generating sets is described by P. J. 
Furlong, Q. S. T., vol. 4, p. 17, February, 1921. 


watts being thus supplied to the tube. If the circuit is operated 
efficiently, 300 watts may be used in the output circuit and 
grid circuit, the remaining 300 watts, or nearly a half horse- 
power, going into heat at the plate. Thus the plates must be 
so constructed as to radiate heat rapidly, and provision must 
be made for cooling the tubes. By operating a number of such 
tubes in parallel a large amount of power can be converted. 

The construction of various types of tube transmitters is de- 
scribed in a paper by T. Johnson, Proceedings Institute Radio 
Engineers, vol. 9. p. 381, October, 1921. A tube transmitter used 
at Clifden, Ireland, for transatlantic work, employing 12 large 
power tubes, and capable of putting over 200 amperes into 
the antenna, is described in a paper by H. J. Round, Radio 
Review, vol. 2, p. 459, September, 1921. 

204. Alternating Current Plate Supply. — In the generating cir- 
cuits previously show^n the power is supplied by a battery or 
by a direct-current generator. In tube transmitting sets the 
power is often supplied by high-voltage, direct-current ma- 
chines. Although such machines are extensively used, they 
are very expensive and are subject to failures of the commu- 
tator and of the armature windings. This is particularly true 
of machines having a commutator voltage in excess of about 
500 volts. For some purposes it is possible to operate the 
transmitting tube by supplying power to the plate from an 
alternating-current source having the effective value of the 
a.c. voltage supplied to the plate approximately the same as 
the rated d.c. plate voltage and still obtain a power output 
and an efficiency as great as that obtained with a d.c. gener- 
ator. The a.c. voltage supplied to the plate can usually be 
safely increased to an effective value considerably above the 
rated d.c. plate voltage of the tube, with a corresponding in- 
crease in the output of the tube. Experimental difficulties will 
be met, however, at the higher voltages, particularly the neces- 
sity for careful insulation of all parts of the circuit. 

The difficulties met in the operation of high-voltage d.c. 
generators are thus avoided. Such a tube transmitter is a 
tone generator, which with crystal or with tube detector recep- 
tion gives a musical note in the telephones corresponding in 
frequency to that of the alternating-current supply. With 
single-phase a.c. supply of frequency f, the radio-frequency 



waves come in pulses of f times per second, and the effective 
decrement of the wave may be appreciable. The output of 
such a generating set is completely modulated — that is, the 
amplitude of the oscillations is periodically reduced to zero. 

If it is possible to secure alternating current of an easily 
audible frequency, such as 800 cycles, this type of transmitter 
is an excellent substitute for the more elaborate electron tube 
tone transmitters whose plates are supplied with d.c. voltage 
and which have either chopper or buzzer modulation. The wave 
form for the output current of such a transmitter is shown in 

Hidio frefuenctf Choke Coil. 

A Circuit for a Tube Transmitter _ 

Supplied with Alter nail no Plate Yoltaae 

Fig. 283, except that with high radio frequencies there will be 
considerably more oscillations per train than could be con- 
veniently drawn. The voltage of the plate supply is also shown 
on this diagram. It is evident that no oscillation can occur 
during the half cycle in which the plate supply is negative. A 
circuit w^hich can be used with a.c. plate supply is shown in 
Fig. 282. An electron tube transmitter of completely modulated 
waves, using 500-cycle modulation, is described in Bureau of 
Standards Scientific Paper No. 381. 

Heterodyne or other beat reception may also be advantageously 
used, as is usual with continuous waves. It is possible, though 



not as desirable, to use for the plate supply voltage, alternating 
current of low commercial frequencies, such as 60 cycles. If it 
is necessary to use alternating current of as low a frequency 
as 60 cycles, more satisfactory results will be obtained with 
heterodyne reception. The heterodyning of course destroys the 
purity of the tone emitted by the transmitter, but gives much 
better reception than a crystal detector or simple tube detector. 
If a low frequency, such as 60 cycles, is used, the received signal 
can be improved by using a " chopper " at the transmitting 
station. (See Sec. 211.) It is preferable, if possible, to use 
for the power supply of the transmitter an alternating current 
of an easily audible frequency, such as 800 cycles. 


It should be noted that this alternating-current modulation 
of plate supply gives only one train of oscillations per cycle, 
corresponding to the intervals when the plate is positive — that 
is, 60-cycle modulation of plate supply gives only the same tone as 
a fixed gap with a 30-cycle a.c. supply, since the latter gives 
two trains of oscillations per cycle. 

By connecting the plates of two tubes to the secondary ter- 
minals of a single-phase transformer, one plate to each sec- 
ondary terminal, both halves of the cycle of supply voltage 
from a single-phase a.c. line can be used to operate the tubes. 
If this is done, it is desirable to use heterodyne reception. It 
is also possible to effectively use two-phase or three-phase 
alternating current as plate supply in power generators ; in this 
case the amplitude of the oscillations is much more nearly con- 
stant, and with three-phase supply does not drop to zero. 

For further information regarding the use of both halves of 
the cycle and two-phase and three-phase plate supply, refer- 


ence may be made to K. B. Warner, Q. S. T., volume 4, page 7, 
December, 1920, and volume 4, page 52, February, 1921; L. M. 
Clausing, Q. S. T., volume 4, page 6, February, 1921; W. C. 
White, U. S. Patent No. 1394056; British Patent 252 of 1914; 
British Patent 127008; French Patent 493222. Details regard- 
ing the use of three-phase a.c. plate supply are given by V. J. F. 
Bouchardon in United States Patent 1373710. 

205. Beat Reception. — If a tuning fork vibrating 256 times per 
second is mounted near to a tuning fork vibrating 260 times 
per second, so that the two forks sound together, a listener 
a short distance away will hear a sound alternately swell- 
ing out and dying away four times per second. These tone 
variations are called "beats." The production of beats has 
been discussed in Section 122. Similarly, if two sources of un- 
damped electrical oscillations of constant amplitude act simul- 
taneously upon the same circuit, one of frequency 51,000 and 
the other of frequency 50,000 cycles per second, the amplitude 
of the resultant oscillation will successively rise to a maximum 
and fall to a minimum at the rate of 1000 times a second, the 
difference between 51,000 and 50,000. If rectified by a tube 
detector or crystal detector, the variations of the resultant 
oscillation will produce an audible note of frequency 1000 in a 
suitable telephone receiver. If one of the two oscillations is 
the received signal in the antenna and the other is generated by 
a circuit in the receiving station, we have " beat " or " hetero- 
dyne " reception. In the receiving telephone a musical note is 
heard whose pitch is readily varied by slight variation of the fre- 
quency of the local generating circuit. The application to radio 
communication of the principle of beats, which had long been 
familiar in sound and other fields of science, is due to Fessenden. 
If the amplitude of the locally generated oscillations is equal 
to the amplitude of the incoming oscillations, the condition of 
" equal heterodyne " is said to exist. In actual practice the 
amplitude of the locally generated oscillations is usually con- 
siderably greater than the amplitude of the received oscillations. 
In fact, it is usually found that the maximum signal in the tele- 
phone receivers is not obtained for " equal heterodyne." 

The principle is shown in Fig. 284. Oscillations of fre- 
quency fi are superimposed on oscillations of frequency f^ ; the 
amplitude of the oscillations of frequency fs is equal to three 



times the amplitude of the oscillations of frequency A. The 
resultant oscillations have a beat frequency of fi — fz, that is, 
the maximum value of the resultant oscillations is attained 

lA I 



(a) Incoming Oscillations -Freciuenct^ f, 



(b) Locally Generated Oscillations al Peceivmg 
Station - Freqaenci^ C 



{c) Resultant Having Beat Frec^aencu (f.-Q 


Fig. 284. 

ix — ti times per second. The value of the resultant at any in- 
stant is obtained by adding together the values at that instant 
of the oscillations from the two sources. When these two 


oscillations are in phase, the resultant oscillation has a peak. 
When the two oscillations are of opposite signs and equal mag- 
nitude, the value of the resultant is zero. In Fig. 284, dur- 
ing the fractional part of a second represented there are 15 
oscillations of frequency fi, 12 oscillations of frequency fz. 
and the niaxirauni value of the resultant is attained 15 — 12^ 
3 times. The amplitude of the resultant oscillations varies from 
four times to twice the amplitude of the oscillations of fre- 
quency fi. The maximum amplitude, 4, corresponds to the 
sum of the amplitudes of f^ and fi (3+1), and the minimum 
amplitude, 2, corresponds to the difference of the amplitudes of 
U and U (3—1). 

When the resultant wave form is received with any form 
of rectifying detector, the part of the resultant wave below the 
zero axis is almost entirely eliminated, as has been explained 
in the discussion of detector action above. The telephone re- 
ceiver diaphragm is acted upon by impulses which vary at the 
beat frequency A — fi and emits the tone corresponding to this 
beat frequency. 

If a regenerative circuit similar to that of Fig. 275 is used 
(L being coupled to the antenna), the same tube may be used as 
a detector and as a generator of local oscillations. This is 
called " autodyne " reception. The procedure is to tune the an- 
tenna circuit to the incoming signals and adjust the local oscil- 
lating circuit so that it is slightly out of tune with the incoming 
signals. Beats are thus produced of an audible frequency equal 
to the difference between the frequency of the incoming oscilla- 
tions and the frequency of the local oscillations. Measurements 
have shown that this method is so sensitive that signals can be 

1 5 
heard when the power received is equal to only j^ watt — that 

is, 0.015 micromicrowatt. The autodyne method is thus much 
more sensitive than the crystal detector or simple detector tube. 
The use of a separate source of oscillations has the advantage 
over the autodyne method that looser coupling can be used with 
resultant sharper tuning, making it easier to tune out interfer- 
ing stations, and that the beat note can be varied without 
changing the tuning adjustments of the receiving circuit. In 
Fig. 239-a, page 427. a circuit is shown which can be used for 
autodyne reception, and is particularly adapted to wave lengths 
of less than 400 meters. 


Of the several methods of receiving continuous waves in radio 
telegraphy which are discussed in Section ISl, the heterodyne 
method is in most general use, and has a number of advantages. 
As just mentioned, the heterodyne method will give readable 
signals when the power received is very small ; in fact, good 
signals can be received by the heterodyne method when the use 
of a " chopper " or " tikker " at the receiving station would not 
give a signal which could be heard. This sensitivity greatly 
increases the range over which a given receiving station can 
receive. With the heterodyne method the note in the telephone 
receivers can be adjusted as desired to correspond to the fre- 
quency at which the telephone receiver diaphragm is most sensi- 
tive, or to suit the ear of the receiving operator, or to be easily 
read through interfering signals from other stations, so that 
interference from other stations is reduced to a minimum. A 
slight difference in the frequency of the interfering signal would 
give a note of entirely different pitch, or a note which would be 
entirely inaudible. For instance, if the local oscillation had 
a frequency of 50,000 (X=6000 meters), the received oscillation 
a frequency of 51,000 (X=5880 meters), and the oscillation from 
the interfering station a frequency of 52,000 (X=5T70 meters), 
the interfering note as heard in the telephone receiver would 
have a frequency of 2000, or be a whole octave higher in pitch 
than the note Miiich it is desired to receive. If the wave of the 
interfering station had a frequency of 55,000 (\=5455 meters), 
its beat tone would be so high as to be inaudible. 

It should be noted that the heterodyne method requires very 
sharp tuning adjustments and that slight changes in the posi- 
tions of leads or objects adjacent to unshielded condensers may 
cause sufficient change in capacity to cause considerable changes 
in the note in the telephone receiver. The method is best 
adapted to long waves. "With comparatively short waves, under 
1000 meters, the tuning adjustments required to get an audible 
beat frequency are so sharp that much difficulty may be expe- 
rienced in adjusting so that any signal at all is heard, and if a 
slight readjustment is inadvertently made the signal will be 
lost again. These difficulties are not so noticeable when receiv- 
ing long waves such as are commonly used by high-power sta- 
tions transmitting undamped waves, which are often longer 
than 10,000 meters. 


The heterodyne method is not well adapted to receiving 
damped waves or modulated continuous waves such as are used 
in radiotelephony, since the incoming waves do not have a 
single frequency but a number of frequencies, and a number 
of beat frequencies are obtained which give a " mushy " note 
which is not clear and is somewhat difficult to read. In radio- 
telephony it is sometimes found desirable to use at the receiving 
station local oscillations of the same frequency as the radio- 
frequency generated at the transmitting station ; in this case a 
clear note w^ill be obtained as long as the frequency of the local 
oscillation is maintained constant. 

In heterodyne reception, if we assume that the amplitude of 
the local oscillations is constant, the amplitude through which 
the resultant oscillations vary is directly proportional to the 
amplitude of the incoming oscillations. This amplitude through 
which the resultant oscillations vary, at the audible beat fre- 
quency, determines the intensity of the signal in the telephone 
receivers. In connection with Fig. 284 we have discussed the 
amplitudes of the different oscillations, using the amplitude of 
oscillations of frequency A as a unit. Using this unit, for the 
case shown in Fig. 284 the amplitude of the resultant oscilla- 
tions varies from 2 to 4 through a range of 2. If we assume a 
case in which the amplitude of the incoming oscillations is 
decreased one-half, but the local oscillations have the same 
amplitude, and use the same unit, it is evident that the ampli- 
tude of the resultant oscillations will vary from 2.5 to 3.5 
through a range of 1 — that is, decreasing the amplitude of the 
incoming oscillations one-half has decreased by one-half the 
amplitude of the resultant oscillations. The signal in the tele- 
phone receiver is correspondingly decreased. 

This relation of direct proportionality for beat reception is 
different from the relation for simple detector reception. For 
the latter the output of the detector tube is proportional to the 
square of the amplitude of the incoming oscillations. The rela- 
tion of direct proportionality constitutes one of the chief ad- 
vantages of beat reception and one of the chief advantages ob- 
tained by the use of continuous waves. These relations were 
pointed out by L. W. Austin, Journal Washington Academy of 
Sciences, volume 6, page 81, February 19, 1916. This advantage 
obviously does not obtain for a spark station or for a station 


transmitting modulated continuous waves for which beat re- 
ception can not be used. 

If at a given station an interfering signal of any liind is 
being received of intensity greater than the signal which it is 
desired to receive, much better results will be obtained in at- 
tempting to copy the weaker signal through the interference 
if beat reception is used than if simple detector reception is 
used. The interference may be due to another station or to 
"strays." (See Sec. 130, p. 289.) Assume that at the same 
receiving station there are two receiving sets, one for beat 
reception and one for simple detector reception, and that at a 
particular moment the strays are three times as strong as the 
voltage oscillations in the antenna of the signal which it is 
desired to receive. Then in the output of the receiving set 
using beat reception having the relation of direct propor- 
tionality the strays will be three times as strong as the signal. 
But in the receiving set using simple detector reception having 
the square law the strays will be nine times as strong as the 
signal. This is one of the principal reasons that a continuous 
wave station of a given power can often maintain communica- 
tion over five times the distance reached by a spark station or 
modulated continuous-wave station of the same power. 

For further information regarding beat reception the reader 
may refer to R. Stanley, Wireless Telegraphy, volume 2, chap- 
ter 8; to H. J. van der Bijl, The Thermionic Vacuum Tube; to 
J. H. Morecroft, Principles of Radio Communication ; to Bu- 
reau of Standards Circular No. 74, page 215; and to a paper 
by M. Latour, Radio Review, volume 2, page 15, January, 1921. 

Reduction of Freqnency of Input of Radio-Frequency Amr 
plifier by Bent Method. — It has been pointed out above that for 
short wave lengths, particularly for wave lengths of less than 
300 meters, radio-frequency amplification is attended with 
much difficulty caused by capacity effects between different 
parts of the circuit. One w^ay to avoid this difficulty is to 
reduce the high frequency of the incoming wave to a lower 
but not audible radio frequency by the beat method. Thus if 
the incoming wave has a wave length of 100 meters — that is, a 
frequency of 3,000,000 cycles — a local generating set may be 
coupled to the antenna circuit to supply a frequency of 
3,100,000 cycles. The resultant current in the antenna circuit 


will have a beat frequency of .100,000 cycles, which can be 
easily amplified with a radio-frequency amplifier. The output 
of the radio-frequency amplifier can then be treated as in the 
usual methods of reception ; it can be detected and amplified 
at audio frequencies or can be made audible by a second 
heterodyne, as described earlier in this section. This method 
requires critical adjustments and considerable skill in manipu- 
lation. This method is very useful in the reception of feeble 
signals with coil antennas, as in direction-finding work. For 
further information the reader may refer to E. H. Armstrong, 
Q. S. T., volume 3, page 5, February, 1920; Proceedings In- 
stitute Radio Engineers, volume 9, page 3, February, 1921. 

E. Radiotelephony. 

206. The Wave Forms "Used in Radiotelephony. — Speech is 
composed of complex vibrations, and a graphic record of the 
sound wave in air which transmits the simplest word shows a 
very complex wave form. The problem of any form of tele- 
phony is to accurately reproduce electrically at the distant 
receiving station the complex sound wave which is spoken into 
the transmitter. The principles of radiotelephony are the same 
as those of radiotelegraphy by undamped waves. In radio- 
telephony the sending key used in radiotelegraphy is replaced 
by apparatus which varies the transmitting antenna current 
in accordance with the sound waves produced by the voice. 
This device is usually the carbon microphone, which is de- 
scribed in Section 60b. 

There are a number of ways in which a graphic record can 
be made of the wave form of the wave in air which corresponds 
to a given sound. A simple method is to record the sound on a 
phonograph record, then play the record slowly, and greatly 
magnify the motion of the needle by a lever arrangement which 
traces the wave. The wave forms corresponding to many dif- 
ferent sounds have been studied.' A tuning fork may give 
nearly a pure sine wave, but the wave forms corresponding to 
most sounds are very complex. 

'' See D. C. Miller, The Science of Musical Sounds ; E. W. Scripture. 
The Study of Speech Curves, Carnegie Institution Publication No. 44 ; 
Scientific American Monthly, vol. 3, p. 361, April, 1921. 


In the transmission of radiotelegraphic signals by undamped 
waves, the pitch of tlie note in the telephone receivers is deter- 
mined in part by the apparatus at the receiving station — as, for 
example, in heterodyne or autodyne reception. For transmission 
of sounds of definite pitch, or for transmission of speech, the 
nature of the received signal must depend, upon the nature of 
the current in the transmitting aerial. In spark transmission 
the note depends upon the number of wave trains per second 
leaving the aerial, this being determined by the speed of the 
rotary gap or the frequency used in charging the primary con- 
denser. Spark, tone, and radiotelephone transmitters differ 
from transmitters of undamped waves in that the strength of 
the radio-frequency antenna currebt is varying at an audio 
frequency. Ordinarily, the radiation from a spark transmitter 
is treated as being composed of successive trains of waves of 
radio frequencies. An alternative method is to describe it as a 
single wave whose amplitude is varying at audio frequencies. 
In Fig. 148 the intensity of the emitted wave is a maximum at 
point D of the curve and is zero during the interval between 
what are usually called the wave trains. 

An alternating current is said to be modulated when the 
amplitude of its oscillations is varied periodically. The fre- 
quency at which the variations occur is necessarily less than 
the frequency of the alternating current which is being modu- 
lated. The nature of the variations may assume almost any 
form. Thus we may have dot-and-dash modulation, " chopper " 
modulation, buzzer modulation, sine-wave modulation (as at 
800 cycles), and speech modulation. Speech modulation of 
radio-frequency currents radiated through space constitutes 
radiotelephony. Chopper, buzzer, and sine-wave modulation 
are often referred to under the general name of " tone modu- 

A modulated wave is symmetrical with respect to the zero 
axis; that is, the part of the modulated wave below the zero 
axis is a reflection of the part of the wave above the zero axis. 

A radio-frequency wave of frequency fr modulated by a sine 
wave of audio frequency /"a can be considered to be the sum of 
three radio-frequency waves having frequencies fr, (fr — fa), and 
(fr-|-/=a). The principal radio frequency fr is called the "car- 
rier " frequency, since it provides the means for carrying or 


transmitting the audio-frequency wave, but it does not in any 
way determine the nature of the sound heard at the receiving 
station when simple detector reception is used. The audio fre- 
quency /"a is called the " modulating " frequency. The waves of 
frequency {fr — fa) and (fr+fa) are called the "side waves," 
and their frequencies are called the " side frequencies." Side 
waves always occur when the amplitude of the radio-frequency 
current is changed in any way. This method of considering a 
modulated wave to be the sum of a carrier wave and side waves 
is particularly useful in determining how a modulated wave will 
affect receiving apparatus. 

When the usual dot-and-dash code signals are transmitted by 
undamped radio-frequency waves which have not been modu- 
lated at the transmitting station by a chopper, buzzer, 800-cycle 
alternating current, or similar method, it is necessary to use 
at the receiving station a chopper, heterodyne, or similar 
method, as described in Section 181. The dot-and-dash inter- 
ruption of the transmitted wave constitutes, however, a varia- 
tion of the transmitted wave, which is a form of modulation, 
and causes " side waves " having wave lengths irregularly dis- 
tributed over a band. When dot-and-dash signals are trans- 
mitted at high speeds by automatic devices the band of w^ave 
lengths between the side frequencies is broader, and greater 
interference is caused. When automatic devices are used for 
both transmitting and receiving, the transmitting station does 
not usually transmit the signals of the International Code, but 
a series of impulses arranged only with regard to the most 
convenient operation of the apparatus. 

When a radio-frequency wave is modulated by an audio- 
frequency wave the amplitude of the resultant wave at each 
instant is determined by the product of the instantaneous value 
of the amplitude of an audio-frequency w^ave into the instan- 
taneous value of the amplitude of the radio-frequency wave at 
that instant. Thus modulating action should be carefully dis- 
tinguished from heterodyne action as described in Section 205, 
since in heterodyne action the instantaneous value of the re- 
sultant is determined by the sum of the instantaneous values of 
the two component radio-frequency waves. 

In modulating action the audio-frequency wave whose ampli- 
tude is multiplied by the amplitude of the radio-frequency wave 


is ordinarily the sum of an audio-frequency wave (alternating 
current) and an unvarying component (direct current). The 
amplitude of the radio frequency is varied periodically above 
and below a certain value which is not zero. 

For rough purposes of illustration of the process of modula- 
tion, the unmodulated radio-frequency wave can be thought of 
as a plastic substance which is molded in a form shaped like 
the form of the audio-frequency modulating wave. An illus- 
tration of a similar process is found in the impression of the 
wave form of a voice on the plastic wax of a master phonograph 
record, from which many records are made which will faith- 
fully reproduce the voice. In radiotelephony the wave form of 
the voice, impressed on the radio-frequency carrier wave, is 
reproduced at many receiving stations. 

The strength of the received signal depends not only on the 
average radio-frequency amplitude but also on the degree to 
which it is changed or modulated. An alternating current is 
said to be completely modulated w^hen the amplitude of its 
oscillations is periodically reduced to zero. Complete modula- 
tion may occur in several different ways. The radio-frequency 
oscillations may be just reduced to zero at one or more points 
during each audio-frequency cycle so that the modulating audio- 
frequency boundary just touches the zero axis. There may be 
no radio-frequency oscillations at all during a part of an audio- 
frequency cycle, as shown for example in Fig. 283. The radio- 
frequency oscillations may be just reduced to zero at one or 
more points during each audio-frequency cycle in such a way 
that the upper and lower boundaries of the modulated wave 
cross the zero axis at these points as shown in Fig. 287 instead 
of simply touching the zero axis; the modulation of Fig. 287 
occurs only when special circuits are used. 

The more usual form of wave for radiotelephony is that shown 
in Fig. 286, in which the amplitude of the audio-frequency wave 
is not sufficient to cause complete modulation. It is, however, 
usually desirable that so far as possible adjustments should be 
made so that for speech of moderate intensity the amplitude of 
the radio-frequency oscillations should be instantaneously re- 
duced just to zero in such a way that the boundaries of the 
modulated wave just touch the zero axis at a point but do not 
cross the zero axis. This would be the case in Fig. 286 if the 

rig.Z85]f\/ave Form of Current on a Telephone 
Line Transmittina the dound of "a" as in father" 

., hiigXOb.J-lntenna Current | vin Hadiotelephom Jransmittina 
theWoound of "a"* as m father] ]ModuJatea rradio- frequency 
Wave which can be received with Simple Detector 

fiqZol Jlntenna Current in nadiotele phony Transmittina 
the Sound of "a' as in father." Radio-frequency Wave so 
h/fodJated that Beat Reception is Required. 

53904°— 22- 




upper and lower boundaries of the modulated wave were pushed 
toward the zero axis so that the points h, h' just touch the zero 
axis. In the circuits commonly used in radiotelephony, if the 
amplitude of the modulating audio frequency becomes too great 
the radio-frequency oscillations entirely cease during a consid- 
erable portion of the cycle, and a marked distortion of speech 
occurs ; this is called " overmodulation." 

The effect of overmodulation in an electron tube radiotele- 
phone transmitting set is similar to the effect during part of 
the cycle in an electron tube generating set having plate supply 
of sine wave alternating current of perhaps 800 cycles. The 
wave form for such a generating set is shown in Fig. 283, page 
500. During the intervals when the plate voltage is negative, 
the radio-frequency oscillations cease. The wave form for a 
complete cycle of the 800-cycle sine w^ave corresponds to the 
modulating audio-frequency wave form in radiotelephony which 
causes overmodulation. 

If the sound of the vowel " a " as in " father " is spoken into 
the transmitter of an ordinary wire telephone system, the wave 
form of the current on the line wire will be substantially that 
shown in Fig. 285. If the same vow^el is spoken into the trans- 
mitter of a radiotelephone system using the ordinary circuits, the 
wave form of the antenna current will be as shown in Fig. 286. 
If the principal frequency of the wave form of Fig. 285 is 800 
cycles, the