SINGLE-PHASE COMMUTATOR MOTORS 419

The same results we can get directly by investigating the com-
mutation current of the overcompensated series motor. This
motor is characterized by:

1/> _ fjl I _ TTf I _ 777

. 6 — xI/1 -j— CQ!!/Q —j~~ C^JCj^j

where c% = 1 + q = reduction factor of compensating circuit
to armature.

2. Jo = Cof, /2 = C2/; /I = /.

Substituting into the fundamental equations of the single-
phase commutator motor gives the results:

1 = ZK'

A= -

ZK

where:

^X = (Za + Z, + jScvZ) + JS\* (c0Z - jSqZ').
To make /ff vanish, it must therefore be:

c X"4 .

or approximately: l/'j1']
— • C9 ^ f'^'j'^
or, with the numerical values of the preceding instance: |;!;j
__ 0.046 - 0.295 j I ;^
Q. a y' »/
That is, the overcompensating component, g, must be approxi- I /.;
mately in quadrature with the current, /, hence can not be pro- \^
duced by this current under the conditions considered here; and !^ 'f
overcompensation, while it may under certain conditions improve ||f I
the commutation, can as a rule not give perfect commutation
in a series alternating-current motor.
229. The preceding study of commutation is based on the
assumption of the short-circuit current under the brush as
alternating current. This, however, is strictly the case only at
standstill, as already discussed in the paragraphs on the repul-
sion motor. At speed, an exponential term, due to the abrupt