FREQUENCY CONVERTER 179

Since the reactance is proportional to the frequency, at the
slip, s, or the secondary frequency, sf, the secondary impedance

_jet the secondary circuit be closed by an external resistance,
r, and an external reactance, and denote the latter by x at
frequency, /, then at frequency, $/, or slip, s, it will be = sx, and
thus:

Z = r + jsx = external secondary impedance.1

Let:

EQ = primary impressed e.m.f. per circuit,
E' = e.m.f. consumed by primary counter e.m.f.,
jj?i = secondary terminal e.m.f.,
' Ijl'i = secondary generated e.m.f.,

e = e.m.f. generated per turn by the mutual magnetic

flux, at full frequency, /,
jTo = primary current,
/oo = primary exciting current,
1 1 = secondary current.

It is then:
Secondary generated e.m.f.:

E'i =
Total secondary impedance :

hence, secondary current:
7 = JLI_ = ___________
il ~Zi + Z (n + r)+ js (X! + x)
1 This applies to the case where the secondary contains inductive react-
ance only; or, rather, that kind of reactance which is proportional to the
frequency. In a condenser the reactance is inversely proportional to the
frequency, in a synchronous motor under circumstances* independent of the
frequency. Thus, in general, we have to set, x = x' + x" 4- a?"7, where x'
is that part of the reactance which is proportional to the frequency, x" that
part of the reactance independent of the frequency, and a/" that part of the
reactance which is inversely proportional to the frequency; and have thus,
at slip, s, or frequency, sf, the external secondary reactance, sx' 4- x" 4—-—
o