SINGLE-PHASE COMMUTATOR MOTORS 399

Substituting now:

Z

z

z'+:

rl = ~r/f = quadrature, or transformer exciting
^ admittance,

2 __ N __ ^f -W/

-. _ ^2 _ \ 2 — JA 2j

X4 - X'4 + jX/74,

7 = A = o:7 — j-^'7 = impedance ratio of the
J two quadrature fluxes,

Z, + co2 (Z0 + Z} = Z8,

and:

e = ei + e2,)

I

Adding (72) and (73), and rearranging, gives:

e = Z2/2 + h (Z* - jScoZ) - /4Z (co - jS);

or:

e
Z

From (73) follows:

or:
and:

62*" = /2 (1 + XS) - /!,

/! = /*(!+ X,) - etY',

(75)

(76)

j-S). (77)

(78)

/, = /, (i - x2) + etY'.
From (74) follows:

0 = /4 (Z + Z,) - h (cQZ + JSZ') + JSZ'I,. (79)

Since 74 is a small current; small terms, as X2, can be neglected
in its evaluation. That is, when substituting (78) in (79), X2
can be dropped:

or:

-/,- etY',
="/i + etY',

approximately.

(80)