SINGLE-PHASE COMMUTATOR MOTORS 405

Using the approximate equation of the commutation current

(94), it is:

r e { 1 - X46 .,,

and, denoting:
it is, expanded:

/. = -^-(1 _ ^

hence, absolute:

X4 = X'4

• j [X"46 - 5ft (c0X'4 + iSfX^O]}; ' (105)

(106)
where [1 — c0X4] denotes the absolute value of (1 — c0X4).

The commutation current is zero, if either S = °° , that is,
infinite speed, which is obvious but of no practical interest, or
the parenthesis in (105) vanishes.

Since this parenthesis is complex, it vanishes when both of
its terms vanish. This gives the two equations:

1 - X'4& + Stb (S\'± - c0X"4) = 0,1
X"4Z> - Stb (c0X'4 + SX"4) = O.j

(107)

From these two equations are calculated the two values, the
speed, S, and the voltage ratio, t, as:

CQ(

- X'4)

to

A 4

X7/42

hence:

For instance, if:

(108)

Z =0.25 + 3j,
Z4 = 5 + 2.5 j: