0195136047.pdf

1.2 LUMPED-CIRCUIT ELEMENTS 35

is such that a currentientering a dotted (undotted) terminal in one coil induces a voltage
M[di/dt] with a positive polarity at the dotted (undotted) terminal of the other coil. If the two
currentsi 1 andi 2 were to be entering (or leaving) the dotted terminals, the adopted convention
is such that the fluxes produced byi 1 andi 2 will be aiding each other, and the mutual and
self-inductance terms for each terminal pair will have the same sign; otherwise they will have
opposite signs.
Although just a pair of mutually coupled inductors are considered here for the sake of
simplicity, complicated magnetic coupling situations do occur in practice. For example, Figure
1.2.11 shows the coupling between coils 1 and 2, 1 and 3, and 2 and 3.

i 1 i 2

(a)

−

+

−

L 11

M

v 1 L 22 v 2

i 1 i 2

(b)

+

−

+

−

L 11

M

v 1 L 22 v 2

Figure 1.2.10Dot notation for a pair of mutually coupled inductors.(a)Dots on upper terminals.(b)Dots
on lower terminals.

2

1 3

Figure 1.2.11Polarity markings for complicated magnetic coupling

situations.

EXAMPLE 1.2.5

Referring to the circuit of Figure 1.2.8, let

L 11 =L 22 = 0 .1H

and

M=10 mH

Determinev 1 andv 2 if:

(a)i 1 =10 mA andi 2 =0.

(b)i 1 =0 andi 2 =10 sin 100tmA.

(c)i 1 = 0 .1 costA andi 2 = 0 .3 sin(t+30°) A.