0195136047.pdf

3.1 SINUSOIDAL STEADY-STATE PHASOR ANALYSIS 119

EXAMPLE 3.1.8

(a) Find the Thévenin equivalent of the circuit shown in Figure E3.1.8(a) at the terminals

A–B.

(b) Determine the impedance that must be connected to the terminalsA–Bso that it is

matched.

(c) Evaluate the maximum power that can be transferred to the matched impedance at the

terminalsA–B.

−

+

20 ∠ 0 ̊ V

I

200 Ω

j 20 Ω

−j 10 Ω

A

B

10 I

(a)

Figure E3.1.8

−

+

20 ∠ 0 ° V

I 200 Ω

(b)

j 20 Ω

−j 100 I −j^10 Ω

+− A

B

−

+

20 ∠ 0 ° V

I A

B

200 Ω

(c)

j 20 Ω

−j 10 Ω

−j 100 I

+−

Isc

I Isc

−

+

Voc =

11.94∠84.3° V

(d)

A

B

ZTh = 14.8∠36.6° Ω

Solution

The circuit is redrawn with the controlled current source replaced by its equivalent controlled
voltage source, as shown in Figure E3.1.8(b).