PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 259

Then the currents of the circuit diagram shown in Figure 3.34 are evaluated by the

algebraic addition of the individual contributions of each source (superposition

principle), yielding the following:

i 1 (t) = IA1 + iB1(t)

i 1 (t) = 5 − √

__

2 cos(10 t − 45°) A

i 2 (t) = IA2 + iB2(t)

i 2 (t) = √

__

2 cos(10 t − 45°) A

i 3 (t) = IA3 − iB3(t)

i 3 (t) = 5 − 2 √

__

2 cos(10 t − 45°) A

R.3.66 Let the Thevenin’s impedance as seen across an arbitrary load ZL be ZTH = RTH +

jXTH. Then maximum power is delivered to the load ZL, when ZL = RTH − jXTH

(note that ZL is the complex conjugate of ZTH), as illustrated in Figure 3.37.

Let us evaluate the power delivered (in watts) to the load ZL.

The total impedance of the circuit is given by

ZT = ZTH + ZL = 2 RTH

Then,

I

V

R

TH PIR

TH

2 RL TH

2

and

P

V

R

R

V

R

ZL TH W

TH

TH

TH

TH

24

(^22)







+

−

VTH

ZTH = RTH + j XTH

ZL = RTH − j XTH

FIGURE 3.37

Condition for maximum power transfer to ZL.