PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

298 Practical MATLAB® Applications for Engineers

MATLAB Solution

% Script file: max _ power _ AC _ RL

% Max. power delivered to ZL=RL+jXL

% where RL varies from 0 to 100 Ohms.

Xth = -50;

RL = 1:1:100;

Rth =10;

Xl = 30;

Zth = Rth+Xth*j;

Zl = RL+Xl*j;

Zt = Zth+Zl;

Pload = (RL.*25)./(abs(Zt).^2);

plot(RL,Pload);grid on;

xlabel(‘RL(Ohms)’);

ylabel(‘Power deliver to ZL(Watts)’);

title(‘Power ZL vs RL, for 0<RL<100’)

text(18,.35,’RL=22.3607 Ohms’)

text(13,.32,’RL=sqrt(Rth^2+(Xth+XL)^2)’)

Rload _ cal=sqrt(Rth^2+(Xth+Xl)^2);

disp(‘*********************************’);

disp(‘The calculated RL ,to deliver max.power is=’);

disp(Rload _ cal);

disp(‘*********************************’);

The script fi le max_power_AC_RL is executed, and the resulting plot is shown in

Figure 3.77.

Observe that maximum power occurs at the theoretical value given by

RRXXL

TH^2 ().TH L^2 22 3607

0 102030405060708090100

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

RL (Ohms)

Power deliver to

ZL

(Watts)

Power ZL versus RL, for 0 <RL<100

RL=22.3607 Ohms

RL= sqrt (Rth^2 +(Xth+XL)^2 )

FIGURE 3.77
Plot of ZL versus RL of Example 3.17.