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 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
R
R
X
X
L
TH
TH
L
ϭ
ϩ
ϩ
ϭ
2
2
22 3607
(
)
.
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
1 0 0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
R L (Ohms)
Power deliver to Z
L (Watts)
Power Z L versus R L , for 0 R L = 22.3607 Ohms
R L = sqrt (Rth
2 +(Xth+X L )
2 )
FIGURE 3.77
Plot of Z L versus R L of Example 3.17.
CRC_47760_CH003.indd 298
CRC_47760_CH003.indd 298
7/23/2008 1:27:51 PM
7/23/2008 1:27:51 PM