PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

296 Practical MATLAB® Applications for Engineers

Example 3.16

The objective of this example is to verify the maximum power transfer theorem, when

the load reactance varies over a given range.

Let the Thevenin’s equivalent circuit of an electrical network be given by VTH =

5 ∠ 0 ° V and ZTH = 10 − j50 Ω. Let the load impedance be given by ZL = 10 + jXL, where

XL varies over the range 0 ≤ XL ≤ 150 Ω, in steps of 1 Ω, as indicated in the circuit

diagram of Figure 3.74.

Create the script fi le max_power_AC that returns the plot of PZL versus XL.

XL

XL = 1:1:150

RL = 10 Ω

ZTH = 10−j 50

VTH = 5 0 ° V ZL = RL + j XL

FIGURE 3.74
Network of Example 3.16

MATLAB Solution

% Script file: max _ power _ AC

% Max. power delivered to the load ZL = RL + jXL

% where XL varies from 0 to 100 Ohms

echo on

Xth = -50;

RL = 10;

Rth = 10;

Xl = 0:1:150;

Zth = Rth+50j;

Zl = RL+Xl.*j;

Zt = Zth+Zl;

magZt = abs(Zt);

magZl = abs(Zl);

Pload = (5./magZt).^2.*magZl;

plot(Xl,Pload);grid on;

xlabel(‘XL(Ohms)’);

ylabel(‘Power deliver to ZL(Watts)’);

title(‘Power ZL vs XL, for 0<XL<100’)

text(41,.118,’XL=50j Ohms’)

The script fi le max_power_AC is executed and the results are indicated in Figure 3.75.

Observe from Figure 3.75 that the maximum power delivered to the load ZL occurs

when |XL| = |XTH|.