PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

170 Practical MATLAB® Applications for Engineers

MATLAB Solution

% script file: Thevenin

% The Thevenin’s equivalent circuit

% can be determined by experimental method

% based on the maximum power theorem

Vs =100;R1 = 20;R2 =60;

RL = 1:1:50; % range of RL

Rpar = (RL.*R2)./(RL+R2);

RT = Rpar + R1;

VL = (Rpar.*Vs)./RT;

PRL = (VL.^2)./RL;

[Pmax,index] = max(PRL);

Rth = RL(index);

Vth = sqrt(4*Rth*Pmax);

%...Display Vth and Rth

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

disp(‘*********R E S U L T S**********’);

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

disp(‘ ‘);

fprintf(‘The Thevenin voltage (in volts) is Vth=%f\n’,Vth);

fprintf(‘The Thevenin resistance (in ohms) is Rth=%f\n’,Rth);

disp(‘ ‘)

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

The script fi le Thevenin is executed, and the results are shown as follows:

>>Thevenin

*******************************************************

*************** R E S U L T S ************************

*******************************************************

The Thevenin voltage (in volts) is Vth =75.000000

The Thevenin resistance (in ohms) is Rth =15.000000

*******************************************************

Note that the calculated results completely agree with the simulated experimental

results.

Example 2.22

Analyze the series RLC circuit shown in Figure 2.68, where the current source i(t) is

given by i(t) = ( (^) π^2 ) (^) ∑
n=odd
15
( (^) n^1 ) sin(n π t). The equation for the current i(t) represents the Fourier
series approximation of a periodic square wave (see Chapter 4 for additional details).
Create the script fi le analysis that returns the following plots:

1. i(t) versus t (verifi es the approximation of the periodic square wave)


2. i^2 (t) versus t

3. ∫

i(t) dt versus t (verifi es the approximation of the periodic triangular wave)

4.

di(t)

____dt versus t