PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

428 Practical MATLAB® Applications for Engineers

Example 4.18

Analyze the circuit diagram shown in Figure 4.74, after the switch “sw” closes at t = 0,

assuming that the initial current through the inductor L is zero.

1. Write the set of loop equations in the frequency domain using Laplace


2. Write the loop matrix equation in the frequency domain


3. Evaluate the loop currents i 1 (t) and i 2 (t), by obtaining the ILT of the solutions of the
   matrix equation of part b


4. Evaluate the loop initial currents i 1 ( 0 ) and i 2 ( 0 ), using the initial value theorem


5. Evaluate the loop fi nal currents i 1 (∞) and i 2 (∞), using the fi nal value theorem


6. Obtain expressions for VR 1 (t), VR 2 (t), and VL(t) for t ≥ 0


7. Obtain plots of the loop currents i 1 (t) versus t, i 2 (t) versus t, and i 2 (t) versus t


8. Obtain plots of the voltages: VL(t) versus t, VR 1 (t) versus t, and VR 2 (t) versus t


9. Discuss the results obtained

The MATLAB solution is given in the following text by the script fi le loop_laplace_eqs.

ANALYTICAL Solution

Part 1

The two loop equations for t ≥ 0, assuming that the loop currents (directions) I 1 (s) and

I 2 (s) are indicated in Figure 4.74, are given by

( 5 + 2 s) I 1 (s) − 2 s I 2 (s) = 100/s

− 2 s I 1 (s) + ( 10 + 2 s) I 2 (s) = 0

The resulting matrix equation is given by

100

0

52 2

2102

1

2

⁄sss

ss

Is

Is



































 



 

()

()

MATLAB Solution

% Script file: loop _ laplace _ eqs

syms s Zs Is Vs it y

100 V

sw closes at t = 0

R 1 = 5 Ω

L = 2 H R^2 = 10 Ω

I 1 (s) I 2 (s)

FIGURE 4.74
Circuit diagram of Example 4.18.