PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 433

V 1 (s) = 50/s

V 2 (s) =

ZL1(s) = s

ZC1(s) = 2/s

R1(s) = 2

R2 (s) = 3

ZL2(s) = 3 s R3 (s) = 4

ZC2(s) = 3/s

I 1 (s)

I 2 (s)

2 V 9 V

3/s

4/s

15

s^2 +9

−

−

+

+

FIGURE 4.78

Equivalent s-domain circuit of Figure 4.77.

Part 3

The Matrix loop equation is given by

50

2

3

1 9 15

9

5

22

3

(^2) 33 4 5
2
ss
ss
s
ss
s
s
s







 


 
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Is
s
Is
1
2
2
()

()

MATLAB Solution

% Script file: IC _ loop _ diff _ eqs

syms s Zs Is Vs it y

Zs = [s+5+2/s -2/s-3;-2/s-3 3*s+7+5/s];

Vs = [50/s+2-3/s;-1/s-9-15/(s^2+9)];

Is = inv(Zs)*Vs;

it = ilaplace(Is);

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

disp(‘************* Frequency domain Results ***************’)

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

disp(‘The loop currents I1(s) and I2(s) are: ‘)

disp(‘I1(s)=’),pretty(Is(1))

disp(‘I2(s)=’),pretty(Is(2))

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

disp(‘The values of the currents (in amps) i1(0) and i2(0), and’)

disp(‘i1(t=inf) and i2(t=inf) using the initial and final value

theorems’)

disp(‘are verified below:’)

i1 _ 0 = limit(s*Is(1),s,inf)

i2 _ 0 = limit(s*Is(2),s,inf)

i1 _ inf = limit(s*Is(1),s,0)

i2 _ inf = limit(s*Is(2),s,0)

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

den = [3 22 37 27 6];

disp(‘The system poles are:’)

rr = roots(den);

abs(rr)

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