Fourier and Laplace
417
Y s
Z s
Y s
R sL
sC
s
s
s
s
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I s
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1
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3
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Since
V s
u t
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£ 50
50
then
I s
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s
i t
I s
e
t
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(
)
(
)
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[( ( )]
si
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50
1
3
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£
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n n( ) ( )
3t u t
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MATLAB Solution
% Script file : analysis _ RLC
t =-1:0.1:8;t0=0;
u = stepfun(t,t0);
it = 50/3*exp(-t).*sin(3*t).*u;
subplot(2,1,1)
plot(t,it);
title(‘i(t) vs t (numeric solution)’)
xlabel(‘time(sec)’)
ylabel(‘Amplitude (amps)’)
axis([0 6 -4 11])
syms s zs
zs = 2+s+(1/(s*.1));
vs = 50/s;
ILs = vs/zs;
IL = ilaplace(ILs);
disp(‘*******************************************’)
disp(‘ **** symbolic result (sw closes at t=0)*****’)
disp(‘The current i(t) (in amps) is :’)
simIL = simplify(IL);
disp(simIL)
subplot(2,1,2)
ezplot(simIL)
title(‘i(t) vs. t (symbolic solution)’)
axis([0 6 -4 11])
xlabel(‘time(sec)’)
ylabel(‘Amplitude (amps)’)
t0=1;
IL = ilaplace((ILs)*exp(-s)); %sw closes at t=1
disp(‘******* *symbolic result(sw closes at t=1) *****’)
disp(‘The current i(t) (in amps) is given by :’)
simIL = simplify(IL);
disp(simIL)
disp(‘***************************************’)
CRC_47760_CH004.indd 417
CRC_47760_CH004.indd 417
7/28/2008 12:26:15 PM
7/28/2008 12:26:15 PM