PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 415

FIGURE 4.62

Circuit diagram of Example 4.12.

C = 1F

R = 1 Ω V 0 (t)

Vi(t) Vi(s)

V 0 (s)

ANALYTICAL Solution

Part 1

Hs

Vs

Vs

R

RsC

s

i s

()

()

() (/ )





0

(^11)
Part 2
Vs
s
Vs
s
i()

() vt()

[ ()]Vs eutt() ( )
11
1
001 0 4

• £from Table .2
  Part 3
  MATLAB Solution
  % Script file :analysis _ RC
  t =-1:0.1:8;
  t0 = 0;
  ut =stepfun(t,t0);
  vo =exp(-t);
  vot =vo.ut;
  subplot(2,1,1);
  plot(t,vot,t,vot,’o’);
  title(‘vo(t) vs. t,numerical solution’);
  xlabel(‘time(sec)’);
  ylabel(‘ Amplitude (volts)’);
  axis([-1 5 -.5 1.3]);
  syms s x
  Hs = s/(s+1);
  Vis =1/s;
  Vos = HsVis;
  vot = ilaplace(Vos);
  subplot(2,1,2);
  ezplot(vot);title(‘vo(t) vs. t, symbolic solution’);
  ylabel(‘ Amplitude (volts)’);
  xlabel(‘time(sec)’);
  axis([0 5 -.5 1.3]);
  The script fi le analysis_RC is executed and the results are shown in Figure 4.63.