280
Practical MATLAB
® Applications for Engineers
ANALYTICAL Solution
For the circuit shown in Figure 3.59 (part a),
Z
C j
j
R C j
L C
( )
( / )( )
( )
( / )( ) ( / )
ϭ
ϩ
ϩ
1
1
1
2
For R = L = C = 1,
Z
j
j
j
( )
( )
( )
( )
ϭ
ϩ
ϩ
2
1
For the circuit shown in Figure 3.60 (part b),
Z
R j
C j
R LC
j
L C
( )
( )
( / )( ) ( / )
( )
( / )
ϭ
ϩ
ϩ
ϩ
2
2
1
1
For R = 1000 Ω, L = 30 mH, and C = 0.47 µF (Figure 3.61),
Z
j
j
j
( )
( )
.
( )
.
( )
ϭ
ϩ
ϩ
Ϫ
Ϫ
Ϫ
1000
1
0 47 10
1000
30 10
0 47 10
2
6
3
6
2
*
*
*
*
*
*
ϩ ϩ
Ϫ
Ϫ
1
30 10
0 47 10
3
6
*
*
*
.
MATLAB Solution
% Script file: circ _ Fig _ 359
% R, L, and C in parallel
% R = C = L = 1.
echo on;
w = 0:0.1:5;
num = [0 0 1];
den = [1 1 1];
ZW = freqs (num, den, w);
subplot(2, 1, 1);
plot(w, abs(ZW));
grid on;
title(‘Magnitude and phase of Z(w)’);
xlabel(‘w(rad/sec)’);
ylabel(‘magnitude’);
subplot(2, 1, 2);
plot(w, angle(ZW)*180/pi);
% Figure 3.61
xlabel(‘w(rad/sec)’);
ylabel(‘phase in degrees’);
grid on;
C
R
L
Z
FIGURE 3.59
Network with R = C = L = 1, over the range 0 ≤
ω ≤ 5 rad/s of Example 3.9.
C
R
L
Z
FIGURE 3.60
Network with R = 1000 Ω, L = 30 mH, and C = 0.47 µF,
over the range 7500 ≤ ω ≤ 9500 rad/s of Example 3.9.
CRC_47760_CH003.indd 280
CRC_47760_CH003.indd 280
7/23/2008 1:27:47 PM
7/23/2008 1:27:47 PM