Alternating Current Analysis 289
ANALYTICAL Solution (series case)|Z()| = |R + j(XL − XC)||Z()| = (^) √
R^2 + (XL − XC)^2
The magnitude equation is given by
ZRL
C
()
^2
1 2
The phase equation is given by
∠
Z
XX
R
( )arc tan LC
ANALYTICAL Solution (parallel case)
Y
RjL jC
()
11 1
1
The magnitude equation is given by
Y
R
C
L
()
^112
2
The phase equation is given by
∠
Y
C
L
R
( ) arc tan
1
1
MATLAB Solution
% Script file: impedance _ plots
clf
R = 10;
L = 5e-3;
C = 12.5e-6;
w = [100:100:10000];
Z = R+ j(wL-1./(Cw)); % series case
subplot(2,2,1);
plot(w,abs(Z));
title(‘Mag. [Z(w)] vs w (series case)’);
ylabel(‘Mag[Z(w)] in Ohms’);
grid on;
subplot(2,2,2);
plot(w,angle(Z)180/pi); grid on;
title(‘Phase[Z(w)] vs w (series case)’);
ylabel(‘Phase angle in degrees’);