Alternating Current Analysis
269
ANALYTICAL Solution
X C () = −j5
X L () = j2
X
X
X
X
X
X
X
j j
j
j
j
C
L
C
L
C
L
( )
( )/ / ( )
( ) ( )
( )
( )
(
ϭ
ϭ
ϩ
ϭ
Ϫ
Ϫ ϩ
ϭ Ϫ
5 2
5
2
10
3
Ω Ω)
X() = j 10
___
3
Z
X
R
X R
X
R
j
j
j
( )
( )/ /
( )
( )
. *
.
.
.
(
ϭ
ϭ
ϩ
ϭ
ϩ
ϭ
ϩ
3 33 4
3 33 4
1 639
1 967 Ω)
and
Y(ω) = 1
_____
Z(ω)
Y
j
j
j
( )
.
.
.
. ( )
ϭ
ϩ ϭ
Ϫ
3 33 4
13 32
0 25
3 sie
MATLAB Solution
% Script file: Z _ Y
W = 1;
C = 1/5;
L = 2;
R = 4;
XC = -j/(W*C);
XL = j*W*L;
X = XC*XL/(XC+XL);
Z = X*R/(X+R);
Y = 1/Z;
disp(‘^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^’)
disp(‘The impedance Z (in Ohms) and admittance (in Siemens) are given
by :’);
Z,Y,
disp(‘^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^’)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The impedance Z (in Ohms) and admittance (in Siemens) are given by:
Z =
1.6393 + 1.9672
Y =
0.2500 - 0.3000i
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Example 3.3
Evaluate the impedance Z of the circuit of Figure 3.51 for ω = 10 rad/s by hand, and by
creating the script fi le imp_Z.
CRC_47760_CH003.indd 269
CRC_47760_CH003.indd 269
7/23/2008 1:27:43 PM
7/23/2008 1:27:43 PM