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E 1
+
–
I 1
1
1′
Z 1
Z 3
FIG. 26.28
Determining z 11.
Thus z 12 �
I 1 � 0 �
and z12 � Z3 (26.28)
For z21, the required network appears in Fig. 26.30, and
E2 � I1Z3 Thus, z 21 �
I 2 � 0 �
and z21 � Z3 (26.29)
For z 22, the determining configuration is shown in Fig. 26.31, and
Thus z 22 �
Z 2
E 2
� I2
E 1
� I2
E 2
� I1
I 2 �
I2 = 0
2
E 2
� Z2 � Z 3
I 1 � 0 �
I 2Z 3
� I2
I 1Z 3
� I1
I 2(Z 2 � Z 3)
��
I2
and z22 � Z2 � Z3 (26.30)
Note that for the T configuration, z 12 � z 21. For Z 1 � 3 � �0°,
Z 2 � 5 � �90°, and Z 3 � 4 � ��90°, we have
z11 � Z1 � Z3 � 3 ��j 4 �
z12 � z21 � Z3 � 4 � ��90° � �j 4 �
z22 � Z2 � Z3 � 5 � �90° � 4 � ��90° � 1 � �90° � j 1 �
For a set of impedance parameters, the terminal (external) behavior
of the device or network within the configuration of Fig. 26.22 is determined.
An equivalent circuit for the system can be developed using the
impedance parameters and Eqs. (26.22a) and (26.22b). Two possibilities
for the impedance parameters appear in Fig. 26.32.
Applying Kirchhoff’s voltage law to the input and output loops of
the network of Fig. 26.32(a) results in
E1 � z11I1 � z12I2 � 0
and E2 � z22I2 � z21I1 � 0
2′
IMPEDANCE (z) PARAMETERS ⏐⏐⏐ 1167
I1 = 0
1
+
E 1
–
1′
E 1
+
–
I 1
Z 1
1
1′
Z 3
+
–
Z 2
E 1
FIG. 26.29
Determining z 12.
Z 1
E 2
+
–
Z 3
2
2′
FIG. 26.30
Determining z 21.
I 2
Z 2
I1 = 0 I2 1 Z1 Z2 2
1′
Z 3
FIG. 26.31
Determining z 22.
2′
+
–
E 2
I2 = 0
2
+
E 2
–
2′
+
E2 –