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1168 ⏐⏐⏐ SYSTEM ANALYSIS: AN INTRODUCTION
1
+
E 1
–
1′
I 1
1
1′
z 11
z 12 I 2
+
–
(a)
Device,
network,
system
(z)
(a)
+
–
z 21 I
1
z 22
I 2 2
+
E 2
–
2′
1
+
E 1
–
1′
which, when rearranged, become
E1 � z11I1 � z12I2 I 1
z 11 – z 12
FIG. 26.32
Two possible two-port, z-parameter equivalent networks.
–
2
2′
+
z 22 – z 12
E 2 � z 21I 1 � z 22I 2
I 2 2
matching Eqs. (26.22a) and (26.22b).
For the network of Fig. 26.32(b),
E1 � I1(z11 � z12) � z12(I1 � I2) � 0
and E2 � I1(z21 � z12) � I2(z22 � z12) � z12(I1 � I2) � 0
which, when rearranged, are
E1 � I1(z11 � z12 � z12) � I2z12 E2 � I1(z21 � z12 � z12) � I2(z22 � z12 � z12) and E1 � z11I1 � z12I2 E2 � z21I1 � z22I2 Note in each network the necessity for a current-controlled voltage
source, that is, a voltage source the magnitude of which is determined
by a particular current of the network.
The usefulness of the impedance parameters and the resulting equivalent
networks can best be described by considering the system of Fig.
26.33(a), which contains a device (or system) for which the impedance
1
1′
I 1
z 11
z 12 I 2
FIG. 26.33
Substitution of the z-parameter equivalent network into a complex system.
(b)
z 12
+
–
(b)
+
–
–
+
(z 21 – z 12 )I 1
z 22
z 21 I 1
I 2
–
2
2′
+
+
E 2
–
2′