Introduction to Electric Circuits

206 Two-port networks

V 1 -- ZllI1 + z1212 (9.1)

V2 = Z21 I, + Z2212 (9.2)

In matrix form these may be written

EVil Zll z12] [11] 93,

v: LZ: Z:: /2

The parameters for this set are called the impedance or z-parameters and they
are defined as follows:

9 Zll is the input impedance (Zi) and is measured as V1/I 1 with 12 = O:

Zll-- (V1/I1)li2=o

9 z~2 is the forward transfer impedance (zf) and is measured as V~/I2 with

I1 - O:

Z12 = (Vl/V2)li,=o

9 Z21 is the reverse transfer impedance (Zr) and is measured as V2/I 1 with
12 = O:
Z21 ~ (V2/I,)112=o

9 Z22 is the output impedance (Zo) and is measured as V2/I 2 with I~ = 0:

z22- (V2/I2)11,=o

(9.4)

(9.5)

(9.6)

Figure 9.2

+0 ~ I1 I2 < 0

Z11~ [~ z22

v,

Z1212~ Z2~l~

-0 0

Since these are all obtained with either the input terminals or the output
terminals open circuited, they are called the open circuit impedance para-
meters. They are measured in ohms.
The circuit shown in Fig. 9.2 satisfies Equations (9.1) and (9.2) and is called
the equivalent circuit for this set.

(9.7)