Introduction to Electric Circuits

220 Two-port networks

We saw in Example 9.7 that for a shunt admittance A = 1, B = 0, C = Y and

D = 1. Also, from Example 9.4 we have, for series impedance, A = 1, B = Z,

C = 0 and D = 1.

Using the matrix Equation (9.52), with A1 = 1, B~ = 0, C~ = Y, D1 = 1,

A 2 = 1, B 2 = Z, C 2 -- 0 and O 2 = 1 we have

V 1 1

Ill ] "- [Y ~1 [10 Z] [/V22]- [C ;3 [/V22]

From Equations (9.53)-(9.56) by matrix multiplication we have

A = [(1 x 1) + (0 x 0)] = 1
B -[(1 x Z) + (0 x 1)] = Z
C = [(Y x 1) + (1 x 0)] = Y
D = [(Y x Z) + (1 x 1)]- 1 + ZY

For the cascaded network, therefore, A = 1, B = Z, C = Y and D = 1 + ZY.
These results agree with those obtained in Example 9.6.

The ABCD-parameters of a 7r-network

The rr- and the T-networks are commonly encountered in electric circuit
theory, for example in filter circuits, attenuator sections and power transmission
circuits. The 7r-network is essentially a delta network and a T-network is a star
connection. As we saw in Chapter 3 it is possible to transform from one to the
other using the delta-star transform or the star-delta transform. The more
appropriate form for any given circuit application can thus be chosen.

Example 9.9

Obtain the transmission parameters for the rr-network shown in Fig. 9.13.

Figure 9.13

+o^11

V1

-o--~

Z

l I

I2

Y V2

o-

Solution

This circuit is made up from three two-port networks connected in cascade as

indicated in Fig. 9.14.