Introduction to Electric Circuits

9.8 Cascaded two-port networks 221

+C I1 ~ 0 0 [

--~y

Figure 9.14

Z I2

] 0 0

Y

-0 0 0 0 0

1 2 3

O+

V2

--O-

For sections 1 and 3, which are shunt admittances, A = 1, B = 0, C = Y and
D = 1. For the series impedance section, A = 1, B - Z, C - 0 and D = 1. Thus
for the rr-network

[I~1] m~ [; ~] [; 1] [; ~;[/V22]

Multiplying the first two matrices on the right-hand side of the equation we

get

-1 Z 1

[iV1]=[y I+ZY][Y ~1[~2]

Finally, multiplying the remaining transfer matrices, we have

Y+(1 + ZY)Y

zl[ ]

I + ZY 12

For the 7r-network, therefore, A=I+ZY, B=Z, C=Y+(I+ZY)Y
= 2Y + ZY 2, D = 1 + ZY. Again A = D, this being a symmetrical two-port
network.

Nominal-TT representation of 'medium length' power
transmission lines

In power transmission the ~r-circuit of Fig. 9.13 is referred to as a nominal-~r
network. It is used to model a medium length transmission line (between 80 km
and 200 km). The whole of the impedance of the line is assumed to be
concentrated at the centre of the line and half the capacitive reactance is placed
at either end of the line. Thus, if we replace Y by I//2, where Y is the total shunt
admittance of the line, we obtain for the ABCD-parameters:

A = D= I + (ZY/2), B= Z, C= Y+ (Zy2/4)