Introduction to Electric Circuits

9.8 Cascaded two-port networks 219

9.8 CASCADED TWO-PORT NETWORKS

+O

vl

--O

Figure 9.11

I~! , ,------Iu

Network

1

+ 11o = 12i +

Iv10 =iv2i

0 0

Network

2

I O+

Two networks connected as shown in Fig. 9.11 are said to be cascaded. The

output port of network 1 is the input port of network 2. The ABCD-parameters

of the cascaded pair are obtained by the multiplication of those of the two

constituent networks. Thus, if the transmission parameters of circuit 1 are A1,

B~, C~ and D~, while those for network 2 are A2, B2, C2 and D2 then

['V1] - [;i ;11] [;i ;221 I/g~ ]'~ I; ;] [V~] (9.52)

where, by matrix multiplication,

A = (A1A 2 + BIC2)

B = (AIB 2 + BAD2)

C = (C1A 2 -+- D1C2)

D = (CIB 2 + O102)

(9.53)

(9.54)

(9.55)

(9.56)

Example 9.8

Obtain the ABCD-parameters for the network of Fig. 9.9.

Solution

The two-port network of Fig. 9.9 may be considered to be a cascaded pair

comprising a shunt admittance followed by a series impedance as shown in

Fig. 9.12.

I1 Ilo I2i Z t I2 ~ O+

+ 0--------~------- ~ ..... 0 ~ I l

t

V1

_o
84

~ Y

...............

o---

Vlo

O I

V2i

,,O

V2

O--

Figure 9.12