Y11 ¼ Ya þ Yc Y12 ¼ Y21 ¼ Yc Y22 ¼ Yb þ Yc
Substituting Ya , Yb , and Yc in (11) into (13), we ﬁnd Y11 ¼
sþ3 5s þ 6
Y12 ¼ Y21 ¼ Y22 ¼
s 5s þ 6
sþ2 5s þ 6
Since Y12 ¼ Y21 , the two-port circuit is reciprocal.
PI-EQUIVALENT OF RECIPROCAL NETWORKS
A reciprocal network may be modeled by its Pi-equivalent as shown in Fig. 13-6. The three elements of the Pi-equivalent network can be found by reverse solution. We ﬁrst ﬁnd the Y-parameters of Fig. 13-6. From (10) we have Y11 ¼ Ya þ Yc Y12 ¼ Yc
[Fig. 13.7ðaÞ [Fig. 13-7ðbÞ
Y21 ¼ Yc Y22 ¼ Yb þ Yc
[Fig. 13-7ðaÞ [Fig. 13-7ðbÞ
from which Ya ¼ Y11 þ Y12
Yb ¼ Y22 þ Y12
Yc ¼ Y12 ¼ Y21
The Pi-equivalent network is not necessarily realizable.
APPLICATION OF TERMINAL CHARACTERISTICS
The four terminal variables I1 , I2 , V1 , and V2 in a two-port network are related by the two equations (1) or (9). By connecting the two-port circuit to the outside as shown in Fig. 13-1, two additional equations are obtained. The four equations then can determine I1 , I2 , V1 , and V2 without any knowledge of the inside structure of the circuit.