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314

TWO-PORT NETWORKS

[CHAP. 13

Y11 ¼ Ya þ Yc Y12 ¼ Y21 ¼ Yc Y22 ¼ Yb þ Yc

ð13Þ

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

ð14Þ

sþ2 5s þ 6

Since Y12 ¼ Y21 , the two-port circuit is reciprocal.

13.5

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

ð15Þ

from which Ya ¼ Y11 þ Y12

Yb ¼ Y22 þ Y12

Yc ¼ Y12 ¼ Y21

ð16Þ

The Pi-equivalent network is not necessarily realizable.

Fig. 13-7

13.6

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.

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
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