CHAP. 13]

Ans:

13.26

TWO-PORT NETWORKS

331

A ¼ 0:1; B ¼ 0; C ¼ 107 =s and D ¼ 10. For high frequencies, the device is similar to the device of Problem 13.21, with N ¼ 10.

The Z-parameters of a two-port device N are Z11 ¼ ks, Z12 ¼ Z21 ¼ 10ks, and Z22 ¼ 100ks. A 1- resistor is connected across the output port (Fig. 13-30). (a) Find the input impedance Zin ¼ V1 =I1 and construct its equivalent circuit. (b) Give the values of the elements for k ¼ 1 and 106 . Ans:

ðaÞ Zin ¼

ks 1 ¼ 1 þ 100ks 100 þ 1=ks

The equivalent circuit is a parallel RL circuit with R ¼ 102 and L ¼ 1 kH: 1 1

and L ¼ 1 H. For k ¼ 106 ; R ¼

and L ¼ 106 H ðbÞ For k ¼ 1; R ¼ 100 100 13.27

The device pN in ﬃ Fig. 13-30 is speciﬁed by its following Z-parameters: Z22 ¼ N 2 Z11 and ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Z12 ¼ Z21 ¼ Z11 Z22 ¼ NZ11 . Find Zin ¼ V1 =I1 when a load ZL is connected to the output terminal. Show that if Z11  ZL =N 2 we have impedance scaling such that Zin ¼ ZL =N 2 . Ans:

13.28

Zin ¼

ZL . N 2 þ ZL =Z11

For ZL  N 2 Z11 ; Zin ¼ ZL =N 2

Find the Z-parameters in the circuit of Fig. 13-31. Ans: Z11 ¼ Z22 ¼ s þ 3 þ 1=s; Z12 ¼ Z21 ¼ s þ 1

Hint: Use the series connection rule.

Fig. 13-31 13.29

Find the Y-parameters in the circuit of Fig. 13-32. Hint: Use the parallel connection rule. Ans: Y11 ¼ Y22 ¼ 9ðs þ 2Þ=16; Y12 ¼ Y21 ¼ 3ðs þ 2Þ=16

Fig. 13-32

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