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186

HIGHER-ORDER CIRCUITS AND COMPLEX FREQUENCY

Ans:

8.34

ðaÞ

Rs=L ; R 1 s2 þ s þ L LC

ðbÞ

1=LC R 1 s2 þ s þ L LC

Obtain the network function HðsÞ for the circuit shown in Fig. 8-34. Ans:

[CHAP. 8

The response is the voltage Vi ðsÞ.

ðs þ 7  j2:65Þðs þ 7 þ j2:65Þ ðs þ 2Þðs þ 4Þ

Fig. 8-34 8.35

Construct the s-plane plot for the transfer function of Problem 8.34. Ans: See Fig. 8-35.

Evaluate Hð j3Þ from the plot.

ð7:02Þð9:0Þ 2:86 þ 38:918 ¼ 3:50 51:418  ð3:61Þð5:0Þ 56:318 þ 36:878

Fig. 8-35 8.36

Obtain HðsÞ ¼ Vi ðsÞ=Ii ðsÞ for the circuit shown in Fig. 8-36 and construct the pole-zero plot.

Ans:

8.37

HðsÞ ¼

sðs2 þ 1:5Þ : s2 þ 1

See Fig. 8-37.

Write the transfer function HðsÞ whose pole-zero plot is given in Fig. 8-38.

Ans:

HðsÞ ¼ k

s2 þ 50s þ 400 s2 þ 40s þ 2000

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
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