Page 197 - Schaum's Outline of Theory and Problems of Electric Circuits

HIGHER-ORDER CIRCUITS AND COMPLEX FREQUENCY
186
Rs=L 1=LC [CHAP. 8
Ans: ðaÞ R 1 ; ðbÞ R 1
2
2
s þ s þ s þ s þ
L LC L LC
8.34 Obtain the network function HðsÞ for the circuit shown in Fig. 8-34. The response is the voltage V i ðsÞ.

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

Fig. 8-34

8.35 Construct the s-plane plot for the transfer function of Problem 8.34. Evaluate Hð j3Þ from the plot.
Ans: See Fig. 8-35.
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 HðsÞ¼ V ðsÞ=I i ðsÞ for the circuit shown in Fig. 8-36 and construct the pole-zero plot.
i
2
sðs þ 1:5Þ
Ans: HðsÞ¼ : See Fig. 8-37.
2
s þ 1
8.37 Write the transfer function HðsÞ whose pole-zero plot is given in Fig. 8-38.

2
s þ 50s þ 400
Ans: HðsÞ¼ k 2
s þ 40s þ 2000