Page 198 - Schaum's Outline of Theory and Problems of Electric Circuits

HIGHER-ORDER CIRCUITS AND COMPLEX FREQUENCY
CHAP. 8]

Fig. 8-36 Fig. 8-37 187

8.38 The pole-zero plot in Fig. 8-39 shows a pole at s ¼ 0 and zeros at s ¼ 50 j50. Use the geometrical
method to evaluate the transfer function at the test point j100.
Ans: Hð j100Þ¼ 223:6 26:578

Fig. 8-38 Fig. 8-39

8.39 A two-branch parallel circuit has a resistance of 20
in one branch and the series combination of R ¼ 10
and L ¼ 0:1 H in the other. First, apply an excitation, I i ðsÞ, and obtain the natural frequency from the
denominator of the network function. Try different locations for applying the current source. Second,
insert a voltage source, V i ðsÞ, and obtain the natural frequency. Ans: 300 Np/s in all cases

þ
8.40 In the network shown in Fig. 8-40, the switch is closed at t ¼ 0. At t ¼ 0 , i ¼ 0 and
di
¼ 25 A=s
dt
Obtain the natural frequencies and the complete current, i ¼ i n þ i f .
Ans: 8:5 Np/s, 23:5 Np/s; i ¼ 2:25e 8:5t 0:25e 23:5t þ 2:5 ðAÞ