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CHAP. 12]

277

FREQUENCY RESPONSE, FILTERS, AND RESONANCE

Fig. 12-9

Hv1 ð!Þ ¼

R2 1 ¼ R2 þ j!L1 1 þ jð!=!x Þ

with !x  R2 =L1 ; that is, 1 jHv j ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ð!=!x Þ2

and

H ¼ tan1 ð!=!x Þ

The magnitude and angle plots are shown in Fig. 12-10. The voltage transfer function Hv1 approaches zero at high frequencies and unity at ! ¼ 0. Hence the name ‘‘low-pass.’’

Fig. 12-10

The other network functions of this low-pass network are obtained in the Solved Problems. EXAMPLE 12.2 Obtain the voltage pffiffiffi transfer function Hv1 for the open circuit shown in Fig. 12-11. frequency, in hertz, does jHv j ¼ 1= 2 if (a) C2 ¼ 10 nF, (b) C2 ¼ 1 nF?

Fig. 12-11

At what

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