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CHAP. 12]

FREQUENCY RESPONSE, FILTERS, AND RESONANCE

309

12.46

In the circuit of Fig. 12-65(b), let R ¼ 1 ; C1 ¼ 1:394 F; C2 ¼ 0:202 F, and C3 ¼ 3:551 F. Find HðsÞ ¼ V2 =V1 and show that it approximates the passive third-order Butterworth low-pass filter of Fig. 12-65(a). Ans: HðsÞ ¼ 1=ð0:99992s3 þ 1:99778s2 þ 2s þ 1Þ

12.47

Show that the half-power cutoff frequency in the circuit of Fig. 8-42 is !0 ¼ 1=ðRCÞ and, therefore, frequency scaling may be done by changing the value of C or R. Ans:

12.48

V2 2 2 1 ; !0 ¼ ¼ ¼  2   V1 R2 C2 s2 þ RCs þ 1 RC s s þ þ1 !0 !0

Find RLC values in the low-pass filter of Fig. 12-65(a) to move its half-power cutoff frequency to 5 kHz. Ans: R ¼ 1 ; C ¼ 31:83 mF; L ¼ 63:66 mH

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
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