Question

5) Consider the following second-order bandpass filter. As input voltage, apply V(t) 100Ω, C-4.7 μF. and L-10mH. sin(wt).R in Vout Fig 9: Second-order band-pass filter a) Determine the frequency response function H(ju) Ve-ju) / Vm(ju) and sketch the magnitude and phase characteristics versus w by calaulation. Calculate the theoretical cutoff frequency of the filter Using PSpice AC analysis, plot magnitude lHju)l and phase ф characteristics of the filter, between 1 Hz-100 KHz b) c)

Answer 1

aAccordingto jw lom uottaqe diuision ru le 10O out Ju in (Juo out J I + , w 476-047 J470 tJu 470.047 | Frequen respon se function magnitude of H(jw) magnitude H- Sa mple Calrularti (w4t0-047j2 6, 283 x 구。 H(jw) = a-95m (^o(6283x410 04g)2 magnitude idHg2 q 2.93 de Scanned with CamScanner Cs -50.59 3

hen 62.832 χ470 -O o295 109 十(62.83 2x470047)2 in da lr(jwjdB. 201ng(Ms) magnitude 30 598 d8 pha se ahgle of H(jo) し.tun. | (on. tan-I/w470.04구 Sam ple Calculations when f:1H , we 2n4-6.283 rad/sec. 89,830 6 rad/sec. 62. 83 f-10Hz) when 88.308 6 when f-100 Hz, ω-anfニ628.3 rad/sec こ73.546" C Scned with CamScanner

Frequency in Hz	w	magnitude	Magnitiude in dB	angle
1	6.285714	0.002954273	-50.590988	89.7
10	62.85714	0.029529969	-30.59474	88.3
100	628.5714	0.283320945	-10.954426	73.4
338.5519	2128.040418	0.707134693	-3.0099571	45
1000	6285.714	0.947122429	-0.4718776	18.7
10000	62857.14	0.999327792	-0.0058407	2.01
100000	628571.4	0.999894283	-0.0009183	0.3

System: H Frequency (Hz): 974 Magnitude (dB): -0.501 System: H Frequency (Hz): 328 iagram Magnitude (dB): -3.15 -10 System: H Frequency (Hz): 97.6 Magnitude (dB): -11.2 20 System: H Frequency (Hz): 10 Magnitude (dB): -30.6 30 40 System: H Frequency (Hz): 1.01 Magnitude (dB): -50.5 50 System: H Frequency (Hz): 10 Phase (deg): 88.3 -60 System: H Frequency (Hz): 1.02 Phase (deg): 89.7 System: H Frequency (Hz): 101 Phase (deg): 73.4 o 45 System: H Frequency (Hz): 1e+03 Phase (deg): 18.7 System: H Frequency (Hz Phase (deg): 0 0 System: H 0 10 Frequency (Hz): 9.68e +0310 Phase (deg): 2.01 10 Frequency (Hz)

) At cutoff seuenty ffo, the magnitud しが70 o. 70구 2. rad/sec Q)2구-23 2THo 2124-23 fo 338-5591 HZ urt-off CS Scanned with CamScanner

e L1 0 10mH 7 4.7u V1 İViac 0Vdc VP 100

100d 20 Od -40 100KHz 10KHz 1.0KHz -100d 100Hz 10Hz 1. 0Hz Frequencu ac_sweep d