Q6. Figure Q6 shows an LCR resonant filter circuit. If the quality factor Q is large enough R Vịn Vout Figure Q6: LCR filter then the frequency transfer function (in terms of the circular frequency w) of this filter can be approximated, 1 H(w) = 1+ 2JRC(w – wo) Taking L=1 mH, C=25 nF and R=2 kQ. (a) Calculate the expected resonant frequency, vo, of this filter (in kHz). (b) Find the -3 dB points (in power) for this filter and hence determine its bandwidth. (c) Determine the value of the quality factor Q for this filter. (d) Using the properties of Fourier transforms and the tabulated selected transforms, determine the impulse response function corresponding to this transfer function. (e) Sketch the form of the real part of the impulse response function. (f) A bandpass filter, such as the one described above, is usually inserted after a chopper or rectifier modulator: explain why and identify the requirements on the resonant frequency and the bandwidth of such a bandpass filter.

Q6. Figure Q6 shows an LCR resonant filter circuit. If the quality factor Q is large enough R Vịn Vout Figure Q6: LCR filter then the frequency transfer function (in terms of the circular frequency w) of this filter can be approximated, 1 H(w) = 1+ 2JRC(w – wo) Taking L=1 mH, C=25 nF and R=2 kQ. (a) Calculate the expected resonant frequency, vo, of this filter (in kHz). (b) Find the -3 dB points (in power) for this filter and hence determine its bandwidth. (c) Determine the value of the quality factor Q for this filter. (d) Using the properties of Fourier transforms and the tabulated selected transforms, determine the impulse response function corresponding to this transfer function. (e) Sketch the form of the real part of the impulse response function. (f) A bandpass filter, such as the one described above, is usually inserted after a chopper or rectifier modulator: explain why and identify the requirements on the resonant frequency and the bandwidth of such a bandpass filter.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

Q6. Figure Q6 shows an LCR resonant filter circuit. If the quality factor Q is large enough
R
Vin
Vout
Figure Q6: LCR filter
then the frequency transfer function (in terms of the circular frequency w) of this filter can
be approximated,
1
H(w) =
1+ 2jRC(w – wo)
Taking L=1 mH, C=25 nF and R=2 kN.
(a) Calculate the expected resonant frequency, vo, of this filter (in kHz).
(b) Find the -3 dB points (in power) for this filter and hence determine its bandwidth.
(c) Determine the value of the quality factor Q for this filter.
(d) Using the properties of Fourier transforms and the tabulated selected transforms,
determine the impulse response function corresponding to this transfer function.
(e) Sketch the form of the real part of the impulse response function.
(f) A bandpass filter, such as the one described above, is usually inserted after a chopper
or rectifier modulator: explain why and identify the requirements on the resonant
frequency and the bandwidth of such a bandpass filter.

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Q6. Figure Q6 shows an LCR resonant filter circuit. If the quality factor Q is large enough Vịn C Vout Figure Q6: LCR filter then the frequency transfer function (in terms of the circular frequency w) of this filter can be approximated, 1 H(w) 1+ 2JRC(w – wo) Taking L=1 mH, C=25 nF and R=2 kQ. (a) Calculate the expected resonant frequency, vo, of this filter (in kHz). (b) Find the –3 dB points (in power) for this filter and hence determine its bandwidth. (c) Determine the value of the quality factor Q for this filter. (d) Using the properties of Fourier transforms and the tabulated selected transforms, determine the impulse response function corresponding to this transfer function. (e) Sketch the form of the real part of the impulse response function. (f) A bandpass filter, such as the one described above, is usually inserted after a chopper or rectifier modulator: explain why and identify the requirements on the resonant frequency and the bandwidth of such a bandpass filter.