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Q6. Figure Q6 shows an LCR resonant filter circuit. If the quality factor Q is large enough 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(@) 1+ 2JRC(w – wo) Taking L=1 mH, C=25 nF and R=2 k2. (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 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(@) 1+ 2JRC(w – wo) Taking L=1 mH, C=25 nF and R=2 k2. (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)
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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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.
Transcribed Image Text: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.
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