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Q5. If the quality factor Q is large enough then the impulse response function of a particular LCR analogue filter can be approximated, (1)e-1/(2RC) RC h(1) = cos wol %3D where wo = 1/VLC. %3D (a) Describe what is meant by the quality factor Q of a filter. (b) Using the properties of Fourier transforms and the tabulated selected transforms, determine the frequency transfer function H(w) corresponding to this impulse response function. (c) Sketch the form of the power spectrum |H(w) of the frequency transfer function. Assume a large Q so you can neglect the term which resonates at w = -Wo. (d) Is this a low-pass, high-pass or a band-pass filter?

Q5. If the quality factor Q is large enough then the impulse response function of a particular LCR analogue filter can be approximated, (1)e-1/(2RC) RC h(1) = cos wol %3D where wo = 1/VLC. %3D (a) Describe what is meant by the quality factor Q of a filter. (b) Using the properties of Fourier transforms and the tabulated selected transforms, determine the frequency transfer function H(w) corresponding to this impulse response function. (c) Sketch the form of the power spectrum |H(w) of the frequency transfer function. Assume a large Q so you can neglect the term which resonates at w = -Wo. (d) Is this a low-pass, high-pass or a band-pass 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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Q5. If the quality factor Q is large enough then the impulse response function of a particular LCR analogue filter can be approximated, h(1) = ()e-1/(2RC) RC cos wot %3D where wo = 1/VLC. %3D (a) Describe what is meant by the quality factor Q of a filter. (b) Using the properties of Fourier transforms and the tabulated selected transforms, determine the frequency transfer function H(w) corresponding to this impulse response function. (c) Sketch ihe form of the power spectrum |H(w)|² of the frequency transfer function. Assume a large Q so you can neglect the term which resonates at w = -wo- (d) Is this a low-pass, high-pass or a band-pass filter? (e) Sketch a basic circuit which would provide this filter functionality. (f) Taking L frequency of this filter (in kHz). 1 mH, C = 80 nF and R 2.5 k2, calculate the expected resonant %3D %3D (g) Using the same component values, find the -3 dB points for this filter and hence determine its bandwidth. (h) A 50% duty-cycle square wave, whose fundamental frequency is of the resonance frequency of this filter, is input into the filter. What form does the output waveform take?
Transcribed Image Text:Q5. If the quality factor Q is large enough then the impulse response function of a particular LCR analogue filter can be approximated, h(1) = ()e-1/(2RC) RC cos wot %3D where wo = 1/VLC. %3D (a) Describe what is meant by the quality factor Q of a filter. (b) Using the properties of Fourier transforms and the tabulated selected transforms, determine the frequency transfer function H(w) corresponding to this impulse response function. (c) Sketch ihe form of the power spectrum |H(w)|² of the frequency transfer function. Assume a large Q so you can neglect the term which resonates at w = -wo- (d) Is this a low-pass, high-pass or a band-pass filter? (e) Sketch a basic circuit which would provide this filter functionality. (f) Taking L frequency of this filter (in kHz). 1 mH, C = 80 nF and R 2.5 k2, calculate the expected resonant %3D %3D (g) Using the same component values, find the -3 dB points for this filter and hence determine its bandwidth. (h) A 50% duty-cycle square wave, whose fundamental frequency is of the resonance frequency of this filter, is input into the filter. What form does the output waveform take?
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