Q5. If the quality factor Q is large enough then the impulse response function of a particular LCR analogue filter can be approximated, h(t) = 1 çu(t)e¬//(2RC) cos wot where wo = 1/VLC. (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)|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 = 1mH, C = 80 nF and R = 2.5 k2, calculate the expected resonant frequency of this filter (in kHz). (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?

Q5. If the quality factor Q is large enough then the impulse response function of a particular LCR analogue filter can be approximated, h(t) = 1 çu(t)e¬//(2RC) cos wot where wo = 1/VLC. (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)|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 = 1mH, C = 80 nF and R = 2.5 k2, calculate the expected resonant frequency of this filter (in kHz). (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?

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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