Answered: in a bandpass filter circuit resonance…

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

in a bandpass filter circuit resonance frequency is 53mhz and bandwidth is 15mhz. design the filter circuit. permitted values of capacitors are: 100μf, 10pf, 470μf, 220μf permitted values of resistance are: 100kω, 10kω, 470kω, 330kω, 1kω, 100ω, 330ω 470ω, 560ω

Expert Solution

Step 1

Let f_H and f_L be the high and low cut-off frequency of the band-pass filter circuit respectively.

Write the expression for the bandwidth.

$\begin{array}{rcl} B W & = & 15 m H z \\ f_{H} - f_{L} & = & 15 m H z . . . . . . (1) \end{array}$

Step 2

Write the expression for the resonant frequency.

$\begin{array}{rcl} f_{r} & = & \sqrt{f_{H} f_{L}} \\ 53 m H z & = & \sqrt{f_{H} f_{L}} . . . . . . (2) \end{array}$

Step 3

Solve the above two equations to get the values of both the cut-off frequencies.

$\begin{array}{rcl} f_{H} & = & 61.02 m H z \\ f_{L} & = & 46.02 m H z \end{array}$

Step 4

Write the expression for the lower cut-off frequency.

$\begin{array}{rcl} f_{L} & = & \frac{1}{2 π R_{1} C_{1}} \\ R_{1} & = & \frac{1}{2 π C_{1} f_{L}} \\ l e t, C_{1} & = & 220 μ F \\ R_{1} & = & \frac{1}{2 π (220 μ F) (46.02 m H z)} \\ = & 15.719 k Ω \end{array}$

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