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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

Assuming that a vi sine signal of variable frequency is applied to the image circuit, it is necessary to calculate its gain as a function of w. What will be the gain in decibels when R1 = R2 = 1MQ, C1 = C2 = 1μF and w = 10rad³/ s

103 rad / s? answers: Avf = -120dB

Expert Solution

Step 1

Given

$R_{1} = R_{2} = 1 M Ω C_{1} = C_{2} = 1 μ F ω = 10^{3} r a d / s e c .$

Taking virtual grounding

Step 2

Applying KCL at node V₀

$\frac{V_{0}}{\frac{1}{s C_{2}}} + \frac{V_{0} - V}{R_{2}} = 0 V_{0} \{s C_{2} + \frac{1}{R_{2}}\} = \frac{V}{R_{2}} . . . . . . . . . . . (1)$

Step 3

Applying KCL at node V

$\frac{V - V_{i n}}{R_{1}} + \frac{V - V_{0}}{\frac{1}{s C_{1}}} + \frac{V - V_{0}}{R_{2}} = 0 V \{\frac{1}{R_{1}} + \frac{1}{R_{2}} + s C_{1}\} - V_{o} s C_{1} = \frac{V_{i n}}{R_{1}} R_{2} V_{0} \{\frac{1}{R_{2}} + s C_{2}\} \{\frac{1}{R_{1}} + \frac{1}{R_{2}} + s C_{1}\} - V_{0} s C_{1} = \frac{V_{i n}}{R_{1}} V_{0} \{\frac{1}{R_{1} R_{2}} + \frac{1}{{R_{2}}^{2}} + \frac{s C_{1}}{R_{2}} + \frac{s C_{2}}{R_{1}} + \frac{s C_{2}}{R_{2}} + s^{2} C_{1} C_{2} - s \frac{C_{1}}{R_{2}}\} R_{1} R_{2} = V_{i n}$

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