Question #1A given differential capacitive sensor is available that is based on the variation inplate distance and whose movable plate is grounded. In order to obtain a ground-referenced output signal proportional to the input displacement in the circuitsshown. Assume that the op-amps are ideal. Determine the conditions to befulfilled by resistors and capacitors in the circuit in order that the output voltageis directly proportional to the displacement and independent of oscillationfrequency.for a variable plate separation:СоC1 =1- xСо& C2 =1+ x where x is the displacement R3R4CaR1R2VsROVoR10СьRsR8

Answered: R4 R3 Ca R9 R1 R2 Vs Vo R10 Сь Rs R8

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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1) From the question the figure is simplified:

Step 2

$A p p l y V o l t a g e d i v i s i o n r u l e a t V_{10} : V_{10} = \frac{R_{10}}{R_{10} + \frac{1}{S C_{b}}} \times V_{1} = V_{1} \frac{S C_{b} R_{10}}{1 + S C_{b} R_{10}} V_{9} = V_{10} [I d e a l o p - a m p p r o p e r t y] A p p l y i n g n o d a l a n a l y s i s a t n o d e 9 V_{9} [\frac{1}{R_{9}} + S C_{a}] = \frac{V_{o}}{R_{9}} + V_{2} S C_{a} \Rightarrow V_{1} \frac{S C_{b} R_{10}}{1 + S C_{b} R_{10}} [\frac{1}{R_{9}} + S C_{a}] = \frac{V_{O}}{R_{9}} + V_{2} S C a - 1) A p p l y i n g v o l t a g e d i v i d e r a t V_{4} : V_{4} = V_{2} \frac{R_{4}}{R_{3} + R_{4}} V_{4} = V_{3}$

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Now apply Nodal analysis at node 3:

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