HW29%20solution

HW29%20solution - x , which can be done using the following...

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ECE 201 Spring 2010 Homework 29 Solutions Problem 40 (a) The following diFerential equation can be written using KCL at the inverting terminal of the op amp and using the virtual ground concept, v s ( t ) R 1 + v out ( t ) R 2 + C dv out ( t ) dt =0 v s ( t )= - 100 u ( t ) = - 100 ,t 0 v out ( t )= 100 R 2 R 1 (1 - e - t/R 2 C ) = 400(1 - e - 2 t ) mV, t 0 Problem not from the book If we denote the voltage at the non-inverting terminal of the op amp as v L ( t ), then using the virtual ground concept, the output voltage is given by V out ( t ) = 10 v L ( t ). Also, v L ( t )= V IN ( t ) - 1000 i L ( t ). The problem then reduces to ±nding i L ( t ). Due to the square wave shape of V IN ( t ), the graph for i L ( t ) will also be periodic with maximum and minimum values of x and - x (say). The task is to ±nd the value of
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Unformatted text preview: x , which can be done using the following equation, i L ( t ) = i L ( ) + [ i L (0)-i L ( )] e-t/ = L R = 2 s x = 2 10-4 + [-x-2 10-4 ] e-. 5 x = 0 . 489 10-4 1 The plot of V out ( t ) for 0 t 2 s is drawn below. Note that V out ( t ) will be periodic with period 2 s . 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10 6 2.5 2 1.5 1 0.5 0.5 1 1.5 2 2.5 t(seconds) V out (t)(Volts) Plot of V out (t) for 0<=t<=2us. Note that it is periodic with period 2us 2...
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HW29%20solution - x , which can be done using the following...

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