ECE 201 Spring 2010 Homework 29 Solutions Problem 40 a The following differential equation can be written using KCL at the inverting terminal of the op amp and using the virtual ground concept vs t vout t dvout t C 0 R1 R2 dt vs t 100u t 100 t 0 100R2 1 e t R2 C vout t R1 400 1 e 2t mV t 0 Problem not from the book If we denote the voltage at the non inverting terminal of the op amp as vL t then using the virtual ground concept the output voltage is given by Vout t 10vL t Also vL t VIN t 1000iL t The problem then reduces to finding iL t Due to the square wave shape of VIN t the graph for iL t will also be periodic with maximum and minimum values of x and x say The task is to find the value of x which can be done using the following equation iL t iL iL 0 iL e t L R 2 s x 2 10 4 x 2 10 4 e 0 5 x 0 489 10 4 1 The plot of Vout t for 0 t 2 s is drawn below Note that Vout t will be periodic with period 2 s Plot of Vout t for 0 t 2us Note that it is periodic with period 2us 2 5 2 1 5 1 Vout t Volts 0 5 0 0 5 1 1 5 2 2 5 0 0 2 0 4 0 6 0 8 1 t seconds 2 1 2 1 4 1 6 1 8 2 6 x 10
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