lab7solutions

lab7solutions - ECE220 Lab7 Solution Created by Rong Guo...

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1 ECE220 Lab7 Solution Created by Rong Guo Problem.7.17. (a) Using Euler s method, approximate the derivative of v with the term, ( ) () v th vt v h +- & (1) where 0 h , and h is a constant. The differential equation in this problem is: ( ) 11 ( ) dvt v t ut d t R C RC += (2) We can replace the derivative of v with v th vt h . ( ) ( ) v v t h R C RC (3) And isolating the v + on the left-hand side. ( ) ( ) hh v v t v t R C RC + = -+ (4) We will use equation (4) to program in MATLAB. The MATLAB code is shown in part (c). If using the step h=0.001, it is too large to get the correct plots, because here C has a very small value which is in the order of micro. If choosing the step h=RC=1us, equation (4) will be simplified to: ( ) ( ) ( ) v v t v t u t + =-+= , which means now v(t+h) does not depend on the v(t) any more. Therefore, we should choose the step h<<RC in order to get the correct and accurate plot. (b) Using analytic method, Complementary solution: 1 1 t RC c v t Ce - = . Particular solution: ( ) p v t = .
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This note was uploaded on 03/30/2009 for the course ECE 220 taught by Professor Nilson during the Spring '08 term at N.C. State.

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lab7solutions - ECE220 Lab7 Solution Created by Rong Guo...

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