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Unformatted text preview: Homework 8 (ECE220 - Fall 2007) Due: Wednesday, November 7 by 2PM in the drop box outside 219 Phillips Hall. Reasoning and work must be shown to gain full/partial credit. WRITE YOUR NAME AND NET ID ON ALL PAGES HANDED IN! 1. (37 points) Consider the LTI system described by the RLC circuit shown in the below figure. x ( t ) is the input and y ( t ) is the output. (a) (5 points) Find the differential equation that relates the input to the output. Solution: V L ( t ) = L dI L ( t ) dt I C ( t ) = C dV C ( t ) dt V C ( t ) = y ( t ) V C ( t ) = x ( t )- RI R ( t )- L dI L ( t ) dt I R ( t ) = I L ( t ) = I C ( t ) V C ( t ) = x ( t )- RC dV C ( t ) dt- L d dt C dV C ( t ) dt y ( t ) = x ( t )- RC dy ( t ) dt- LC d 2 y ( t ) dt 2 LC d 2 y ( t ) dt 2 + RC dy ( t ) dt + y ( t ) = x ( t ) (b) (10 points) Determine the frequency response of the system. Let R = 1, C = 1 F , and L = 1 H . Solution: Y ( ) = H ( ) X ( ) Y ( ) X ( ) = H ( ) Y ( )( LC ( j ) 2 + RCj + 1) = X ( ) H ( ) = 1 LC ( j ) 2 + RCj +1 H ( ) = 1- 2 + j +1 (c) (5 points) Determine the output of the system in part a) if the input is x ( t ) = sin ( t )....
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This note was uploaded on 05/31/2008 for the course ECE 2200 taught by Professor Johnson during the Fall '05 term at Cornell University (Engineering School).
- Fall '05