10Fall_Exam2soln - 1. Problem 1 (25 points) These problems...

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Unformatted text preview: 1. Problem 1 (25 points) These problems are intended to be quick and easy: (a) For the following circuit. v in ( t ) v out ( t ) . 1 F 2 (3 pt) i. Find the frequency response H ( ) . Sol: Phasor voltage divider: H ( ) = 1 jC 1 jC + R = 1 1+ jRC = 1 1+ jRC = 1 1+ j . 2 (1 pt) ii. Is H ( ) the frequency response of a high pass, low pass or a band pass filter? Sol: Lowpass ( H (0) = 1 , H ( ) = 0 , monotonically decreasing) (3 pt) iii. If v in ( t ) = 2 + cos(5 t + 4 ) , then v out ( t ) =? Sol: v in ( t ) composed of two co-sinusoidal components with frequencies 0 and 5: o V in phasor H ( o ) V out phasor = V in H ( o ) v out ( t, o ) 2 e j 1 2 2 5 1 e j 4 1 1+ j = e- j 4 2 1 2 e j ( 4- 4 ) = 1 2 1 2 cos(5 t + 0) v out ( t ) = 2 + 1 2 cos(5 t ) (2 pt) (b) What is the resonance frequency of the following circuit....
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This note was uploaded on 03/05/2011 for the course ECE 210 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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10Fall_Exam2soln - 1. Problem 1 (25 points) These problems...

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