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

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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 Ω (3 pt) i. Find the frequency response H ( ω ) . Sol: Phasor voltage divider: H ( ω ) = 1 jωC 1 jωC + R = 1 1+ jωRC = 1 1+ jωRC = 1 1+ jω · . 2 (1 pt) ii. Is H ( ω ) the frequency response of a high pass, low pass or a band pass filter? Sol: Lowpass ( H (0) = 1 , H ( ω → ∞ ) = 0 , monotonically decreasing) (3 pt) iii. If v in ( t ) = 2 + cos(5 t + π 4 ) , then v out ( t ) =? Sol: v in ( t ) composed of two co-sinusoidal components with frequencies 0 and 5: ω o V in phasor H ( ω o ) V out phasor = V in H ( ω o ) v out ( t,ω o ) 2 e j 1 2 2 5 1 e j π 4 1 1+ j = e- j π 4 √ 2 1 √ 2 e j ( π 4- π 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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10Fall_Exam2soln - 1 Problem 1(25 points These problems are...

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