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Homework 11 Solution

# Homework 11 Solution - MEEN 260 Introduction to Engineering...

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MEEN 260 Introduction to Engineering Experimentation Homework 11: Passive and Active Filters Solutions Assigned: Thursday, 10 Apr. 2008 Due: Thursday, 17 Apr. 2008, 9:00 am Homework Problems: Problem 1) Passive Filter Circuits For the filter circuits shown: a) Derive the transfer function ( ) ( ) j ω V j ω V in out . b) Determine expressions for the magnitude and phase spectrum, and sketch them (by hand or using Excel, Matlab, etc.). c) Identify the filter type. d) Determine the frequency where the maximum magnitude occurs, in terms of R, L, and C. e) Given R L =2 k , R=1 k , C= 2 μ F and a 1 H inductor, determine the bandwidth of the filter where ( ) ( ) dB 3 c in c out j ω V j ω V (below the peak value) f) Determine V 0 (t) for V in (t) = 5cos(200 π t- π /4)+2sin(500 π t+ π /3)

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Solution: 1) For the filter circuit shown: a) 1/ C Z jC ω = Thus, the relationship between the input and output voltages are; V in (j ω ) = I(j ω )[Z R +Z C//RL ] and, ( ) ( ) [ ] // out RL C V j I j Z ω ω = Therefore, the relationship between the input and output voltages can be determined as follows: b) Determine expressions for the magnitude and phase spectrum, and sketch them (by hand or using Excel, Matlab, etc.). Magnitude response of the filter can be expressed as; And also the phase of the spectrum is determined by the angle of the complex transfer function; The plots have been provided for part (e) of the problem.
c) Identify the filter type. The filter type based on the spectrum of the frequency response is identified as a low pass filter.

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Homework 11 Solution - MEEN 260 Introduction to Engineering...

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