10Fall_hw07soln - ECE210 Fall 2010 Homework 07 Solutions 1...

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Unformatted text preview: ECE210 - Fall 2010 - Homework 07 Solutions 1. Use the circuit from the Textbook problem 4.11 with the following modifications; replace the input voltage source with a general voltage source v in ( t ) , replace the 2 F capacitor with a 10 μ F capacitor, and the 1 H inductor with a 1 mH inductor. (a) Get the frequency response of the system H ( ω ) = V ( ω ) V in ( ω ) . (b) Plot the magnitude frequency response | H ( ω ) | , as a dB plot from 10 1 to 10 7 rad sec . (Check p. 175 for explanations on dB plots) Solution : (a) H ( ω ) =- 1 k Z C 1+ Z L =- 1 / ( jωC ) 1+1 / ( jωC ) 1+ jωL =- 1 (1+ jωL )(1+ jωC ) =- 1 ( 1+ jω 10 3 )( 1+ jω 10 5 ) (b) There will be a “flat” amplitude response for ω 10 3 rad sec . In the range 10 3 rad sec ω 10 5 rad sec there will be a -20 dB per decade slope and for ω 10 5 rad sec the slope will be- 40 dB per decade. Figure 1: Magnitude Frequency Response | H ( ω ) | . 2. Textbook problem 5.5 1 3. Starting from the circuit of Ex 5.1 (p. 182) analyze the circuit using phasors. Assume that v ( t ) and i ( t ) may be written as the real part of a complex constant times e jωt , and express the current and the voltage across the inductor and the capacitor. Explain exactly the meaning of this solution in a short paragraph, that is clearly written. One or two sentences is required. Use clear English. (a) Describe the current phasor relative to the input voltage phasor (b) Discuss the phasor describing the voltage across the inductor re the input phasor. (c) Discuss the phasor describing the voltage across the capacitor re the input phasor. (d) What is the meaning of this solution given that C has an initial charge? (Hint: The solution gives the steady-state response of v c ( t ) for all t ∈ (-∞ , ∞ ) . What would happen if at some point in time t o the capacitor C is forced to have an unknown charge v c ( t o ) = v o .) (e) Determine the power absorbed in the capacitor for the circuit of Ex 5.1 (p. 182) . Solution: Grader Note: For the discussion of parts (a)-(c), full credit should be given if a clear discussion of any aspect of the phasor is provided. A simple aspect to discuss is the magnitude response, particularly at extreme points, which allows us to determine what type of filter the circuit is as seen by each measurement, however, any relevant aspect, such as phase or power, could be discussed as well.any relevant aspect, such as phase or power, could be discussed as well....
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10Fall_hw07soln - ECE210 Fall 2010 Homework 07 Solutions 1...

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