ps10 - EE 350 PROBLEM SET 10 DUE: 10 December 2007 Reading...

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EE 350 PROBLEM SET 10 DUE: 10 December 2007 Reading assignment: Lathi Chapter 6, Sections 6.4 and 6.5 Laboratory sections meet the week of December 3. Problem 50: (20 points) Consider the circuit shown in Figure 1. - - - 1 6 F + f(t) + x(t) + y(t) 1 F 2 10Ω 15Ω Figure 1: Second-order RC network. 1. (2 points) In order to calculate the transfer function of the circuit, assume that all initial conditions are zero and sketch the circuit in the frequency domain. 2. (6 points) Write the node equations (in the frequency domain) associated with the node voltages X ( s ) and Y ( s ). 3. (3 points) Using your results in part 2, ±nd the transfer function H ( s ) relating the output y ( t ) to the input f ( t ). 4. (6 points) Find the zero-state response y ( t ) if the input voltage f ( t )= e - t u ( t ). 5. (3 points) From the transfer function, write the differential equation relating y ( t )to f ( t ). Problem 51: (20 points) Consider the circuit shown in Figure P6.4-5 on page 465 of the text. 1. (7 points) Obtain an ordinary differential equation that governs the behavior of y 1 ( t ) for t 0. 2. (3 points) Take the Laplace transform of the ordinary differential equation obtained in part 1, and ±nd an expression for Y 1 ( s ). 3. (4 points) Determine the value of the terms y 1 (0 - ) and ˙ y 1 (0 - ) that appear in the expression obtained in part 2. Note that it is not necessary to determine the value of either y 1 (0 + )or ˙ y 1 (0 + ), as was the case when solving a differential equation using the classical solution method described in section 2.5 of the text.
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This note was uploaded on 07/23/2008 for the course EE 350 taught by Professor Schiano,jeffreyldas,arnab during the Fall '07 term at Pennsylvania State University, University Park.

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ps10 - EE 350 PROBLEM SET 10 DUE: 10 December 2007 Reading...

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