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

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