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HW8Soln

HW8Soln - E i s = R 1 Ls I 1-LsI 2 E o s = 1 Cs I 2 3 0 = R...

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ME 375 Homework 8 : Solution March 17, 2009 Problem 1 Obtain the transferfunction E o (s)/E i (s) of the circuit shown Figure 1: Prob B6-8 We convert the circuit from the time-domain to the s-domain. We get the following system. Figure 2: Prob B6-8 - s-domain 1

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We obtain the following equations: E i ( s ) = ( Ls + ( R 1 + R 2 ) 1 Cs R 1 + R 2 + 1 Cs ) I 1 ( s ) E o ( s ) = R 2 I 2 ( s ) I 2 ( s ) = 1 Cs R 1 + R 2 + 1 Cs I 1 ( s ) The transfer function is : E o ( s ) E i ( s ) = R 2 R 1 (1 + LCs 2 ) + R 2 (1 + LCs 2 ) + Ls 2
Problem 2 Obtain the transferfunction E o (s)/E i (s) of the circuit shown Figure 3: Prob B6-10 We convert the circuit from the time-domain to the s-domain. We get the following system. Figure 4: Prob B6-10 - s-domain We obtain the following equations:

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Unformatted text preview: E i ( s ) = ( R 1 + Ls ) I 1-LsI 2 E o ( s ) = 1 Cs I 2 3 0 = R 2 I 2 + 1 Cs I 2 + LsI 2-LsI 1 The transfer function is : I 2 = Ls Ls + 1 Cs + R 2 I 1 E o ( s ) E i ( s ) = 1 Cs R 1 Ls ( Ls + 1 Cs + R 2 ) + R 2 1 Cs 4 Problem 3 Obtain the transferfunction E o (s)/E i (s) of the circuit shown Figure 5: Prob B6-12 The equation for the impedances: Z 1 = Ls = Lωj Z 2 = 1 Cs R 1 Cs + R = R 1 + CRωj The transfer function is : E o ( s ) E i ( s ) = Z 2 Z 1 + Z 2 = R 1+ CRs Ls + R 1+ CRs = R Ls + R + CLRs 2 5...
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HW8Soln - E i s = R 1 Ls I 1-LsI 2 E o s = 1 Cs I 2 3 0 = R...

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