hw8sol - Purdue University, School of Electrical and...

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Unformatted text preview: Purdue University, School of Electrical and Computer Engineering Prof. DeCarlo ECE 202 L INEAR C IRCUIT A NALYSIS II (S P 10) Homework #8 Solution (2932) Problem 29 (a) H ( s ) = V out ( s ) V in ( s ) = 2 s + 6 s 2 + 4 s + 16 is excited by the input v in ( t ) = 2cos ( 2 t + 45 ) V. Then the output will be v out ( t ) = 2 H ( j 2 ) cos ( 2 t + 45 + ( H ( j 2 )) ) V H ( j 2 ) = 6 + 4 j 12 + 8 j = . 5 v out ( t ) = cos ( 2 t + 45 ) V (b) H ( s ) = ( s + 1 )( s 1 ) s ( s + 4 ) has output v out ( t ) = 3cos ( 3 t + 45 ) V. Then the input will be v in ( t ) = 3 H ( j 3 ) cos ( 3 t + 45 ( H ( j 3 )) ) V H ( j 3 ) = 9 1 9 + 12 j = ( 2 / 3 ) 53 . 1301 v in ( t ) = 4 . 5 cos ( 3 t 8 . 1301 ) V (c) R 1 = R 2 = R = 1 , L = . 2H, C = . 25F 1/ 8 Purdue University, School of Electrical and Computer Engineering Prof. DeCarlo V C ( s ) = R 1 R 1 Cs + 1 R 1 R 1 Cs + 1 + R 2 Ls R 2 + Ls V in ( s ) = R 2 + Ls R 2 LC s 2 + ( R 1 + R 2 R 1 R 2 ) 1 C s + 1 LC V in H ( s ) = 1 RC s + 1 LC s 2 + 2 RC s + 1 LC = 4 s + 20 s 2 + 8 s + 20 v in ( t ) = 20cos ( 4 t ) V v out ( t ) = 20 H ( j 4 ) cos ( 4 t + ( H ( j 4 )) ) V H ( j 4 ) = 20 + 16 j 4 + 32 j = . 7942 ( 44 . 2152 ) v out ( t ) = 15 . 8842 cos ( 4 t 44 . 2152 ) V (d)...
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hw8sol - Purdue University, School of Electrical and...

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