Exam 1 Spring 2007 - ECE 313 Examination #1 February 23,...

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ECE 313 Examination #1 February 23, 2007
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1. Consider the circuit shown below. v 1 ( t ) v 2 ( t ) i ( t ) 1 Ω 1 F + + - - (a) [10 pts] Find the transfer function from v 1 ( t ) to v 2 ( t ) . (b) [20 pts] Find the step response and impulse response. Find also v 2 ( t ) when v 1 ( t ) = 3 1( t ) 2 δ ( t ) and v 2 (0) = 0 . (a) KVL ⇒ − V 1 ( s ) + 1 I ( s ) + (1 /s ) I ( s ) = 0 I ( s ) = V 1 ( s ) / (1 + 1 /s ) . V 2 ( s ) = (1 /s ) I ( s ) G ( s ) = V 2 ( s ) /V 1 ( s ) = 1 / ( s + 1) . (b) Step response: V 1 ( s ) = 1 /s V 2 ( s ) = 1 s ( s + 1) = 1 s + 1 s + 1 v 2 ( t ) = (1 ǫ t ) 1( t ) . Impulse response: V 1 ( s ) = 1 V 2 ( s ) = 1 s + 1 v 2 ( t ) = ǫ t 1( t ) . Response due to given input and initial condition: v 2 ( t ) = 3(1 ǫ t ) 1( t ) 2 ǫ t 1( t ) = (3 5 ǫ t ) 1( t ) . 1
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2. Consider the system shown below. r
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Exam 1 Spring 2007 - ECE 313 Examination #1 February 23,...

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