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Unformatted text preview: 1 1 Summary of Lecture #8 9/10/2010 Cramers rule and matrix inversion Nodal analysis Loop or mesh analysis Thevenin and Norton equivalents Superposition Examples 7 Ex.7. Find H(s) = V out (s)/V in (s) by nodal analysis . KCL to node V a in out a b a out a in a V V ) s 2 1 ( V ) s 2 2 ( 1 V V ) s 2 /( 1 V V 1 V V = + + = + + + 2 /s 1/ 2s Ignore initial conditions, if any. Also note V b = V out . 8 KCL to node V b Solve for V out , and obtain H(s) 1 s 2 s 1 ) s ( V ) s ( V ) s ( H 2 in out + + = = V )) 2 / s ( 1 ( V s / 2 V 1 V V b a b a b = + + = + Recall V b = V out out a V )) 2 / s ( 1 ( V + = 9 Ex. 8 Given i L (0 ) = 1 A , v c (0 ) = 1 V and i in (t) = (t) A , find v c (t) and v L (t) for t > 0 . s 1 s V 1 V V : V 1 1 1 V V s / 1 V 1 V : V L C L L L C C C C = + + = + + node to KCL node to KCL 1/s 1s sdomain circuit Account for initial conditions 10  = + + 1 2 V V s 1 s 1 s 2 L C In matrix form Solve for V C (s) and V L (s) Inverse Laplace transform 2 2 2 2 2 L 2 2 2 2 2 C 1 ) 1 s ( 1 3 1 ) 1 s ( 1 s 2 s 2 s 2 s ) s ( V 1 ) 1 s ( 1 1 ) 1 s ( 1 s 2 2 s 2 s 1 s 2 ) s ( V + + + + + = + + = + + + + + = + + + = V ) t ( u )] t sin( 3 ) t [cos( e ) t ( v V ) t ( u )] t sin( ) t cos( 2 [ e ) t ( v t L t C = = 11 Ex. 9. Find H(s)=V out (s)/V in (s)....
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 Spring '06

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