C23-act - ELECTRIC CIRCUITS ECSE-2010 Class 23 Activity...

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1 ELECTRIC CIRCUITS ECSE-2010 Class 23 Activity 23-1 ± Forming a complete solution to s- Domain Circuit Analysis: ² Activity 23-1 ACTIVITY 23-1 v(t) R 1 H 1 F 400 L .1v L v +− i in I(s) Find H (s) V(s) = C v + C V( s ) Find H(s) V(s) = C Find Differential Equation Relating v (t) to v(t) Draw s-domain diagram ACTIVITY 23-1a V(s) R s 400 s L .1V L V + s-domain I(s) C V + Assume No Initial Stored Energy when finding H(s) Simple s-domain models for L and C ACTIVITY 23-1a V(s) R s 400 s L .1V L s-domain I(s) C V + Constraint Equation: L s ) s I ( s ) = in I(s) Let's Use Mesh Equations to find H (s) V(s) = ACTIVITY 23-1b V(s) R s 400 s L .1V L + s-domain I(s) C V + Mesh Equation: () ( ) L 400 I. 1 V sRI V s −+ + = I(s) L .1V
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2 ACTIVITY 23-1b () ( ) L 400 I. 1 V sRI V s −+ + = L V( s ) s I ( s ) = ( ) 400 1 s I sRI V s += 400 Is R 4 0 V s ⎛⎞ ++ − = ⎜⎟ ⎝⎠ 2 I s (R 40)s 400 sV +− + = in 2 I(s) s H( s ) V(s) s (R 40)s 400 == +− + ACTIVITY 23-1d V(s) R s 400 s L .1V L V + s-domain I(s) C V + C Node Equation at V : C L V I(s) .1V 400 s =+
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This note was uploaded on 10/21/2010 for the course ECSE 2010 taught by Professor Millard during the Spring '08 term at Rensselaer Polytechnic Institute.

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C23-act - ELECTRIC CIRCUITS ECSE-2010 Class 23 Activity...

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