ECE201_Lecture17

ECE201_Lecture17 - ECE201 Linear Circuit Analysis I Lecture...

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1 ECE201 Linear Circuit Analysis I Lecture 17 Topic: Inductor/Capacitor Combinations (Duality) 1. Inductor Combinations (1) Principles: #1. Inductors in series add to form L eq . L eq = L 1 + L 2 + … L n #2. For n inductors in parallel eq 1 2 n 1 11 1 L LL L = + ++ (Reciprocal of sum of reciprocals law.) Derivation of Principle #1 :
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2 Derivation of Principle #2 eq in in in eq in L (t) v dt (t) di dt (t) di L (t) v = = 1 1 in in 1 1 2 2 in in 2 2 33 in in 3 3 di (t) di v v (t) L dt dt L di (t) di v L dt dt L di (t) di v L dt dt L = ⇒= = = in 1 2 3 i i i i (kCL) =++ 3 in 1 2 in in in in eq 1 2 3 di (t) di (t) di (t) di (t) dt dt dt dt v vvv L LLL eq 1 2 3 1 111 L LL L Remark: Inductor combinations follow the same formula as resistors.
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3 (2) Voltage division formula in 11 in in eq 1 in eq 1 2 3 di vL dt di dt L v L LL L = = = = ++ General: kk n in i i1 v L = = (n: total # of L’s) (3) Current Division Formula General: n in i 1 iL i 1 L = =    (n: total # of parallel inductors) Derivation: t 1 in 1 t in in eq 1 i (t) v ( )d L 1 v ( )d L −∞ −∞ = = = = = 3 1 1 1 1 ) 1 ( 1 1 1 ) ( ) ( i i eq in L L L L t i t i
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4 2. Capacitor Combinations (1) Principles: #3. For n capacitors in series eq 1 2 n 1 11 1 C CC C = + ++ #4. Capacitors in parallel add
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ECE201_Lecture17 - ECE201 Linear Circuit Analysis I Lecture...

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