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# 196 Review Sheet for ECE 20100 with Professor Tan at Purdue

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 24 views.

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Date Created: 02/06/15
ECE201 Linear Circuit Analysis I Prof H Z Tan Topic First order Circuits zero input response 1 ISt order circuits 1 Circuits that consist of sources resistors and ONE capacitor 0r ONE inductor dz dv 2 L L amp 39 C VL dt 1 dt 3 KVL amp KCL amp Ohm s Law for R still work 4 Circuit equations are Islorder linear differential equations 2 A general solution to Isl order differential equations 1 A general circuit equation m dt xt ft Initial condition Xt0 X0 where Xt can be i or V 7 is a constant ft is a function of t The equation is valid for t 2 t0 eg diL t 25 50 39V 1Lt dt IL 159 SACT 109 L1H 1L0 1A x iL 1 721m 50 to 0 x0 1A 2 derivation of solution Step 1 multiply both sides by e39M 77 e 7M 7M 7 t ft dt 6 X e Step 2 integrate both sides over to t t left side I eMM M t dt X Ed t Note that 77 and xlttgtltMe dt e7 M dX t Aeihxa dt Then t left side e39MX39c tO eimxt e7M0 Xt0 t right side It G39Mf39clt 0 Step 3 multiple both sides by e2 left side xt el t xt0 t right side I eMtiTf39cd39c tO Step 4 solve for Xt left side right side t Xt eMti toXt0 I eMti If39rd39c to This is a solution to both the general 1st order differential eqn and the initial condition 3 Source freezero input RL circuits 1 circuit equation 2 circuit response 7507 iLte L l W vLr V iLrR L di t L zt iLtR M 5 iL t dt L initial condition iLt0 for t 2 t0 0 1L In 3 circuit time constant iL to r e liLao m 0368iL to 139 determines how fast iLt decays exponentially 4 Source freezero input RC circuits 1 circuit equation l39 t 1quot m0 V zrR l dv t R C F V00 Va RC7 dV tLVCI dt RC initial condition Vc t0 2 circuit response for t 2 t0 1 7 07 vCr e RC 0 we 3 circuit time constant A r Vct0 r RC sec e lvcag m 0368Vct0 139 determines how fast Vct decays exponentially 5 Example of zero input response 6 For more general source less circuits replace R with Rm Linear Resistive Circuit No sources Linear Resistive Circuit No sources I J WU l 7 Review of 3 Methods for Computing Rm when dependent sources are present 4vlt VW OA 1 Method 1 Rm vaciSC Find V0C and isc then calculate Rm Open AB for calculating V0c keep indep sources Short AB for calculating Isc keep indep sources note direction of Isc is A gt B To nd V001 How to label the VCCS To nd isc How to label the direction of isc 4v What value is the VCCS 4V A 15c 08 29 39 V00 8 Solve for Rm Rth 1OQ 1SC 08 2 Method 2 Add imaginary voltage source v5 1quot nd is then Rm 1s Howto label 51V theVCCS 1s o A 29 is a 4 B vsisx32xis34 321lfj vs10V 10V Rm l A IOQ Comments Method 1 does not always work Why Method 2 and 3 always work

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