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Unformatted text preview: ECE 201 Lecture 26 OpAmp basics: dependent source models 2 nd Order Circuit with Input Given v C (0 ), i L (0 ) and v in (t) Write the equation for v C (t), t>0 By KCL: nonzero input Assume constant input General Form of Differential Equations and given with Problem is to solve the inhomogeneous differential equation: Nonzero forced input Its homogeneous version is: obtained by setting F=0 Relation between the solutions to the above two equations? Homogeneous and Inhomogeneous Equations Homogeneous equation has general solution (case 1) (case 2) (case 3) Claim: the general solution to the inhomogeneous equation is Inhomogeneous equation has one particular solution When a=1 When a=1 Initial Conditions The general solution to (case 2) (case 3) (case 1) compare with the given initial conditions. Solve K 1 and K 2 (A and B) from the two equations derive dx/dt To determine the constants K 1 and K 2 (or in case 3, A and B), Final Value The solution to (case 2) (case 1) If the two roots s 1...
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 Spring '08
 EUDEY
 Macroeconomics

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