first-order - LDN / feb. 06 page 1/3 First-order transients...

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LDN / feb. 06 page 1/3 First-order transients First-order circuits Thévenin/Norton equivalents Circuit equations Circuit of resistances and sources C R C v Vt KCL (single node): 0 = + dt dv C R Vt v RC Vt RC v dt dv = + Circuit of resistances and sources L LR i In KVL (right mesh): 0 ) ( = + In i R dt di L In L R i L R dt di = + (circuits shown after a sudden change at t = 0) Generic form: τ Xs x dt dx = + R L or RC = = (ref.: Hambley, Ch. 4)
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LDN / feb. 06 page 2/3 (1) Inhomogeneous equation: τ Xs x dt dx = + (t > 0) Xs = forcing function . Xs = constant => particular solution: Xs t x = ) ( (2) Homogeneous equation (no forcing function): 0 = + x dt dx Complementary solutions (“eigen functions”): / ) ( t e K t x = (1+2) Solution to fit initial condition x(0+) = Xo: / ) ( ) ( t e Xs Xo Xs t x + = Final value is x( ) = Xs.
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This note was uploaded on 05/14/2008 for the course HIST 101 taught by Professor Wormer during the Spring '08 term at Academy of Art University.

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first-order - LDN / feb. 06 page 1/3 First-order transients...

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