SummaryFirstOrderCircuits(2pp)

SummaryFirstOrderCircuits(2pp) - CIRCUITS WITH ONE ENERGY...

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Unformatted text preview: CIRCUITS WITH ONE ENERGY STORING ELEMENT , ) ( ); ( ) ( ) ( 1 > = + = + t x x t f t x a t dt dx a For ANY circuit variable, x , the model is ) ( ; x x f x dt dx TH = + = + τ The normalized equation is If all INDEPENDENT sources are constant then the solution is 2 1 ; ) ( t t e K K t x t t ≥ + = − − τ ) ( = t The math ODE approach would be to use the general solution ∫ − − − + + = t TH t t d f e x e t x ) ( ) ( ) ( α α τ α τ Circuits approach tries to determine the required constants and avoids the use of the general formula We have presented two approaches to determine the constants. Both require the initial condition but differ in the way they determine the constants K1, K2, tau STEP IC1: ANALYZE THE CIRCUIT FOR t<0. IF ALLOWED USE STEADY STATE ASSUMPTION DETERMINE CURRENT THROUGH INDUCTORS AND VOLTAGES ACROSS CAPACITORS STEP IC2: ANALYZE THE CIRCUIT AT t=0+ INDUCTORS ARE CURRENT SOURCES CAPACITORS ARE VOLTAGE SOURCES TO DETERMINE INITIAL CONDITION ) ( + x known is...
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SummaryFirstOrderCircuits(2pp) - CIRCUITS WITH ONE ENERGY...

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