HighOrderCircuitsSp03

# HighOrderCircuitsSp03 - MODELS FOR LINEAR CIRCUITS...

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MODELS FOR LINEAR CIRCUITS We discuss methods for writing equations for linear circuits containing any number of inductors and capacitors. STEP 1: SELECT ANALYSIS TECHNIQUE This selection is based on the interconnection (topology) of the circuit Basically count nodes and loops Candidate for loop analysis Candidate for node analysis + - Candidate for node analyis + - dt dv C i dt di L v C C L L = = , doubt. .. in when Loop analysis replaces voltages in terms of currents Node analysis replaces currents in terms of voltages

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STEP 2 WRITE EQUATIONS + ) ( t v S EXAMPLE: RLC Series Circuit R L C i LOOP ANALYSIS + R v + L v + C v 0 = + + + C L R S v v v v Replace voltages in terms of loop current(s) Law) s (Ohm' Ri v R = Law) e (Inductanc dt di L v L = Law) ce (capacitan = t C dx x i C v ) ( 1 equation) al differenti - (integro 0 ) ( 1 = + + + t S dx x i C dt di L Ri v dt dv i C dt di R dt i d L S = + + 1 2 2 EXAMPLE RLC Parallel Circuit ) ( t i S RL C v NODE ANALYSIS R i L i C i 0 = + + + C L R S i i i i Replace currents in terms of node voltage(s) law) s (Ohm' R v i R = Law) e (Inductanc = t L dx x v L i ) ( 1 Law) ce (Capacitan dt dv C i C = equation) al differenti - (integro 0 ) ( 1 = + + + dt dv C dx x v L R v i t S dt di L v dt di R dt v d C S = + + 1 2 2 STEP 3: ELIMINATE INTEGRALS BY DIFFERENTIATION AND ARRANGE TERMS
+ - L C 1 R 2 R S v + O v O v for equation al differenti the Find LOOP ANALYSIS 1 i 2 i 0 ) ( 1 ) ( 1 1 2 2 1 1 = + + + t S dx x i C i R i i R v 0 ) ( 1 2 1 2 = + i i R dt di L Eliminate integrals and arrange 0 ) ( ) ( 1 2 1 2 1 2 1 1 2 1 = + = + + i i R dt di L dt dv C i dt di R dt di R R S NODE ANALYSIS C v 1 v S v 0 : 2 1 = + R v v dt dv C C C C v @ =

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HighOrderCircuitsSp03 - MODELS FOR LINEAR CIRCUITS...

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