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L13- First Order 1 - Firstordercircuits...

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3/18/12 1 First order circuits Circuits contains on dynamic element ( capacitor or inductor) Examples: v s ( t ) R L i s ( t ) R L R C v s ( t ) R C i s ( t ) RL circuit RL circuit RC circuit RC circuit i s ( t ) R L i L ( t ) v L ( t ) i R ( t ) i s = i L + i R KCL: i s = i L + v R i s = i L + 1 R L di L dt ! " # $ % & di L dt + R L i L = R L i s The circuit diferen±al equa±on in terms o² i L a) RL circuit Analysis of Frst order circuits
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3/18/12 2 Check Dimensions! di L dt + R L i L = R L i s R = Volt current L = flux current = volt ! time current L R = volt ! time current ! current volt = time Defne: L R = ! Circuit ±me constant! Note : L R = = s v s = v c + v R KVL: v s = v c + i c R v s = v c + R C dv c dt ! " # $ % & dv c dt + 1 RC v c = 1 RC v s The circuit diFeren±al equa±on in terms o² v c i c ( t ) v c ( t ) i R ( t ) R C v s ( t ) v R ( t ) i c = i R b) RC Circuit
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3/18/12 3 Check Dimensions! R = Volt current C = ch arg e volt = current ! time volt Defne: RC = ! Circuit ±me constant! Note : RC = = s dv c dt + 1 RC v c = 1 RC v s RC = volt current ! current ! time volt = time t = o V s R L t = o V s R C Step Response of Frst order circuits Sudden application or variation of a DC sources.
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