ECE201_Lecture19

# ECE201_Lecture19 - 1 EE201 Linear Circuit Analysis I...

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Unformatted text preview: 1 EE201 Linear Circuit Analysis I Lecture 19 Topic: First-order circuits: Step response Review (1) general dx ( t ) dt = Ξ» x ( t ) + f ( t ) x ( t o ) = x o x ( t ) = e Ξ» ( t β t o ) x o + t o t β« f ( Ο ) e Ξ» ( t β Ο ) d Ο (2) zero-input/source-free x ( t ) = e Ξ» ( t β t o ) x i L ( t ) = e β R L ( t β t o ) i L ( t o ) v c ( t ) = e β t β t o RC v c ( t o ) 1. RL circuits with constant input (1) Circuit Equation KVL & Ohmβs Law: v L ( t ) = V s β Ri L ( t ) Inductor: v L ( t ) = L di L ( t ) dt L di L ( t ) dt = V s β Ri L ( t ) di L ( t ) dt = β R L i L ( t ) + V s L Initial condition: i L ( t o ) +- V s R L β i L (t) + v L (t) β 2 (2) Response i L (t) for t β₯ t o . i L ( t ) = e β R L ( t β t o ) i L ( t o ) + t o t β« V s L β e β R L ( t β Ο ) d Ο = e β R L ( t β t o ) i L ( t o ) + V s L e β R L t β L R e R L Ο t t o = e β R L ( t β t o ) i L ( t o ) + V s R 1 β e β R L ( t β...
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ECE201_Lecture19 - 1 EE201 Linear Circuit Analysis I...

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