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Chapter 13: The Laplace Transform in Circuit Analysis

ECEN 2633 Page 1 of 12 Chapter 13: The Laplace Transform in Circuit Analysis Circuit Elements in the s-Domain Creating an s-domain equivalent Circuit requires developing the time domain Circuit and transforming it to the s-domain Resistors: Inductors: (initial current ) Configuration #2: an impedance sL in parallel with an independent current source I0/s If the initial current is zero the s-domain Circuit for both representations simplifies to just the impedance sL. Capacitors: Configuration #2: an admittance sC in series with an independent voltage source V0/s Time-domain s-domain Where 0 Time-domain: s-domain: Configuration #1: an impedance sL in series with an independent voltage source LI0 0 Time-domain s-domain Configuration #1: an admitt

solution satisfied the given initial conditions and final behavior. ... Transfer Function: the s-domain ratio of the Laplace transform of the output (response) to the Laplace transform of the input (source) ℒ ℒ Example. Finding the transfer function of an RLC circuit If the voltage is the desired output: ...

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