ECE201_32_Jung

ECE201_32_Jung - Click to edit Master subtitle style ECE...

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Unformatted text preview: Click to edit Master subtitle style ECE 201 Lecture 32 Impedance and Admittance of 2-Terminal Devices Announcements • Last Lecture #31: – Phasors: Ohm’s Law, KVL & KCL • This Lecture #32: – Z & Y of 2-Terminal Devices Motivating Example Initial condition Input Output Homogeneous equation: Characteristic equation with Particular solution to the inhomogeneous eq: General solution: Guess: Differential equation becomes Motivating Example (cont.) General solution to is Constant K is chosen so that vC(0)=v0 Transient response goes to zero as time goes to ∞ Steady state response is a sinusoid with the same frequency as Vs After a sufficiently long period of time, the full response will have only the steady state response, no matter what v0 is Transient response Steady state response Decomposition of response: Second Order Example Initial condition Input Output Suppose the characteristic equation has two roots Transient response Steady state response ϖ d is intrinsic ϖ is forced Then solutions are Applying Complex Representation in SSS Analysis Complex forcing function Procedures to obtain the response for Vs=cos( ϖ t) 1. Replace Vs=cos( ϖ t) by the complex forcing function Vs=ej ϖ t; 2. Compute the (complex) response for the new forcing function; 3. Take the real part of the response, this will be the response for Vs=cos( ϖ t) equivalent real part of Why This Works?...
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This note was uploaded on 10/26/2010 for the course ECON 002 taught by Professor Eudey during the Spring '08 term at UPenn.

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ECE201_32_Jung - Click to edit Master subtitle style ECE...

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