ASU EEE 302 - Lecture Notes (12 pages)

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Lecture Notes



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Lecture Notes

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Lecture Notes


Pages:
12
School:
Arizona State University
Course:
Eee 302 - Electrical Network II
Electrical Network II Documents

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EEE 302 Electrical Networks II Dr Keith E Holbert Summer 2001 Lecture 16 1 Laplace Circuit Solutions In this chapter we will use previously established techniques e g KCL KVL nodal and loop analyses superposition source transformation Thevenin in the Laplace domain to analyze circuits The primary use of Laplace transforms here is the transient analysis of circuits Lecture 16 2 LC Behavior Recall some facts on the behavior of LC elements Inductors L The current in an inductor cannot change abruptly in zero time an inductor makes itself felt in a circuit only when there is a changing current An inductor looks like a short circuit to d c Capacitors C The voltage across a capacitor cannot change discontinuously a capacitor makes itself felt only when there exists a changing potential voltage difference A capacitor looks like an open circuit to d c Lecture 16 3 Laplace Circuit Element Models Here we develop s domain models of circuit elements Voltage and current sources basically remain unchanged except that we need to remember that a dc source is really a constant which is transformed to a 1 s function in the Laplace domain Note on subsequent slides how without initial conditions we could have used the substitution s j Lecture 16 4 Resistor We start with a simple and trivial case that of the resistor R Begin with the time domain relation for the element v t R i t Now Laplace transform the above expression V s R I s Hence a resistor R in the time domain is simply that same resistor R in the s domain this is very similar to how we derived an impedance relation for R also Lecture 16 5 Capacitor Begin with the time domain relation for the element d v t i t C dt Now Laplace transform the above expression I s s C V s C v 0 Interpretation a charged capacitor a capacitor with non zero initial conditions at t 0 is equivalent to an uncharged capacitor at t 0 in parallel with an impulsive current source with strength C v 0 Lecture 16 6 Capacitor cont d Rearranging the above



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