3-Lesson_Notes_Lecture11_ee205 - Lecture 11 This lecture...

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Lecture 11 This lecture covers the following topics 1) Introduction to the non zero-input circuit. 2) Derivation of the state matrix equation for circuits with nonzero inputs. 3) State equation analysis for nonzero input circuits After finishing this lecture, you should be able to 1) Understand the basics of the non zero-input circuit. 2) Derive state matrix equation for nonzero circuits 3) Perform the State equation analysis for nonzero input circuits Circuits with Non zero Inputs R L i L v L v R + + _ _ v C + _ C v s F i g u r e 1 3 - 1 Consider the series RLC circuit shown in figure 13-1. Consider the inductor current i L and capacitor voltage v c as the state variables. Since for the inductor voltage
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L L Ldi v dt = ( 1 3 - 1 ) Then by KVL, L s R C di Lv v v dt =− − + (13-2) L cs L di LR i v v dt =− − + (13-3) From which, we will find our state equation as 11 L L di R ivv LLL dt + (13-4) Also 1 c L dv i C dt = (13-4) We have already seen when v s = 0, we can write the the state equation in the form () dX t AXt dt = (13-5) however, when v s
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This note was uploaded on 01/16/2010 for the course EE ee205 taught by Professor Profsyed during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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3-Lesson_Notes_Lecture11_ee205 - Lecture 11 This lecture...

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