3-Lesson_Notes_Lecture6_ee205 - 1 Electric Circuits II...

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1 1 Electric Circuits II Natural Response of a Parallel RLC Circuit Lecture #4
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2 2 The material to be covered in this lecture is as follows : o Introduction to the natural response of a parallel RLC circuit o The general solutions of the second order differential equation o The form of the natural Response of A Parallel RLC circuit After finishing this lecture you should be able to : ¾ Understand the natural response of a parallel RLC circuit ¾ Solve circuits with second order differential equation ¾ Know The forms of the natural Response of A Parallel RLC circuit
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3 3 Introduction to the natural response of a parallel RLC circuit Parallel RLC Circuit I 0 , initial current i C +i L +i R =0 0 0 1 0 t dv v Cv d t I LR dt ⎛⎞ ⎜⎟ ⎝⎠ ++ + = 8.1 Derive both sides. 2 2 1 0 dv v d v C dt dt = 8.2 Arrange equation 8.2 by dividing by C
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4 4 2 2 1 0 dv v d v LC RC dt dt ++ = 8.3 Equation 8.3 is an ordinary second-order differential equation with constant coefficients The general solutions of the second order differential equation: If we assume that the voltage is of the form st vA e = 8.4, where A and s are constants if (8.4) is a solution of (8.3), then 2 0 st st st Ase Ae As e RC LC = 8.4 2 1 0 st s Ae s RC LC ⎡⎤ ⎢⎥ ⎣⎦ = 8.5 if 0 A and 0 st e then
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5 5 2 1 0 s s RC LC ⎡⎤ ⎢⎥ ⎣⎦ ++ = 8.6 The roots of the equation 8.6 are 2 1 11 1 22 S RC RC LC ⎛⎞ ⎜⎟ ⎝⎠ =− + 2 2 1 S RC RC LC Parameter Terminology Value I natural response S 1 ,S 2 α 0 ω Characteristics roots Neper frequency
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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_Lecture6_ee205 - 1 Electric Circuits II...

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