215+Ch6NEW+Student - 6 RLC Circuits Second Order Circuits A...

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6. RLC Circuits
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Second Order Circuits A second order circuit is characterized by a second order differential equation Resistors and two energy storage elements Determine voltage/current as a function of time Initial/final values of voltage/current, and their derivatives are needed
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Initial Conditions
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Initial/Final Conditions v C, i L do not change instantaneously Get derivatives dv C/ dt and di L/ dt from i C , v L Capacitor open, Inductor short at dc Guidelines
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Series RLC Circuit : General Solution
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Series RLC Circuit : General Solution
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Ex6-2 solution
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Ex6-3 Solution
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Parallel RLC Circuit Overdamped ( α > ϖ 0) Critically Damped ( = 0) Underdamped ( < 0) Same form of diff. equation as series RLC LC I LC i dt di RC dt i d s 2 2 1 = + + s I dt dv C i R v = + + dt di L v = 2 0 2 2 , 1 - ± - = s RC 2 1 = LC 1 0 = ( 29 ( 29 t s t s e A e A i t i 2 1 2 1 + + = ( 29 ( 29 ( 29 2 1 t e t B B i t i - + + = ( 29 ( 29 ( 29 t D t D e i t i t d 2 d 1 sin cos + + = -
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Oscillators If R=0 in a series RLC circuit or ∞ in a parallel RLC circuit, the circuit becomes an oscillator
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Singularity Functions Unit Impulse Function For any function f ( t ):
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Definition
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This note was uploaded on 01/19/2012 for the course EECS 215 taught by Professor Phillips during the Fall '08 term at University of Michigan.

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215+Ch6NEW+Student - 6 RLC Circuits Second Order Circuits A...

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