Wk_13_Lecture_1

# Wk_13_Lecture_1 - Second-order Circuit Characterized by a...

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1 Second-order Circuit • Characterized by a second-order differential equation RLC, R C C , R L L Two way of excitations • Source-free –Free of independent sources, may have dependent source 1 BME 311 Network Theory John X.J. Zhang, UT Austin sources • Independent sources (dc, sinusoidal, exponential) Second-order Circuit Four combinations: – The source-free RLC circuit (series, parallel) – Step response of RLC circuit (series, parallel) 2 BME 311 Network Theory John X.J. Zhang, UT Austin

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2 The Source-free Series RLC Circuit The circuit is being excited by the energy initially stored in the capacitor ( V 0 ) and inductor ( I 0 ). Find current i . 3 BME 311 Network Theory John X.J. Zhang, UT Austin The Source-free Series RLC Circuit 0 2 2 LC i dt di L R dt i d Two initial conditions: (1) ? (2) ? Assume i=Ae st Characteristic equation 4 BME 311 Network Theory John X.J. Zhang, UT Austin
3 The Source-free Series RLC Circuit 0 2 2 LC i dt di L R dt i d Two initial conditions: (1) ? 0 1 2 LC s L R s (2) ? Assume i=Ae st Characteristic equation 5 BME 311 Network Theory John X.J. Zhang, UT Austin The Source-free Series RLC Circuit 0 2 2 LC i dt di L R dt i d Two initial conditions: (1) ? (2) ? 0 1 2 LC s L R s LC L R L R s LC L R L R s 1 ) 2 ( 2 1 ) 2 ( 2 2 1 2 1 Assume

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## This note was uploaded on 05/19/2011 for the course BME 311 taught by Professor Zhang during the Spring '08 term at University of Texas.

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Wk_13_Lecture_1 - Second-order Circuit Characterized by a...

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