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E E 2315 Lecture 11 Natural Responses of Series RLC Circuits

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Natural Response of Series RLC (1/5) KVL for t 0: but

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Natural Response of Series RLC (2/5) KVL for t 0: Differentiate:

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From experience with 1st order problems: Substitute into last KVL equation: Divide outthen Natural Response of Series RLC (3/5)

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Natural Response of Series RLC (4/5) Solve for a: Letand

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Then Three types of response: real and unequal (both negative) real and equal (negative) complex conjugate pair Natural Response of Series RLC (5/5)

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Overdamped Series RLC (1/6)

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Overdamped Series RLC (2/6)

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Now use initial conditions to find k 1 and k 2. then Overdamped Series RLC (3/6)

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Overdamped Series RLC (4/6)

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Overdamped Series RLC (5/6)

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Overdamped Series RLC (6/6)

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Critically Damped Series RLC (1/6)

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Critically Damped Series RLC (2/6)

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Critically Damped Series RLC (3/6) Solve for g 1 & g 2 using initial conditions: then &

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Critically Damped Series RLC (4/6)

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Critically Damped Series RLC (5/6)

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Critically Damped Series RLC (6/6)

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Underdamped Series RLC (1/7)

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but and Underdamped Series RLC (2/7)

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Underdamped Series RLC (3/7)

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Solve for and with initial conditions: Underdamped Series RLC (4/7)

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Underdamped Series RLC (5/7)

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Underdamped Series RLC (6/7)

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Underdamped Series RLC (7/7)

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