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E E 2315 Lecture 11 Natural Responses of Series RLC Circuits
Natural Response of Series RLC (1/5) KVL for t 0: but
Natural Response of Series RLC (2/5) KVL for t 0: Differentiate:
From experience with 1st order problems: Substitute into last KVL equation: Divide outthen Natural Response of Series RLC (3/5)
Natural Response of Series RLC (4/5) Solve for a: Letand
Then Three types of response: real and unequal (both negative) real and equal (negative) complex conjugate pair Natural Response of Series RLC (5/5)
Overdamped Series RLC (1/6)
Overdamped Series RLC (2/6)
Now use initial conditions to find k 1 and k 2. then Overdamped Series RLC (3/6)
Overdamped Series RLC (4/6)
Overdamped Series RLC (5/6)
Overdamped Series RLC (6/6)
Critically Damped Series RLC (1/6)
Critically Damped Series RLC (2/6)
Critically Damped Series RLC (3/6) Solve for g 1 & g 2 using initial conditions: then &
Critically Damped Series RLC (4/6)
Critically Damped Series RLC (5/6)
Critically Damped Series RLC (6/6)
Underdamped Series RLC (1/7)
but and Underdamped Series RLC (2/7)
Underdamped Series RLC (3/7)
Solve for and with initial conditions: Underdamped Series RLC (4/7)
Underdamped Series RLC (5/7)
Underdamped Series RLC (6/7)
Underdamped Series RLC (7/7)
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