E E 2315 Lecture 11 Natural Responses of Series RLC Circuits.

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Presentation transcript:

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)