Lecture 12 - Natural Response of Parallel RLC Circuits

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Presentation transcript:

Lecture 12 - Natural Response of Parallel RLC Circuits E E 2315 Lecture 12 - Natural Response of Parallel RLC Circuits

Natural Response of Parallel RLC Circuit (1/5) KCL for t  0: but then

Natural Response of Parallel RLC Circuit (2/5) Differentiate KCL: From experience with 1st order problems:

Natural Response of Parallel RLC Circuit (3/5) Substitute into differentiated KCL equation: Divide out

Natural Response of Parallel RLC Circuit (4/5) Solve for a: Let and

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

Overdamped Parallel RLC (1/5)

Overdamped Parallel RLC (2/5) then

Overdamped Parallel RLC (3/5)

Overdamped Parallel RLC (4/5)

Overdamped Parallel RLC (5/5)

Critically Damped Parallel RLC (1/4)

Critically Damped Parallel RLC (2/4) Use initial conditions to find g1 and g2.

Critically Damped Parallel RLC (3/4)

Critically Damped Parallel RLC (4/4)

Underdamped Parallel RLC (1/6)

Underdamped Parallel RLC (2/6)

Underdamped Parallel RLC (3/6) Using initial conditions: and then

Underdamped Parallel RLC (4/6)

Underdamped Parallel RLC (5/6)

Underdamped Parallel RLC (6/6)