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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:.

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E E 2315

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E e 2315

E E 2315

Lecture 12 - Natural Response of Parallel RLC Circuits


Natural response of parallel rlc circuit 1 5

Natural Response of Parallel RLC Circuit (1/5)

KCL for t  0:

but

then


Natural response of parallel rlc circuit 2 5

Natural Response of Parallel RLC Circuit (2/5)

Differentiate KCL:

From experience with 1st order problems:


Natural response of parallel rlc circuit 3 5

Natural Response of Parallel RLC Circuit (3/5)

Substitute

into differentiated KCL

equation:

Divide out


Natural response of parallel rlc circuit 4 5

Natural Response of Parallel RLC Circuit (4/5)

Solve for a:

and

Let


Natural response of parallel rlc circuit 5 5

Natural Response of Parallel RLC Circuit (5/5)

  • Three types of response:

    • real and unequal (both negative)

    • real and equal (negative)

    • complex conjugate pair

Then


Overdamped parallel rlc 1 5

Overdamped Parallel RLC (1/5)


Overdamped parallel rlc 2 5

Overdamped Parallel RLC (2/5)

then


Overdamped parallel rlc 3 5

Overdamped Parallel RLC (3/5)


Overdamped parallel rlc 4 5

Overdamped Parallel RLC (4/5)


Overdamped parallel rlc 5 5

Overdamped Parallel RLC (5/5)


Critically damped parallel rlc 1 4

Critically Damped Parallel RLC (1/4)


Critically damped parallel rlc 2 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 (3/4)


Critically damped parallel rlc 4 4

Critically Damped Parallel RLC (4/4)


Underdamped parallel rlc 1 6

Underdamped Parallel RLC (1/6)


Underdamped parallel rlc 2 6

Underdamped Parallel RLC (2/6)


Underdamped parallel rlc 3 6

Underdamped Parallel RLC (3/6)

Using initial conditions:

and

then


Underdamped parallel rlc 4 6

Underdamped Parallel RLC (4/6)


Underdamped parallel rlc 5 6

Underdamped Parallel RLC (5/6)


Underdamped parallel rlc 6 6

Underdamped Parallel RLC (6/6)


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