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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). 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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  1. E E 2315 Lecture 12 - Natural Response of Parallel RLC Circuits

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

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

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

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

  6. 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

  7. Overdamped Parallel RLC (1/5)

  8. Overdamped Parallel RLC (2/5) then

  9. Overdamped Parallel RLC (3/5)

  10. Overdamped Parallel RLC (4/5)

  11. Overdamped Parallel RLC (5/5)

  12. Critically Damped Parallel RLC (1/4)

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

  14. Critically Damped Parallel RLC (3/4)

  15. Critically Damped Parallel RLC (4/4)

  16. Underdamped Parallel RLC (1/6)

  17. Underdamped Parallel RLC (2/6)

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

  19. Underdamped Parallel RLC (4/6)

  20. Underdamped Parallel RLC (5/6)

  21. Underdamped Parallel RLC (6/6)

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