1. Lecture 12 - Natural Response of Parallel RLC Circuits
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:
Let
and

6. 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

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)