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

2. Natural Response of Series RLC (1/5) KVL for t  0: but

3. Natural Response of Series RLC (2/5) KVL for t  0: Differentiate:

4. Natural Response of Series RLC (3/5) From experience with 1st order problems: Substitute into last KVL equation: Divide out then

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

6. Natural Response of Series RLC (5/5) Then • Three types of response: • real and unequal (both negative) • real and equal (negative) • complex conjugate pair

7. Overdamped Series RLC (1/6)

8. Overdamped Series RLC (2/6)

9. Overdamped Series RLC (3/6) Now use initial conditions to find k1 and k2. then

10. Overdamped Series RLC (4/6)

11. Overdamped Series RLC (5/6)

12. Overdamped Series RLC (6/6)

13. Critically Damped Series RLC (1/6)

14. Critically Damped Series RLC (2/6)

15. Critically Damped Series RLC (3/6) Solve for g1 & g2 using initial conditions: then &

16. Critically Damped Series RLC (4/6)

17. Critically Damped Series RLC (5/6)

18. Critically Damped Series RLC (6/6)

19. Underdamped Series RLC (1/7)

20. Underdamped Series RLC (2/7) but and

21. Underdamped Series RLC (3/7)

22. Underdamped Series RLC (4/7) Solve for a and b with initial conditions:

23. Underdamped Series RLC (5/7)

24. Underdamped Series RLC (6/7)

25. Underdamped Series RLC (7/7)