1. Lecture 10 - Step Response of Series and Parallel RLC Circuits
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Lecture 10 - Step Response of Series and Parallel RLC Circuits

2. Step Response DC Sources are present after switches change
Transient parts have same form as in natural response
Use Steady-state response and initial conditions to determine constants
In steady-state with DC sources:
inductors are as short circuits
capacitors are as open circuits

3. Series RLC Step Response (1/5)
Switch has been closed for a long time.
Initial Conditions:
Steady-state
Conditions:

4. Series RLC Step Response (2/5)
Since series RLC, start with capacitor voltage:

5. Series RLC Step Response (3/5)
Now find current in capacitor as:
Use initial conditions:
then

6. Series RLC Step Response (4/5)

7. Series RLC Step Response (5/5)

8. Parallel RLC Step Response (1/6)
Switch has been open for a long time.
Initial Conditions:
Steady-state
Conditions:

9. Parallel RLC Step Response (2/6)
From experience, we know this is a damped sinusoid. Therefore, start with that form.

10. Parallel RLC Step Response (3/6)
Evaluate at initial conditions.

11. Parallel RLC Step Response (4/6)
Evaluate at initial conditions.

12. Parallel RLC Step Response (5/6)

13. Parallel RLC Step Response (6/6)