Lecture 10 - Step Response of Series and Parallel RLC Circuits

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Presentation transcript:

Lecture 10 - Step Response of Series and Parallel RLC Circuits E E 2415 Lecture 10 - Step Response of Series and Parallel RLC Circuits

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

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

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

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

Series RLC Step Response (4/5)

Series RLC Step Response (5/5)

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

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

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

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

Parallel RLC Step Response (5/6)

Parallel RLC Step Response (6/6)