Solving natural/step response in RL/C circuits

ACLerok

when solving a RL or RC circuit, what's the easiest way to tell if it is a natural response problem or step response?

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SGT

The step response is the response of your circuit to a step input, with all initial conditions set to zero. I don´t know exactly what you mean by natural response, but I believe that it is the response of your circuit to the initial conditions, when no input is applied.

Astronuc

Staff Emeritus
In the case of the natural response, the inductor has a constant current or the capacitor has a constant voltage (stored energy). The inductor or capacitor is then discharged through a resistance at the reference time, t=to.

In the step response case, the initial current is zero in the inductor, or the voltage is zero across the capacitor, until time t=to when a constant (dc) current or voltage is applied.

In the case of a parallel RLC circuit, the natural response consists of finding the voltage across the parallel branches that arises due to the release of energy that has been stored in the inductor, capacitor or both. The step response of a parallel RLC circuit implies finding the voltage that appears across the parallel branches as a result of a sudden application of a dc, or constant, current source.

The natural response of a series RLC circuit consists of finding the current in the series-connected elements that arises due to the release of stored energy in either the inductor, capacitor or both. The step response of series RLC circuit implies finding the current in the series-connected components when a sudden dc voltage is applied.
James W. Nilsson, Electric Circuits, 2nd Ed, 1985.

Electric Circuits w/PSpice, 7th Edition
By James Nilsson, Susan Riedel. 2004
Published by Prentice Hall (now publishes former Addison-Wesley science and engineering texts).

1. Circuit Variables.
2. Circuit Elements.
3. Simple Resistive Circuits.
4. Techniques of Circuit Analysis.
5. The Operational Amplifier.
6. Inductors, Capacitors, and Mutual Inductance.
7. Response of First-Order RL and RC Circuits.
8. Natural and Step Responses of RLC Circuits.
9. Sinusoidal Steady-State Analysis.
10. Sinusoidal Steady-State Power Calculations.
11. Balanced Three-Phase Circuits.
12. Introduction to the Laplace Transform.
13. The Laplace Transform in Circuit Analysis.
14. Introduction to Frequency-Selective Circuits.
15. Active Filter Circuits.
16. Fourier Series.
17. The Fourier Transform.
18. Two-Port Circuits.

Appendix A. The Solution of Linear Simultaneous Equations.

Appendix B. Complex Numbers.

Appendix C. The Decibel.

Appendix D. Bode Diagrams.

Appendix E. An Abbreviated Table of Trigonometric Identities.

Appendix F. An Abbreviated Table of Integrals.

Appendix G. Answers to Selected Problems.

ng

astronuc,isnt natural response called transient response as well?
ng

Astronuc

Staff Emeritus
Both natural and step responses involve a transient, and I have heard transient response used in reference to both natural and step responses. Usually the transient response is within t= a few time constants of the initial event and beyond say t=10 time constants, the response is considered steady-state.

Corneo

As I recall, transient response is the circuits response to some sort of excitation. This is the period before the circuit reaches the steady state response.

Astronuc

Staff Emeritus
The term 'transient' infers a change in state, e.g. voltage/current applied abruptly, or a switch closed or open. Steady-state implies equilibrium, i.e. some long time (e.g. t > ~ 10 time constants) where the subsequent state changes very little (effectively steady-state) or really settles to some 'constant' value.

SGT

Transient response is due to the natural modes of the circuit and involves an exponential with negative exponent, so it tends to zero after some time(hypothetically for t = infinity, in practice 4 or 5 time constants).
Steady state response is due to the excitation. If the excitation is zero (natural response), the steady state is zero. If the excitation is a constant, the steady state is also a constant and if the excitation is a sinusoid, the steady state is a sinusoid of the same frequency, but with a different phase.

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