Transient response
Inelectrical engineeringandmechanical engineering,atransient responseis the response of a system to a change from an equilibrium or asteady state.The transient response is not necessarily tied to abrupt events but to any event that affects the equilibrium of the system. Theimpulse responseandstep responseare transient responses to a specific input (an impulse and a step, respectively).
In electrical engineering specifically, the transient response is the circuit’s temporary response that will die out with time.[1]It is followed by the steady state response, which is the behavior of the circuit a long time after an external excitation is applied.[1]
Damping[edit]
The response can be classified as one of three types of damping that describes the output in relation to thesteady-state response.
- Underdamped
- Anunderdampedresponse is one that oscillates within a decayingenvelope.The more underdamped the system, the more oscillations and longer it takes to reach steady-state. Heredamping ratiois always less than one.
- Critically damped
- Acritically dampedresponse is the response that reaches the steady-state value the fastest without being underdamped. It is related tocritical pointsin the sense that it straddles the boundary of underdamped andoverdampedresponses. Here, the damping ratio is always equal to one. There should be no oscillation about the steady-state value in the ideal case.
- Overdamped
- An overdamped response is the response that does not oscillate about the steady-state value but takes longer to reach steady-state than the critically damped case. Here damping ratio is greater than one.
Properties[edit]
Transient response can be quantified with the following properties.
- Rise time
- Rise timerefers to the time required for a signal to change from a specified low value to a specified high value. Typically, these values are 10% and 90% of the step height.
- Overshoot
- Overshootis when a signal or function exceeds its target. It is often associated withringing.
- Settling time
- Settling timeis the time elapsed from the application of an ideal instantaneous step input to the time at which the output has entered and remained within a specified error band,[2]the time after which the following equality is satisfied:
- whereis the steady-state value, anddefines the width of the error band.
- Delay-time
- The delay time is the time required for the response to initially get halfway to the final value.[3]
- Peak time
- The peak time is the time required for the response to reach the first peak of the overshoot.[3]
- Steady-state error
- Steady-state error is the difference between the desired final output and the actual one when the system reaches asteady state,when its behavior may be expected to continue if the system is undisturbed.[4]
Oscillation[edit]
Oscillation is an effect caused by a transient stimulus to an underdamped circuit or system. It is a transient event preceding the finalsteady statefollowing a sudden change of a circuit[5]or start-up. Mathematically, it can be modeled as adamped harmonic oscillator.
Inductorvolt-second balanceand capacitorampere-second balanceare disturbed by transients. These balances encapsulate the circuit analysis simplifications used for steady-state AC circuits.[6]
An example of transient oscillation can be found in digital (pulse) signals in computer networks.[7]Each pulse produces two transients, an oscillation resulting from the sudden rise in voltage and another oscillation from the sudden drop in voltage. This is generally considered an undesirable effect as it introduces variations in the high and low voltages of a signal, causing instability.
Electromagnetics[edit]
Electromagnetic pulses(EMP) occur internally as the result of the operation of switching devices. Engineers usevoltage regulatorsandsurge protectorsto prevent transients in electricity from affecting delicate equipment. External sources includelightning,electrostatic dischargeandnuclear electromagnetic pulse.
WithinElectromagnetic compatibilitytesting, transients are deliberately administered to electronic equipment for testing their performance and resilience to transient interference. Many such tests administer the induced fast transient oscillation directly, in the form of adamped sine wave,rather than attempt to reproduce the original source. International standards define the magnitude and methods used to apply them.
The European standard for Electrical Fast Transient (EFT) testing isEN-61000-4-4.The U.S. equivalent is IEEE C37.90. Both of these standards are similar. The standard chosen is based on the intended market.
See also[edit]
References[edit]
- ^abAlexander, Charles K.; Sadiku, Matthew N. O. (2012).Fundamentals of Electric Circuits.McGraw Hill. p. 276.
- ^Glushkov, V. M.Encyclopedia of Cybernetics(in Russian) (1 ed.). Kyiv: USE. p. 624.
- ^abOgata, Katsuhiko (2002).Modern Control Engineering(4 ed.). Prentice-Hall. p. 230.ISBN0-13-043245-8.
- ^Lipták, Béla G. (2003).Instrument Engineers' Handbook: Process control and optimization(4th ed.). CRC Press. p. 108.ISBN0-8493-1081-4.
- ^Nilsson, James W, & Riedel, S.Electric Circuits, 9th Ed.Prentice Hall, 2010, p. 271.
- ^Simon Ang, Alejandro Oliva,Power-Switching Converters,pp. 13–15, CRC Press, 2005ISBN0824722450.
- ^Cheng, David K.Field and Wave Electromagnetics, 2nd Ed.Addison-Wesley, 1989, p. 471.