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In
electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
and
mechanical engineering Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, an ...
, a transient response is the response of a system to a change from an equilibrium or a
steady state In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p'' ...
. The transient response is not necessarily tied to abrupt events but to any event that affects the equilibrium of the system. The
impulse response In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (). More generally, an impulse response is the react ...
and
step response The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the out ...
are 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. It is followed by the steady state response, which is the behavior of the circuit a long time after an external excitation is applied.


Damping

The response can be classified as one of three types of damping that describes the output in relation to the steady-state response. ;Underdamped :An
underdamped Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples inc ...
response is one that oscillates within a decaying
envelope An envelope is a common packaging item, usually made of thin, flat material. It is designed to contain a flat object, such as a letter or card. Traditional envelopes are made from sheets of paper cut to one of three shapes: a rhombus, a sho ...
. The more underdamped the system, the more oscillations and longer it takes to reach steady-state. Here
damping ratio Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples inc ...
is always less than one. ;Critically damped :A
critically damped Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples inc ...
response is the response that reaches the steady-state value the fastest without being underdamped. It is related to critical points in the sense that it straddles the boundary of underdamped and
overdamped Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples in ...
responses. 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

Transient response can be quantified with the following properties. ;Rise time :
Rise time In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value. These values may be expressed as ratiosSee for example , and . or, equivalen ...
refers 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 : Overshoot is when a signal or function exceeds its target. It is often associated with ringing. ;Settling time :
Settling time In control theory the settling time of a dynamical system such as an amplifier or other output device is the time elapsed from the application of an ideal instantaneous step input to the time at which the amplifier output has entered and remained ...
is 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, the time after which the following equality is satisfied: :: , h(t)-h_, \leqslant \epsilon : where h_ is the steady-state value, and \epsilon defines 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. ;Peak time :The peak time is the time required for the response to reach the first peak of the overshoot. ; Steady-state error :Steady-state error is the difference between the desired final output and the actual one when the system reaches a
steady state In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p'' ...
, when its behavior may be expected to continue if the system is undisturbed.


Oscillation

Oscillation is an effect caused by a transient stimulus to an underdamped circuit or system. It is a transient event preceding the final
steady state In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p'' ...
following a sudden change of a circuit or start-up. Mathematically, it can be modeled as a
damped harmonic oscillator In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force ''F'' proportional to the displacement ''x'': \vec F = -k \vec x, where ''k'' is a positive constan ...
. Inductor
volt-second balance In physics, the weber ( ; symbol: Wb) is the unit of magnetic flux in the International System of Units (SI), whose units are volt-second. A magnetic flux density of one Wb/m2 (one weber per square metre) is one tesla. The weber is named after t ...
and capacitor
ampere-second balance The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...
are disturbed by transients. These balances encapsulate the circuit analysis simplifications used for steady-state AC circuits. An example of transient oscillation can be found in digital (pulse) signals in computer networks.Cheng, David K. ''Field and Wave Electromagnetics, 2nd Ed''. Addison-Wesley, 1989, p. 471. 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

Electromagnetic pulse An electromagnetic pulse (EMP), also a transient electromagnetic disturbance (TED), is a brief burst of electromagnetic energy. Depending upon the source, the origin of an EMP can be natural or artificial, and can occur as an electromagnetic fie ...
s (EMP) occur internally as the result of the operation of switching devices. Engineers use
voltage regulator A voltage regulator is a system designed to automatically maintain a constant voltage. A voltage regulator may use a simple feed-forward design or may include negative feedback. It may use an electromechanical mechanism, or electronic components ...
s and
surge protector A 'surge protector'' (or spike suppressor, surge suppressor, surge diverter, surge protection device (SPD) or transient voltage surge suppressor (TVSS) is an appliance or device intended to protect electrical devices from voltage spikes in al ...
s to prevent transients in electricity from affecting delicate equipment. External sources include
lightning Lightning is a naturally occurring electrostatic discharge during which two electrically charged regions, both in the atmosphere or with one on the ground, temporarily neutralize themselves, causing the instantaneous release of an average ...
,
electrostatic discharge Electrostatic discharge (ESD) is a sudden and momentary flow of electric current between two electrically charged objects caused by contact, an electrical short or dielectric breakdown. A buildup of static electricity can be caused by tribocha ...
and
nuclear electromagnetic pulse A nuclear electromagnetic pulse (nuclear EMP or NEMP) is a burst of electromagnetic radiation created by a nuclear explosion. The resulting rapidly varying electric and magnetic fields may couple with electrical and electronic systems to produc ...
. Within
Electromagnetic compatibility Electromagnetic compatibility (EMC) is the ability of electrical equipment and systems to function acceptably in their electromagnetic environment, by limiting the unintentional generation, propagation and reception of electromagnetic energy whic ...
testing, 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 a damped 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 is EN-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

* Acoustic transient * Astronomical transient *
Attractor In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain ...
*
Carrying capacity The carrying capacity of an environment is the maximum population size of a biological species that can be sustained by that specific environment, given the food, habitat, water, and other resources available. The carrying capacity is defined as ...
*
Control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
*
Dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...
*
Equilibrium point In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation. Formal definition The point \tilde\in \mathbb^n is an equilibrium point for the differential equation :\frac = \ma ...
*
Limit cycle In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity ...
*
List of types of equilibrium {{Unreferenced, date=September 2022 This is a list of various types of equilibrium, the condition of a system in which all competing influences are balanced. Biology * Equilibrioception, the sense of a balance present in human beings and animals ...
*
Race condition A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events. It becomes a bug when one or more of ...
*
Simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the ...
*
State function In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a syste ...
*
Systems theory Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structu ...
*
Transient state A system is said to be transient or in a transient state when a process variable or variables have been changed and the system has not yet reached a steady state. The time taken for the circuit to change from one steady state to another steady stat ...


References

{{Reflist Electricity concepts Engineering concepts Control theory Oscillation