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capacitors A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of a c ...
and
inductors An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
as used in
electric circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, c ...
s are not ideal components with only
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
or
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
. However, they can be treated, to a very good degree of approximation, as being ideal capacitors and inductors in series with a resistance; this resistance is defined as the equivalent series resistance (ESR). If not otherwise specified, the ESR is always an AC resistance, which means it is measured at specified frequencies, 100 kHz for switched-mode power supply components, 120 Hz for linear power-supply components, and at its self-resonant frequency for general-application components. Additionally, audio components may report a "
Q factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy lo ...
", incorporating ESR among other things, at 1000 Hz.


Overview

Electrical
circuit theory Circuit may refer to: Science and technology Electrical engineering * Electrical circuit, a complete electrical network with a closed-loop giving a return path for current ** Analog circuit, uses continuous signal levels ** Balanced circui ...
deals with ideal
resistor A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active ...
s,
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passivity (engineering), passive electronic component with two termi ...
s and
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a ...
s, each assumed to contribute only resistance, capacitance or inductance to the circuit. However, all components have a non-zero value of each of these parameters. In particular, all physical devices are constructed of materials with finite
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallel ...
, so that physical components have some resistance in addition to their other properties. The physical origins of ESR depend on the device in question. One way to deal with these inherent resistances in circuit analysis is to use a
lumped element model The lumped-element model (also called lumped-parameter model, or lumped-component model) simplifies the description of the behaviour of spatially distributed physical systems, such as electrical circuits, into a topology consisting of discrete e ...
to express each physical component as a combination of an ideal component and a small
resistor A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active ...
in series, the ESR. The ESR can be measured and included in a component's
datasheet A datasheet, data sheet, or spec sheet is a document that summarizes the performance and other characteristics of a product, machine, component (e.g., an electronic component), material, subsystem (e.g., a power supply), or software in sufficie ...
. To some extent it can be calculated from the device properties.
Q factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy lo ...
, which is related to ESR and is sometimes a more convenient parameter than ESR to use in calculations of high-frequency non-ideal performance of real inductors, is quoted in inductor data sheets. Capacitors, inductors, and resistors are usually designed to minimise other parameters. In many cases this can be done to a sufficient extent that ''parasitic'' capacitance and inductance of a resistor, for example, are so small as not to affect circuit operation. However, under some circumstances parasitics become important and even dominant.


Component models

Pure capacitors and inductors do not dissipate energy; any component which dissipates energy must be treated in an equivalent circuit model incorporating one or more resistors. Actual passive two-terminal components can be represented by some network of lumped and distributed ideal inductors, capacitors, and resistors, in the sense that the real component behaves as the network does. Some of the components of the equivalent circuit can vary with conditions, e.g., frequency and temperature. If driven by a periodic sinewave (
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which ...
) the component will be characterised by its
complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
impedance ''Z''(ω) = ''R'' + ''j'' ''X''(ω); the impedance can involve several minor resistances, inductances and capacitances in addition to the main property. These small deviations from the ideal behavior of the device can become significant under certain conditions, typically high frequency, where the reactance of small capacitances and inductances can become a significant element of circuit operation. Models of lesser or greater complexity can be used, depending upon the accuracy required. For many purposes, a simple model with an inductance or capacitance in series with an ESR is good enough. These models, however simple or complex, can be inserted into a circuit to calculate performance. Computer tools are available for complex circuits; e.g., the SPICE program and its variants.


Inductors

An inductor consists of a conducting insulated wire coil usually wound around a ferromagnetic core. Inductors have resistance inherent in the metal conductor, quoted as DCR in
datasheet A datasheet, data sheet, or spec sheet is a document that summarizes the performance and other characteristics of a product, machine, component (e.g., an electronic component), material, subsystem (e.g., a power supply), or software in sufficie ...
s. This metallic resistance is small for small inductance values (typically below 1 Ω). The DC wire resistance is an important parameter in transformer and general inductor design because it contributes to the impedance of the component, and current flowing through that resistance is dissipated as
waste heat Waste heat is heat that is produced by a machine, or other process that uses energy, as a byproduct of doing work. All such processes give off some waste heat as a fundamental result of the laws of thermodynamics. Waste heat has lower utility ( ...
, and energy is lost from the circuit. It can be modeled as a resistor in series with the inductor, often leading to the DC resistance being referred to as the ESR. Though this is not precisely correct usage, the unimportant elements of ESR are often neglected in circuit discussion, since it is rare that all elements of ESR are significant to a particular application. An inductor using a core to increase inductance will have losses such as
hysteresis Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
and
eddy current Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magne ...
in the core. At high frequencies there are also losses in the windings due to proximity and
skin effect Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the con ...
s. These are in addition to wire resistance, and lead to a higher ESR.


Capacitors

In a non-electrolytic capacitor and electrolytic capacitors with solid electrolyte, the metallic resistance of the leads and electrodes and losses in the dielectric cause the ESR. Typically quoted values of ESR for ceramic capacitors are between 0.01 and 0.1 ohms. ESR of non-electrolytic capacitors tends to be fairly stable over time; for most purposes real non-electrolytic capacitors can be treated as ideal components. Aluminium and
tantalum Tantalum is a chemical element with the symbol Ta and atomic number 73. Previously known as ''tantalium'', it is named after Tantalus, a villain in Greek mythology. Tantalum is a very hard, ductile, lustrous, blue-gray transition metal that is ...
electrolytic capacitor An electrolytic capacitor is a polarized capacitor whose anode or positive plate is made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel e ...
s with non solid electrolyte have much higher ESR values, up to several ohms; electrolytics of higher capacitance have lower ESR. ESR decreases with frequency up to the capacitor's self-resonant frequency. A very serious problem, particularly with aluminium electrolytics, is that ESR increases over time with use; ESR can increase enough to cause circuit malfunction and even component damage, although measured capacitance may remain within tolerance. While this happens with normal aging, high
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
s and large
ripple current Ripple (specifically ripple voltage) in electronics is the residual periodic variation of the DC voltage within a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alt ...
exacerbate the problem. In a circuit with significant ripple current, an increase in ESR will increase heat accumulation, thus accelerating aging. Electrolytic capacitors rated for high-temperature operation and of higher quality than basic consumer-grade parts are less susceptible to become prematurely unusable due to ESR increase. A cheap electrolytic capacitor may be rated for a life of less than 1000 hours at 85 °C. (A year is 8760 hours.) Higher-grade parts are typically rated at a few thousand hours at maximum rated temperature, as can be seen from manufacturers' datasheets. If ESR is critical, specification of a part with higher temperature rating, "low ESR" or larger capacitance than is otherwise required may be advantageous. There is no standard for "low ESR" capacitor rating. Polymer capacitors usually have lower ESR than wet-electrolytic of same value, and stable under varying temperature. Therefore, polymer capacitors can handle higher ripple current. From about 2007 it became common for better-quality computer motherboards to use only polymer capacitors where wet electrolytics had been used previously.Capacitor Lab - Types of Capacitors - Polymer Capacitors
The ESR of capacitors larger than about 1 μF is easily measured in-circuit with an
ESR meter An ESR meter is a two-terminal electronic measuring instrument designed and used primarily to measure the equivalent series resistance (ESR) of real capacitors; usually without the need to disconnect the capacitor from the circuit it is conne ...
.


See also

* Capacitor plague * Polymer capacitor *
Dissipation factor In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of oscillation (mechanical, electrical, or electromechanical) in a dissipative system. It is the reciprocal of quality factor, which represents the "quality" or d ...
*
RC circuit A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses. A first order RC ci ...
*
Output impedance The output impedance of an electrical network is the measure of the opposition to current flow (impedance), both static ( resistance) and dynamic ( reactance), into the load network being connected that is ''internal'' to the electrical source. The ...
*
Equivalent series inductance Equivalent series inductance (ESL) is an effective inductance that is used to describe the inductive part of the impedance of certain electrical components. Overview The theoretical treatment of devices such as capacitors and resistors tends to ...
(ESL)


References

{{Reflist


External links


Determining the Equivalent Series Resistance (ESR) of Capacitors

Application note of ESR of capacitors

"Capacitors: Equivalent Series Resistance (ESR)"
General Atomics General Atomics is an American energy and defense corporation headquartered in San Diego, California, specializing in research and technology development. This includes physics research in support of nuclear fission and nuclear fusion energy. Th ...
Engineering Bulletin, pp. 2–9 Capacitors Electrical parameters Electronics concepts de:Equivalent Series Resistance