Equivalent series resistance
Encyclopedia
Practical capacitors and inductors as used in electric circuits are not ideal components with only capacitance
or inductance
. However, they can be treated to a very good approximation as ideal capacitors and inductors in series with a resistance
; this resistance is defined to be the equivalent series resistance (ESR).
s, capacitors and inductors, 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
, 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
to express each physical component as a combination of an ideal component and a small resistor
in series, the ESR. The ESR can be measured and included in a component's datasheet
. To some extent it can be calculated from the device properties.
Q factor
, 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.
If driven by a periodic sinewave (alternating current
) the component will be characterised by its (complex 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.
Pure capacitors and inductors do not dissipate energy; any process which dissipates energy must be treated as one or more resistors in the component model.
s.
This metallic resistance is small for small inductance values (typically below 1 Ω
). The DC resistance is an important parameter in switch-mode power supply design. It can be modeled as a resistor in series with the inductor, therefore 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
and eddy current
losses in the core. At high frequencies there are also additional losses in the windings due to proximity and skin effect
. These are in addition to wire resistance, and lead to a higher ESR.
Aluminium and tantalum
electrolytic capacitor
s have much higher ESR values, and ESR tends to increase with frequency due to effects of the electrolyte. 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
s and large ripple current exacerbate the problem. In a circuit with significant ripple current, an increase in ESR will increase heat dissipation, much accelerating ageing.
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 about 9000 hours). Higher-grade parts are typically rated at a few thousand hours at maximum rated temperature, as can be seen from manufacturers' datasheets. Electrolytics of higher capacitance have lower ESR; if ESR is critical, specification of a part of larger capacitance than is otherwise required may be advantageous.
The ESR of capacitors of relatively high capacity (from about 1 μF), which are the ones likely to cause trouble, is easily measured in-circuit with an ESR meter
.
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
or inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
. However, they can be treated to a very good approximation as ideal capacitors and inductors in series with a resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
; this resistance is defined to be the equivalent series resistance (ESR).
Overview
Electric circuit theory deals with ideal resistorResistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
s, capacitors and inductors, 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
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
, 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
Lumped element model
The lumped element model simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions...
to express each physical component as a combination of an ideal component and a small resistor
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
in series, the ESR. The ESR can be measured and included in a component's datasheet
Datasheet
thumb|A floppy disk controller datasheet.A datasheet, data sheet, or spec sheet is a document summarizing the performance and other technical characteristics of a product, machine, component , material, a subsystem or software in sufficient detail to be used by a design engineer to integrate the...
. To some extent it can be calculated from the device properties.
Q factor
Q factor
In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency....
, 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
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
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
) the component will be characterised by its (complex impedance
Electrical impedance
Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...
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
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
tools are available for complex circuits; e.g., the SPICE
SPICE
SPICE is a general-purpose, open source analog electronic circuit simulator.It is a powerful program that is used in integrated circuit and board-level design to check the integrity of circuit designs and to predict circuit behavior.- Introduction :Unlike board-level designs composed of discrete...
program and its variants.
Pure capacitors and inductors do not dissipate energy; any process which dissipates energy must be treated as one or more resistors in the component model.
Inductors
Inductors have resistance inherent in the metal conductor, quoted as DCR in datasheetDatasheet
thumb|A floppy disk controller datasheet.A datasheet, data sheet, or spec sheet is a document summarizing the performance and other technical characteristics of a product, machine, component , material, a subsystem or software in sufficient detail to be used by a design engineer to integrate the...
s.
This metallic resistance is small for small inductance values (typically below 1 Ω
Ohm
The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...
). The DC resistance is an important parameter in switch-mode power supply design. It can be modeled as a resistor in series with the inductor, therefore 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
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...
and eddy current
Eddy current
Eddy currents are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of...
losses in the core. At high frequencies there are also additional losses in the windings due to proximity and skin effect
Skin effect
Skin effect is the tendency of an alternating electric current to distribute itself within a conductor with the current density being largest near the surface of the conductor, decreasing at greater depths. In other words, the electric current flows mainly at the "skin" of the conductor, at an...
. These are in addition to wire resistance, and lead to a higher ESR.
Capacitors
In a non-electrolytic capacitor the metallic resistance of the leads and electrodes and losses in the dielectric comprise the ESR. Typically quoted values of ESR for ceramic capacitors are between 0.01 and 0.1 Ω. 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 capacitor
The tantalum capacitor is a highly reliable type of electrolytic capacitor, available in both solid-bodied and separately encased forms. The encased "wet" variant is not used often in modern designs...
electrolytic capacitor
Electrolytic capacitor
An electrolytic capacitor is a type of capacitor that uses an electrolyte, an ionic conducting liquid, as one of its plates, to achieve a larger capacitance per unit volume than other types. They are often referred to in electronics usage simply as "electrolytics"...
s have much higher ESR values, and ESR tends to increase with frequency due to effects of the electrolyte. 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
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
s and large ripple current exacerbate the problem. In a circuit with significant ripple current, an increase in ESR will increase heat dissipation, much accelerating ageing.
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 about 9000 hours). Higher-grade parts are typically rated at a few thousand hours at maximum rated temperature, as can be seen from manufacturers' datasheets. Electrolytics of higher capacitance have lower ESR; if ESR is critical, specification of a part of larger capacitance than is otherwise required may be advantageous.
The ESR of capacitors of relatively high capacity (from about 1 μF), which are the ones likely to cause trouble, is easily measured in-circuit with an ESR meter
ESR meter
An ESR meter is a two-terminal electronic measuring instrument designed and used primarily to measure the equivalent series resistance of real capacitors—the ESR of an ideal capacitor is zero—usually without the need to disconnect the capacitor from the circuit it is connected to...
.
Typical values of ESR for capacitors
| Type | 22 µF | 100 µF |
|---|---|---|
| Standard aluminum | 0.1 - 3.0 Ω | 0.05 - 0.5 Ω |
| Ceramic | <0.015 Ω |