Equivalent Series Resistance

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 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 measured with standardized frequencies.

Contents [hide]

1 Overview

2 Component models

2.1 Inductors

2.2 Capacitors

2.2.1 Typical values of ESR for capacitors

3 See also

4 References

5 External links

Overview[edit]

Electric circuit theory deals with ideal resistors, 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-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.

Component models[edit]

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) 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.

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