Component models Equivalent series resistance

1 component models

1.1 inductors
1.2 capacitors

1.2.1 typical values of esr capacitors

component models

pure capacitors , inductors not dissipate energy; component dissipates energy must treated in equivalent circuit model incorporating 1 or more resistors. actual passive two-terminal components can represented network of lumped , distributed ideal inductors, capacitors, , resistors, in sense real component behaves network does. of components of equivalent circuit can vary conditions, e.g., frequency , temperature.

if driven periodic sinewave (alternating current) component characterised complex impedance z(ω) = r + j x(ω); impedance can involve several minor resistances, inductances , capacitances in addition main property. these small deviations ideal behavior of device can become significant under conditions, typically high frequency, reactance of small capacitances , inductances can become significant element of circuit operation. models of lesser or greater complexity can used, depending upon accuracy required. many purposes simple model inductance or capacitance in series esr enough.

these models, simple or complex, can inserted circuit calculate performance. computer tools available complex circuits; e.g., spice program , variants.

inductors

an inductor consists of conducting insulated wire coil wound around ferromagnetic core. inductors have resistance inherent in metal conductor, quoted dcr in datasheets. metallic resistance small small inductance values (typically below 1 Ω). dc wire resistance important parameter in transformer , general inductor design because contributes impedance of component, , current flowing through resistance dissipated waste heat , lost circuit. can modeled resistor in series inductor, leading dc resistance being referred esr. though not precisely correct usage, unimportant elements of esr neglected in circuit discussion, since rare elements of esr significant particular application.

an inductor using core increase inductance have losses such hysteresis , eddy current in core. @ high frequencies there losses in windings due proximity , skin effects. these in addition wire resistance, , lead higher esr.

capacitors

in non-electrolytic capacitor , electrolytic capacitors solid electrolyte metallic resistance of leads , electrodes , losses in dielectric cause esr. typically quoted values of esr ceramic capacitors between 0.01 , 0.1 ohms. esr of non-electrolytic capacitors tends stable on time; purposes real non-electrolytic capacitors can treated ideal components.

aluminium , tantalum electrolytic capacitors non solid electrolyte have higher esr values, several ohms; electrolytics of higher capacitance have lower esr. esr decreases frequency capacitor s self-resonant frequency. serious problem, particularly aluminium electrolytics, esr increases on time use; esr can increase enough cause circuit malfunction , component damage, although measured capacitance may remain within tolerance. while happens normal aging, high temperatures , large ripple current exacerbate problem. in circuit significant ripple current, increase in esr increase heat dissipation, accelerating aging.

electrolytic capacitors rated high-temperature operation , of higher quality basic consumer-grade parts less susceptible become prematurely unusable due esr increase. cheap electrolytic capacitor may rated life of less 1000 hours @ 85°c (a year 8760 hours). higher-grade parts typically rated @ few thousand hours @ maximum rated temperature, can seen manufacturers datasheets. if esr critical, specification of part higher temperature rating, low esr or larger capacitance otherwise required may advantageous. there no standard low esr capacitor rating.

polymer capacitors have lower esr wet-electrolytic of same value, , stable under varying temperature. therefore, polymer capacitors can handle higher ripple current. 2007 became common better-quality computer motherboards use polymer capacitors wet electrolytics had been used previously.

the esr of capacitors larger 1 μf measured in-circuit esr meter.

typical values of esr capacitors