Impedance is one of the key parameters to consider when choosing a capacitor for a specific application.

Although today’s integrated circuits operate at higher frequencies and have higher current demands, they are optimized to operate at relatively low voltages to minimize build-up of heat. Such high performance integrated circuits demand decoupling capacitors with low impedance. Apart from low impedance, capacitors for high performance circuits are also required to have high ripple current capability and excellent surge performance.

**RESISTANCE, REACTANCE, AND IMPEDANCE OF A CAPACITOR**

The resultant opposition to flow of alternating current (AC current) in a capacitor is referred to as impedance. It is a function of equivalent series resistance (ESR), inductive reactance, and capacitive reactance. The impedance of a capacitor is a complex value that consists of a real part (resistance) and an imaginary part (reactance).

For an ideal capacitor, the effective impedance is negative and dependent on frequency and capacitance of the component. This impedance is equal to the capacitive reactance of the component, and decreases with an increase in frequency. For a practical capacitor, the effective impedance is composed of three components: capacitive reactance, inductive reactance, and resistance.

An ideal capacitor acts like a purely reactive component. Such a perfect reactive component has zero resistive effects and does not dissipate energy. However, practical capacitors have dissipative properties.

**EQUIVALENT SERIES RESISTANCE (ESR)**

The equivalent circuit model of a practical (non-ideal) capacitor consists of capacitance, series resistance, and series inductance. All resistive forces at a specific set of measurement conditions are lumped together to form equivalent series resistance. This resistance comprises of various components including resistance in components, resistance in contacts, resistance due to the dielectric material, resistance due to defects, and so on. The equivalent series resistance for an ideal capacitor is zero. For a given capacitor, the equivalent series resistance is not a constant. It varies depending on the operating conditions.

In a capacitor, the dielectric material is the primary contributor of the resistive component. When electric fields change, this material reacts by producing heat. The amount of heat produced by a dielectric material increases with an increase in frequency. Wire resistance contributes a small part to this component. Compared to inductors, capacitors have less resistive effects and dissipate less power.

The dielectric resistivity consists of two resistances: one resistive component in series with a pure capacitance and another in parallel with it. Dielectric losses vary from one capacitor to another mainly depending on the dielectric material used. Some dielectric materials have more resistive effects than others. Capacitors that are constructed from dielectric materials with high resistive effects are unsuitable for electronic circuits that demand low impedance components.

**CAPACITIVE REACTANCE (X**_{C}**)**

_{C}

When an AC current flows through a capacitor, it is opposed by resistance and reactance. Capacitive reactance is a function of capacitance and frequency. It is measured in Ohms and is inversely proportional to the operating frequency.

The capacitive reactance of a capacitor decreases towards zero with an increase in frequency. As the frequency decreases towards zero, the capacitive reactance of a capacitor increases towards infinity. At a frequency approaching zero, a capacitor has very high reactance and acts as an open circuit. An increase in capacitive reactance results in an increase in impedance, and vice versa.

**INDUCTIVE REACTANCE (X**_{L}**)**

_{L}

For aluminium electrolytic capacitors, the equivalent circuit consists of capacitance, equivalent parallel resistance, equivalent series resistance, and equivalent series inductance. At low frequencies, the equivalent series inductance of a capacitor is extremely small. The reactance from this inductance is small and can be regarded as negligible.

Practical capacitors exhibit parasitic inductance. Unlike capacitive reactance, inductive reactance reduces the effective impedance of a capacitor. At very high frequencies, the inductive reactance can be extremely large, and this can cause the capacitor to behave like an inductor. For this reason, most high frequency applications demand low inductance capacitors.

**TEMPERATURE AND FREQUENCY DEPENDENCE OF AC IMPEDANCE**

The impedance of a capacitor is a function of equivalent series resistance, capacitive reactance, capacitance, and inductive reactance. Since some of these components vary with changes in temperature, the effective impedance is affected too. For aluminium electrolytic capacitors, the impedance increases up to 10 times when temperature decreases from 25^{0}C to the low temperature limit and decreases by about 5% when temperature increases to the high temperature limit.

The impedance of a capacitor is greatly determined by frequency. At self-resonant frequency (SRF), the impedance of a capacitor is minimum and equal to the equivalent series resistance of the capacitor at that frequency. The contribution of the capacitive reactance and the inductive reactance is zero at the self-resonant frequency. At frequencies below the SRF, the capacitive reactance increases significantly with a decrease in frequency. The ESR also increases slightly with a decrease in frequency.

The inductive reactance of a capacitor increases as the frequency increases from the self-resonant frequency. Changes in the ESR are negligible as frequency increases above the SRF.

**CONCLUSION**

An ideal capacitor is a purely reactive device. However, a real capacitor has capacitance, parasitic resistance and parasitic inductance. The impedance of a practical capacitor comprises three components: equivalent series resistance, inductive reactance, and capacitive reactance. These components vary depending on the operating conditions of a capacitor. At self-resonant frequency, the impedance of a capacitor is equal to the equivalent series resistance. In addition, at this frequency, the impedance of a capacitor is minimum and purely resistive. The impedance of a capacitor is also significantly affected by temperature.

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