Capacitor Impedance with ESR

Formula

Description

A real capacitor has equivalent series resistance (ESR) that prevents its impedance from ever reaching zero. The total impedance is the vector sum of the resistive ESR component and the reactive capacitance component. At low frequencies, Xc dominates and the impedance is mostly capacitive. Near the self-resonant frequency, Xc and ESL cancel, leaving only ESR as the minimum impedance. Below this minimum, the capacitor acts capacitive; above it, the parasitic inductance (ESL) dominates and the component behaves as an inductor.

Variables

• Z — Total capacitor impedance (Ω)
• ESR — Equivalent series resistance (Ω)
• Xc — Capacitive reactance at the frequency of interest (Ω)

Practical Notes

Ceramic capacitors have very low ESR (1-10 mΩ), making them excellent for high-frequency bypassing. Electrolytic capacitors have ESR from 10 mΩ to several ohms, which limits their effectiveness at high frequencies but provides damping in power supply output filters. Low-ESR electrolytics are specifically designed for switching power supply output filtering.