# Capacitor ESR Calculator

This tool calculates the Equivalent Series Resistance of a Capacitor. It uses the loss tangent, capacitor value and frequency.

## Background

A real capacitor is modeled as a lossless ideal capacitor in series with an equivalent series resistance (ESR).

The loss tangent is defined by the angle between the capacitor’s impedance vector and the negative reactive axis.

The resistor results in a voltage drop and heat dissipation. It means that the capacitor is not the perfect capacitor many of us might expect it to be. In a good capacitor the ESR is very small, and in a poor capacitor the ESR is large.

### What is the effect of ESR?

Any electrical system that uses capacitors, such as power supplies or audio equipment, can be affected by ESR.

In high-frequency applications, the capacitance of the capacitor becomes less significant, and the ESR becomes more crucial. High ESR can lead to increased ripple voltage and decreased regulation. Moreover, the resistive component of the ESR results in power dissipation, leading to heating of the capacitor. In the case of electrolytic capacitors, this heat can further damage the electrolyte, causing the ESR to increase even more.

Hence, selecting a capacitor with low ESR is essential to ensure proper performance and longevity of electronic devices.

### Can ESR be measured with a multimeter?

No, the Equivalent Series Resistance of a capacitor cannot be measured with an ohmmeter or a multimeter.

Sometimes a capacitor vendor will provide ESR values (in which case you don’t need to calculate them).

## Formula

ESR = (tan δ)/(2*π*f*C)

where,

• C = Capacitance
• tan δ = Loss Tangent
• f = Frequency at which the loss tangent is measured

The value of loss tangent can be found in the capacitor data sheet.

The frequency of measurement is 120 Hz.

## Example Calculation

For a capacitor value 100 μF rated to 16V, tan δ=0.20, f=120 Hz the ESR is 2.65 Ω.

As can be seen from the table above, capacitors that are rated to higher DC voltage levels have lower loss tangent values and as a result – lower ESR.