# Calculating capacitor ESR from Tan(δ)

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Capacitor equivalent series resistance (ESR) is often a characteristic of interest, that is not directly specified in parametric data or a device datasheet. Information about a device’s loss angle (δ) is usually available in these cases, which allows calculating an ESR value.

A capacitor’s total complex impedance is represented on a real-complex plane as the vector sum of a real component, (the ESR) and a complex (reactive) component representing the ‘ideal’ capacitor that things like ESR mess up in all actual components. The angle between the total impedance and its complex component is called the ‘loss angle,’ and is a figure used to summarize the ratio between the ideal and non-ideal components of a capacitor’s overall impedance.

The tangent of the loss angle is usually provided, which actually simplifies things a bit. Taking the formula for the impedance of an ideal capacitor and doing a bit of algebra, one finds that an ESR value can be obtained by dividing that value from the datasheet by two pi, the test frequency, and the capacitor value. Taking part number 1189-1546-3-ND as an example, the tan(δ) and f values can be found on page one of the datasheet.

From that point, it’s a simple matter of putting the actual numbers into the equation:

Note that this value applies only at the indicated test conditions (temperature, frequency, etc.) and will vary as conditions change.