Calculating capacitor ESR from Tan(δ)

Passives Capacitors
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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.
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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.

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

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

2 Likes
3

Hi Rick,
I am also figuring the ESR of capacitor!
The capacitor is (Kemet, ESK226M100AE3AA: 22 µF, 100 V)
Datasheet: KEM_A4004_ESK-1103206.pdf
According to the datasheet DF at (120 Hz 20°C (tanδ %)) is 10
I tried to calculate ESR=10%/(2pi x 120 x 22uF) =6.0286 (Ohms)
That value is looked like impossible and weird
Need help!!
Thank you

4

Haven’t checked your math, but IME, 6 ohms on a low value, economy grade, small package electrolytic capacitor is not unreasonable.

Checked Wikipedia and sure enough 6 is considered actually better than average for that capacitor type.

5

Hi PaulHutch, The one I used is from Kemet called radial aluminum electrolytic capacitors, so you thought it matched with Standard aluminum type?

Type 22 µF 100 µF 470 µF
Standard aluminum 7–30 Ω 2–7 Ω 0.13–1.5 Ω
Low-ESR aluminum 1–5 Ω 0.3–1.6 Ω
Solid aluminum 0.2–0.5 Ω
Sanyo OS-CON 0.04–0.07 Ω 0.03–0.06 Ω
Standard solid tantalum 1.1–2.5 Ω 0.9–1.5 Ω
Low-ESR tantalum 0.2–1 Ω 0.08–0.4 Ω
Wet-foil tantalum 2.5–3.5 Ω 1.8–3.9 Ω
Stacked-foil film < 0.015 Ω
Ceramic < 0.015 Ω

Thank you

6

Yes it’s a basic standard aluminum electrolytic with radial leads.