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About dissipation factor (D.F.) / tanδ

The aluminum electrolytic capacitor loss tangent (also commonly referred to as: tanδ, D.F., dissipation tangent, tan delta) is the property that expresses output phase difference relative to the ideal capacitor.
This is one of the metrics used to express capacitor loss. In an ideal capacitor, there is no resistance element and loss does not exist, so D.F. is zero.
Defining D.F.(tanδ)
ω
: 2πf
f
: For catalog standards 120 [Hz]
π
: Pi (3.1415・・・)
C
: Capacitance [F]
R
: Equivalent Series Resistance(ESR) [ω]
Method of using D.F. to calculate ESR
From the definition of D.F., we know that ESR can be calculated if the measured frequency and the capacitance are known. Solving for R in formula (1) results in formula (2).

When calculating ESR from the D.F. indicated as the specification value of the product, it is necessary to note that the rated value includes a large margin and is only for the specified frequency of 120Hz.

Due to the impact of the D.F. rated value margin and the capacitance tolerance, even when calculating ESR at 120Hz, there could be a discrepancy ranging from several dozen percent to several times greater.
Also, you cannot use calculation to derive the ESR value of differing frequencies.

Based on the above, using D.F. to calculate ESR requires the actual measured value for D.F. and that the measured frequency matches the frequency of the desired conditions. Generally speaking, in such cases, ESR is measured directly. While it is understood that ESR can be calculated theoretically, practically speaking it is never used.

Example:
D.F. measured value
: 0.011
D.F. measured frequency
: 120 [Hz]
Capacitance measured value
: 97 [μF/120Hz]
Role of D.F. today

In a classic power source circuit using a transformer and a rectifying circuit, D.F. does not depend on the voltage and capacitor loss at 120Hz can be expressed so this value was convenient for expressing the merits and demerits of capacitor properties.
Today, however, switching circuits have become common. As these are operated at several dozen to several hundred kHz, the value of D.F. at 120Hz has no significant meaning.
As such, we mainly define ESR or impedance at 100kHz for capacitors used on the secondary side.

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