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Why so many ways to measure a capacitor?

The methods used are proprietary. Someone might know.

Real capacitance is not a simple RsC//Rp and has additional RC values that cause the "memory effect". So accurate values can differ by the methods used. Film Caps are more ideal in the model than electrolytic but also have high tolerance error.
The calibration method also matters.

The e-Caps may be measured in different ways;

- large signal step response causing C=Ic dt/dV with the correct polarity

- if the tester has no polarity demand, then it will use a small signal fixed frequency response to modulated currents

- an impedance ratio method with a fixed frequency modulated current source to measure amplitude and phase from Z(f)=2pi*f*C+ESR

- Good RLC meters will measure at 3 different frequencies like the E4981A 120 Hz / 1 kHz / 1MHz and get different results. This is normal.
- 120 Hz is the DF standard for e-Caps used for bulk DC rectification and the caps will specify Dissipation Factor rather than ESR.
- These are generally standard e-Caps and not low ESR types.
- Low ESR e-Caps need 100kHz and 1 MHz where C*ESR=Tau =~ 0.5 to 10 us while std e-Caps =~100 to 250 us for most

- the most accurate method would be a tester that measures spectral impedance with Zc and ESR vs frequency on a log-log scale.

The method you choose depends on your consequences for errors in verification and accuracy.

My background was in design in R&D since '75 then a Test Engineer.
 
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