Finding ESR from a capacitor's impedance curves

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#2
Most accomplished handheld LCRs have 100Hz 120Hz 1kHz 10kHz 100kHz selection so 1kHz is the more indicative for a two way. If having an expensive bench unit with almost free frequency selection in many steps, best is to measure nearest to the specific crossover's frequency of course.
 
#3
You don't need any expensive bench unit, only a way of measuring impedance magnitude and phase. We usually do that with free measurement programs that we have mentioned more than a few times here. The next step is to calculate esr from these data. Very easy to do.
 
#4
OK I just traced a capacitor for impedance magnitude and phase from 20Hz to 20kHz in 100 points. I used Woofer Tester 2 for that. Can you tell what its ESR is at closest data points to 100Hz 1kHz and 10kHz? I will reveal the capacitor model and value plus the calibrated DER EE LCR meter's Rs measurements at those three frequencies after that answer so we can see how reliable the affordable gear curves method can be. The tracing results are attached in a text file.
 

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#6
It must be due to the WT2's constant current method I thought so I bypassed the cap with a 100 Ohm resistor providing its CCS a DC path also. Here I attached the new data. And how they get graphed when loaded in REW.
 

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#7
Your second attempt appears much better. Now imagine a right triangle, the hypotenuse(Z), adjacent(ESR) and opposite(Xc). ESR is the real part, and Xc imaginary part of the complex number. The angle between Z and ESR is the phase angle in degrees.

ESR=Z*cos(phase)
Xc=1/(2*pi*f*C); f=frequency in Hz; C=capacitance in Farads

So at 100.23 Hz; ESR=2.686; C=32.74 uF

The rest of the frequencies you can do yourself.
 
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#8
Time to reveal the capacitor and the DER EE DE-5000 LCR meter's readings. Its a Nichicon ES non polar 100uF/50V showing 99.68uF value and 0.3R ESR at 100Hz 97.52uF 0.068R at 1kHz and 97.8uF 0.048R at 10kHz.
 
#11
A lot is depending on calibration and interface type or control options. This is my last best Nichicon attempt with WT2. The 100Hz ESR result still sucks. Higher up its closer to true. Shown graphically side by side with your Visaton Elko data.

In my view to use the curves method it takes having a reliable LCR meter to spot frequency check the setup's tracing results first. Absolutely essential in a new non dialed in rig. On the other hand the ESR differences between typical crossover frequencies in the mid range do not appear to be crucially far from a 1kHz spot check result. For example 0.186R 500Hz 0.140R 1kHz and 0.115R 2.5kHz in the Visaton Elko data. Wouldn't affect much a speaker's crossover simulation.
 

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  • Nichicon ES.png
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#12
Salas said:
The 100Hz ESR result still sucks. Higher up its closer to true.
Click to expand...

Normally the high frequency impedance is accurate because the value converge to a minimum value at resonance (where impedance equals esr). But what is your reference to say that the 100Hz esr still sucks?

Your measured esr at 100, 1k and 10k is:
0.3, 0.068, 0.048
and calculated from the graph is:
0.66, 0.14, 0.1

As can be seen above, error or accuracy is similar for the 3 frequencies.
 
#14
That is the suspicious data for xcapz2 (where impedance at 100.237 is 48.5779). Your later data for Nichicon and Lojzek Visaton both shows similar curve (where impedance at 100 is around 15).

I think your phase number is wrong. Not 80 but 87.53.
 
#17
It maybe just runs out of adequate constant current in LF for high uF caps (?)

Anyways, all this shows that the tracer rig must be fully proper and cross checked before taking any or some of its results literally.
 
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