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LCR Impedance Viewer for Picoscope+Keysight+R&S Bode Plot Data (open source)
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_Wim_:
Hi Hans,

I am not following your explanation why the result is wrong, could you elaborate a bit more?

To be honest, I do not think the result is wrong, I think the difference is in the end goal we want to achieve. The calculation I have implemented is to find the equivalent series capacitance and equivalent series resistance for the DUT. The second calculation (that I have not implemented), would calculate the equivalent parallel capacitance and equivalent parallel resistance for the DUT. These should be 2 different results, and I think this is how it is commonly done for an LCR/impedance meter. This is also confirmed by the fact the analog discovery had a very similar result. Your suggestion that series/parallel can be calculated with the same equations does not seem logical to me (why else would almost every LCR meter have a separate mode for this)

I think your goal is to calculate the capacitor independent of the series / parallel resistor. But this does not characterize the DUT as a whole. With an extreme example of a capacitor with a 100 ohm resistor in parallel, the series mode is indeed useless but still correct (this did confuse me also however, I would have expected a more reasonable result). I should have implemented both modes when I was writing the app, but as my main goal for the app was to check capacitor quality at frequencies high than my HP could handle (tops out at 20kHz), series mode (aka ESR) was all I needed.

There are for sure many different ways to do all of this. Keysight has and impedance measurement handbook (https://www.keysight.com/be/en/assets/7018-06840/application-notes/5950-3000.pdf) that has probably sufficient info to build a really high end system, but I only stuck to the very basics.

Wim
Hans Polak:
Hi Wim,

What I tried to explain is that you cannot simply invert a complex number and still keep using the original imaginary part.
As I have shown, you have to rearrange the formula and split it again in real and imaginary.
You didn't do that, which is mathematically wrong.
The result B/(A^2+B^2) instead of 1/B that you are using happens to be true for very small values of A, thus very small values of Resr, which is the case with a serial connection.

The formula that could fit parallel connections would then be for very small values of B, because in that case you will get B/A^2.
But in the images below you can see that in this B/A^2 only fits at very low frequencies, far below the 100Hz where the graph starts, whereas B/(A^2+B^2) does the job as expected.

So with the series connection 1/B happens to go well, but with the parallel connection 1/B fits very bad, in this very case there is only some overlapping above 1Mhz.
So this is just to say that there is no separate formula for parallel connections.
When you disagree, I would welcome that formula.

Maybe someone reading this correspondence who is fit in complex calculation can confirm my calculation.
My goal is to find the capacitance for an unknown circuitry and not for a single series cap. For that I can use my cap meter.

Hans
_Wim_:

--- Quote from: Hans Polak on May 13, 2021, 07:36:00 pm ---So this is just to say that there is no separate formula for parallel connections.
When you disagree, I would welcome that formula.

--- End quote ---
See page 6 for conversion between series and parallel capacitance.

http://www.componentsengineering.com/wp-content/uploads/pdfs/LCR-Measurement-Primer.pdf


--- Quote from: Hans Polak on May 13, 2021, 07:36:00 pm ---What I tried to explain is that you cannot simply invert a complex number and still keep using the original imaginary part.
As I have shown, you have to rearrange the formula and split it again in real and imaginary.
You didn't do that, which is mathematically wrong.
The result B/(A^2+B^2) instead of 1/B that you are using happens to be true for very small values of A, thus very small values of Resr, which is the case with a serial connection.

--- End quote ---

The attached figure shows I think best why this is done. When we express Z_DUT in 2 ways:
  Z_DUT = Resr            – j / (2*π* f*C)
  Z_DUT = Zmag* cosα + j* Zmag*sinα

From this we see that
  Resr = Zmag * cosa
 -1  / (2*π* f*C) = Zmag * sina

=> both are not complex numbers any longer, and all calculations are done in an algebraic way.

Edit: forgot to add the minus sign
_Wim_:
An important paragraph why we should not expect the values to be the same
Hans Polak:
Wim,
I think we should leave the subject, because we are not coming together as it seems.
When 1/jwC=A+JB, it is mathematically wrong to conclude that jwC=1/jB, because one j is in the numerator and the other j is in the denominator.
Correct is: jwC= IM(1/(A+JB). Solving this leads to wC=B/(A^2+B^2).
And as mentioned, for very small values of A as in serial connections, this becomes the 1/B that FRA Imp Viewer uses.

But after this all, here's a really positive thing that I would like to mention, which is the calibration.
I asked you a few days ago to possibly include the probe's capacity in the calculation, but I found a much better way, making this question completely  obsolete.
With FRA4PS I record the chain without a DUT, but of course with the necessary measuring probes in place. Ideally this should give a flat Bode diagram with phase permanently at zero degrees.
Look at the first image below how the Bode diagram looks in my case.
And altough this doesn't look to bad, only 0.06dB and 6 degrees removed from the ideal, the effect of this can be quite massive as we will see.

Now store this Bode diagram as a .csv file, open it in Excel and make a second set with Log Freq, -1*Gain in dB  and -1*Phase.
This second set will be your future correction set.
To show the effect, I took a 1x probe as a DUT.
Without any correction, results are shown in the second image.
But when correcting this recording in Excel by adding the gain in dB and phase of the correction set, the now corrected data produces quite a different plot, see the the third image.
So this is way more accurate than just specifying the capacity of the measuring probe.
What you see are resp. Impedance, Resr and two plots for the Capacity, one is using 1/B as in FRA and the second using B/(A^2+B^2),  [with A and B being resp. the RE and IM part of Z].
Result is very good after correctio,  isn't it.

Hans


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