Do I misunderstand ESR measurement? Frequency dependence of ESR

[G0HZU]

Same test jig, same test frequency but ESR of the model increased to 0.25R. You can see two of the three voltages are now subtly different and this is why you need a really good voltmeter for this stuff. The source has to be clean and stable too.

It calculated 0.2497R for the ESR at 10kHz.

[G0HZU]

Often when I try and share knowledge and experience on the web, an ‘expert’ stubbornly refuses to accept my input. This time there’s two of them  and they are posting up lots of equations and theory

Maybe because the shared knowledge and experience is flawed 

If you make three scalar voltage measurements you can reverse engineer the ESR of the DUT using just an AC voltmeter even if the ESR is much smaller than the reactance. This technique has been around for many years but it does require a few equations to work out the vectors from three scalar measurements.

Don't think this is possible, so calling you out this. Care to share your many years old 3 scaler measurements technique and methods to enlighten us old schoolboys

According to both of you, this can’t be done because of your schoolboy reasoning about the reactance being much bigger than the ESR.

Might be time to revisit some old elementary electronics schoolboy texts to get a grasp on complex values, what reactance/impedance means and how to evaluate such

Best

Mawyatt's comments above aren't going to age well on this thread... 

[tggzzz]

I'm quite busy at the moment so I can't spend much time on this, but I've dug out my old excel spreadsheet for this stuff. Give me some more time and I'll set up some 'real' tests with real test gear.

I've used a simulation (shown below) to get the AC voltages and then put them into the spreadsheet. ...

You show the results of a simulation of something using some hidden calculations.

Show the equations used to specify the calculations, defining the terms as appropriate.

[tggzzz]

Mawyatt's comments above aren't going to age well on this thread... 

 

Mesdames et Messieurs, faites vos jeux s'il vous plaît.

[G0HZU]

I'm quite busy at the moment so I can't spend much time on this, but I've dug out my old excel spreadsheet for this stuff. Give me some more time and I'll set up some 'real' tests with real test gear.

I've used a simulation (shown below) to get the AC voltages and then put them into the spreadsheet. ...

You show the results of a simulation of something using some hidden calculations.

Show the equations used to specify the calculations, defining the terms as appropriate.

I can't find the IEEE paper yet but it should be obvious that you can sometimes reverse engineer angles (vectors) from multiple scalar measurements. This isn't rocket science.

I may have to log in to work to get IEEE access or you could just google for "three voltage method impedance" or something like that. This should find numerous papers on this but they might not have accurate equations. Probably lots of diagrams and lots of equations though...

Note: If you want to try this yourself using test gear, don't use three different voltmeters to speed up the process. It's best to just use one even though it takes longer to do it. Otherwise the accuracy may suffer.

[mawyatt]

I'm quite busy at the moment so I can't spend much time on this, but I've dug out my old excel spreadsheet for this stuff. Give me some more time and I'll set up some 'real' tests with real test gear.

I've used a simulation (shown below) to get the AC voltages and then put them into the spreadsheet. ...

You show the results of a simulation of something using some hidden calculations.

Show the equations used to specify the calculations, defining the terms as appropriate.

I can't find the IEEE paper yet but it should be obvious that you can sometimes reverse engineer angles (vectors) from multiple scalar measurements. This isn't rocket science.

I may have to log in to work to get IEEE access or you could just google for "three voltage method impedance" or something like that. This should find numerous papers on this but they might not have accurate equations. Probably lots of diagrams and lots of equations though...

Note: If you want to try this yourself using test gear, don't use three different voltmeters to speed up the process. It's best to just use one even though it takes longer to do it. Otherwise the accuracy may suffer.

How are we supposed to utilize the 3 scalar measurements to resolve the real part of the capacitor impedance. We all can make these measurements, we just did on a 1uF film cap utilizing a KS34465A for all 3 measurements and verified the C and Rs at 10KHz by IM3536 LCR measurement, so we know what the correct answer is!!

A quick preliminary look at the math by a page of scribbles indicates the result is a quadratic in Rs which "hints" that the results might be highly influenced my measurement inaccuracies!!

Please enlighten us with how to apply these 3 scalar measurements, we are eager to learn something new

Best

[G0HZU]

FFS just google

three voltage method impedance

For the theory and equations.

if I measured a 1uF WIMA cap at 10 kHz the reactance is going to be about -15 ohms. The ESR is probably going to be less than 0.2R.

In your (and TimFox's) interpretation of reality I can't possibly measure this with scalar measurements because the reactance is 80 times greater than the ESR at 10kHz.

In my reality, I think the three voltage method will be able to get quite close to the correct ESR of 0.2R at 10 kHz. I know this because I've made these measurements many times.

For sure it isn't going to deliver metrology grade accuracy but it will be able to deliver similar results to a hobby grade handheld LCR/ESR meter. Which is why I suggested it as a way to cross check the results from a typical LCR meter to see if they are sensible.

[G0HZU]

Give me some time this evening and I'll set this up. I'll measure the ESR of a 1uF WIMA cap at 10kHz and then I'll put a precision 1 ohm  1% resistor in series with it and measure it again. The second reading should be ESR + 1 ohm. I know this is going to work well because this was the way I evaluated this process many years ago. So I'll be measuring a ~1 ohm ESR for a cap with about -15 ohm reactance for the second reading.

To do this properly requires a fixture with two test sockets. Obviously, I can't use a soldering iron to make any connections or it will cause thermal drift. So I'll need to add another test socket with the 1R resistor at the ground end.

It isn't going to compete with $$$ lab instruments but it will at least prove to the 'experts' and doubters here that it is possible to reverse engineer vector based information from a set of three scalar measurements. This technique is decades old but it does require a very good voltmeter and a clean and accurate and stable signal source if you want to measure capacitors like a 1uF WIMA at a few kHz

[mawyatt]

Well we just made the measurements based upon the AI description. Curious why you won't post your methods and "hidden" calculations?

AI claims solution by constructing a vector diagram and solve by using law of cosines? This doesn't make sense as how do you construct a Vector Diagram with 3 Scalars?  Anyway we followed the description and the result for Rs was 0.395Ω at 10kHz with KS34465A, we repeated the 3 measurements and computations with same result.

However, our measurements of the same capacitor (1uF film) on our IM3536 (1.00236uF and 28.14mΩ) with a leaded TH26048A fixture at 10kHz. So we repeated the measurement on our TH2830 at 10kHz, at 1.00238uF and 28.51mΩ.

Edit: Checked another 1uF Film Type Knscha MPX/MKP, measured 1.02550uF 18.12mΩ with IM3536, using the 3 scalar technique described by AI we get RS = 118mΩ!!

Went back and measured with the 3 scalar technique, same result, Rs = 0.395Ω.

Not sure what to make of this 3 scalar technique, maybe we messed up the measurements/calculations (per AI)

BTW still waiting for your technique details and "hidden" calculations

Best

[armandine2]

...in my AI search I added loss angle , better suited than esr , to 3 voltmeter method 

.. and my google search for 3 voltmeter method showed how to measure and calculate power factor (albeit in an inductive load).

[G0HZU]

This is getting a bit like Youtube where everything is declared 'fake' by all knowing keyboard warriors   

Anyway, it took me less time than expected to set this up and I tested with the raw 1uF cap, then with 0.1R inline and then with 1R inline. I have to say the results came out better than expected but this time I used an old Agilent ESGD sig gen to output an LF signal at 10 kHz as this has very low distortion and is very accurate and stable.

The images below are screenshots from my EeePC for all three cases. You can see that the ESR was about 0.16R at 10kHz. With the 0.1R 1% resistor it was 0.27R and with the 1R 1% resistor it was 1.17R.

By all means study the voltage readings and try and prove the basic ESR measurement is fake or wrong or whatever Some of the other onscreen cell data was added as useful info but these cells may contain nuts as I only really look at ESR and reactance etc.

[G0HZU]

You can also see in the top right corner of the EeePC GUI I added a crude uncertainty indicator. There are test conditions where this setup can give huge measurement uncertainty if an unsuitable sense resistance or test frequency is used. So the cells in the top corner show how much the results change with a voltage error for at least one of the voltage readings. I can't remember how I set this bit up but it can be very useful as it easily spots cases where I've used the wrong sense resistor and/or test frequency.

[gf]

Well we just made the measurements based upon the AI description. Curious why you won't post your methods and "hidden" calculations?

AI claims solution by constructing a vector diagram and solve by using law of cosines? This doesn't make sense as how do you construct a Vector Diagram with 3 Scalars?  Anyway we followed the description and the result for Rs was 0.395Ω at 10kHz with KS34465A, we repeated the 3 measurements and computations with same result.

Here's how Gemini explains and derives the ESR estimation with the 3-voltmeter method:
https://g.co/gemini/share/c2a7524730d0
I checked it only briefly, but the calculation seems plausible.

Even more interesting would be error propagation, i.e. how the relative uncertainty of the estimated ESR depends on volt meter uncertainty, Q of the DUT, and the choice of Rref.

[G0HZU]

...in my AI search I added loss angle , better suited than esr , to 3 voltmeter method 

.. and my google search for 3 voltmeter method showed how to measure and calculate power factor (albeit in an inductive load).

Yes, in recent years, I've moved across to using an Analog Discovery 2 for measuring components so this is the first time I've used the Excel spreadsheet or the EeePC program in quite a while. The AD2 is much faster and it may well be more accurate most of the time. It can use a sense resistor too and it can measure phase so it can compute ESR a different way.

Many years ago I used to use a two channel scope to measure ESR by measuring amplitude and phase but this was quite clunky and not as accurate. I use a different tab of that excel sheet when using a scope. I've also used my HP8405A vector voltmeter for this stuff too. But not many people will have an AD2/3 or a vector voltmeter. The AC voltage + sense resistor method can give good results as long as a decent AC voltmeter is used. If the wrong choice of sense resistor is used for a chosen component or an unsuitable test frequency is chosen then it can give crazy results. So some experience is needed.

[G0HZU]

Mawyatt: How do you propose to extract the Real part (R) of a complex impedance ({R -j/(wC)} of Cap DUT) unless the capacitive reactance 1/(wC) is << than R?

I think this extraction of R has now been demonstrated to be possible with the online info and my test results. In my example with the 1uF WIMA cap, the ESR was about 90 times lower than the reactance. Yet this method gave pretty good results.

You claimed the reactance has to be << than R which is obviously wrong by at least two orders of magnitude in my example with the 1uF cap.

Do you now agree you were quite wrong here?

[TimFox]

Your first four posts did not specify three voltage measurements, but you did in the fifth post.
I can see how the law of cosines could calculate a real and imaginary part;  when I have time, I’ll consider the resolution for the “minority component”, ESR in this case, due to subtracting large numbers.
My original comments related to using the external resistor to measure the current through the part, then measuring the voltage across the part, giving the impedance magnitude, based on your original description.

[G0HZU]

Your first four posts did not specify three voltage measurements, but you did in the fifth post.
I can see how the law of cosines could calculate a real and imaginary part;  when I have time, I’ll consider the resolution for the “minority component”, ESR in this case, due to subtracting large numbers.
My original comments related to using the external resistor to measure the current through the part, then measuring the voltage across the part, giving the impedance magnitude, based on your original description.

Go back and look again. You were still claiming scalar measurements were no good in post #120.

TimFox: Again, the magnitude (or scalar) measurements can only give the magnitude (complex absolute value) of the device’s impedance.  Phase-sensitive (or vector) measurements are required to separate the real (resistance) and imaginary (reactance) components of that impedance.

So you were still wrong in post #120.

[G0HZU]

G0HZU post #117:
If it helps, I’m measuring the AC voltages around the sense resistor. I measure the input voltage, the voltage across the series sense resistor and the voltage across the DUT capacitor and from this I can calculate both the reactance and the ESR.

G0HZU post #118: If you make three scalar voltage measurements you can reverse engineer the ESR of the DUT using just an AC voltmeter even if the ESR is much smaller than the reactance. This technique has been around for many years but it does require a few equations to work out the vectors from three scalar measurements.

Mawyatt #119: Don't think this is possible, so calling you out this. Care to share your many years old 3 scaler measurements technique and methods to enlighten us old schoolboys

Do you now accept that this is actually possible?

[mawyatt]

Mawyatt: How do you propose to extract the Real part (R) of a complex impedance ({R -j/(wC)} of Cap DUT) unless the capacitive reactance 1/(wC) is << than R?

I think this extraction of R has now been demonstrated to be possible with the online info and my test results. In my example with the 1uF WIMA cap, the ESR was about 90 times lower than the reactance. Yet this method gave pretty good results.

You claimed the reactance has to be << than R which is obviously wrong by at least two orders of magnitude in my example with the 1uF cap.

Do you now agree you were quite wrong here?

No, because the 3 Scalar results we got were not even close to the actual value we measured with 2 different capacitors and the 3 Scalar measurements producing results of 395mΩ vs 28mΩ for the LCR meter, which is a factor of >14 in error, also measured the other capacitor as 18mΩ vs 118mΩ. Neither of these 3 scalar measurements are even close to the actual capacitor Rs value and we are using your suggested 1uF film type. We get better results with a T7 than the 3 Scalar technique

This confirms what we stated earlier about this measurement technique as it could be sensitive to uncertainties. The fact we can't get values even close to the quality lab grade bench LCR meters indicates this measurement is unrealistic and worthless for any kind of useful purpose. In fact we can't get any useful results with any of the capacitors we've measured with this 3 Scalar technique, and these now include a 1000uF 16V, a 4.4nF Soviet mica, and a 10nF film, all producing results not even close to the IM3536 LCR meter. Suspect this might be due to having to change the frequency and/or the sense resistor for the higher Z capacitors, but still useless!!

Anyway, for now we'll stand by what we said and also state what we've found with this 3 Scalar technique, it's worthless for any kind of quality capacitor Rs measurements where semi-accurate results are required.

Hopefully others will attempt this technique and report results, maybe even prove us wrong

Best

[mawyatt]

Mawyatt #119: Don't think this is possible, so calling you out this. Care to share your many years old 3 scaler measurements technique and methods to enlighten us old schoolboys

Do you now accept that this is actually possible?

Yeah, about as possible as measuring the temperature drift and aging of a LTZ1000 with a Simpson VOM 

Best

[TimFox]

Your first four posts did not specify three voltage measurements, but you did in the fifth post.
I can see how the law of cosines could calculate a real and imaginary part;  when I have time, I’ll consider the resolution for the “minority component”, ESR in this case, due to subtracting large numbers.
My original comments related to using the external resistor to measure the current through the part, then measuring the voltage across the part, giving the impedance magnitude, based on your original description.

Go back and look again. You were still claiming scalar measurements were no good in post #120.

TimFox: Again, the magnitude (or scalar) measurements can only give the magnitude (complex absolute value) of the device’s impedance.  Phase-sensitive (or vector) measurements are required to separate the real (resistance) and imaginary (reactance) components of that impedance.

So you were still wrong in post #120.

OK:  my post 120 was in reply to mawyatt's post 119, and I had not noticed your post 117 by then.
I'm still dubious about the three-voltage measurement for high-Q capacitors, but I haven't done the math yet.

[G0HZU]

Mawyatt #119: Don't think this is possible, so calling you out this. Care to share your many years old 3 scaler measurements technique and methods to enlighten us old schoolboys

Do you now accept that this is actually possible?

Yeah, about as possible as measuring the temperature drift and aging of a LTZ1000 with a Simpson VOM 

Best

Mawyatt: Any scalar voltage measurement (DVM ACrms) reveals the magnitude [sqrt(Imaginary^2 + Real^2)] of the voltage measurement, wether across a resistor (Real), ideal capacitor/inductor (Imaginary) or complex impedance (both Real and Imaginary like Cap DUT).

How do you propose to extract the Real part (R) of a complex impedance ({R -j/(wC)} of Cap DUT) unless the capacitive reactance 1/(wC) is << than R?

I've shown you how to extract R when the ESR is less than the reactance and shown you that your schoolboy claim above is wrong and there are plenty of papers about the 3 voltage method online that show your claim to be wrong. By all means conjure up an extreme case where the technology struggles but the same can be done with any measurement technique.

Mawyatt; How do you propose to extract the Real part (R) of a complex impedance ({R -j/(wC)} of Cap DUT) unless the capacitive reactance 1/(wC) is << than R?

If it helps this statement is the one that really exposes your ignorance with respect to this 3 voltage technique. You obviously didn't have a clue how it works.


Just admit that you were wrong and you weren't aware of this three voltage technique and we can all go home

[mawyatt]

Well we just made the measurements based upon the AI description. Curious why you won't post your methods and "hidden" calculations?

AI claims solution by constructing a vector diagram and solve by using law of cosines? This doesn't make sense as how do you construct a Vector Diagram with 3 Scalars?  Anyway we followed the description and the result for Rs was 0.395Ω at 10kHz with KS34465A, we repeated the 3 measurements and computations with same result.

Here's how Gemini explains and derives the ESR estimation with the 3-voltmeter method:
https://g.co/gemini/share/c2a7524730d0
I checked it only briefly, but the calculation seems plausible.

Even more interesting would be error propagation, i.e. how the relative uncertainty of the estimated ESR depends on volt meter uncertainty, Q of the DUT, and the choice of Rref.

This link doesn't agree with the AI Overview response generated when searching "three voltage method impedance". We didn't check the math but the AI shows a result for Zx (Real part of Z) which has the denominator as 2*V2*V3, whereas the gemini link above shows equivalent of 2*V2^2.

Need to spend some time looking at the math behind all this, but we threw in the measured values we acquired earlier with the 1uF Film and the result from the gemini solution is still in significant error.

Edit: We found another Google AI reference that follows the denominator of 2*V2^2, where V2 is the voltage across the series resistor R or Vref, so this seems correct. We also verified this is correct by means of a simple circuit which evaluated correctly for Rs, the other AI (2*V2*V3) did not. Also noted the Gemini reference has a date of 10/9/2025 at 4:48 PM and published at 5:00PM? Not sure what this means?

Best

[mawyatt]

I've shown you how to extract R when the ESR is less than the reactance and shown you that your schoolboy claim above is wrong and there are plenty of papers about the 3 voltage method online that show your claim to be wrong. By all means conjure up an extreme case where the technology struggles but the same can be done with any measurement technique.

And we've followed your described 3 Scalar method using 2 different quality DMMs (KS34465A and DMM6500), altho we had to search as you wouldn't disclose the details as requested by a couple folks, which hints that you have something to hide, otherwise why not post the requested information to support your claims, and we even utilized the same value and type capacitor 1uF film you claimed along with the same 100Ω sense (actually 99.5158Ω @ 10KHz). Yet our results weren't close to the LCR measurements made by quality LCR meters which both agreed quite well.

Since you seem to be hiding something wrt the 3 Scalar computations (multiple requests), we searched on line and now gf has posted another AI link which differs as we mentioned. Which one is correct and what are your results based upon?? 

So basically what you've claimed to have shown doesn't work for us with the same type 1uF film cap and 100Ω sense resistor at same 10kHz and you are still hiding your details after multiple requests, so what's to acknowledge??

Best

[G0HZU]

I'm not trying to hide anything.

If you look at my software, I must have looked at this about 10 years ago. I probably generated the excel spreadsheet a year or two before this. So I've had two PCs and several HDDs since then. So I've long since lost my notes on this stuff.

However, take a look at the vector diagram below of the three voltages I measured with my Keithley 2015 meter.

Do you accept that it is possible to work out the angle shown in the diagram below based on the three voltages that make up the triangle? There should only be one solution for this angle.

This is how this system is able to extract vector information from scalar measurements.

Once this angle is known then it's possible to work out the magnitude of the reactance and also the ESR using more equations.