Do I misunderstand ESR measurement? Frequency dependence of ESR

[joeqsmith]

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And now, an important question comes up: Are the errors of the measured voltages correlated, or not?
Correlated versus uncorrelated makes a big difference! (I observed factor 5...10)
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Assuming three subsequent AC voltage readings of a stable signal, with all three readings performed on the same range and at the same frequency, I would expect the voltage errors to be highly correlated (close to to 1.0), and rather the correlated estimated would apply. But please correct me, if this assumption is wrong.
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From my previous post you could get some idea what the drift and noise looks like.  Of course, I am moving leads around, touching stuff.... for each measurement. 

To plot the amplitude drift, the HP34401A was attached directly to the RF generator, which was set to 10kHz.   Shown is the drift over a 10 minute period, assuming I am very slow at taking these measurements. For a 1V signal, about 70uV of drift.  Really though, it maybe takes me 2 minutes to make all three readings. (plus it will settle as the temps stabilize)   

***
Forgot to mention, when I had replicated GOHZU's application, it seems they have some sort of mux attached to their meter.  Notice the button next to each reading.  I would imagine this could improve things, just in that I could cover things up with a beach towel and not be fingering it. 

[G0HZU]

I had hoped G0HZU would have chimed in by now.   Hopefully it's not a case where they so badly wanted people to admit they were wrong,  that the idea of them potentially being right was more than they could handle. 

Simulating the sensitivity to the voltage measurement, I am holding everything constant and just adding error to the DUT's voltage measurement.  Shown using a 1.5uF cap tested at 10kHz.  If the cap's ESR is 10 ohms, and I sweep the measured voltage of the cap 1mV (a very poor meter) the error is less than 0.2%.   

The PP part I am trying to test has a typical ESR of 0.004 ohms.   Sweeping the cap's measured voltage 10uV causes about 2% error in the ESR.

While my calculations could very well be wrong (no AI was used),  the jest is higher Q devices will place a heavy demand on the instruments to get any level of accuracy when using this method.

I've been in hospital for three weeks for an op. But I'm back now.

I never suggested using this to replace an ESR meter, just as a means for a beginner to do a one off sanity check of a reading from a low cost ESR meter. Otherwise it is just too slow and clunky for regular use. The voltmeter needs to have good linearity and it's best to choose a sense resistor that gives similar voltage readings for all three voltages if you want the best from it.

I don't have much free time at the minute as I'm back in hospital tomorrow. But I should be home again the same day. But back again in hospital Monday. Then I might have more time.

This isn't the metrology forum it's the beginner's forum and I never intended anyone to explore the limits for high Q caps. I suggested 0.1R ESR and 15R reactance as an example that a beginner might want to measure. Something like a basic 1uF WIMA cap for example. This might get used in a filter or oscillator for example.

[G0HZU]

You do have to make the three measurements quickly with a decent bench DVM like a Keithley 2015 THD and it's best to do it via GPIB and to use connectors and a twisted pair wire to the DVM. I can do it all in about 5 seconds for example using that old VB6 app. I've been using this technique since about 2015 with good results but this takes some experience.

I've never tried to measure high Q caps with this method. For example, I would expect that the measurement of a 1-2uF cap with 0.004R ESR at 10kHz is going to be very challenging for any low cost ESR meter.

To be fair to my original claim, limit the ESR to about 0.1R and use a sensible choice for the sense resistor like 10-15R for the 1uF cap at 10kHz. I've already provided example measurements that were OK using an old Keithley 2015 THD meter.

Can a DE-5000 measure a 1-2uF cap with 0.004 ohms ESR at 10kHz for example? I've never used a DE-5000. What does the display show for a DE-5000 for the 0.004R ESR? I'll be impressed if it can measure this with a good result...

Otherwise, where will this lead? Is someone going to find a cap with even lower ESR than 0.004R? But can a low cost (beginner's) ESR meter also measure it?

[David Hess]

Can a DE-5000 measure a 1-2uF cap with 0.004 ohms ESR at 10kHz for example? I've never used a DE-5000. What does the display show for a DE-5000 for the 0.004R ESR? I'll be impressed if it can measure this with a good result...

I have some Tektronix oil filled plastic film capacitors (used for timing) in that range and a DE-5000.  Hmm, their ESR is about 0.05 ohms, so not low enough.  At 100 Hz the DE-5000 reports overload for their Q measurement and a D of 0.000, so that makes sense.

The capacitors may be better than that while the DE-5000 test setup is not good enough.

[gf]

Can a DE-5000 measure a 1-2uF cap with 0.004 ohms ESR at 10kHz for example?

The DE-5000 datasheet specifies an ESR accuracy of 0.3% of |Z|. For a 1 µF capacitor at 10 kHz, that would be 0.3% of ~16 Ω, or ±48 mΩ. Sure, the specified accuracy is Maximum Permissible Error (MPE), and it is usually quite conservative, so actual accuracy is probably better (but not guaranteed).

For decent ESR meters, the basic accuracy for angle measurements seems to be somewhere in the region around 0.03°. This translates to an ESR accuracy of ~0.03*π/180*|Z|, or ~0.05% of |Z|. Depending on the operating conditions, additional uncertainties are added on top of the basic accuracy. For a 1 µF capacitor at 10 kHz, 0.05% of ~16 Ω would be ±8 mΩ.

[mawyatt]

Can a DE-5000 measure a 1-2uF cap with 0.004 ohms ESR at 10kHz for example?

The DE-5000 datasheet specifies an ESR accuracy of 0.3% of |Z|. For a 1 µF capacitor at 10 kHz, that would be 0.3% of ~16 Ω, or ±48 mΩ. Sure, the specified accuracy is Maximum Permissible Error (MPE), and it is usually quite conservative, so actual accuracy is probably better (but not guaranteed).

For decent ESR meters, the basic accuracy for angle measurements seems to be somewhere in the region around 0.03°. This translates to an ESR accuracy of ~0.03*π/180*|Z|, or ~0.05% of |Z|. Depending on the operating conditions, additional uncertainties are added on top of the basic accuracy. For a 1 µF capacitor at 10 kHz, 0.05% of ~16 Ω would be ±8 mΩ.

Where did this come from?

This is much better than our Hioki IM3536 and Tonghui 2830 claim. Below is from the IM3536 manual and shows basic accuracy table for variable A and B which are used to calculate the basic instrument accuracy as shown in the next image.

At 10KHz Z accuracy variables A=0.2 and B=0.02 while Phase accuracy variables A=0.1 and B=0.01 in the 100Ω range.

With these the Z accuracy of a 1uF Cap at 10KHz equates to +-0.305% and Phase +-0.153 Degrees. Of course one "expects" a quality instrument to be better!!

Edit: The data sheet table for the DE-5000 shows a basic Phase accuracy of +-0.171 Degrees if we followed the notes correctly  {our old friend HP32S II has died so no RPN and done on phone calculator} 

Best 

[G0HZU]

I'm back from hospital again today but still suffering from drug side effects.

However, reading how this thread has degraded since I left it has been a bit disappointing. I can't explain why Joe and Mawyatt are getting such poor results but then again I've seen Joe make errors before so I'm not that surprised about this.
What I don't understand is how you can both f*ck this up so badly despite all the hints and tips I've posted to minimise uncertainty.

One thing I have got here now is a huge red 1uF safety cap I got from work. This should have low ESR at 10 kHz. Sadly I only have one of them. It should have an ESR lower than 0.1R at 10 kHz.

I know I'm completely wasting my time but I can demo (again) that this method can give good results but it does require someone who knows how to operate the (correct) test gear properly and process the results properly.

[G0HZU]

OK, I just measured the big 1uF safety cap and it has an ESR of 0.033R at 10kHz. See the third image below.

I also measured a basic 1uF WIMA cap and it has an ESR of 0.159R at 10kHz.

I then put them in parallel and measured them again and got an ESR of 0.048R and this agrees with theory. See the second image below.

Compare this to whatever Joe and Mawyatt are doing with their test gear and their maths. They are getting crazy results and i'm getting really tight results.

[G0HZU]

I then added the 0.1R 1% resistor inline with the big safety cap and saw an ESR of 0.142R. It should have been 0.133R if the previous 0.033R ESR measurement was valid and if the 0.1R resistor is accurate and there isn't any ESR in my test fixture socket.
Either way, its a pretty good result.

[G0HZU]

I then tried putting two 0.1R resistors in parallel (to make 0.05R) and added this series with the 0.033R ESR of the safety cap.

I measured 0.09R (should have been 0.0833R) which is pretty good considering I'm using a socket system to make it easy to put things in series and parallel.

[G0HZU]

I'm not sure what else to suggest, but for this test type, my test fixture uses a series termination resistor of about 50R just before the voltage measurement point. This helps keep the sig source terminated and probably puts less strain on any ALC system it may use. It's also worth using a source that is accurate, stable and clean with low harmonics. I also use averaging inside the DVM for all three voltage measurements.

I tried a different bench DVM and got very similar results. However, I do think it becomes risky to explore below 0.1R ESR in this case as there will be increasing uncertainty as the ESR is lowered. I'm not sure why Joe chose 0.004R ESR to test this method as this is also asking a lot of any cheap beginner's ESR meter to measure.

[gf]

For decent ESR meters, the basic accuracy for angle measurements seems to be somewhere in the region around 0.03° ...

Where did this come from?

This is much better than our Hioki IM3536 and Tonghui 2830 claim. Below is from the IM3536 manual and shows basic accuracy table for variable A and B which are used to calculate the basic instrument accuracy as shown in the next image.
...

I had asked Google to name a few decent LCR meter models and their phase angle accuracy. Screenshot attached.

Now, I also looked at the datasheet for your Hioki IM3536, and it also says 0.03°. See screenshot.
However, this only applies to a few measurement conditions. Additional uncertainties are added on top for other measurement conditions.

What I actually wanted to show is that, even if the accuracy were 0.03° (which can be considered decent), the ESR accuracy for 1 µF at 10 kHz would not be better than ±8 mΩ.

[mawyatt]

For decent ESR meters, the basic accuracy for angle measurements seems to be somewhere in the region around 0.03° ...

Where did this come from?

This is much better than our Hioki IM3536 and Tonghui 2830 claim. Below is from the IM3536 manual and shows basic accuracy table for variable A and B which are used to calculate the basic instrument accuracy as shown in the next image.
...

I had asked Google to name a few decent LCR meter models and their phase angle accuracy. Screenshot attached.

Now, I also looked at the datasheet for your Hioki IM3536, and it also says 0.03°. See screenshot.
However, this only applies to a few measurement conditions. Additional uncertainties are added on top for other measurement conditions.

What I actually wanted to show is that, even if the accuracy were 0.03° (which can be considered decent), the ESR accuracy for 1 µF at 10 kHz would not be better than ±8 mΩ.

Our note was directly from the Hioki IM3536 manual (as shown) on accuracy estimates with the 1uF DUT Cap (16Ω at 10KHz), which should include the effects of the DUT, frequency, and range settings. So not just a generic accuracy spec (maybe sweet spot) but specific to the 1uF DUT under consideration at 10KHz. The actual IM3536 should be better than this, as quality instruments tend to generally outperform.

Anyway, thanks for the info.

Best

[G0HZU]

Here's an image of the ESR simulation/prediction for the two caps in parallel a few posts ago. You can see it agrees with the 0.048R I measured using the 3 voltage method.

I tried taking another read of all the stuff from Joe and spotted he had used an old Marconi 2024 sig gen to generate the test signal. I'm not sure this is a good idea as this is operating the RF sig gen right down at its lowest frequency and these are budget mid range sig gens at best. Worse than this, the  levelling (ALC) system they use is not great but is 'adequate' for most RF tasks. The ALC detector (and its impact on the source impedance etc) will probably be quite stretched down at 10 kHz. The spectral purity will probably be compromised and I doubt it will give enough drive level if the test fixture has the series termination resistor that I recommend the use of.

Try using something decent for the signal source rather than stretching the limits of an old low budget sig gen from Marconi. I would suggest using a function generator as long as it has good spectral purity. I used to use an analogue function generator most of the time for this stuff as I wasn't that fussed about accuracy. This cost me about £40 many years ago.

I've tried using three DVMs and four function generators and get similar results. I'm currently using the LF function generator output from an Agilent ESGD sig gen but also used other types and get similar results.

[G0HZU]

I really shouldn't have to explain this but if the signal source has harmonic distortion (like a Marconi 2024) and you feed the low impedance source directly to the sense resistor then any harmonics will add to the Vrms measurement of the Vin voltage and poison it if this is within the bandwidth of the DVM. Even quite low level harmonics can be a problem here.
After the sense resistor, the relative levels of these harmonics can change due to the RC effect of the test fixture with the DUT attached.

This will introduce systematic errors that can cause unexpected results and confusion. Some of my function generators have harmonic distortion down at about -80dBc and this should be OK for this stuff.

I can't be responsible for the incompetence and lack of experience of people who pretend to be experts on this forum.

[joeqsmith]

I'm back from hospital again today but still suffering from drug side effects.

However, reading how this thread has degraded since I left it has been a bit disappointing. I can't explain why Joe and Mawyatt are getting such poor results but then again I've seen Joe make errors before so I'm not that surprised about this.
What I don't understand is how you can both f*ck this up so badly despite all the hints and tips I've posted to minimise uncertainty.

One thing I have got here now is a huge red 1uF safety cap I got from work. This should have low ESR at 10 kHz. Sadly I only have one of them. It should have an ESR lower than 0.1R at 10 kHz.

I know I'm completely wasting my time but I can demo (again) that this method can give good results but it does require someone who knows how to operate the (correct) test gear properly and process the results properly.

....

I can't be responsible for the incompetence and lack of experience of people who pretend to be experts on this forum.

You can tag people if to notify them when you revive a thread.  Guessing the hospital stay, drug and failing health are contributing to your higher than normal levels of lashing out.   Looking back to when you dropped out:   

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This thread and the one it referenced started with film caps.  Q was brought up by Tim and G0HZU claimed "none of that matters".   
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A good film capacitor will have Q > 100, so the expected ESR can easily be < 0.1 ohms, depending on dielectric.
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None of that matters in this case. The sense resistor method will still be able to predict that the ESR is <0.1 ohms at 100 kHz. It can’t tell if it is a capacitor or an inductor but usually that doesn’t matter so the reactance can be assumed to be capacitive in this case.

A decent AC voltmeter with 5 digits and good accuracy and low drift is important as this helps to minimise uncertainty.

I am expecting G0HZU to chime in to demonstrate in detail what I am doing wrong as they have been very clear that this method gives good results when used within their constraints.  After all, it was important to them for members to admit they were wrong, suggesting they are right.  I am the king of fuckups and have no problems with them pointing out my mistakes.  So give them a chance to respond. 
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Of course, I measured a various low Q high ESR parts using your recommended method with decent results using both the Marconi and other generator/meter combos.  I didn't think that was ever in question.   It gets down to your original comment that Q does not matter.   A few of us jumped on it, and rather than owning that mistake, you doubled down and started to lash out at members.  In retrospect,  I assume this was due to health failing.

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I've never tried to measure high Q caps with this method. For example, I would expect that the measurement of a 1-2uF cap with 0.004R ESR at 10kHz is going to be very challenging for any low cost ESR meter.

To be fair to my original claim, limit the ESR to about 0.1R and use a sensible choice for the sense resistor like 10-15R for the 1uF cap at 10kHz.
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Otherwise, where will this lead? Is someone going to find a cap with even lower ESR than 0.004R? But can a low cost (beginner's) ESR meter also measure it?

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I'm not sure why Joe chose 0.004R ESR to test this method as this is also asking a lot of any cheap beginner's ESR meter to measure.

I chose this low ESR high Q part to show that your original blanket claims of it not mattering for your measurement was wrong.  Who owns what products if if they can or can not measure it have no bearing on the inaccuracy of your post.   Now you can whine and carry out with your childish comments but it will not change the outcome.   

[G0HZU]

It gets down to your original comment that Q does not matter.

No, I obviously don't mean that Q doesn't matter. That is due to the irrational way you misinterpreted my response to TimFox who was saying that my method can't work unless the reactance is much less than the resistance. It doesn't matter if the reactance is greater than the resistance with this 3 voltage method. Obviously, there are realistic limits to anything but I gave an example where the reactance was 150 times greater than the ESR. He thought it had to be the other way around.

In your version of reality this means an open book to reduce the ESR down to really low levels towards infinite Q. Why stop at 0.004R why not 0.000000004R? 

It's not my fault or my problem if you can't interpret my posts in a rational way. I gave the 0.1R ESR and -15R reactance example many times.

Attempting to test this using a Marconi 2024 (with its harmonic distortion) as the signal source shows a complete lack of understanding of what contributes to the overall uncertainty. Again not my fault or my problem that you can't work this out for yourself.

[G0HZU]

To anyone still reading this thread, the 3 voltage method I proposed is a really elegant way to check a questionable result achieved using a low cost ESR meter.

Meanwhile Joeqsmith thinks I'm proposing something that can measure Q levels up towards infinity (seriously?) because he thinks I claimed infinite Q doesn't matter. Even though I quoted 0.1R ESR many times and initially stated I'd never measured a 1uF cap at 10 kHz with an ESR below about 0.1R using this method. But Joe still thinks I claimed it can measure unlimited Q based on his irrational misinterpretation of one of my posts to TimFox.

[joeqsmith]

It gets down to your original comment that Q does not matter.

No, I obviously don't mean that Q doesn't matter. That is due to the irrational way you misinterpreted my response to TimFox who was saying that my method can't work unless the reactance is much less than the resistance. It doesn't matter if the reactance is greater than the resistance with this 3 voltage method. Obviously, there are realistic limits to anything but I gave an example where the reactance was 150 times greater than the ESR. He thought it had to be the other way around.

In your version of reality this means an open book to reduce the ESR down to really low levels towards infinite Q. Why stop at 0.004R why not 0.000000004R? 

It's not my fault or my problem if you can't interpret my posts in a rational way. I gave the 0.1R ESR and -15R reactance example many times.

Attempting to test this using a Marconi 2024 (with its harmonic distortion) as the signal source shows a complete lack of understanding of what contributes to the overall uncertainty. Again not my fault or my problem that you can't work this out for yourself.

You were asking for parts you could procure to run a independent test and I had these parts on-hand. 

The Marconi worked fine for measuring the lower quality parts.  The fact you continue to focus on that generator is a bit odd as it was only used for a couple of quick sanity tests.   

To anyone still reading this thread, the 3 voltage method I proposed is a really elegant way to check a questionable result achieved using a low cost ESR meter.

Meanwhile Joeqsmith thinks I'm proposing something that can measure Q levels up towards infinity (seriously?) because he thinks I claimed infinite Q doesn't matter. Even though I quoted 0.1R ESR many times and initially stated I'd never measured a 1uF cap at 10 kHz with an ESR below about 0.1R using this method. But Joe still thinks I claimed it can measure unlimited Q based on his irrational misinterpretation of one of my posts to TimFox.

Those readers can always view what was posted.  Again, I'll state your recommended method seems like a really stupid idea.  For low quality parts, I would imagine most RLC meters will get you in the ballpark.  A quick plug it in and measure.  Your crazy setup requiring high end meters, muxs to make fast measurement.....  just dumb.  There's really no benefit outside giving you something to blab about.   

[G0HZU]

Quote from: TimFox on October 08, 2025, 12:49:09 pm
1 uF at 100 kHz has a reactance of 1.6 ohms, and 16 ohms at  10 kHz.
Adding (real) 0.1 ohms to the (imaginary) 1.6 or 10 ohms reactance will not change the magnitude of the impedance much, nor affect the current through the device.
A good film capacitor will have Q > 100, so the expected ESR can easily be < 0.1 ohms, depending on dielectric.
It's easier to design an ESR meter for electrolytic capacitors with much lower reactance and higher ESR.

None of that matters in this case. The sense resistor method will still be able to predict that the ESR is <0.1 ohms at 100 kHz. It can’t tell if it is a capacitor or an inductor but usually that doesn’t matter so the reactance can be assumed to be capacitive in this case.

A decent AC voltmeter with 5 digits and good accuracy and low drift is important as this helps to minimise uncertainty.

I'm assuming that this is the post where Joe thinks I'm claiming the ability to measure infinite Q and infinitely low ESR with this 3 voltage  method.  I just meant to explain that TimFox's own example of adding 0.1R ESR to a reactance of 16R would be within the limits of the 3 voltage method. It doesn't matter if 0.1R ESR is small wrt the -16R reactance

Also there is no MUX required, just a clean function generator and a decent DVM. I can do the whole thing in a few seconds. It took Joe two minutes. Maybe Joe has a disability so I don't want to be too critical here.

[G0HZU]

Again, I really shouldn't have to explain this but the 3 voltage method is really elegant. The DVM mainly has to have good linearity because the three voltages make up the sides of a triangle. It therefore doesn't have to have a recent high end calibration, it just has to be healthy and linear.

As long as the signal source is clean (i.e. don't be a dumbass and use a Marconi 2024) and the sense resistor value is chosen carefully and its resistance is accurately known then you can compute ESR quite easily.
The nice thing is the theory behind it is well proven. It's a nice way to confidently check a low cost ESR meter if there is any doubt about the reading it shows on its LCD display.


Maybe this thread can end now because I'm growing tired of laughing at Mawyatt and joe's lame attempts to try and prove me wrong about this...

[joeqsmith]

Again, I really shouldn't have to explain this but the 3 voltage method is really elegant.

Even for you, that's a dumb statement.  Who in their right mind would think this would be more elegant than a low cost RLC.  The DE-5000 is elegant.   What you have shown is some off the wall, overly complex, old time way.  Most of us have moved on Gramps.

I think the fact that you are backing away from measuring high quality parts like we were discussing says we are at the end.   It was a stupid comment to make, but we are used to that sort of thing from you every now and then. 

***
status quo bias...

[joeqsmith]

Also there is no MUX required, just a clean function generator and a decent DVM. I can do the whole thing in a few seconds. It took Joe two minutes. Maybe Joe has a disability so I don't want to be too critical here.

To give your method the best chance of working with these high quality film caps, I was allowing it to settle after moving the leads.  As I mentioned, the mux your software shows would allow a hands off approach, allowing better control.

Now that you understand that your method really offers no advantage and you are only looking at jelly bean parts, all that slow reading goes out the window.  Then again, I can just plug the part into my RLC meter with zero setup time, one instrument, and very fast.   I guess for Gramps, that's not elegant.

[mawyatt]

Again, I really shouldn't have to explain this but the 3 voltage method is really elegant. The DVM mainly has to have good linearity because the three voltages make up the sides of a triangle. It therefore doesn't have to have a recent high end calibration, it just has to be healthy and linear.

As long as the signal source is clean (i.e. don't be a dumbass and use a Marconi 2024) and the sense resistor value is chosen carefully and its resistance is accurately known then you can compute ESR quite easily.
The nice thing is the theory behind it is well proven. It's a nice way to confidently check a low cost ESR meter if there is any doubt about the reading it shows on its LCD display.


Maybe this thread can end now because I'm growing tired of laughing at Mawyatt and joe's lame attempts to try and prove me wrong about this...

No one has been able to reproduce your self-proclaimed "elegant" approach with various capacitors and multiple attempts. So until others can consistantly reproduce your self-proclaimed "elegant" results, guess we're all laughing at you my friend

Best,

[G0HZU]

Again, you are misinterpreting what I mean. Elegant is often used to describe an engineering solution to a problem where the solution is relatively simple and the solution can be calculated using simple equations and (in this case) using proven test equipment. In other words, there is some theory behind the solution.

Even for you, that's a dumb statement.  Who in their right mind would think this would be more elegant than a low cost RLC.  The DE-5000 is elegant.

Read the thread again. I offered this as an elegant way to do a one off sanity check of a suspect reading from a low cost hobby meter. I never suggested this could replace the meter for everyday use. Just check a reading of ESR in the ballpark of 0.1R for a 1uF WIMA cap at 10 kHz.

So if someone has a dodgy reading from a cheapo ESR meter and they don't have another ESR meter (but they do have a decent DVM and function generator) they can so a sanity check of the reading.

If you can accept the bit in bold then we can all go home.