EEVblog #544 - Fluke 5450A Resistance Calibrator Teardown

[ddavidebor]

Why not? The grey beard woukd try to make it's best to hit the desired value!

This would end in a bell type distribution. (gauss curve)

[Dr. Frank]

The SI ampere is still defined via the force between two conductors. But that is impractical to realize, so standard labs derive it via Ohm's law. There is some work going on to redefine the SI ampere based on the charge of a proton. But the BIPM members are discussing that for years now, and they don't seem to be in a hurry to do the change.

Naa, that's not correct. The Proton experiment was too unprecise so it's not followed up.

The proposed and really planned change of the SI system is described here:
http://www.bipm.org/en/si/new_si/why.html  (Go through the details on the left side)

It begins with the redefinition of the kg by a (1) Si sphere and (2) the Watt balance, then defining fixed (exact) values of e, h and NA.

As soon as the new kg definition can be realized to a better level than the kg prototype in Sèvres (currently looses weight compared to copies), i.e. as soon as those two experiments agree better than 2x 10^-8, this new SI definition will be set active by BIPM. The status of the experiments  is checked every two years.

The Ampere would be then automatically defined by counting electrons (e.g. charge pump), and at a first step realized = mise en pratique by the - only then - exact definitions of Volt and Ohm by Josephson and von-Klitzing quantum standards.

Currently, Volt and Ohm are precise within SI to a level of about 3x10^-7 only (!), but can be practically realized to levels of about 10^-19 to 10^-9, depending on whether you compare e.g. different Volt standards on cryogenic level (SQUID) or at room temperature (problem of thermo voltages).

In a second, later step, if the charge pump experiments (counting electrons, SET) some day delivers currents big enough (nA) and without any missing electron counts, it would be possible to close the Metrological Triangle, i.e the values for e and h would be over determined by the measurements of U ~ f x h/e, R ~ h/e^2, I ~ e x f, and their numerical values could be measured exactly depending on the definition of the Second, instead of initially fixing their values arbitrarily.

As the current SI defintion of the Ohm is precise to 10^-7 Until only, such Ohm standards as the venerable Fluke 5450A and others, are fully sufficient.

Frank

[rs20]

The resistors will have something like a "bell curve" normal distribution.  If they've got a standard normal distribution, the chance of getting all four of them at the very bottom or very top of the range is very slim.  The very worst case would be that the percentage error in the combined resistance would be as bad as the percentage error on one of them.  But the average case is much better than that, even if you're not specially selecting the resistors in matched sets.

You can't assume a normal distribution (although the Fluke engineers might have had additional information), especially not one centered around the nominal value, so worst case is that you should assume a uniform distribution within the stated tolerance. Still, the standard deviation (and any confidence interval you care to calculate) of the parallel (or series) combination will be smaller than the single resistor. I believe the freely available book 'Analog SEEKrets' by Leslie Green contains a decent discussion of this topic.

When fluke describes the resistors as matched sets, they're doing something far better than relying on reducing standard deviations. As mentioned in the video, they'll be binned, that is, very accurately measured and grouped ("binned") according to measured value. Take a resistor from the 50.004 ohm bin and pair it with a resistor from the 49.996 bin, and hey presto, you're doing much, much better than the root-4 improvement you can expect to get from random chance.

[alm]

If you read the question AG6QR was responding to, you'll note it was about Dave mentioning the improvement in tolerance before he discovered they were selected, i.e. picking your resistors at random. Obviously you can get the error arbitrary small if you spend enough time selecting them.

[cengland0]

Dave said something that interested me.  There were four 40 ohm resistors in parallel to make 10 ohms.  Each resistor was at 0.05% tolerance and he said having four of them makes that better than 0.05%.  Why would that be?  Obviously later in the video he discovers they are all specially matched which could make this true but he said this before knowing that detail.

So each 40 ohm resistor could have a resistance between 39.98 and 40.02 ohms and still be within tolerance.  If each resistor just happened to be 39.98, you would have a total resistance of 9.995.  That is still 10 ohms at 0.05%.

The resistors will have something like a "bell curve" normal distribution.  If they've got a standard normal distribution, the chance of getting all four of them at the very bottom or very top of the range is very slim.  The very worst case would be that the percentage error in the combined resistance would be as bad as the percentage error on one of them.  But the average case is much better than that, even if you're not specially selecting the resistors in matched sets.

If you're randomly selecting the resistors, you can only put a statistical confidence level on the likelihood of the worst case not happening.  But if you individually select the resistors, combining high ones with low ones and medium ones with each other, you can guarantee that the worst possible case doesn't happen.

Not sure I agree with this because the 0.05% is already a worse case scenario on a single resistor and I can see the manufacturing process having an entire batch being either high or low.

I don't even know how to do the math on this one.  So assuming you are correct, if I connect four 0.05% resistors in parallel, what is the formula to determine the final tolerance of all combined?

[cengland0]

When fluke describes the resistors as matched sets, they're doing something far better than relying on reducing standard deviations. As mentioned in the video, they'll be binned, that is, very accurately measured and grouped ("binned") according to measured value. Take a resistor from the 50.004 ohm bin and pair it with a resistor from the 49.996 bin, and hey presto, you're doing much, much better than the root-4 improvement you can expect to get from random chance.

I understand that but my question was about Dave's comment before he noticed the schematic called for specially matched sets.  I would then have thought the resistors were randomly selected and would still have a better tolerance than a single resistor alone.  I'm asking for help understanding the math on that aspect because I can see how if you select a random set of four, on average the resistance should be on a normal distribution but each resistor is probably on a normal distribution too.  Only a few would be on the extreme value but that's why there's a normal curve instead of them all being an exact value.  However, can it be stated mathematically that if you combine four items on a normal curve, the final product will have a non-normal curve but will be more narrow?  How does that math work?

[alm]

I'm asking for help understanding the math on that aspect because I can see how if you select a random set of four, on average the resistance should be on a normal distribution but each resistor is probably on a normal distribution too.  Only a few would be on the extreme value but that's why there's a normal curve instead of them all being an exact value.  However, can it be stated mathematically that if you combine four items on a normal curve, the final product will have a non-normal curve but will be more narrow?  How does that math work?

I believe the freely available book 'Analog SEEKrets' by Leslie Green contains a decent discussion of this topic.

See chapter 3. Google should give you a link to the (legal) PDF version within a few seconds, hosted on this very site. It explains when and when not to use statistical tolerances, and gives some rules of thumb.

But I'll explain the basic case with the assumption that the resistors follow a normal distribution, which is not necessarily a fair assumption (see the book for reasons why and how to handle that). To keep it simple I'll first explain the series case. Assume the resistance of the 40 Ohm resistors is normally distributed with a mean of 40 Ohm and a standard deviation (or any multiple of the standard deviation, like a 95% confidence interval) of 0.05% * 40 Ohm, or 0.02 Ohm. The probability distribution of the total resistance of the four resistors in series is the sum of four normal distribution, which is another normal distribution with mean = sum of the means and variance (which is the standard deviation squared) = sum of the variances. If the total variance is the sum of the variances, then the total standard deviation is the root of the sum of squared standard deviations. So in this case the mean total resistance would be 160 Ohm with a standard deviation of sqrt(4*0.02^2) = 0.04 Ohm. This is 0.025% of the mean, i.e. half that the tolerance of the original resistors. A quicker way to calculate this for identical standard deviations is sd / sqrt(n), where sd represents the standard deviation of the individual resistor and n the number of resistors.

For the parallel case you can show that for normal distributions which are well above zero, the distribution of the reciprocal value is another normal distribution with mean 1/40 Ohm and standard deviation 0.05% * 1/40 Ohm. You can then add conductances to get the conductance of the four resistors in parallel, and again get a factor sqrt(4) improvement in standard deviation.

Note that this is about what the majority (eg. 99%) of the circuits is doing, as you note the worst case does not improve.

[cengland0]

If you were to design a resistance reference box like this today, wouldn't it be better to use solid state relays instead?  You wouldn't have to worry about contact resistance issues and the leakage is very low like 0.006 pA at 80 degrees C.  And only 0.003 pA at 40 degrees C.  And if you're concerned about that small leakage, putting a couple in series couldn't hurt because they are only around $1 each.

Without doing much research about the best ones to use, I picked a random one and looked at the specs and they are pretty good compared to a conventional relay.  http://www.clare.com/home/pdfs.nsf/www/CPC1016N.pdf

With conventional relays, the contact resistance can be low in the beginning but increase in time as the contacts become worn and seems that can mess with the calibration as you use it.  With the solid state relays, I would think the resistance would be consistent throughout the life of the product.  The internal resistance of the IC could be compensated with different value resistors if that is important.

[cengland0]

See chapter 3. Google should give you a link to the (legal) PDF version within a few seconds, hosted on this very site. It explains when and when not to use statistical tolerances, and gives some rules of thumb.

But I'll explain the basic case with the assumption that the resistors follow a normal distribution, which is not necessarily a fair assumption (see the book for reasons why and how to handle that). To keep it simple I'll first explain the series case. Assume the resistance of the 40 Ohm resistors is normally distributed with a mean of 40 Ohm and a standard deviation (or any multiple of the standard deviation, like a 95% confidence interval) of 0.05% * 40 Ohm, or 0.02 Ohm. The probability distribution of the total resistance of the four resistors in series is the sum of four normal distribution, which is another normal distribution with mean = sum of the means and variance (which is the standard deviation squared) = sum of the variances. If the total variance is the sum of the variances, then the total standard deviation is the root of the sum of squared standard deviations. So in this case the mean total resistance would be 160 Ohm with a standard deviation of sqrt(4*0.02^2) = 0.04 Ohm. This is 0.025% of the mean, i.e. half that the tolerance of the original resistors. A quicker way to calculate this for identical standard deviations is sd / sqrt(n), where sd represents the standard deviation of the individual resistor and n the number of resistors.

For the parallel case you can show that for normal distributions which are well above zero, the distribution of the reciprocal value is another normal distribution with mean 1/40 Ohm and standard deviation 0.05% * 1/40 Ohm. You can then add conductances to get the conductance of the four resistors in parallel, and again get a factor sqrt(4) improvement in standard deviation.

Note that this is about what the majority (eg. 99%) of the circuits is doing, as you note the worst case does not improve.

Hey, thanks.  I actually understand that explanation and it makes sense. 

[rs20]

If you were to design a resistance reference box like this today, wouldn't it be better to use solid state relays instead?  You wouldn't have to worry about contact resistance issues and the leakage is very low like 0.006 pA at 80 degrees C.  And only 0.003 pA at 40 degrees C.  And if you're concerned about that small leakage, putting a couple in series couldn't hurt because they are only around $1 each.

Without doing much research about the best ones to use, I picked a random one and looked at the specs and they are pretty good compared to a conventional relay.  http://www.clare.com/home/pdfs.nsf/www/CPC1016N.pdf

With conventional relays, the contact resistance can be low in the beginning but increase in time as the contacts become worn and seems that can mess with the calibration as you use it.  With the solid state relays, I would think the resistance would be consistent throughout the life of the product.  The internal resistance of the IC could be compensated with different value resistors if that is important.

Sorry about misinterpreting your earlier question about resistor combinations.

Where are these 0.006pA leakage current solid state relays? The one you linked has 1uA leakage, which is certainly unacceptable. I'd be pleasantly surprised if you could find a reasonably priced solid state relay that had a reasonably low on-state resistance (all the ones on digikey are basically immediately too high for 2-wire measurement; as I mentioned in an earlier post, though, on-state resistance is irrelevant in four-wire mode unless the relays are burning out or loading down the current source) and low leakage current (beware the distinction between control-to-relay leakage, and off-state leakage).

One point that comes to mind, at least for two-wire measurement, is that the on-state resistance would be a function of relay drive voltage. If you want the on-state resistance to be very repeatable (a far greater concern than absolute value), this is a very bad trait. At least a relay is very much either on or off.

[sync]

Without doing much research about the best ones to use, I picked a random one and looked at the specs and they are pretty good compared to a conventional relay.  http://www.clare.com/home/pdfs.nsf/www/CPC1016N.pdf

It has an on-resistance of max. 16 ohm. A mechanical replay can get easily 16 milliohm. That's 3 orders of magnitude better. And the resistance of the solid state relay changes with temperature. That's unacceptable for a calibrator.

[cengland0]

Where are these 0.006pA leakage current solid state relays? The one you linked has 1uA leakage, which is certainly unacceptable. I'd be pleasantly surprised if you could find a reasonably priced solid state relay that had a reasonably low on-state resistance (all the ones on digikey are basically immediately too high for 2-wire measurement; as I mentioned in an earlier post, though, on-state resistance is irrelevant in four-wire mode unless the relays are burning out or loading down the current source) and low leakage current (beware the distinction between control-to-relay leakage, and off-state leakage).

One point that comes to mind, at least for two-wire measurement, is that the on-state resistance would be a function of relay drive voltage. If you want the on-state resistance to be very repeatable (a far greater concern than absolute value), this is a very bad trait. At least a relay is very much either on or off.

It says it in the graph titled "Typical Leakage vs. Temperature Measured Across Pins 3&4"  The pA was too small on the pdf so I had to copy and paste it into a text editor to confirm it was pA and not uA or mA.  Regarding repeatable on-state resistance, a relay doesn't seem repeatable because it degrades as the contacts become worn.

It has an on-resistance of max. 16 ohm. A mechanical replay can get easily 16 milliohm. That's 3 orders of magnitude better. And the resistance of the solid state relay changes with temperature. That's unacceptable for a calibrator.

I did see that the on-resistance was 16 ohms and I also stated you can compensate for that with different value resistors.  I would be more worried about conventional relays having an unpredictable resistance as time goes on as the device gets used.  At least this shouldn't change for a solid state device.  I did not initially see the graph that showed the solid state relay resistance changing with temperature and now that I see that, I can understand why they are not used.  Consider that a stupid question now.  Oops.

[ralph]

It says it in the graph titled "Typical Leakage vs. Temperature Measured Across Pins 3&4"  The pA was too small on the pdf so I had to copy and paste it into a text editor to confirm it was pA and not uA or mA.

On that graph I read :
- 0.006µA @ 80°C
- 0.002µA @ 20°C

[cengland0]

It says it in the graph titled "Typical Leakage vs. Temperature Measured Across Pins 3&4"  The pA was too small on the pdf so I had to copy and paste it into a text editor to confirm it was pA and not uA or mA.

On that graph I read :
- 0.006µA @ 80°C
- 0.002µA @ 20°C

Sorry to beat a dead horse on this but how do you know it's uA and not pA?  I couldn't see it clearly on the graph so I copied the text and pasted into a text editor and it says PA in all caps.  I'm curious if the greek letters are being pasted into my text editor incorrectly now.  Can you copy and paste and tell me what you get?

[stackoverflow]

Great video!! @ 27min I'm guessing the low resistor are wound on mica card.

[codeboy2k]

@cengland0:  I see uA too
graph attached.

[cengland0]

@cengland0:  I see uA too
graph attached.

Thank you for posting the enlarged image.  It's clear that it is uA but could you do me a favor and copy that and paste it into notepad, wordpad, ultraedit or some other text editor?  All three that I tried on both Mac and PC paste it as PA.  The only thought that I have is it's an ASCII 80 but in a special font that doesn't correlate with the regular alphabet.  When pasting ASCII 80 into a regular text editor, it loses font detail.  If someone else confirms it happens to them, I might be able to sleep at night knowing I'm not going crazy.

[Dr. Frank]

Dave,
great video again, thanks for showing the entrails of that delicate box!

I just love those old designs/schematics and layouts, that's great engineering.
Today, that would cost too much, so those things are not done any more, I fear.

Anyhow, some comments on you video:

The 5450A is not a transfer standard, as you have stated.

It delivers 17 absolute Ohm values, but it is not capable of doing resistance transfers.

A transfer standard normally has less absolute uncertainty, but is capable of transferring one absolute value to another random value with very high uncertainty, perhaps one decade apart.

Examples of transfer standards:

ESI SR1010: transfers Ohm values per decade, uncertainty 1ppm.
Fluke 720A: transfers voltage to random values to 0.1ppm of input. Ex.: 10V to 1.018659V is transferred to 1ppm uncertainty of input (+/-10µV).
Fluke 752A transfers voltages to 10:1 and 100:1 levels. Example: 1000V can be compared against a 10V reference standard (i.e. 0.5ppm of input, much better than the 720A!)
HP3458A is able to transfer volt and ohm to an uncertainty of 0.05 ... 0.02 ppm of input, better than the 720A.
The Fluke 5440, 57xx an the Gertsch/Singer AC transformers/Bridges are further examples of transfer standards.

The 5450A could be redesigned much more compact and more stable today :
The processor board would be a one chip embedded solution, occupying <1/20 of the inital area.
The resistor standards board would also make use of relays and Teflon stand ups, but perhaps more compact bistable ones.

The FLUKE ww resistors would be replaced by more stable (vs. T and t) industrial metal foil resistors from Vishay.

Flukes was great on making selected sets of precision resistors.
They were selected for uncertainty, but mainly for identical temperature coefficients.
So, those 4 paralleled resistors could have a selected T.C. of < 1ppm/K
Today, a single Vishay metal foil types can achieve that at least without selection.
And Vishay oil filled type resistors timely drift would be < 2ppm/6yr, compared to the mediocre 12.5ppm/year of the old style Fluke technology.

Btw.: Thanks for the link to the FLUKE manual of the 5450A, it's not visible in EU, currently.

Frank

[Bored@Work]

The SI ampere is still defined via the force between two conductors. But that is impractical to realize, so standard labs derive it via Ohm's law. There is some work going on to redefine the SI ampere based on the charge of a proton. But the BIPM members are discussing that for years now, and they don't seem to be in a hurry to do the change.

Naa, that's not correct. The Proton experiment was too unprecise so it's not followed up.

... then defining fixed (exact) values of e, ...

But that is the charge of a proton, isn't it? I thought the idea was fixing e (one value in Coulomb = As), and then "simply" deriving the Ampere from the charge.

[Dr. Frank]

But that is the charge of a proton, isn't it? I thought the idea was fixing e (one value in Coulomb = As), and then "simply" deriving the Ampere from the charge.

Yes, you are right, in that could also define the charge of an electron, and therefore the Ampère, theoretically.

But it's not easy to make the experiment ( mise en pratique) with high enough precisision...

Therefore, BIPM and all metrology institutions decided on going the way described in the resolution I have linked.

Frank

[nitro2k01]

Great video!! @ 27min I'm guessing the low resistor are wound on mica card.

Is there any particular reason why it would be mica, other than just to use the absolute best material? I can't see any particular justification to use it for electrical resistivity, thermal conductivity or dielectric properties in this application.

[ddavidebor]

Because not only is the best but also is cheap and practical

[Ronald1962]

Great tear down!!!

Dave talked about special connectors for input and sense.

Does anybody knows what type / brand it is?

[ddavidebor]

It's a tellurium-copper low emf connector

[CHexclaim]

I have just finished watching the video but looking at the big relays, and taking into account that this is a precision gear, it is understandable to see the big Sprague filter capacitor there. Think when all relays are on plus the digital logic.

Great teardown.

CH!