HP34401 - Measurement of Linearity

[Dr. Frank]

The most important characteristic of an A/D converter or a DMM is its linearity.
The number of digits displayed (and promoted) is often spoiled by the bad non linearity.
A good linearity on the other hand allows to make a transfer from a reference value  to another random value.
That's the purpose of a transfer standard, like the famous Fluke 720A.

I made a quick 'n dirty measurement on the venerable HP34401A, whose A/D concept is derived from the best linear one, sitting in the HP3458A.

The 34401A specification claims 2-3ppm A/D linearity (3458A: typ. 0.02ppm = real 8 digits).

To perform such a high precision measurement, one may get about 7 stable digits from the 34401A over GPIB, or by the averaging function initiated by  MinMax.

I measured 15 values, averaged over ~100 samples each, between 11.00000V and 0.000000V, generated by a Fluke 5442A, which itself  is linear to better than 0.1ppm.

This latter characteristic had been verified by a linearity comparison of the 5442A against the HP3458A, see figure 1.

The DNL (differential non linearity) is computed relative to FS (full-scale) = 10V, by first applying a best fit to remove zero and gain error, and then calculating the difference between best fit and output, divided by 10V.

DNL relative to output is calculated the same way, but divided by each individual output value.

The first DNL calculation is specified in the datasheets.

The 2nd DNL calculation, which is getting worse towards small values due to less and less resolution there, gives an idea, how precise for example a 10:1 or a 100:1 transfer might be.

In figure 2, you can see, that the 34401A is linear to around 0.2ppm of FS (input), and from figure 3, that a 10:1 transfer, e.g. 10V => 1V, can be made precise to 1ppm.
A direct 100:1 transfer would yield 15ppm, so a 10V => 100mV transfer would be done in two subsequent steps, 10V=>1V and 1V =>100mV, for 2 ppm accuracy instead.

Another practical application of that very linear characteristic of the HP34401A is shown in picture 1.

The fixed, direct output of an LTZ1000, Ref_2 = 7.1479734V (as measured by the 3458A) is amplified to a nominal of 10.00000V. This yields a precise cardinal calibration value.

The ratio of nominal 10V/7.1479734V =  1.3989979 can be measured by the 34401A directly, to trim the amplifier output to the exact 10.00000V value with an accuracy of around 1ppm, limited by the single shot resolution of the ratio function.
This allows to re-calibrate the 10V output at any time, as this value drifts much more than the raw output of the LTZ1000.

By measuring the input and output values separately, and averaging over the GPIB, the accuracy of the ratio transfer can be driven to around 0.4ppm.

Frank

[Rick Law]

Dr. Frank,

Very interesting.  I learned something about linearity and transfer accuracy which I was just wondering about exactly what it is.  Your post is very educational.

Rick

[Joe Geller]

See my later post below, the technique seems fine, and very convenient! as long as both the sense value (e.g. 7 V) and the Vin value (e.g. 10 V) are on the same DMM scale. 

The detailed notes pertain to cross scale DCV ratio work, such as using both the 10 V and 1V scales.

Frank,

  I think the way the DCV Ratio function works on hp Agilent DMMs is by measuring the sense input (Sense) on an auto-ranged scale and then measuring the input voltage (Vin) and doing the math by microprocessor.  That is, the DMM is not doing a true ratiometric "raw" conversion using one input in place of the internal reference, and then digitizing Vin based on the "sense reference".  Instead, it is simply literally making two separate measurements based on the one internal reference.

  Unfortunately, I do not think there is a way to effectively substitute the internal reference or scale calibrations with a voltage standard at the sense input (or Vin) while excluding effects of the internal reference.

   Edited post: Replaced cross range (10 V & 1 V example) in separate following post.

   As an aside, I ran overnight with the Fluke 732B 10 V connected to the 34461A sense input, and the HiZ (just a R divider) 732B 1.018 V connected to the Vin, manual range 1 V, HiZ selected.  After some tens of thousands of points, I think around 45k, the central ratio average was 101.81683 with one standard deviation of 45.625 n.  There was very little temperature drift with more than a 3 degree C change (not recorded, but the normal night time setback).  It seems that whatever is temperature sensitive (in spec, but curious) in my 61A (presumably in the reference chain, suspected now to be the Rs in the first gain stage, hmm, or it still could be the ADC, anything in common gain with the 1 V and 10 V scales) is cancelled out by both measurements!  Then, I want to say, I bootstrapped the 1.018 V measurement by my 10.000 00 V from the 732B to read it's own 1.018V output as 1.018 163, my best measurement yet! But not.  Because although super stable and free of the DMM tempco (successfully cancelled!), the 101.81683 depends on the absolute calibration of both my 10 V scale and my 1 V scale.  Bummer.

  I do agree that the reason the Fluke dividers of the past such as the 720 and 752 are no longer needed is because of the amazing linearity of the hp 3458A. 

Joe

[Joe Geller]

Here is a better example being sure to use both the 10V scale (for the auto-range sense measurement) and the 1V scale manually set (always HiZ when using a Fluke 732B 1.018 resistor divider output).

The premise is that hp / Agilent DMM performs the DCV ratio function by making independent measurements at the Vsense terminals and the Vin terminals as opposed to a "true" ratiometric measurement (e.g. using one input to stand-in temporarily for the internal reference)

All measurements were made using an Agilent 34461A 6.5 digit DMM using a 10 power line cycle (plc) integration time with statistics averaging.  Averaging was used to run "full out" in resolution.  It is understood that thermal emfs likely caused errors rendering these values off "absolute" at 6 to 7 digits (unimportant for the experiment / demonstration of DCV ratio).

A)  Measure the FLUKE 732B 10 V and 1.018 V outputs using the DCV function with statistics averaging
100 samples, 10 plc, 10 V 10 Meg, 1.018 V HiZ

1.018 V: 1.018 165 0 V
10 V: 9.999 987 V

Ratio: (30 samples) R101.816 93 m (ratio, no units)

B) Intentionally change the 34461A 1 V scale calibration (gain) by about +30 uV (30 ppm for a 1 V full scale)

EDC 520A, set 1 V on 61A: 1.000 004 5 V
EDC 520A, set +30 uV error signal: 1.000 035 7 V (about +30 uV)
Calibrate 34461A DCV 1 V scale to 1.000 035 7 V, by telling cal procedure, that 1.000 035 7 V is 1.000 000 0 V
EDC 520A, set +30 uV error signal: 1.000 035 7 V (about +30 uV): 34461A now reads 0.999 999 8 V

C) Repeat step A) with cal error of step B)

1.018 V: 1.018 129 5 V    (compare with before: 1.018 165 0 V)
10 V: 9.999 985 V

Ratio: (30 samples) R101.813 3 m (ratio, no units)    (compare with before: R101.816 93 m)

Conclusion: The DCV ratio function is dependent on Vin, Vsense, the linearity of the ADC, the calibration (gain and offset) of the 1 V DCV scale, and the calibration (gain and offset) of the 10 V scale when comparing a 10 V or a 7 V reference signal (Vsense) to a 1 V source (Vin) under calibration.  My understanding is that the 34401A DC Ratio function works the same way.  The later more accurate 34410A (the "10A") dropped the DCV Ratio function.

Probably, short of a short term calibrated hp 3458A, one of the best ways to approach a 1 V absolute calibration, based on a 10 V "known" absolute "correct" value, is still by the Fluke 752A Hamon method.  Hamon experiments can be done in a small lab, understanding that results are only short term valid (if at all) to some precision.  Here are some references: http://www.gellerlabs.com/752AJunior.htm .

For 5.000 00 V, It would also seem valid to use two 5 V adjustable reference sources and have the series connection (yes, you need to worry about the sum of TE junctions in the connections) nulled to a known 10 V calibration source.  Then one could reverse the connections and check for zero volts and iterate until both 10 V is matched and each 5.000 V source matches each other (I suppose that could be a null check 5 V to 5 V too).  The idea is that both reference need to be both the "same value" and the "same value" that adds up to "exactly" match the 10 V reference. 

Then, one of the 5.000 00 V cal references might be suitable for short term checking the DMM 10 V scale at 5 V, or for setting by null techniques a third reference to one of the 5.000 00 V set references.  As with any calibration exercise, to be rigorous, one would need to try to identify possible errors, and set the resulting range of uncertainty accordingly. 

[sync]

Looking at the 34401A schematic I don't think it can do radiometric ratio measurement. But is this a problem?

[Joe Geller]

yes, you might be right (not a problem).  The original proposal is to make both measurements of the ratio calculation on the same 10 V scale.  Most of my concern is cross scale, e.g. the calibration source on the 10 V scale and the value being calibrated by ratio on the 1 V scale.

However, if both the 7 V reference and the 10 V reference are measured on the same 10 V scale, whatever gain and offset error is associated with the 34401A 10 V scale, short term is the same for both measurements (which was probably Frank's original point).  And, as was noted, the 10 V absolute calibration of the 34401A is less of an issue, perhaps insignificant.

There might be some merit to the technique as long as it uses a common voltage scale, convenient at that!  I think maybe it does work, so long as both measurements are on a common scale.

[Andreas]

Hello,

here you will find the "poor man's" linearity adjustment+check which I do for my ADCs (LTC2400) to get from 4-15 ppm down to around 1 ppm linearity error.

The LTC2400 is relatively easy to linearize since the error curve is nearly a simple parabolic function. (see AN86 of Linear Technology).

The measurement setup consists of the ADC (left) a buffer amplifier (mid left) and the "calibrator" (right) and a stable LM399 source (background). All is supplied with floating supplies (batteries).
The calibrator is a galvanometer amplifier with a output resistor string of 20 resistors (R1-R20). The feedback of the galvanometer amplifier is tapped between R14+R15 giving up to 10V with 500mV steps from a 7V reference.
The resistor string consists of 1K 0.1% low TC (25ppm/K in this case) film resistors.
The buffer amplifier is necessary to decouple the low ohmic input impedance of the ADC from the resistor string.
The plastic pincer is needed to keep heat transfer away from the connectors during "switching". This reduces the stabilisation time during measurement. A thermal stable environtment and a temperature compensated/stabilized ADC is necessary (less than 1 ppm drift during measurement).


Measurements (example in mid scale). Integration time is 1 minute due to noise reduction.
1.) offset both lines connected at same tap (is subtracted automatically from all further measurements) (IMG1459w)
2.) R1-R10 full scale (around 5V)  (e.g. 4900.7528 mV) (IMG1460w)
3.) R5-R10 upper part resistor string (5V - 2.5V) (e.g. 2450.6078 mV) (IMG1461w)
4.) R1-R5   lower part resistor string (2.5V-0V)   (e.g. 2450.0172 mV) (IMG1462w)
Repeat all steps with all other taps to check the parabolic function.
Check offset and full scale for drift (< 1ppm)

If there is no linearity error then the value 2) is the sum of 3) + 4).
In this case 0.1278 mV as sum are missing near mid-scale. (each measurement 64 uV)
With a projection to exact mid scale a correction of +13.2 ppm (+66uV of 5V) is necessary at 2500 mV

With best regards

Andreas

[Dr. Frank]

Here's an update of the linearity characterization.

The front panel functions as MinMax and Ratio will do a clipping of the extended 7-digit- resolution.

And yes of course, the Ratio function performs 2 separate DCV measurements and calculates the ratio. So the achievable resolution is already limited by the calculation and rounding algorithm to around 1ppm.
It is necessary, that both measurements (DUT and reference) are done on the same range. I think, that's fulfilled, if the instrument is set to Manual Range.

Instead of the front panel functions, now I used the agilent DMM Utility, Dave already has shown in one of his blogs blog #562.
(It's a pity, that I don't have an iPhone for remote measurement  ).

This utility logs the results to 1µV resolution for each measurement value, over GPIB, i.e. to 7 digits, see fig. 1.

The noise for NLPC 100 / 6 Digits Slow is less than  +/- 2 digits, or +/- 0.2ppm.

With additional averaging, i.e. over 20 samples, the standard deviation is around 1µV, that means one will achieve stable 7 digits from the 34401s A/D, see table 1.
All readings are done on the 10V range!

The results for the linearity FS and Out are identical, see fig. 2 & 3,  but now confirmed by statistics.

So, calculating volt transfers by such raw data instead of Ratio may really yield < 1ppm of uncertainty.

As a bonus, I measured the stability of the HP34401A over 16h , at constant 21.5°C (+/- 0.2°C), see fig. 4.

I did not expect that old box (25 years or so) to be that stable (~0.3ppm)!

Frank

[Dr. Frank]

....
  I do agree that the reason the Fluke dividers of the past such as the 720 and 752 are no longer needed is because of the amazing linearity of the hp 3458A. 

Joe

Hello Joe,

I don't think those transfer standards are obsolete, especially not the Hammon type Fluke 752A.

The 3458A beats the 720A, that's right, but not the 752A at high voltages.

The 752A is uncertain to 0.5ppm @ 1kV, whereas the 3458A is specified > 12ppm @ 1kV only.

That's due to the uncompensated heating effect of the 100:1 divider inside the 3458A.

Even the HP34401A performs much better at that point.

Other long scale DMMs, which compensate for that effect, also achieve 2ppm @ 1kV only.

I built my own Hammon transfer standard, mitigating that heating effect to less than 1ppm.

Perhaps I'll add an interior photo, as this fits into the Transfer Standard discussion here.

The 2nd photo illustrates a 10V => 100V transfer by means of this "Reference Divider".
That setup indicates, that the (uncalibrated) HP34401A is off by +30ppm.

Frank

[sync]

Nice build!
Can you post the schematic?
What resistors do you used?

I planned to build a simple 10:1 Hammon divider. Maybe i will add a 100:1 mode too. I think the 752A manual will be a good read.

[Dr. Frank]

Nice build!
Can you post the schematic?
What resistors do you used?

I planned to build a simple 10:1 Hammon divider. Maybe i will add a 100:1 mode too. I think the 752A manual will be a good read.

Yes, the 752A manual is very instructive, as it describes in detail all the error sources.
You should download the complete version, including the schematics.

Fluke does not explain, how the resistors are matched to achieve that independence from heating effects.

On the web you will also find several interesting scientific / metrological articles about the design and evaluation of decade and High Voltage transfer standards.
Search for : EUROMET.EM-K8.pdf, for example.

Well, in my design, I made a different  approach compared to the 752A, to avoid the special T.C. matching which Fluke does in every of their divider designs, see principle schematics.

I used 104 identical metal foil resistors, FLCY from Alpha Electronics, 25kOhm, 0.1%, 0.14ppm/K typ. @ RT, available from rhopoint components Germany.
10 years ago, I paid around 200€ in total.

Lower grade resistors won't do the job for < 1ppm transfer uncertainty, because that would be too unstable regarding thermal fluctuations.

R1 - R100 are used for the divider, the 4 other resistors are used for the 2 arms (2* 50k) of the Wheatstone Bridge.
That's not shown in the schematics.

Selected metal film resistors trim the seven parts of the divider ( 3* 750k, 3* 75k, 1* 25k) to equivalence within a few ppm (34401A or better required).

3 trimmers are used to balance the Wheatstone Bridge, and to calibrate the 100:1 and 10:1 divider chains.

The custom specific ELMA switch provides low EMF, low resistance and low leakage.
It is not specified for HV, but up to now, did withstand 1kV without problems.

The cables are Teflon isolated ones.

I achieved uncertainties of 0.2 / 0.5 ppm for 10:1 / 100:1 at input voltages up to 100V, measured by Fluke 5442A and HP3458A.

The 1kV transfer is around 1ppm by design, and also confirmed by measurement  with the Fluke 5442A, which itself contains auto calibrating transfer standards.

I did not yet measure the heating effect at 1kV directly.
Using the HP3458A fast digitizing feature at 10V level, the magnitude of this thermal drift in the first several 100ms  could be detected.

Frank

 

[robrenz]

I would love to see this linearity test done on the Fluke 8846A (tek 4050) if anyone has one.

[bingo600]

I would love to see this linearity test done on the Fluke 8846A (tek 4050) if anyone has one.

RR you know it would fail  ... It's "just" a Fluke 

/Bingo

[robrenz]

My money says it is better than the 34401A

[sync]

The spec are the same for both: 2ppm of reading + 1ppm of range. A real measurement would be interesting. Just send your 8846A to Dr. Frank.

[robrenz]

quarks has one and is much closer to Dr. Frank.  I think he has the equipment to measure it himself also.

[sync]

Hello Frank,

Thank you very much for the schematic and the other information. I have read the 752A manual. Very good indeed.

200€ for the resistors sounds like a good price. When I saw your photo I expected they cost over 1000€. Fortunately I'm not aiming for sub-ppm precision. So I hope to find a bit cheaper ones.

[quarks]

quarks has one and is much closer to Dr. Frank.  I think he has the equipment to measure it himself also.

Hello robrenz,

unfortunately I have missed this thread until now.
I can do a test maybe tommorrow, just let me know what setup you like me to check for you.

Bye
quarks

[robrenz]

quarks has one and is much closer to Dr. Frank.  I think he has the equipment to measure it himself also.

Hello robrenz,

unfortunately I have missed this thread until now.
I can do a test maybe tommorrow, just let me know what setup you like me to check for you.

Bye
quarks

A repeat of what Dr. Frank did on his first post and reply #7 would be great if you don't mind going to go to all that work.

[quarks]

Unfortunately I do not have enough spare time to do all the same measurements, but here are some TEK 4050 results.

Setup:
All gear warmed up > 4h
4050 in Manual Range 10VDC, 6.5 Digit, 100PLC, HIGHZ
and also in ANALYZE STATS Mode with better resolution of 1µV from below 10V to 1V
All measurements are made against my WAVETEK 4808, set in 10 VDC Range to the nominal value (with no tweaks/corrections)

The 4050 is almost perfectly identical to the 4808 linearity.

[Dr. Frank]

I just made the calculation
See xls sheet. German version only, sorry.

Linearity of input is around 0.35 ppm.

Linearity of Wavetek 4808 is not specified in the catalogue, or I did not find detailed specifications.
Obviously 0.3ppm linearity also.

Frank

[robrenz]

Thank you quarks and Dr. Frank for your work!   

[cellularmitosis]

Hello,

here you will find the "poor man's" linearity adjustment+check which I do for my ADCs (LTC2400) to get from 4-15 ppm down to around 1 ppm linearity error.

The LTC2400 is relatively easy to linearize since the error curve is nearly a simple parabolic function. (see AN86 of Linear Technology).

The measurement setup consists of the ADC (left) a buffer amplifier (mid left) and the "calibrator" (right) and a stable LM399 source (background). All is supplied with floating supplies (batteries).
The calibrator is a galvanometer amplifier with a output resistor string of 20 resistors (R1-R20). The feedback of the galvanometer amplifier is tapped between R14+R15 giving up to 10V with 500mV steps from a 7V reference.
The resistor string consists of 1K 0.1% low TC (25ppm/K in this case) film resistors.
The buffer amplifier is necessary to decouple the low ohmic input impedance of the ADC from the resistor string.
The plastic pincer is needed to keep heat transfer away from the connectors during "switching". This reduces the stabilisation time during measurement. A thermal stable environtment and a temperature compensated/stabilized ADC is necessary (less than 1 ppm drift during measurement).


Measurements (example in mid scale). Integration time is 1 minute due to noise reduction.
1.) offset both lines connected at same tap (is subtracted automatically from all further measurements) (IMG1459w)
2.) R1-R10 full scale (around 5V)  (e.g. 4900.7528 mV) (IMG1460w)
3.) R5-R10 upper part resistor string (5V - 2.5V) (e.g. 2450.6078 mV) (IMG1461w)
4.) R1-R5   lower part resistor string (2.5V-0V)   (e.g. 2450.0172 mV) (IMG1462w)
Repeat all steps with all other taps to check the parabolic function.
Check offset and full scale for drift (< 1ppm)

If there is no linearity error then the value 2) is the sum of 3) + 4).
In this case 0.1278 mV as sum are missing near mid-scale. (each measurement 64 uV)
With a projection to exact mid scale a correction of +13.2 ppm (+66uV of 5V) is necessary at 2500 mV

With best regards

Andreas

Hello Andreas,

I am having some trouble understanding how you are able to perform this linearity measurement.  I'd soon like to set up an LTC24XX-based vref scanner project of my own, so I'd love to be able to perform a similar linearity characterization.

I'm having trouble imaging what the schematic of your calibrator looks like, so I'll start by posting my best guess, and then maybe someone can correct it from there (see attachment).

I am also having trouble understanding the theory of operation.  Are you using a bench DMM to measure what the voltages at each tap should be, and then comparing that to your LTC2400?  I don't think that's what you are doing, because that would only match the linearity of your DMM.

[Andreas]

Hello,

no when I first made this linearity test my best DMM had 80000 counts.
So no chance to do a 1 ppm linearity check.

With my cirquit I fully rely on the (short term) stability of the resistors.
Additional on the fact that the sum of 2 voltages (VTotal) should be always V1 + V2.
(if not then I have a linearity deviation, assuming that offset is calculated out).
Maybe that you will need additional measurements/assumptions if your ADC has not a parabolic (symmetrical) INL-behaviour.


The principle of your cirquit is right. (except that I never would use a additional voltage divider if I have already one on hand).

The battery powered LM399  (or LTZ1000) is connected on J1 (neighboured pins on D-SUB).
After input filtering and buffering with a AZ-Op-Amp (today I would use a LTC2057) the voltage feeds the resistor string.
C2 is for dampening oscillations.
Power supply is done by 2 * 9V NiMH-Blocks.
Negative voltage supply is a diode drop.
The positive voltage is stabilized by a low noise LTC1761.

Output is via 2 jumpers to a D-Sub connector.
Of course you will need a additional buffering of the output voltage
if you have a dynamic load (not high impedant > 10 Gig) like a sigma delta adc.

with best regards

Andreas

[cellularmitosis]

Ah, after reading over your post again and looking over the datasheet again, I think I understand now.

By the nature of A + B = C, if both "part" measurements are high (or both are low), you know what the total error is (e.g. where you should have 1.5V + 3.5V = 5V, but you measure 1.6V + 3.6V = 5.2V, the total error is 0.2V).  The trick then is trying to figure out how to divide that error up among the two measurement points.

When you take a tapped measurement, the two measurements will naturally be centered around the half-way point (e.g., measuring 5V at the 1.5V tap yields measurements of 1.5, 3.5, and 5V).  If we then make the assumption that the LTC2400 error is a perfect parabola (or any shape symmetric about the half-way point), then we can make the assumption that half of the error belongs to each "part" measurement.

In practice, the error will not be a perfect parabola.  Our remaining "unknown" error is then determined by how much the actual error curve differs from a perfect parabola (how asymmetric it is).  However, this remaining error should be much smaller than what we started out with, so this is a big improvement using modest equipment.

Very cool!  Thanks for replying so quickly.

I also understand why the resistors need to hold their value long enough to complete one set of measurements (full scale, bottom half of tap, and top half of tap).  If they drift due to temperature, that introduces some additional error.