Statistical arrays

[iMo]

But the number of variants is huge. A colleague of mine says with 8 resistors it is 8! that is 40320, but that is just a guess, imho. With equal resistors some of the arrangements cancel out, what is not the case with none equal resistors. With the given divider ratio the majority will not fit, but the number of close fit arrangements could be still high..

Would be great to develop a brute force solver for that problem..

PS: "N none equal resistors" means an array with resistors you measured before the calculation, as I expect their values differ a little bit. Also it could be an array (or set of two arrays) with quite different resistor values, like the LT5400 series..

[Kleinstein]

With many of the configurations some resistor positions are excangable (e.g. in a series configuration the sequence does not matter) - so the 8! number is not really applicable.

The resistors in the arrays are usually quite close to each other. Often the relative specs are better than 1% and the actual spread may very well be considerably closer. So while the guarantied limit may be less than 1% difference, it may be hard to find actual more than 0.1% difference and when using more resistors there is still averaging with better matching resistors.

So there is little use of meassuring and selecting the right ones for a specific combination.  This would be only a minor deviation from the equal resistor case that comes with the price of individual PCBs for the specific units. Such smaller trims ( < 0.1% range) are relatively easy with a separate resistor. So I doubt this would be worth the effort of individual measurements.

[iMo]

There is still an option with arrays like LT5400 and similar. My current understanding is you can mix two separate arrays (each one with good ratio matching TC) such the TC matching ratio stays the same. For example there are arrays with 1k+1k+9k+9k, 1k+1k+5k+5k,  1k25+1k25+5k+5k, etc. you may combine.

PS: anyhow, my first post above was re existing calculator for this problem - such you enter the resistors params and divider ratio and after a couple of seconds/minutes you'll get the optimal setup for given divider ratio..

[Kleinstein]

One can combine multiple arrays, but this comes with some difficulties. The matching between different arrays is usually not that great, especially not if from different batches.  So this may add additional chances for drift.

Especially with equal resisstors one may combine them to have the same weight from both arrays. E.g.  combine pairs of resistors from both arrays in parallel of series to get some kind of average. Here one can mix parallel and series. With different resistor ratios this usually no longer works well.  It may also need extra resistors to get equal mixing (e.g. use 2 in parallel and 2 in series instead of 1 resistor to get mixing of 2 chips).

[Ole]

I´ve got a question regarding the LT5400´s datasheet:
The datasheet mentions shelf life stability at 25°C, unbiased for 1 Year as +- 5ppm,
is this for the ratio or the absolute values?

[miro123]

I´ve got a question regarding the LT5400´s datasheet:
The datasheet mentions shelf life stability at 25°C, unbiased for 1 Year as +- 5ppm,
is this for the ratio or the absolute values?

Good question. I dont know the exact answer - just guessing
 I think that +-5ppm is for absolute value
 - Looking at "Change in Matching vs Time" - shows +2ppm max @2000h

[julian1]

Is anything known about the on-die organisation of the 4 resistors in a lt5400?.

Is the (desposition?) layer physically interleaved with each other, to increase temperature matching/coupling? It would seem like a good design/manufacturing strategy.

If a signal feeds through several lt5400 (series and parallel), does it make sense to select a different resistor position for each package. To equalize proximity of all signals to each other, and reduce cross- TCR?

[antintedo]

Attached is a poor quality photo of 4x10k LT5400. Individual golden color terminations are visible, there could be as many as 40 resistive elements. Connections seem to be done through at least 2 metal layers, one on top and one under the surface. Resistors are interleaved but not to the fullest extent possible, they are paralleled in groups first. It probably has to do with limited number of metal layers being available. Silicon substrate seems to be used, it did not look like ceramic. I did not strip the passivation layer so no idea about the geometry or whether they are trimmed.

[miro123]

I wonder does someone tested NOMCA statistical dividers for long term.
On paper they must shine in this area.

[dietert1]

The parts i used for my tests in 2019 are still there, one could use them to repeat those tests. Getting precision on the relative resistance values that determine a divider ratio and the TCs was fairly simple. Guess it will take some time though. Other projects here.

Regards, Dieter

[Kleinstein]

I did some test with 2 NOMCA arrays in my ADC. They performed quite good in the TC and were also reasonable stable, as far as I can tell. However the 1/f noise is rather anoying. There is a chance that the processes leading the excess noise can also lead to drift in the long run.  I would prefer the related NiCr version (without the A at the end), that is supposed to have less noise.

AFAIR the specs are also not that great, but with some of the parameters in the datasheet the question is if this refects the actual part performace, the acceptance creterion or just a test limit - so how good are the instruments used to check the parts.

[dietert1]

So we should rather test NOMC (not NOMCA) arrays instead. In N. Beevs paper they appeared at a noise index of about -70 dB and eight resistor arrays are available from Mouser. Maybe they exhibit similar TC properties.

Regards, Dieter

[miro123]

So we should rather test NOMC (not NOMCA) arrays instead. In N. Beevs paper they appeared at a noise index of about -70 dB and eight resistor arrays are available from Mouser. Maybe they exhibit similar TC properties.

Regards, Dieter

Thanks for feedback. I've just looked at NOMC/NOMCT datasheet. I still don't know what is the better choose for my application
 - NOMC and PBfree NOMCT have Ti2N version Datasheet page 1 Note - Available upon request. Resistance value range and performance differs from passivated nichrome standard electrical specifications on datasheet, consult factory
 - NOMCT subtrate is SI no ised what will be in Ti2N version
 - NOMCA is automotive specified - mostly means quarantined long term parameters, and more resistant in harsh environment.

I have one questions about NOMCA .
-  How bad is the noise performance of NOMCA? If I do match calculation. I come to very low numbers NI=-30..-40dB is still very low.
-  Is there some some data for frequency below 0.01Hz - lets say 1h, 1day or 1week

[branadic]

You can expect the slope to go on for lower frequencies, but effects like temperature variation to show up too, unless you have everything temperature stabilized.

-branadic-



*https://www.eevblog.com/forum/metrology/statistical-arrays/msg3137942/#msg3137942
*https://www.eevblog.com/forum/metrology/diy-high-resolution-multi-slope-converter/msg3392180/#msg3392180

[dietert1]

Once more:
According to N. Beev (link to research paper above) NOMCA and NOMC are different in respect to noise index, NOMC give 30 to 40 dB lower noise . NOMC are nichrome film resistors, while NOMCA is a variation of NOMC with tantalum nitride instead.
Today i ordered some of these: NOMCT16035001AT1

Regards, Dieter

[miro123]

Thanks  Branadic and Dieter,
Sorry that my question was not clear!
I am interested in noise at 1uHz...100mHz = 10e-6Hz...10e-1Hz. Can I draw straight 1/F approximation line to infinity?
I know that the answer is no
I'm not interest from solution that gives me 0.1ppm lower noise. I'm more interested in solution that gives me 5ppm/year better stability.

The paper shows the noise spectrum until 0.1Hz. I assume it comes from industry standard 0.1...10Hz measurements. I understand CERN decision, they are also not interested in any long term analysis, since they calibrate the equipment frequently with stable HP3458

PS: I already build an small oven with stability of 1mK @24h. Still  not enough time to document it. The problem is that multyloop MIMO controller requires manual tuning.

[Kleinstein]

The excess noise can extend quite a bit down. Usually the limit is not from the 1/f noise gettling less, but more from temperature or similar variations taking over.
How far down the 1/f noise extends is a good question and it can depend on the DUT. Even though on a log scale, like the same noise power per decade in frequency, there obviously needs to be a lower limit.  From the physics side 1/f noise would require some kind the memory for the past and the time how long the old state is remembered shoud about limit the 1/f noise. This could be something like the lifetime of defect states involved.

[iMo]

..
I am interested in noise at 1uHz...100mHz = 10e-6Hz...10e-1Hz. Can I draw straight 1/F approximation line to infinity?

Yes (the slope will be the same in 1pHz to 0.01Hz).

[dietert1]

Meanwhile 10x NOMC 8x 5 KOhm resistor arrays arrived here from mouser.
They were put onto SMD adapters with 0.5 mm pins and cleaned.

Using a setup with a Keithley 2700 DVM including a 7706 scanner,
the 2019 NOMCA test jig  (9 channels of 4W resistance with offset
compensation) and an incubator wired to an Arroyo Tecsource 5235
these are the results:

- First diagram shows temperature cycle as seen by TecSource
and by PT1000 sensor included in test jig. There is some temperature
offset and a time lag. Data analysis is based on the temperature
measured by PT1000 sensor. One 18°C to 28°C oven cycle takes about
4 hours, largely unattended.

- Second and third diagram demonstrate resistance and TC
determination by line fit. There are no anomalies like hysteresis
nor higher order TC. Stability and noise of setup appear to be
good enough.

- Table shows results of all 10 arrays tested. There is some
resolution for all data necessary to judge stability of dividers
built with these parts.

- Two more diagrams illustrate scatter of TCs and resistances.
The TCs show a regular pattern while the resistance deviations
are more random. TCs are within +/- 5 ppm/K and TC tracking
within an array is +/- 1 ppm/K. Array 5 is a good candidate for
making a zero TC 10K resistance standard.

Two of the NOMC arrays were put into a drypack to repeat the tests
after some weeks. Meanwhile the 2019 measurements of NOMCA
parts will be repeated.
   
Regards, Dieter

[miro123]

Thanks for sharing.
The TC shape in 4-th graph is similar across arrays R1 and R8 has lover TC than de rest.
Can be an systematic error from the test setup

[dietert1]

 "Systematic error" means some mechanism/explanation.
The repetition of my 2019 NOMCA measurements will be a check on systematic errors, as in 2019 a small oven was used instead of the incubator and a HP 3456A with a DIY relay scanner instead of the K2700.
In 2019 i also wired zero TC voltage dividers with NOMCA arrays and they behaved as expected. Another possible check whether one can trust the TC determinations.

Regards, Dieter

[dietert1]

Meanwhile i looked into two possible sources of systematic errors.

First the SMD adapter i am using for the arrays has copper traces of different length. The traces of the outer resistors R1 and R8 are longer than the others and copper contributes with a strong positive TC of 3930 ppm/K. The trace resistance was determined to be about 25 mOhm, so the variation due to different trace lengths may be half of that. Each resistor has this twice (on each of two terminals). So i am getting
25 mOhm / 5000 Ohm * 3930 ppm/K = 0,02 ppm, much smaller than the observed effect.
A similar calculation applies to bonding and frame inside the array, so this may be part of the observed pattern. And then it isn't a systematic error of the measurement, but an explanation why the parts show that pattern.

Second i changed the scanner process to take two measurements for each channel. The standard deviation between the two measurements is about 1.5 ppm, with no systematic difference, except for the PT1000 sensor that shows a shift of +22 ppm due to self heating. This shift is equivalent to 5.6 mK.

Regards, Dieter

[miro123]

Thanks for sharing.
I want to start experimenting with either NOMCA or NOMC resistor networks.
You have experience with both of then. I have few questions.
How do they compares in terms of
 - TC
 - TCR
 - Temperature hysteresis
 - stability
Thanks
Miro

[dietert1]

It all depends on the application.
When i started measurements in 2019 i wanted to use those NOMCA arrays to make voltage dividers for LTFLU1 or LTZ1000 references. Then everybody wrote that NOMCA arrays are noisy and not good enough. So i made some references with other parts and they turned out to be good for 0.1 ppm, e.g. after a 5 month power-down.
Then others found NOMC arrays to be less noisy.
With my test setup, the determination of TCs within an array works well, to about +/- 0.05 ppm/K. I can say that the TCs are immune against humidity change (1 week in dry pack at 0% RH).
The resistance measurements look good as well. The NOMCs stay within some ppm. Except my resistance measurements suffer from the contact resistance of the socket. For a 5 K resistor, 1 ppm is 5 mOhm, and the biggest unexpected change i have seen is 3 ppm. Need to order another set of NOMC arrays and measure them using SSOP32 adapters - with the 4-wire ohms connection point on the adapter (behind the socket).
Measured all NOMCAs once more and started to combine the results with those of 2019, to see what happened within two years. Need more time.

Regards, Dieter

[miro123]

Thanks,
I've  found few interesting articles. on this subject.
This is what manufacturer says about their products.
https://www.vishay.com/docs/60019/spm.pdf
https://www.vishay.com/docs/49562/49562.pdf

Nichrome Thin Film have typically been used in applications requiring excellent performance but have exhibited catastrophic failure under harsh moisture environments, unless protected in hermetic packages. Tantalum Nitride resistor films have typically been the film of choice but require performance trade offs for precision application