[volt-nuts] Matched resistors

[Randy Evans]

Tony,

Sorry for not reading further.  I will give it some thought. Interesting
idea.

Randy


On Thu, Jul 24, 2014 at 5:13 AM, Tony Holt <vnuts at toneh.demon.co.uk> wrote:

> Randy,
>
>
> On 24/07/2014 04:22, Randy Evans wrote:
>
>> Tony,
>>
>> Your improvement factor of SQRT(n) assumes that each resistor in the group
>> has random changes uncorrelated to all others in the group.  For similar
>> type resistors, I would think that is not likely to be true.
>>
>
> Yes/,/ I'm well aware of that which is why I discussed that point further
> down in my post. It was a long post though so I don't blame you for getting
> bored and not getting that far!
>
>
>  For shelf life
>> stability it is likely that they all "age" in a similar way.  Unless the
>> resistors are in a hermetic package, humidity would impact all the
>> resistors in a similar manner.
>>
>> Randy
>>
> Exactly. Since they are being used in a 1:1 divider configuration, if they
> age in a similar way, the tracking ratio stability will be good. The
> reality however is that there will be some variance between components, and
> using multiple resisters will reduce that overall variance. Part of the
> variance between individual resisters will likely follow a Guassian
> distribution and thus the improvement factor for that element will be
> SQRT(N).
>
> Some of the variance will likely be due to random factors which have a
> rather different distribution, probably highly skewed with long tails, and
> thus the improvement probably won't be SQRT(N). My conjecture (ok random
> speculation) is that factors such as stress differences due to
> microcracking in the ceramic substrate or at the terminations may cause
> some of the latter. Nevertheless, even though part of the variance doesn't
> follow SQRT(N) the variance will still reduce by using multiple identical
> resisters (if there are enough*). The problem is knowing how much - it
> probably can only be determined by lengthy experimentation, unless some
> good empirical data can be obtained from manufacturers or research papers.
>
> Another complication is that I believe that thin film resistor stability
> and TCR characteristics improve as the resistance reduces. This is not
> usually reflected in the datasheet but using multiple resistors in series
> allows lower values to be used which may perform better. On the other hand,
> thermal EMF problems may increase proportionally.
>
> TCR tracking is much easier to measure, so it might be interesting to see
> how it improves with increasing numbers of resisters. However, I understand
> that ratio stability is likely to be a bigger problem than TCR tracking.
>
> The other end of the spectrum, using a single Vishay VHD foil divider is
> certainly the simplest; however bear in mind that Vishay's stated typical
> tracking TCR of < .1ppm is just that, and the one that you buy may be
> anything but typical. And if you can work out the maximum tracking TCR from
> the VHD144/200 datasheet, you're a better man than I. My guess is that its
> probably better than .5ppm which is likely good enough for your
> application. But would it perform better than, say $30 worth of Vishay DFN,
> 3ppm 4-resister networks, 1 year shelf life ratio stability < 20ppm? I
> don't know.
>
> Of course there's nothing to stop you using multiple VHDs if you can get
> them at a good price. Ebay maybe?
>
> *) If all resisters are identical expcept that 1 in a 100 is markedly
> different, then any 10 will have a good chance (90%) of being identical;
> using 100 will have a good chance (64%) that at least one is different and
> thus the overall error would be at least 1/100 of the difference.
>
> Tony H
>
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