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 vn...@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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