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 > > _______________________________________________ > volt-nuts mailing list -- volt-nuts@febo.com > To unsubscribe, go to https://www.febo.com/cgi-bin/ > mailman/listinfo/volt-nuts > and follow the instructions there. > _______________________________________________ volt-nuts mailing list -- volt-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/volt-nuts and follow the instructions there.