Tony, I should have mentioned that I am primarily referring to stability, not accuracy. As i stated before, accuracy is relatively unimportant but stability is essential.
Randy On Wed, Jul 23, 2014 at 8:22 PM, Randy Evans <randyevans2...@gmail.com> 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. 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 > > > On Wed, Jul 23, 2014 at 6:36 PM, Tony <vn...@toneh.demon.co.uk> wrote: > >> Randy, >> >> Have you considered using multiple identical resistors to reduce the >> variance? Depending on who you believe, you can reduce the variance of the >> overall resistance by SQRT(N) where N is the number of resistors in >> series/parallel. Its not that easy to create a good search query for this >> but here is one such explanation: >> >> http://paulorenato.com/joomla/index.php?option=com_content& >> view=article&id=109:combining-resistors-to-improve- >> tolerance&catid=4:projects&Itemid=4 >> >> Ideally they should all come from the same batch - ie. manufactured by >> the same machine from the same batch of materials. Obviously there's no way >> to guarantee that without close liaison with the manufacturer (you did want >> 10 million parts at $.10 each didn't you!) but hopefully a set of resistors >> which come off the same reel would come close. >> >> The absolute value isn't important however, but 'statistical gain' will >> also apply to the TCR and stability of the overall divider. The following >> assumes that both factors are similarly improved by SQRT(N), but in fact >> they may be rather better than that. >> >> That80€ or $108 for one sealed Vishay foil divider will buy a lot of >> lower spec parts: >> >> Approx 12558 x Susumu RR0510P .5%, 25ppm 0402 (Digikey, $86/10k). 6279 in >> series and parallel in each leg of the 1:1 divider<http://media.digikey. >> com/photos/Susumu%20Photos/RR%200402%20SERIES.jpg> might reduce the >> variance to 25ppm/SQRT(6279) = .32ppm. Can't see any spec for stability, >> but it may also improve similarly. Would take a while to solder them onto >> stripboard though! >> >> Slightly more sensible might be 1078 x TE Connectivity RP73 1%, 10ppm >> 1206 (Digikey, $100.18/1K). Stability .5% (no qualifers in datasheet) >> => 10ppm/SQRT(539) = .43ppm, stability => 215ppm >> >> Or 372 x KOA Speer RN731JTTD4021B5 .1%, 5ppm (Mouser, $29/100). Stability >> not on data sheet but typical endurance is +/- .02% for 1000 hrs @ 70C >> on/off 1.5hours/.5hours. >> => 5ppm/SQRT(138) = .37ppm, endurance => 14.7ppm (Stability should be >> rather better than that). Note that the Mouser part no. is for a 25ppm part >> but their manufacturer's part number is the 5ppm part as is the >> description. Also, the price is way too high for 25ppm parts. >> >> Or 28 x Susumu RG2012L .01%, 2ppm (Digikey, $39.6/10). Stability not >> quoted but typical Load Life is .01% (1000 x 1.5hours on/.5hours off at 85C) >> => 2ppm/SQRT(14) = .53ppm, endurance => 27ppm >> >> You could also use multiple resistor networks. Eg: >> >> 104 x Susumu RM2012B-103/103-PBVW10 .1%, 5ppm tracking, 2 >> resistors/device (Digikey $104/100). Stability not quoted, endurance 500ppm >> (1000 x 1.5hours on/.5hours off at 85C) >> => 5ppm/SQRT(104) = .49ppm, endurance => 49ppm >> >> 35 x TT Electronics SFN08B4701CBQLF7, .25%, 5ppm tracking 7 >> resistors/device (Digikey, $76/25) . Stability not quoted, high temperature >> exposure < 1000ppm >> => 5ppm/SQRT(122) = .52ppm >> >> 33 x TT Electronics 668A1001DLF .5%, 5ppm tracking 8resistors/device >> (Digikey, $82/25). Stability not quoted, load life < 1000ppm >> => 5ppm/SQRT(33 * 4) = .45ppm >> >> 16 x Vishay DFN .1%, 3ppm tracking with 4 resistors/device (Digikey, >> $5.24/1). Shelf life ratio stability is specced at 20ppm (1 year at 25C). >> (That may be a typical rather than a maximum - your parts may all be much >> worse than typical). The 3ppm tracking TCR may also be a typical figure as >> its headlined in a section titled 'TYPICAL PERFORMANCE' but in the >> specification table its not qualified with '(typical)' as they sometimes do >> in other datasheets. Its hard to tell. >> => 3ppm/SQRT(32) = .53ppm shelf life stability => 3.5ppm >> >> 5 x Vishay DSMZ metal foil dividers, .5ppm tracking max (probably >> performs rather better than this over restricted temperature range, but >> don't believe the Vishay typical figure of < .1ppm/C) (Digikey, $22.93/1). >> Shelf life ratio stability not quoted but 'typical limit' for Load Life >> ratio stability is 50ppm (2000 hours at 70C). Who knows what a typical >> limit is? Again, probably best to treat Vishay 'typical' figures with a >> pinch of salt given the experience of another poster on volt-nuts. >> => .5ppm/SQRT(5) = .22ppm, load life => 22ppm >> >> Interestingly Digikey quote a price of only $5400 for 1k parts for the >> similar DSM divider (1ppm tracking), which is a huge difference from >> $22.93. Might be worth considering a bulk buy if there enough volt-nuts >> with the same problem. They aren't stocked though so that price might not >> be 'real'. However: >> 20 x Vishay DSM dividers, 1ppm (Digikey, $5400/1000) Load life ratio >> stability 'typical limit' 50ppm >> => 1ppm/SQRT(20) = .22ppm, load life => 11ppm >> >> Multiple LT5400 networks could also be used and may give the best >> results, but the much larger absolute tolerance, +/-15% would cause those >> with the highest value for series connected/lowest for parallel to dominate >> and reduce the statistical improvement. Do your own calculations. >> >> Its interesting that all these different components end up providing >> pretty much the same performance for the same cost - in other words the >> cost is inversely proportional to the TCR^2 >> >> My gut feeling is that the tracking TCR will improve rather better than >> the SQRT(N) calculated, if they do indeed come from the same batch, as I >> would expect them to have similar absolute TCRs. Thus you might be able to >> get away with rather less parts to achieve < 1ppm. The SQRT(N) factor comes >> from assuming that the variation in the value is random, and I believe, has >> a particular distribution (Guassian or normal?). Component specifications >> are often derived from the distribution parameters measured from a large >> set of production samples, with the max/min values determined from a >> multiple (typically 6?) of the standard deviations of the distribution? The >> worst case specifications for TCR and stability may (I don't know, just >> hypothesizing) be derived very differently. For example, the TCR may be >> affected not only by the characteristics of the bulk resistive material, >> but also due to stresses on the element due to thermal expansion of the >> substrate/packaging. It may be that the former is almost identical for all >> components from the batch, but the latter is less predictable. The >> specification max/min would have to allow for the worst cases which might >> be due to a relatively few which for some reason (microcracking in the >> substrate perhaps) have much larger variance from the majority. The >> distribution of TCRs from a set of resistors could be very skewed with long >> tails and the SQRT(N) reduction in variance may be well off the mark. >> >> Stability is more difficult because the shelf life stability is rarely >> specified, but is likely to be the closest to your usage. For reference, >> the Vishay DFSMZ datasheet specifies ratio stability of .015% for 2000 hour >> at 70C and .002% for shelf life ratio stability. The 7.5X difference might >> be useful for estimating shelf life stability for resistors that only quote >> load life or endurance specs. But it might not! I'm not sure that the >> endurance spec is very useful either as it subjects the resistor to a large >> number of large temperature cycles which won't be anywhere near your usage. >> >> I would expect the long term tracking stability to be much better than >> (worst case datasheet stability)/SQRT(N) as I would expect the vast >> majority to age in similar ways, if not by the same magnitude. Whilst the >> specs show stability to be +/- xx% I would expect that most will age in the >> same way - probably slowly increasing resistance over time. I also expect >> there are experienced posters here who know otherwise! Similarly to TCR, it >> could be that for example, the stability of most resistors in a batch may >> be quite good, but the specs reflect that a few may be much worse due to >> random faults in individual samples - such as defects in the protective >> coating of the element allowing corrosion to occur in a few samples. You'd >> need a very good understanding of the factors that determine the resistor >> stability to calculate the overall stability of multiple resistors. >> >> I would expect similar factors to apply to ratio tracking due to humidity >> changes. No doubt there is some useful information out their in application >> notes/research papers on the variance in long term stability between >> resistors of various types (and maybe even for parts taken from the same >> batch) just waiting for some interested volt-nut to discover? >> >> The fewer the parts, the more chance of statistical outliers reducing the >> improvement over a single part, but you could test each divider for the >> best matching, if you've got a decent meter, fairly easily by applying a >> voltage from a stable, low noise source (a battery would be good if its >> temperature is kept very stable), and measure the voltage at the centre >> tap. Then put the resistor network in a plastic bag and immerse it in >> boiling water to raise the temperature by 75C or so; .5ppm tracking would >> give 9.4uV/V maximum change; you'd probably need to reverse the meter leads >> a few times to null out thermal EMFs. Alternatively measure the voltage >> difference between the divider under test and another driven by the same >> voltage source and kept at a stable temperature - ie. in a bridge >> configuration. A simple high gain amplifier (say 1000x) with adjustable >> offset would allow testing with a more realistic lower temperature >> difference of say 20C and/or a cheap meter. >> >> Accuracy is not particularly important - you probably don't need to know >> the temperature tracking coefficient to better than 20%. >> >> Component layout would need to ensure any thermal gradients apply equally >> to both legs of the divider by interleaving upper and lower resistors. >> >> Tony H >> >> >> On 17/07/2014 16:26, Randy Evans wrote: >> >>> Frank, >>> >>> The high cost is my concern, although high performance demands high price >>> typically. I am trying to double the voltage reference from either an >>> LM399 or LTZ1000, hence the need for precision matched resistors for a x2 >>> non-inverting amplifier (using a LT1151 precision op amp). An >>> alternative >>> I am investigating is using the LTC1043 in a voltage doubling circuit as >>> shown in Linear Technology app note AN 42, page 6, Figure 16. It states >>> that Vout = 2xVin +/- 5 ppm. I am less concerned about the absolute >>> accuracy than I am about the long term stability. I assume that a high >>> quality capacitor is required (low leakage, low ESR, low dielectric >>> absorbtion, etc.) but the circuit does not appear to be dependent on the >>> absolute value of the capacitors. I'm not sure if the two 1uF caps need >>> to be matched. If they do then that would be a show stopper. >>> >>> Does anyone have any experience using the LTC1043 in such a circuit? >>> >>> Thanks, >>> >>> Randy >>> >>> >>> On Wed, Jul 16, 2014 at 9:40 PM, Frank Stellmach < >>> frank.stellm...@freenet.de >>> >>>> wrote: >>>> Randy, >>>> >>>> resistor matched in T.C. are extremely expensive, as the manufacturer >>>> (or >>>> yourself) would have to select these from a batch of many samples. >>>> >>>> reistors with very small T.C. (<1ppm/K) would do the job also, but they >>>> also need to be stable over time, in shelf life opereation mode, i.e. >>>> P<10mW. >>>> >>>> That means, you need those hermetically sealed VHP202Z from Vishay, T.C. >>>> is typically < 1ppm/K and they are stable to < 2ppm over 5years. But >>>> they >>>> cost already 80€ each, depending on tolerance. >>>> >>>> I made a longterm observation of these and found these parameters >>>> confirmed. >>>> >>>> Frank >>>> _______________________________________________ >>>> 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. >>> >> >> _______________________________________________ >> 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.