[volt-nuts] Matched resistors

[Randy Evans]

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 <vnuts at 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.stellmach at 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
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