Matched resistors
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@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@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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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 randyevans2688@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 vnuts@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@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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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
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@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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At risk of being flamed for suggesting scrapping an instrument, selecting
the best pair from the K-V divider of an old Null Voltmeter may be an
option. A simple bridge with the test resistors in a heated oil bath and
the other pair kept constant will give an indication of match. Take care
not to mechanically or thermally stress the resistors when removing them.
The resistors will have been well matched originally and will be well aged.
Robert G8RPI.
On 17 July 2014 05:40, Frank Stellmach frank.stellmach@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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