0.01% resistors

[Spehro Pefhany]

Someone should work out all the voltages possible from an LM317 and a quad
r-pack.

Okay, here's a first cut, assuming all equal values and ignoring the
adj pin current, using the circuits John D listed:

# Circuit Ratio LM317 LT1964 LT1761 TL431
TLV431
13 "(a|b) + (c+d)", 0.800 2.81 -2.75 2.75 5.61
2.79
19 "(b | (a+c)) + d FB a-c" 0.800 2.81 -2.75 2.75 5.61
2.79
4 "a+ (b+c+d)", 0.750 2.92 -2.85 2.85 5.82
2.89
2 "a + (b+c)", 0.667 3.13 -3.05 3.05 6.24
3.10
7 "(a|b) + c", 0.667 3.13 -3.05 3.05 6.24
3.10
9 "a + (b + (c|d))", 0.600 3.33 -3.25 3.25 6.65
3.31
11 "a + ((b|c)+d)", 0.600 3.33 -3.25 3.25 6.65
3.31
17 "(b|(a+c))+d", 0.600 3.33 -3.25 3.25 6.65
3.31
1 "a+b", 0.500 3.75 -3.66 3.66 7.49
3.72
5 "(a+b) + (c+d)", 0.500 3.75 -3.66 3.66 7.49
3.72
15 "((a|b) + (c|d))", 0.500 3.75 -3.66 3.66 7.49
3.72
12 "(a+(b|c)) + d", 0.400 4.38 -4.27 4.27 8.73
4.34
14 "((a|b)+c) + d", 0.400 4.38 -4.27 4.27 8.73
4.34
3 "(a+b) + c", 0.333 5.00 -4.88 4.88 9.98
4.96
8 "a + (b|c)", 0.333 5.00 -4.88 4.88 9.98
4.96
6 "(a+b+c) + (d)", 0.250 6.25 -6.10 6.10 12.48
6.20
10 "(a+b) + (c|d)", 0.200 7.50 -7.32 7.32 14.97
7.44
16 "(a) + (b|(c+d))", 0.200 7.50 -7.32 7.32 14.97
7.44
18 "a + (b | (c+d)) FB c-d" 0.200 7.50 -7.32 7.32 14.97
7.44

 

[Klaus Kragelund]

The one time that I had occasion to actually try to source such things I

found that many of those arrays don't guarantee matching -- they're

basically some number of "plain old" precision resistors all on one

substrate, with no guarantees about matching beyond what you'd get from a

bag of similar-precision resistors.

That´s not my experience. They are made on the same substrate and then sprayed with vaporized metal film (if that's the correct term) and the reasonthat they match so well on a quad pack is that within the small area of the resistor pack, the vapor density is uniform, so that each element "sees" the same amount of metal

Cheers

Klaus

 

[Spehro Pefhany]

It would be more irritating if there were more applications where you could=
exploit this. I've known about ratio transformers for about forty years no=
w, but have yet to find an application where I could use one.

Bridges for precision temperature measurement and capacitance bridges
are two "common" applications for the physics types.

And they don't have to be rack-mounted to be that good.

By "that good", I presume you mean "fairly decent", not 1ppb!

Not all the rack mount ones are as good as 1ppb, some are as bad as
0.1ppm/K (100x worse).

Probably assembling ~1,000 similar Z-foil resistors into a
series-parallel divider would get well within an order of magnitude,
of the good ones, but..

 

[John Devereux]

Bridges for precision temperature measurement and capacitance bridges
are two "common" applications for the physics types.


By "that good", I presume you mean "fairly decent", not 1ppb!

Not all the rack mount ones are as good as 1ppb, some are as bad as
0.1ppm/K (100x worse).

Probably assembling ~1,000 similar Z-foil resistors into a
series-parallel divider would get well within an order of magnitude,
of the good ones, but..

Fluke use a "statistical array" made from resistor networks in their
voltage standards.

<http://www.mksa.dii.univpm.it/bibli...menti/Campioni/appnote/DCVref_maintaining.pdf>

See fig 4, I think it's possible there are more elements than that
shown.

(This is what I was using the LT5400 and my gain calculating program
for).

Anyone know what are these "Taitanium-Nitrate" arrays? I think they mean
tantalum nitride but even if so have not been able to find any with
anywhere near required ratio tracking.

Perhaps they use hundreds of them as you suggest.

 

[Spehro Pefhany]

Fluke use a "statistical array" made from resistor networks in their
voltage standards.

<http://www.mksa.dii.univpm.it/bibli...menti/Campioni/appnote/DCVref_maintaining.pdf>

See fig 4, I think it's possible there are more elements than that
shown.

(This is what I was using the LT5400 and my gain calculating program
for).

Anyone know what are these "Taitanium-Nitrate" arrays? I think they mean
tantalum nitride but even if so have not been able to find any with
anywhere near required ratio tracking.

http://www.vishay.com/company/press/releases/2013/130620resistors/

Maybe they are custom thin-film arrays.. if the stability of the TaN
resistors is good enough, a clever arrangement on a thin-film
substrate might make it work. Something like the transistor arrays
used in MOSFET-input op-amps.

Perhaps they use hundreds of them as you suggest.

If they're all on one substrate it might not be all that costly.

They're pretty tight-lipped about what exactly is inside the LT5400.

 

[Bill Sloman]

The one time that I had occasion to actually try to source such things I
found that many of those arrays don't guarantee matching -- they're
basically some number of "plain old" precision resistors all on one
substrate, with no guarantees about matching beyond what you'd get from a
bag of similar-precision resistors.

Quite a few resistor arrays are intended to be used as pull-ups or pull-downs and don't need to be at all precise.

Clearly we weren't looking in the right place, or perhaps the market has
developed in the last 12 years. Or we weren't looking in exclusive
enough boutiques.

I first got enthusiastic about them when I - briefly - worked for Chessell Recorders in 1979. Chessell didn't end up using them - the twit who took over the project didn't see the point. He also rejected a positive feedback of 1.0003 because he feared that it might cause oscillation.

We ended up solving that problem another way. Had there been a $30/ea
solution, I think that we would have still solved the problem with that
alternate method -- like Joerg, the group I was in had an aversion to
boutique parts. In his case it's often expense; in ours it's because we
were building products with 10-15 year lifetimes.

The 1979 parts were closer to $3 than $30. I think they came from Beckman.

http://www.bitechnologies.com/products/passive.htm

 

[Bill Sloman]

Well, they're used all the time in capacitive gauges.

Ratio transformers? Ferrite-core ratio transformers wound with Litz wire?

A little more information could be interesting.

I imagine you are thinking of the Baratron capacitative pressure sensors - my Ph.D. thesis included a discussion of that approach back in 1969, based on work that had been published by the Philips Laboratory quite a bit earlier.

 

[Bill Sloman]

Bridges for precision temperature measurement and capacitance bridges
are two "common" applications for the physics types.

One of my colleagues at Cambridge Instruments used one in a calibrator for 6-digit DVM (20-bit). Not for Cambridge Instruments - it took longer than expected at his previous employer, who carped enough that we got him - and were very glad about it.

By "that good", I presume you mean "fairly decent", not 1ppb!

The quality is determined by the physics, not the size. More space does give you more room to be picky about the lead dress.

Rayner and Kibble devote quite a lot of their book to singing the praises of ratio transformers. You don't have to work too hard to get 1ppb absolute accuracy out of a bifilar-wound ratio transformer. The more useful beasts with eleven intertwined windings are hard to get better than 100pbb.

http://www.amazon.com/books/dp/0852743890

Since it's all fixed by geometry, thermal drift isn't much of an issue (below the Curie point of the core).

Not all the rack mount ones are as good as 1ppb, some are as bad as
0.1ppm/K (100x worse).

Bad design.

Probably assembling ~1,000 similar Z-foil resistors into a
series-parallel divider would get well within an order of magnitude,
of the good ones, but..

Worse design.

--
Bill Sloman, Sydney (but in Nijmegen at the moment)

 

[Spehro Pefhany]

One of my colleagues at Cambridge Instruments used one in a calibrator for 6-digit DVM (20-bit). Not for Cambridge Instruments - it took longer than expected at his previous employer, who carped enough that we got him - and were very glad about it.


The quality is determined by the physics, not the size. More space does give you more room to be picky about the lead dress.

Rayner and Kibble devote quite a lot of their book to singing the praises of ratio transformers. You don't have to work too hard to get 1ppb absolute accuracy out of a bifilar-wound ratio transformer. The more useful beasts with eleven intertwined windings are hard to get better than 100pbb.

http://www.amazon.com/books/dp/0852743890

Since it's all fixed by geometry, thermal drift isn't much of an issue (below the Curie point of the core).

I didn't see much information on details of construction in the thin
R&K book.

There's a lot more detail in B. Hague/TR Foord's excellent book on
bridge methods (and even more in the copious references), enough to
lead me to think I might not be able to make a 1ppb/K transformer the
first time or second time.

Here's my (commercial) one.
http://www.tegam.com/product.asp?modelNumber=PRT-73&redirected=1

At 30lbs and >$12K new it's not very practical as a component.

Bad design.

Apparently. And that one is not by an unknown name. McGregor et al. at
NBS found they had to ovenize the ratio transformer (they were
shooting for a few ppb total error).

Worse design.

Certainly could be, and perhaps silly and/or obvious.

Any other ideas for getting a DC ratio stable to within, say, 10ppb/K,
and WITHOUT ovenizing?



Best regards,
Spehro Pefhany

 

[Spehro Pefhany]

I don't understand that. LM317 ref voltage is 1.25, so some obvious
available voltages should be 1.25 and 2.50.

Good point. I'll check it later tonight.


Best regards,
Spehro Pefhany

 

[Bill Sloman]

I didn't see much information on details of construction in the thin
R&K book.

There's a lot more detail in B. Hague/TR Foord's excellent book on
bridge methods (and even more in the copious references), enough to
lead me to think I might not be able to make a 1ppb/K transformer the
first time or second time.

Rayner and Kibble isn't short of references, and is a bit more explicit about plugging you into the National Standards Laboratory literature.

Hague and Foord is thicker, but it's also a lot older. What Amazon is now advertising is the sixth edition from 1971. IIRR the first edition came out in the 1920's.

Neither book is exactly into using modern integrated circuits - Rayner and Kibble do talk about some active circuits, but their whole approach is justas conservative as you'd expect from National Standards Labs employees,

If you did get a bit more creative, you could probably do better (but it would be a time-consuming development, and not all that cheap).

Here's my (commercial) one.

http://www.tegam.com/product.asp?modelNumber=PRT-73&redirected=1

At 30lbs and >$12K new it's not very practical as a component.

But it looks big enough and old-fashioned enough to appeal to National Standard Labs type customers.

Apparently. And that one is not by an unknown name. McGregor et al. at
NBS found they had to ovenize the ratio transformer (they were
shooting for a few ppb total error).

It always makes life easier.

Certainly could be, and perhaps silly and/or obvious.

Any other ideas for getting a DC ratio stable to within, say, 10ppb/K,
and WITHOUT ovenizing?

You don't get a DC ratio from a ratio transformer. You are shifting a very well-defined AC ratio into the direct-current domain by some kind of demodulation or rectification.

My sole venture into this area was a precise - if slow - isolation circuit for 1V to 5V (4mA to 20 mA) signals. The isolating transformer had three windings, only one of which had to carry much current. It spent most of it's time being driven so that the second and third windings generated the desired DC voltages on either side of the isolation barrier.

This current was monitored, and whenever it got too high, it was driven down to the opposite end of the tolerable range. The two feedback windings hadto be isolated - and the output voltage maintained by a sample-and-hold - while this was going on. The errors were essentially the off-set voltages of the op-amps involved - 748's as it happened (since this was back in 1975)..

I'm not recommending this as a solution for your problem - whatever it is -but more as an example of a bit of lateral thinking in the general area.

 

[John Devereux]

I didn't see much information on details of construction in the thin
R&K book.

There's a lot more detail in B. Hague/TR Foord's excellent book on
bridge methods (and even more in the copious references), enough to
lead me to think I might not be able to make a 1ppb/K transformer the
first time or second time.

Here's my (commercial) one.
http://www.tegam.com/product.asp?modelNumber=PRT-73&redirected=1

At 30lbs and >$12K new it's not very practical as a component.


Apparently. And that one is not by an unknown name. McGregor et al. at
NBS found they had to ovenize the ratio transformer (they were
shooting for a few ppb total error).


Certainly could be, and perhaps silly and/or obvious.

Any other ideas for getting a DC ratio stable to within, say, 10ppb/K,
and WITHOUT ovenizing?

We had a nice thread "SMD TC" about precision PWM (and precision
resistors) last year.

<https://groups.google.com/forum/#!s...i.electronics.design/eHx0O3vg0t4/zBynI1Mht7AJ>

In particular James Arthur came up with a nice scheme to cancel supply
ripple effects which would otherwise create errors, reproduced below in
full.

Of course I don't know if this will get to 10ppb but I would think some
PWM scheme would be the way forward. I think flukes calibrators use PWM
and do approach this level.

(James' original post follows)
===========================================================================


OK, after six months, six or seven days most weeks (and, due to
committing to a not-so-clearly defined project, mostly for free), I've
just gotten my gadget in shipping-shape.

So, time to play!

Here's the basic PWM:

.........................
:
Vref >----/\/\/-----O :
R1 \ : R3
\ : 1M
O-----/\/\/---+-----> Vout
: |
R2 : --- Cf
0 >----/\/\/-----O : ---
: |
........................: |
===
Fig. 1


To me, 16 bits on the cheap is plenty cool. But if the bar is doing
something extraordinary, like 1ppm, then it seems fair to use fancier
parts.

So, let's assume an FPGA and 100MHz clock rate, driving the switch.
The switch can either be the FPGA output, or an extra gate (or
paralleled gates).

We can get 1ppm modulating 100Hz in 10nS chunks. Or 40Hz in 25nS
chunks, etc. Whatever works out with our switch-speed.

Switch mis-match (R1-R2) produces a code-related error, maximized at
mid-scale. With R3=1M, my algebra says <0.5ppm non-linearity from
switch mis-match requires |R1-R2| <= 1 ohm. Y(A)MV.

Paralled gates, analog switches, or a BSS138 buffer stage could do
that. I measured (characterized) some 74ACxx parts a ways back for
this.


Another, liberating possibility is to bootstrap the switches,
canceling most of their effective resistance:


Vcomp >-------------.
|
|
......................... .-.
: | | R4
Vref >----/\/\/-----O : | |
R1 \ : '-'
\ : | R3
O----+--/\/\/---+-----> Vout
: |
R2 : --- Cf
0 >----/\/\/-----O : ---
: |
........................: |
===
Fig. 2


If Vcomp is such that i(R4) = i(R3), the voltage drops (errors) across
R1 and R2 disappear. This next version does that.


C1
Vpwm >-----+----||----.
.-. .-. | |
_| |__| |_ =2Vrefp-p| |
| .-.
.....................V... | | R4
: . : | | 100K, 1%
Vref >----/\/\/-----O . : '-'
R1 : \ : | R3
: \ : | 100K, 1%
: O---------+---/\/\/---+-----> Vout
: : |
R2 : : --- Cf
0V >----/\/\/-----O : R4=R3 ---
: : |
.................:......: |
===
Fig. 3


C1-R4 re-create the same currents as flow in R3. Effective switch
resistance (R1, R2) is lowered by about two orders of magnitude,
allowing us to reduce R3 and lower the output impedance.

Filtering the 100Hz PWM to 1ppm takes 14 time-constants = 140mS.

So, Fig. 3 is a working solution. It's linear and accurate, but needs
a hi-z buffer amp and it's slow. A 16-bit version could be faster,
with lower-z output. Or, splitting the DAC up into two sections
improves both those properties too.


C1
Vpwm(hi) >------------+---||---.
.-. .-. | |
_| |__| |_ =2Vrefp-p| |
| |
.....................V... .-.
: . : | | R4
Vref >----/\/\/-----O . : | |
R1 : \ : '-'
: \ : | R3, 0.05%
: O-------+--/\/\/---+---/\/\/--+-----> Vout
: : | Rf |
R2 : : | --- Cf
0V >----/\/\/-----O : R4=R3 | ---
: : | |
.................:......: | |
| ===
|
|
Vpwm(lo) >------------. |
| |
| |
.....................V... .-.
: . : | | R7
Vref >----/\/\/-----O . : | | = 1000 x R3, 0.05%
R5 : \ : '-'
: \ : |
: O------------------'
: :
R6 : :
0V >----/\/\/-----O :
: :
.................:......:

Fig. 4


If the upper and lower DACS cover 1,000:1 each, we could lower the
clock frequency to, say, 10MHz, pump it with a uC, and still have a
10kHz composite waveform that one-pole-filters to 1ppm in 14 * 100uS =
1.4mS.

The R7-R3 ratio is critical to absolute accuracy and monotonicity.
The top DAC divides Vref accurately into 1,000 parts, so a 1% error in
the R7-R3 divider ratio represents an error of 1 part in 100 of
1/1,000th, or 1 part in 100,000 overall. 0.05% ensures 0.5ppm.

Likewise, to ensure monotonicity to 1ppm, the lower DAC's contribution
of 1,000 lsb's cannot be off by >1 part (lsb) in those 1,000 lsb's, or
0.1%

The low DAC represents a small, code-related d.c. load on R1, R2 via
R7. That needs to be either kept small, or compensated.

Back to the topic of this thread, the effect of T/C errors in the
divider resistors is reduced by the divider ratio, a factor of 1,000.

So, there's a stable, accurate, 1ppm PWM DAC made with non-critical
parts.

--
Cheers,
James Arthur

======================================================================
(end quote)

 

[Raveninghorde]

My question is why? Even brewing beer does not take that kind of precision.

On an existing design I use a Howland current pump for high side
current measurement. For a new application of the board I need to
improve the current range at the low current end and found I was
getting too much variation. That means accurate measurement of 1mV
with a varying high side voltage around 16V.

I've tried it on some existing boards having changed the op amp to an
OPA2180 and get a 2 to 1 variation in readings forthe same current.
Most boards are OK.

So I either need better resistors or a better method of high side
current measurement.

 

[John Devereux]

On an existing design I use a Howland current pump for high side
current measurement. For a new application of the board I need to
improve the current range at the low current end and found I was
getting too much variation. That means accurate measurement of 1mV
with a varying high side voltage around 16V.

I've tried it on some existing boards having changed the op amp to an
OPA2180 and get a 2 to 1 variation in readings forthe same current.
Most boards are OK.

So I either need better resistors or a better method of high side
current measurement.

The howland current pump is a crappy circuit (as has been pointed out to
me here).

What about something like this

<http://ee.devereux.me.uk/current-sensor.jpg>

Reflects the current so it is referred to the 0V rail, stripped of it's
16V offset.

 

[Bill Sloman]

On an existing design I use a Howland current pump for high side
current measurement. For a new application of the board I need to
improve the current range at the low current end and found I was
getting too much variation. That means accurate measurement of 1mV
with a varying high side voltage around 16V.

I've tried it on some existing boards having changed the op amp to an
OPA2180 and get a 2 to 1 variation in readings for the same current.

Most boards are OK.

So I either need better resistors or a better method of high side
current measurement.

Or perhaps an instrumentation amplifier

http://www.analog.com/static/imported-files/application_notes/AN-244.pdf

http://www.analog.com/static/imported-files/data_sheets/AD8422.pdf

John Devereux's precision voltage to current converter would probably be cheaper. Rail-to-rail input op-amps will work with their inputs pretty close to the positive rail.

So does the venerable LM301A though performance isn't guaranteed close to the positive rail.

http://www.ti.com/lit/ds/symlink/lm101a-n.pdf

The op amp output has to drive the input of a P-channel MOS-FET and can be kept well away from the 16V rail.

Stability may need some attention at very low currents.

 

[John Devereux]

Or perhaps an instrumentation amplifier

http://www.analog.com/static/imported-files/application_notes/AN-244.pdf

http://www.analog.com/static/imported-files/data_sheets/AD8422.pdf

John Devereux's precision voltage to current converter would probably
be cheaper. Rail-to-rail input op-amps will work with their inputs
pretty close to the positive rail.

So does the venerable LM301A though performance isn't guaranteed close to the positive rail.

http://www.ti.com/lit/ds/symlink/lm101a-n.pdf

The op amp output has to drive the input of a P-channel MOS-FET and can be kept well away from the 16V rail.

Stability may need some attention at very low currents.

I meant to post a link to Linears AN105 too:

<http://www.linear.com/docs/12479>

Linears application notes are a bit like Wikipedia; they can inflate
your apparent IQ by 30 points on usenet

 

[Bill Sloman]

I meant to post a link to Linears AN105 too:

<http://www.linear.com/docs/12479>

Linears application notes are a bit like Wikipedia; they can inflate
your apparent IQ by 30 points on usenet

Only if you know enough about what you are posting to avoid posting duff information. Some Wikipedia articles, like some application notes, are not to be relied on.

 

[Spehro Pefhany]

The howland current pump is a crappy circuit (as has been pointed out to
me here).

What about something like this

<http://ee.devereux.me.uk/current-sensor.jpg>

Reflects the current so it is referred to the 0V rail, stripped of it's
16V offset.

That's what I normally do- the Howland thing is seriously sub-optimal.

You may have to add a zener or something like that to keep the input
within the op-amp's common mode range (between the two upper resistors
and 16V, and maybe a resistor to ground) or to keep the supply voltage
of the op-amp low enough for a low-voltage R-R input op-amp.


Best regards,
Spehro Pefhany

 

[John Devereux]

That's what I normally do- the Howland thing is seriously sub-optimal.

You may have to add a zener or something like that to keep the input
within the op-amp's common mode range (between the two upper resistors
and 16V, and maybe a resistor to ground) or to keep the supply voltage
of the op-amp low enough for a low-voltage R-R input op-amp.

Oh yes of course I was just showing the principle. With the FET output
most of the circuit could ride up near the supply, so it could work with
very high voltages in principle, even with a 5V opamp say.

But there is e.g. OPA170 which is a $0.40, 36V, rail to rail opamp.

 

[Raveninghorde]

The howland current pump is a crappy circuit (as has been pointed out to
me here).

What about something like this

<http://ee.devereux.me.uk/current-sensor.jpg>

Reflects the current so it is referred to the 0V rail, stripped of it's
16V offset.

As far as I can see that doesn't work if the output is shorted.