Ultra low-noise, short-term stable references

[bsdphk]

Apologies for not spotting this sooner and sharing my own related experience.

At one point I tried to implement digital control of the Vadj on an OCXO with an integrator instead of a DAC, to avoid the oven around the DAC+Vref.

That is basically the same thing you are trying to do, only I had an input which could be be brought high or low for some amount of time to adjust the voltage as necessary.

My direct inspiration was the integrator circuit in the HP5061 and HP5065 atom frequency standards, which use a 5µF Polyethylene capacitor.

My target time constant was much longer than HP's, hours and days rather than milliseconds, so I spent (too much) time trying to find a better capacitor.

My findings were roughly:

I didn't try vacuum capacitors - too bulky for their small capacitance, but I suppose they would be close to perfect (if kept in darkness!)

Silver-mica was very stable, but since they come only in very low capacitance, even fA leakage dooms the idea.

Tiny ceramics have the same problem, but worse stability.

High capacitance ceramics are sensitive to everything, up to and including what you ate the day before.

Anything with liquids in it is hideously sensitive to temperature and air-pressure.

Stabilizing the temperature only got me to a nonlinear barometric sensor.

(I only tried ultracaps up to about 5F in the usual cylindrical housing.)

That more or less left film capacitors, and they were all over the place, even for what is supposed to be the same kind of film from the same manufacturer.

Dont even think about paper.

Teflon is supposed to be the superior plastic, but impossible to get hold of in relevant capacitance. (Probably because of Wassenaar 3.A.1.e.2)

Back then eBay sellers from Russia sold what they claimed was teflon capacitors, but at prices and with appraisals which literally screamed audiohomoeopathy, so I figured they didn't have any teflon in them in to begin with.

Taking a clue from HP's use of PE, I spent a fair bit of time on plastic film capacitors.

Around this time AoE III came out and said basically the same thing: kV plastic films.

The good news is that those are cheap, so you can afford to experiment.

With µF sized capacitors rated for 1kV voltage, and everything washed in iso-propanol after soldering, leakage current is a non-issue, my HP3458 had a hard time measuring the self-discharge on my timescale of hours and days.

They were heavy enough that I saw no signs of microphonics until I literally struck them with a pencil.

I could not attribute anything to humidity, but could also not yet rule it out.

Some of them were light sensitive, but a good box fixes that.

Air pressure mattered, not much, but relevant.  I saw both signs, so I figured I could probably compensate that out with a set of handpicked capacitors.

But temperature mattered a lot, and with the selection of dielectrics I tried, the sign was always the same, so ovenizing would be required.

Since that was exactly what I had tried to avoid in the first place, I sort of gave up around that point.

I should note that I saw "pop-corn" changes in the voltage, and since their rate seemed to be roughly proportional to the physical volume of the capacitors I made a note to find out if cosmic rays or background radiation were relevant.  Never got to it.

As I understand it, you are targeting a timescale of "a day in the lab"-ish.

You can probably ignore the air-pressure, provided you check the barometer before and after to see that it didn't change too much[1].

I'm less convinced you can avoid an oven, or at least thermal insulation, so I'll conclude with a cheap trick for high stability work in both frequency and voltage:

Find an old fridge, ignore the compressor.

Convenient door.  Good thermal insulation.  Faraday shielded.  Easy to drill holes for wires.

Preinstalled tubing to run water through, if you want to do active temperature control[2]

Add a couple of bricks on the top and bottom shelves for increased thermal impedance.

Have fun :-)

/phk

[1] My thoughts go out to Kleinstein and PTB: Looks like some really bad weather coming your way.

[2] Please get a qualified cooling technician to evacuate the gas so you don't contribute to atmospheric pollution.

[dietert1]

We also made an oven with two 380 uF film caps (see https://www.eevblog.com/forum/metrology/making-an-array-of-ltz1000/msg4772546/#msg4772546). The advantage of the film cap filter: It might be used in a calibrator, i mean a source with variable output voltage.
The advantage of the ultra-cap solution: It can be used without a buffer amplifier. I mean any reasonable voltmeter comes with a good input buffer anyway, some with leakage currents in the low pA.
After branadics test i thought i should look into this, as i made TEC ovens before that are short-term stable to some microK. The TC of my ultracap set is roughly 1 mV / 10 V /K = 100 ppm/K. So a 10 uK oven should be sufficient for 1 ppb voltage stability. For this application we neither need to calibrate temperature to that level nor guarantee long-term stability to that level.

Regards, Dieter

[Echo88]

Took me a few days to rethink the idea. I stepped away from the idea of OP -In feedback connecting directly to the supercap, due to the ridiculous size the compensation cap (in the single Farad range) would need to have according to the rule of thumb from the mentioned article "To start, the value of C1 is chosen such that R3C2 = C1R2" https://www.analog.com/en/resources/technical-articles/simulation-shows-how-real-op-amps-can-drive-capacitive-loads.html
I havent yet done a phase margin analysis on the circuit to see how it could be properly compensated, quite frankly because im not familiar with it.

Now im trying to use a simple Riso between the OP and the supercaps and doing what Dieter suggested: compensating the leakage current. When going the analog way one can for example inject a suitable current to compensate the Riso voltage drop or go with the old trick of using two caps in series with a suitable middle connection bias voltage.

Regarding the current injection method: Still unsure about the necessary feedback look for near perfect current compensation, LTSpice indicates a high voltage gain leads to better compensation?
Regarding the series cap method: Hybrid caps cant be discharged to 0V, so the top caps have to be standard supercaps with higher leakage/lower capacitance with regards to physical size, meanwhile the bottom caps can be of the hybrid type.

Both variants are attached.
Please ignore the supercap capacitance values in the schematics/simulations, they are relatively small. Now i got a new chamber and can use way bigger supercaps and am no longer so limited in the physical size regard.

@ iMo: The +Star is never allowed to connect to ground as that would short the supercaps and lead to mayhem.

The digital solution might be really the way to go to properly design a complete solution in the end. But for now ill stay with the analog design as a prototype to try to get familiar with the supercapacitor behavior itself.
The DA of those caps is enormous as expected and since all supercap datasheets spec the leakage spec after 72h at nominal voltage the true leakage will be buried under the DA.

Some relevant papers dealing with supercaps and one with low noise diodes:
https://www.mdpi.com/2079-9292/9/8/1245#B28-electronics-09-01245
https://iopscience.iop.org/article/10.1088/1742-6596/1015/5/052011/pdf
https://www.researchgate.net/publication/3950664_Very_low_noise_high_accuracy_programmable_voltage_reference
https://www.wellesu.com/10.1063/1.4870248
https://www.wellesu.com/10.1142/s021947750700388x A diode based low noise voltage source variant, no supercaps.

[MiDi]

Noise tests for NCR18650A & BR2032 Panasonic gave very low noise, NCR18650A is even below NF of ULF-ULNA (see attachments).
3xNCR18650A in series (11.8V) have a TC of ~280µV/K (~24ppm/K) at 22°C and self-discharge of ~2.6nV/s (~82mV/a).
The TC is in the range of unheated LTZ/ADR1000.

[guenthert]

[..]
Now im trying to use a simple Riso between the OP and the supercaps and doing what Dieter suggested: compensating the leakage current. When going the analog way one can for example inject a suitable current to compensate the Riso voltage drop or go with the old trick of using two caps in series with a suitable middle connection bias voltage.

Is this actually needed here?  The voltage drop over Riso would be before the star point and hence irrelevant, no?

[Kleinstein]

A TC of only 24 ppm/K for the super cap / LI cell looks promissing. This should be better than most film capacitors.  With essentially no power loss in the capacitor a thermal stabilization could be relatively easy at least for the shorter times.
Also just the 100 ppm/k reported by Dietert look OK and managable.

With the Li based "super-caps" there is a chance that the TC depends on the actual voltage per cell and not just the capacitor type.

The main advantage of a film capacitor would be less DA and other relaxation effects (e.g. after mechanical stress). The lower capacitance still would need really low leakage currents.

[dietert1]

Noise tests for NCR18650A & BR2032 Panasonic gave very low noise, NCR18650A is even below NF of ULF-ULNA (see attachments).
3xNCR18650A in series (11.8V) have a TC of ~280µV/K (~24ppm/K) at 22°C and self-discharge of ~2.6nV/s (~82mV/a).
The TC is in the range of unheated LTZ/ADR1000.

With our ultra-caps the discharge rate would be 120 uA from 125 F, about -1 uV/sec, about a factor 400x higher than  your result. If i compare to the LiC cap specs, that would still be about 40x. Seems like those lithium batteries are a good choice. Are the Allen diagrams TC compensated? What kind of oven was used for this?

Regards, Dieter

[iMo]

..3xNCR18650A in series (11.8V) have a TC of ~280µV/K (~24ppm/K) at 22°C and self-discharge of ~2.6nV/s (~82mV/a)..

What about to "trickle charge" the battery with a couple of nA such you compensate for the voltage_drop/sec??

[MiDi]

Are the Allen diagrams TC compensated?
What kind of oven was used for this?

There is no TC-compensation for the NSD plots, the cells were just inside an alu case on the bench in my basement with quite stable temperature (around ±0.1°C over a day during those measurements).
Allan deviation for 18650 and NF ULF-ULNA attached (as 18650 is below NF, it mainly shows ULF-ULNA NF)

What about to "trickle charge" the battery with a couple of pA such you compensate for the voltage_drop/sec??

Roughly compensate self-discharge with a low noise constant current and let the LS reference take over the fine adjustment, main question is where to set the transfer point?
As already stated, it needs to sit in an ovenized, sealed and sturdy case that rejects influence of temperature, pressure and humidity enough.

[iMo]

I added above a naive sim, with 251nA you may compensate the 2.6mV/Megsec drop at the 100F battery.. Not sure about the 1/f noise impact of a trickle charging current source though.. 

[dietert1]

The backup battery pack of our ADR1399 has 5 Li-Ion cells of 2 AH and would need a 960 F capacitor to simulate. It has been running for a year or so at a stable 20 V voltage, directly controlled by the reference voltage. It has a 200R safety resistor and i see about 35 uV across that resistor, in other words 175 nA leakage current. This includes some leakage of the voltage balancer and is almost 700x less than the 120 uA i have with our ultra-cap set. Seems to confirm MiDis numbers. I started a log to determine the average over one day/night temperature cycle.

Regards, Dieter

Edit:
Looking at a complete day/night temperature cycle of 0.4 °C i got an average leakage current of 460 nA, a factor 260x less than the 120 uA of the ultra-caps. Estimated TC is about -20 ppm/K, also similar to what MiDi reported. The time constant of the setup should be about 2000 F * 200R = 400 000 seconds. Part of the voltage change gets compensated by the charger.

[MiDi]

The current noise & drift of the trickle charger should not be a problem.
Self-discharge for those 18650 is ~40µA and differential capacity is ~14.000F/cell (dV=0.5V, I=1.45A, t=80min from DS).
With worst case 3x1Ω ESR (typ. 0.3Ω/cell) the noise attenuation factor at 10V is ~83k (typ. ~250k).
For 10µHz (1.2 days) the noise attenuation factor at 10V is ~55k (typ. ~70k) - 100ppm current noise/drift gives <0.002ppm voltage noise/drift.

[Kleinstein]

The leakage compensation can likely be combined with the loop that links the capacitor part to the long term stable ref. (e.g. LTZ1000). I see no real need for extra current source. Chances are this part would be some kind of PID regulator.

[iMo]

One issue I see with the 18650 cells is you cannot create 10V easily out of them (nor filter the 10V)..
3 cells at 3.33333V each in series - that is well below their voltage minimum..
Even filtering 7V with 2 cells in series is not feasible, imho.
With those 2.7V max supercaps you may use 4 in series and you are at 10V (and with 3 at 7V and with 2 at 5V)..

[KT88]

LFP cells would work. they also have a fairly flat discharge curve.

[MiDi]

One issue I see with the 18650 cells is you cannot create 10V easily out of them (nor filter the 10V)..
3 cells at 3.33333V each in series - that is well below their voltage minimum..
Even filtering 7V with 2 cells in series is not feasible, imho.
With those 2.7V max supercaps you may use 4 in series and you are at 10V (and with 3 at 7V and with 2 at 5V)..

The safe minimum voltage for NMC is 2.7V .. 3V.
So 3.33V should be fine, but at the low end of SOC (could decrease lifetime).
Could you please give a bit more info on your statement?
What do you mean with "filter"?

[iMo]

To use it as a simple RC filtering capacitor with 10V (when there is 10V at the 3x18650 in series)..

[dietert1]

Meanwhile i got some basic data concerning LiFePo4 batteries for a voltage reference low pass filter. I have been looking at no-name AA size cells IFR14500 (600 mAh), two sets of 3 cells each.
Leakage current/self discharge is known to be 2-3 % per month. For a 600 mAh cell that amounts to about 20 uA. Measured values of my two battery sets are 3 and 8 uA, with little dependence on temperature (tested at 22 and 28 °C). TCs of the two sets were found to be 14 ppm/K and 7 ppm/K. One could try to select cells from a larger set in order to improve those results.
Series resistance of the cells is specified as < 80 mOhn. That means each 10 V set will be < 0.24 Ohm. A filter with a 100 Ohm resistor can certainly suppress 1 uV zener noise to about 2 nV or better.

Today i tested a 0603 PTC fuse, Digikey part number 507-0ZCM0001FF2GCT-ND. Cold resistance is 20 Ohm and steady short circuit current is about 50 mA (about 200 Ohm). Should be good enough to protect the cells from a short. Don't know yet how much thermal EMF the part causes.

Also there is some progress building the constant humidity, pressure and temperature oven. Pressure leakage time constant increased to about 400 days. Currently i am trying to embed the cells into a piece of copper in order to improve temperature control.

Regards, Dieter

[Kleinstein]

A TC of some 7 and 14 ppm/K looks very promissing. That is better than the saturated Hg ref. cells (AFAIR some 40 ppm/K). I don't think the internal resistance is that critical. With some active feedback to compensate the leakage current one would likely not have a simple low resistor from the reference side, but more a controlled current source with a much higher resistance. So not simple RC time constant by a larger resistor and some electronic / digital gain.

The PTC fuse looks good. If really needed one could use a high voltage one, or possibly 2 in parallel to average thermal EMF. Testing the thermal EMF would make sense. I have tested a THT part (more suitable to protect a DMM input) and found surprosingly low thermal EMF. So the changes good to find a suitable version. AFAIK there are 2 types: ceramic and polymer ones.
In a stable temperature case there should also be small gradients.

One could consider 2 temperature stabilized parts:
1) the Li-cells and some parts with essentially zero (<< 1mW) power consumption: this needs a really stable temperature, but low power makes it easy
2) the amplifiers and maybe the LTZ1000 (or similar) reference part: may not need that stable a temperature, but has significant power consumption

[Korchahin]

I would like to know the thermal stability of LTO Li Akku. Theoretically, it should be better than LiFePO4. It is also interesting to use it in parallel with a zener diode as a buffer, as in the current experiment.
Usually everything tantalum is many times more stable and surprisingly higher. I looked at Moser prices for some Vishay capacitors (>300usd) and involuntarily wondered why and where are these used? 

[Kleinstein]

More expensive does not necessary mean better.  It is hard to predict the TC of different battery chemistries. So hard to tell up front if the LTO would be even better than LiFePO4, that turned out surprisingly good.

The wet tantalum capacitors are an old technology used for high reliabilty / low temperature. So expect space and avionics or militry - so areas where component costs is not that relevant and numbers are small.
Tantalum is not necessary more stable. The old style tag tantalums from the 1970/1980s have a pretty bad reputation. There is a little sense behind the idea, as tantalum is relatively expensive. So they would only use it if the products of some advantage over cheaper alternative products. For the tantalum capacitors the main point is however more low ESR also at low temperature.

[dietert1]

Meanwhile i have some measurements of thermal EMF of the 20 Ohm PTC mentioned above. In a typical setup with low thermal gradients it adds 8.2 nV of thermal EMF with about 2 nVrms extra noise. In comparison a current limiter made with two back-to-back JFETs (R = 400 Ohm) adds 10.4 nV with about 1 nVrms extra noise. The PTC is a bit more sensitive with temperature changes.

Regards, Dieter

[Echo88]

Here are some preliminary pictures from my setup and chamber stability results.
I chose to go with stainless steel chambers with standard vacuum conflat flanges, held at temperature via an analog heater PI-controller + kanthalwire, while thermally insulated by about 5cm styrofoam surrounding it.
While more expensive i wanted to have a very sturdy, shielding and virtually zero pressure leakage chamber for these longterm refstability tests.
To keep the chamber at constant temp kanthalwire was applied to the mantle and bottom, with a standard OP-Amp PI-Controller keeping the walltemp at 30°C.
Normally this heater controller would sit inside the chamber, but for preliminary tests it was sitting outside of the chamber as visible on the photo.
Chamber humidity was kept at 0° RH by using fresh dried silica gel.
That shouldnt be necessary for the reference though, as i have no idea how 0° RH will influence the capacitor stability.
In the pictures the unpopulated stacked rev 0 pcbs can be seen:
Heater Controller/Sensors BME280 + TMP117/Signal feedthrough - OPA206 + PTF56 + NTC + BJT-Driver, thermally coupled to the chamber by a thermal mat
ADR1399-Ref - LTZ1000 or ADR1000 would be better, but to test the feasibility of this project i chose to go with the simpler/cheaper ADR1399
Supercap-pcb - series connected standard and lithium hybrid supercaps, the hybrid supercaps compensate the standard supercap leakage current
Thermal shielding/baffle-pcbs that surround the Ref-pcb
The visible radial fan in the chamber is necessary to circulate the air for uniformly temp distribution (thanks TiN).
Without a fan the BME280 inside the chamber indicated way worse thermal stability (about factor 30 thermal attenuation vs roomtemp change) than measured by a NTC + HP34465A connected directly to the outside chamber wall.
PCBs that support a version which uses the big visible PP-cap + tantalum caps for leakage compensation are also on the way.
The PP-cap should provide way less headache/time constant waiting due to way lower DA.

Preliminary stability results explanation:
BME280 inside and outside of the chamber were sampled by a Raspberry Pi 4 for about a week.
A standard rubber gasket was used, the two Swagelok signal feedthrough ports were closed with fittings, which were sealed with "Uhu Endfest" epoxy.
The fan was running inside the chamber and the heater controller sat outside the chamber, which gives slightly worse thermal attenuation values compared to it sitting at constant temp inside the chamber.
The visible curves start after the heater has stabilized the chamber temperature and therefore pressure.
The silicagel had time to absorb nearly all chamber humidity.
The environmental temperature and also the chamber wall temperature were measured via a HP34465A and HP34461A + PT100 running in parallel to the BME280 logging, to ensure proper measurement values.
As can be seen the roomtemp changed by about 8K (i intentionally disabled the room radiator for the test), meanwhile the chamber temp changed 0.05K -> Thermal attenuation is about 160, which was confirmed by the DMMs.
The chamber pressure stability is about 0,3hPa, while the environmental pressure changed by about 43hPa.
The chamber relative humidity keeps on playing dryness limbo, while the environmental humidity changed by about 12%.

A chamber can house either two independent supercap filtered references or one PP-cap filtered reference.
Two opposition mode connected filtered references allow for easier noise measurement with a nV-meter.

The new improved heater controller design should yield slightly better thermal attenuation values of about 200, limited by the styrofoam insulation - i dream of cheap, large and millable aerogel-cubes

[dietert1]

That looks interesting.
When i tried to get a quantitative model of chamber pressure measurements i found three components:
- Sensor drift. In my case the test chamber runs at 37.4 °C and drift was determined as -1.7 Pa/day. Drift is caused by the over pressure of the reference volume inside the sensor caused by running the sensor at higher temperatures. The membrane slowly gives in and makes the chamber pressure appear less. For low sensor drift the chamber better operates near ambient temperature.
- In a closed gas volume temperature changes will be visible as pressure changes at about 3 hPa/K. That means a temperature variation of 20 mK is expected to show up as a 6 Pa pressure variation and it does in my BMP388 data. The gas thermometer measures average temperature inside the chamber.
- Chamber leakage depends on pressure difference between chamber and ambient. One needs to understand the other factors before one can check leakage and make claims about it.

Regards, Dieter

[dietert1]

Meanwhile i tested a current limiter with 2x BSP135 and a 100R resistor, as proposed in another thread.
Resistance as measured by multimeter is 160 Ohm. Current limit is about 8.3 mA at 30 V.
Diagram shows a 24h log. Thermal EMF is about 23 nV where temperature is flat. Maybe it can be built different in order to further reduce temperature gradients.
This time the 20R PTC appears with about 5 nV.

Regards, Dieter