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)..