Ultra low-noise, short-term stable references

[Kleinstein]

For testing the noise of the L cells one could look at the difference between 2 cells or 2 stacks. So only a small DC voltage and thus the possibility for DC coupled amplification. DC couples and thus with low resistors the OPA189 and most other AZ amplifiers would be OK, as the Li cells are low impedance.

For AC coupling the AZ amplifiers like OPA189 would need rather large coupling capacitors, which may be more sensitive to temperature and mechanical stress than LI cells. I don't think one would need a serious low pass filter - the LI cells should be very low noise over quite some frequency range. It would be really hard to amplifiy with AC couling. A moderate LPF may be wanted to filter out AZ amplifier artifacts.

[miro123]

One stupid question arise when I start playing with those LiFePO4 cells.
How do you deal with power off state of supported electronics. Imagine power goes of and all clamping diodes acivates

[dietert1]

In my tests i used some BS170 mosfets to disconnect the electronics automatically, as shown in the schematic i posted above. They are driven by a very simple circuit with a pnp transistor, a zener and some resistors to avoid any glitches during power on or off. Later three PC817 optocouplers were added per device so the MCU can select the charger operation mode, disconnect the chargers and disconnect the device output. The fourth opto drives the trickle current PWM.
The schematic doesn't show the necessary output protection circuit.

Regards, Dieter

[mzzj]

The diode array comes with a TC of about -2 mV/K / 600 mV = -3300 ppm/K, while the LiFePo4 batteries i tested have around 12 ppm/K, a 278x advantage. In the paper they are looking above 0.1 Hz. Certainly ambient temperature variations are easier to suppress at short time scales.
I think the LiFePo4 averager can work at time scales of hours or days. And yes, the cells are terribly slow for development and tests. While i glued the cells into the copper block they already lost some charge. When i connected them again, i made a minor mistake that changed the state of the cells even more. One definitely needs an automatic controller to charge and balance the cells as fast as possible and make them finally track the zener reference. Otherwise the idea is useless.
The schematic is a possible starting point. It still needs some level shifters. As Kleinstein wrote above, resistor R13 won't be necessary, so optional or switchable. I have been using it to measure leakage current.

Regards, Dieter

Edit: The schematic isn't more than a sketch. The amplifier can't feed the 10R charger resistor. And there should be a hardware protection when reaching 3x 3.6V = 11 V total voltage for whatever reason. And the nullmeter needs its own battery tap in order to measure battery voltage independent of charger current and during output off.

Came across your post when I was looking for LiFePo4 voltage tempco.

Some LiFepo4 batteries seem to have considerably lower self discharge rate than others. 100Ah cell I'm currently measuring seem to have about 0.4% per month self discharge rate.
Coupled with the flattest portion of the  LiFepo4 discharge curve (stage 1 lithiation between 80-90% SOC) we would get -0.000184 volts per month or 2ppm per day.
Didn't see that coming but explains why self-discharge measurement can be a bugger.

[dietert1]

Yes, a good disciplined LiFePo4 standard requires a continuous charger current to compensate self discharge. In my case that circuit is digital in order to achieve a large time constant for adjustments of the charger current. There is one DAC that controls charger current for all three cells.
Those larger cells used for energy storage often incude safety circuits that are incompatible with this application. E.g. the power mosfets of a charge balancing circuit will certainly increase discharge current.

Regards, Dieter

[Kleinstein]

With the low load there is likely no need to really worry about balaning between the cells. Chances are one could leave that part to maintenance, maybe every 10 years or so.

A digitally controlled charge current does make sense. It could be the same current source / DAC as used to link the Li cells to the long term reference (e.g. Zener based).

A still open point may be the question on how to handle voltage scaling.
It could make sense to have 3 Li cells and 10 V directly and than scale from 10 to 7.x (or 6.6 V with an ADR1000) for the long term corrections.
I consider this better than 2 Li cells to directly follow the 7.x V and scale the 7.x V to 10 V as a separate step.
In both cases the buffer after the Li cells would be included in the long term corrections.

[mzzj]

30 minute stability of 3S LiFePo4 pack sitting idle  at somewhere 70...85% SOC




Was not certainly in my books that cheapest LiFePo4 battery is indistinquishable from  3458A 0.1ppm 10 minute DC transfer stability.

[Kleinstein]

Chances are that much of the noise is from the meter. To really see the noise / stability one could chave 2 battery packs connecting to directly looking at the difference.
It is only over a long time (like hours or days - depending on the temperature stability and stress effects) that the zener reference will be more stable.

[Kleinstein]

I did some crude tests one some old Li-ion cells:
One part noted is that the temperature coeffient depends on the charge state / voltage.
For some 3.5 V cell voltage I get a temperature effect of some -80 µV/K. The number is however not very accurate as the cells were still drifting from prior (some 12 hours before) charging.
The drift part after significant charging / discharging could be an issue - it may need a few days or weeks to really stabilize.

For a different cell (but same type) that was stored at 4.08 V (und thus rather full) the thermal effect is opposite, something on the order of +20 µV/K  (only a crude test).
Overall the temperature effect is that bad. For comparison the old mercury Weston cell has some -40 µV /K with only a little over 1 V per cell.

The interesting point here is that at some voltage (likely in the 3.6 to 4 V range and can depend on cell details) there should be near zero temperature effect.

[Kleinstein]

I did a few more tests:
For the cells I used for testing (old Makita tool batteries 1.5 Ah per cell, 2 cells in parallel each) the zero crossing for the TC is close to 3.6 V per cell.
At the right voltage this gives at least a short time stable voltage, even without an extra stable temperature. For a direct reading one gets the DMM reference noise.
To get around this, I checked the difference between 2 batteries of 4 cells each. So 2 x 14 V wired back to back. This allows to have the voltmeter in the low range (200 mV) and have rather low noise. One of the cells is still drifting a little from recent charging. So a linear drift part is subtracted.
The residual difference is at some 30 mV for the test. The 1 PLC reading mode has a noise BW of about 12.5 Hz (2x20 ms integration of the input with little gaps). 

The noise is reasonable low, though not much better than for a LTZ1000 reference.

[Kleinstein]

Much of the lower frequency noise still seems to be thermal, like thermal EMF at the cables. It gets better in a box.
Still need to wait a bit more for drift (after charging) to calm down.

[MiDi]

How did you measure the ZTC point?
The high noise is untypical, especially with 4 cells in series, even CR2032 cells have <1nV/rtHz.
If you do not have a stable temperature chamber at hand, a cooling box filled with water bottles gives quite some isolation from temperature changes.

Edit: attached the measurement for CR2032 & 18650 (both at the NF of the ULF-ULNA, omitting the noise bump of CR2032 between 0.1Hz and 1kHz)

[Kleinstein]

Much of the noise was from thermal effects. As it is so fast likely more the cabeling and contacts (nickle strips) and thermal EMF. It got much better in a protective box.
The test was done to check if there is additional noise from reformation of the surfaces after charging / discharging. It does not look like this would be an issue - at least not at that time scale. The issue is still the drift / settling after charging so there are still processes going on the cells that could cause extra noise. One such thing is Li ions diffusing between the surface and bulk of the electrode. Chances are this would be a good part of the slow settling after charging.

The TC was mainly tested crude with changes of the room temperature with a 10 K NTC sensor at the battery pack. The TC values are not super accurate though. One can clearly see the TC changing sign depending on the voltage. Getting really close the zero TC is tricky, as after charging it takes days before the cells somewhat stabilizes. This could also effect the TC somewhat.

For 2 cells in series my closest 2 points so far:
 +30...40 µV/K   at 7.235 V 
 ~     -30 µV/K   at 7.19 V

[miro123]

I performed a series of tests using two 18650 LiFePO4 cells embedded in an aluminum block. Two NTC thermistors were also placed inside the aluminum block. The block and cables were wrapped with a thick insulation layer and taped externally to make the setup as airtight as possible.

First, I will post the preliminary measurements taken at high voltage. They do not tell the complete story, but they provide a useful indication of the general direction. The measurements were performed using a Keithley DMM6500 on the 10 V range.

The pictures show one of my aged ADR1399 TO-46 references at 6.95 V versus a 2S 18650 pack at roughly 6.7 V, vs the DMM inputs shorted on the 10 V range.

It is clear that the DMM is currently the bottleneck here, but the results already provide some indication of the next direction for further investigation.

Why I chose LiFePO4:
1. The chemical structure is more stable and robust. In theory, this should result in lower electrochemical noise.
2. The voltage-versus-charge (U/C) curve of LiFePO4 has a relatively flat region between approximately 10% and 90% state of charge.
3. At this stage, I am not particularly interested in the temperature coefficient (TC), since the main goal is to achieve ultra-low-noise, short-term stable voltage references.

[miro123]

test of two LiFePO cells with common ground. diff measurements. DMM6500 at 100mV range. No pre-amplifier. It is little to distiguisch short vs batery cell diff noise. The isotermal block and wire labyrinth in insolation layer seems to work. Measurements ware done is sunny days on my rooftop room. Temperature fluctuated between started with 23C went to 26C and finished at 25C. It is time to represent the noise measurements using my home grown x1000 DC diff amplifier

[miro123]

I used a differential amplifier based on the OPA2189 with a gain of 1100. The resistor values were R1 = 100 Ω and R2 = 110 kΩ, with a 10 nF C0G capacitor connected in parallel. The circuit was powered from a 2S LiFePO4 pack providing approximately ±3.3 V. The center tap was used as a virtual ground. The enclosure was made from aluminum sheet, although it was not airtight.

Some clarification:
The shorted-input measurements were performed with the setup fully exposed to ambient conditions, while the LiFePO4 measurements were performed with the entire setup covered using cotton sheets for additional thermal insulation.

My conclusions:

1. The differential measurement between two LiFePO4 cells exhibits extremely low noise. The noise level is well below the capability of my current measurement setup, at least an order of magnitude lower than a good selected and aged ADR1399.
2. Using moderately charged cells, allowing them to balance for several days, and then leaving them in open-circuit condition for at least 8 hours appears to be the proper way to use such cells for ultra-low-noise reference experiments.
3. Any charging or discharging activity, even at very low current levels, creates strange low-frequency voltage fluctuations. At this stage, I am not sure whether these effects are caused by noise, thermochemical processes, relaxation effects, or some other type of drift.

Using a single LiFePO4 cell as a voltage-ratio reference in a dual-ADC setup currently seems to be the most promising approach for me. The input bias current and current injection effects of the OPA189 appear to be negligible in this application.