Supercapacitors for reference voltage filtering?

[maxwell3e10]

I am wondering if anyone has tried to use supercapacitors to build an RC filter for filtering a voltage reference?

I am thinking of making an RC filter with a time constant of about 100000 sec (say 1 MOhm and 0.1F) with a JFET follower. The question is how stable would the voltage on the capacitor be as a function of temperature. I got some large Electric double-layer capacitors and regular aluminum electrolytic capacitors on order, but I wonder if anyone has already tried something like that?

[MK]

what are the leakage currents like? that is a source of noise and may well be quite temperature dependant. but it is always worth exploring these ideas.

[T3sl4co1l]

ESR as well.  And absorption; ionic devices tend to have long, ill-defined time constants, because of ionic diffusion (sqrt(f) dependency).

Tim

[zhtoor]

hello,

please see the following regarding use of supercaps and *really super* caps.

https://www.eevblog.com/forum/metrology/poor-man's-reference/msg1232798/#msg1232798

regards.

[EmmanuelFaure]

The answer is a yes. Have a look :
http://www.ginogiusi.com/wp-content/uploads/2014/10/J39.pdf

[David Hess]

Leakage (and weirder effects) versus temperature and time will trash the reference accuracy.

[Kalvin]

How about using a capacitance multiplier instead of super-capacitor: https://en.wikipedia.org/wiki/Capacitance_multiplier You could use a good capacitor and use a good op amp to make a high value, well-behaving capacitor.

[maxwell3e10]

Thanks for suggestions, everyone.

EmmanuelFaure, this is a very useful article. I've seen other papers by Ciofi, he has been working in this area for years, but haven't come across this one. He says that supercapacitors are better than aluminum or tantalum ones. I guess its not a completely crazy idea.

The leakage current is a concern for accuracy, but not for short-term stability, since any changes in the equilibrium voltage will be filtered out. Another potential problem is change in the capacitance value with temperature. Here, I am not actually sure what will happen, if the capacitance of a charged capacitor changes, one cannot conserve simultaneously the stored charge and the stored energy. So it will be interesting to measure the voltage after a sudden temperature change.

Kalvin, capacitance multiplier is a cool trick that I haven't come across. I wonder to what extend the imperfections of the capacitor and amplifier will also be multiplied.  It seems one can't get something for nothing.

[T3sl4co1l]

Kalvin, capacitance multiplier is a cool trick that I haven't come across. I wonder to what extend the imperfections of the capacitor and amplifier will also be multiplied.  It seems one can't get something for nothing.

One can use feedback to improve anything; the downside is current consumption, and the inevitable noise of the amplifier itself.

Noise itself can be improved with feedback; in a typical inverting amplifier, if the amplifier is low enough noise, then the feedback resistor is effectively "refrigerated".  That is, its noise is reduced, and it physically gets cooler as a result -- not that you could ever* measure the temperature change, as it's a single degree of freedom at the resistor terminals, not a bulk effect.

*Perhaps in a cryogenic circuit with microscopic components, so that the amplifier and other components can be made very quiet, and the resistor's ever-so-small amount of power has a sensible power density.

Tim

[amspire]

Voltage change will be proportional to the square root of the capacitance change. So if temperature causes a 1% change to the capacitance, the voltage will change by 0.01%.

Basically if you could characterise the change of capacitance with temperature - say it was 1% decrease per degree C - and say you would want the effect of temperature changes to have less then 1ppm. To achieve this you would want the capacitance temperature change to be less then 0.1 degC (with this -1%/C capacitor) within the RC time constant as an approximation. The bigger the RC time constant, the more you will have to slow down the capacitor's temperature changes.

If the RC time constant of the supercapacitor was 10 minutes, you would want to make sure the capacitor's maximum rate of temperature change was lower then 0.1 deg C in 10 minutes.

[maxwell3e10]

Voltage change will be proportional to the square root of the capacitance change. So if temperature causes a 1% change to the capacitance, the voltage will change by 0.01%.

This assumes that energy CV^2 is constant. But what about total charge q=CV? It requires some charge to become bound or unbound.
Also, if voltage change is proportional to the square root of the capacitance change, changing capacitance by 1% will cause voltage to change by 0.5%, not 0.01%.

[amspire]

Voltage change will be proportional to the square root of the capacitance change. So if temperature causes a 1% change to the capacitance, the voltage will change by 0.01%.

This assumes that energy CV^2 is constant. But what about total charge q=CV? It requires some charge to become bound or unbound.

You are probably right. I was thinking energy was going to be conserved, but I guess charge has to be conserved. That makes the voltage proportional to the capacitance which is much worse.  That would reduce that 0.1 degC/10 minutes maximum rate of change above to 0.0001 degC/10 minutes in my example.

In other words, if heat pulls the capacitor's plates further apart, the work involved increases the total energy in the capacitor and so the energy is not constant. Makes sense.

You are starting to become hugely dependant on the mechanical and dielectric stability of the supercapacitor. And that doesn't take into account other factors like capacitor leakage and noise.

Thanks for the correction.

Also, if voltage change is proportional to the square root of the capacitance change, changing capacitance by 1% will cause voltage to change by 0.5%, not 0.01%.

No if the relationship was squared, then 0.01² = 0.0001 (0.01%).

[T3sl4co1l]

You are probably right. I was thinking energy was going to be conserved, but I guess charge has to be conserved. That makes the voltage proportional to the capacitance which is much worse.  That would reduce that 0.1 degC/10 minutes maximum rate of change above to 0.0001 degC/10 minutes in my example.

Note that this means stored energy is changing, and that energy goes with the heat applied or removed.  A charged capacitor (that has a strong tempco) will therefore have a slightly higher heat capacity (Cp) than otherwise.

Tim

[zhtoor]

Voltage change will be proportional to the square root of the capacitance change. So if temperature causes a 1% change to the capacitance, the voltage will change by 0.01%.

Basically if you could characterise the change of capacitance with temperature - say it was 1% decrease per degree C - and say you would want the effect of temperature changes to have less then 1ppm. To achieve this you would want the capacitance temperature change to be less then 0.1 degC (with this -1%/C capacitor) within the RC time constant as an approximation. The bigger the RC time constant, the more you will have to slow down the capacitor's temperature changes.

If the RC time constant of the supercapacitor was 10 minutes, you would want to make sure the capacitor's maximum rate of temperature change was lower then 0.1 deg C in 10 minutes.

hello,

temperature dependent capacitance shall contribute to current through it (leakage) according to the formula:-

i = d(cv)/dt.

now if v across the cap is constant then:-

i = v d(c)/dt

regards.

[David Hess]

How about using a capacitance multiplier instead of super-capacitor: https://en.wikipedia.org/wiki/Capacitance_multiplier You could use a good capacitor and use a good op amp to make a high value, well-behaving capacitor.

Usually what I see is the capacitor bootstrapped so that the voltage across the capacitor is zero.

[splin]

Voltage change will be proportional to the square root of the capacitance change. So if temperature causes a 1% change to the capacitance, the voltage will change by 0.01%.

Also, if voltage change is proportional to the square root of the capacitance change, changing capacitance by 1% will cause voltage to change by 0.5%, not 0.01%.

No if the relationship was squared, then 0.01² = 0.0001 (0.01%).

1 = 1/1.005 x sqrt(1.01). Ie. a voltage change of 1% results from a capacitance change of .5% (If Q is unchanged).

[maxwell3e10]

Usually what I see is the capacitor bootstrapped so that the voltage across the capacitor is zero.

I am not sure if that is possible. In the circuit you have attached, its the 20 uF capacitors that do the filtering, with voltage across them. The 1 uF capacitor doesn't do much, it would be irrelevant for an ideal op-amp.

[David Hess]

Usually what I see is the capacitor bootstrapped so that the voltage across the capacitor is zero.

I am not sure if that is possible. In the circuit you have attached, its the 20 uF capacitors that do the filtering, with voltage across them. The 1 uF capacitor doesn't do much, it would be irrelevant for an ideal op-amp.

The voltage across the top capacitor is reduced to a fraction of its normal value so the leakage through that capacitor is also reduced.

I do not know why the resistor was added inside the feedback loop since the LT1001 has input bias current cancellation (Phase margin?  But an LT1001 is pretty slow.) but given that it was, the feedback capacitor makes sense to lower high frequency noise from the operational amplifier itself.  But the reason I gave it as an example is to show the bootstrapping of the capacitor to lower leakage and the buffer has nothing to do with that.

[maxwell3e10]

So, I did some rough testing with 3 capacitors, Polypropylene 100 microF, Aluminum Electrolytic 100 milliF and supercap "BestCap" 22 mF (largest supercap with a 12 V maximum voltage rating).
I charged the capacitors to 10V and left them for some length of time. I also very roughly measured the temperature dependence by holding the capacitor in hand for about 10 minutes.
                       1 hour   12 hour   5 days   2 weeks      Temp change (+5-10C)
Polyprolylene     9.959    9.958      9.956     9.953         +0.1%
Aluminum          9.72       9.55      9.41     9.14             -0.1%
Supercap            8.15       6.70      4.39     4.00            -0.1%

Not surprisingly, the supercap capacitor has very strong dielectric absorption that occurs on time scale of several days. The polypropylene capacitor can hold charge better than Aluminum electrolytic that is 1000 times larger. They all have similar temperature dependence, on the order of 100-200 ppm.

Without active temperature control, it wouldn't make sense to make the RC time constant longer than the thermal time constant, which is about 10 minutes for these large capacitors.  So maybe a sweet spot is to use an RC filter after a voltage reference with about 200 Ohm resistor and 100mF capactor with the goal of getting noise around 1 nV/sqrt(Hz) at 1 Hz but long term temperature stability still provided by the voltage reference.  One could also use a 200kOhm resistor and 100 microF capacitor, but then it would require a FET-input amplifier after the filter, with larger noise.

[floobydust]

Usually what I see is the capacitor bootstrapped so that the voltage across the capacitor is zero.

Yes, bootstrapping the capacitors is explained on pg. 14 Intersil App note 177
Otherwise capacitor leakage currents cause an error in the filter.
Also, consider the long time constant to settle to say 0.01% of final value.