Precision, low DA and low value capacitor (1-10pF)?

[Atomillo]

Hi:

I'm trying to design a current integrator in order to measure accurately really small currents (pA-fA). I'm choosing an integrator in order to avoid the high TC, uncertainties and other unpleasant side effects of using a Gohm order feedback resistor in a TIA.

Unfortunately it seems that 1/10pF capacitor with low DA and tolerances of around 1% are not readily available. Does anyone know of any source?

Many thanks!

[bob91343]

Make one yourself.

[Kleinstein]

For the low values one could build an air capacitor. When you carefully measure the dimensions one may even calculate the capacitance from first principles. This especially works as a 3 wire capacitor with a separate shield / ground. So one has a shield plane with a hole and an isolated plate to both sides that covers the whole hole.

Normal SMD parts would not help, as the is usually parasitic capacitance of a few 100 fF around a 0805 size part.

Alternatively one would build the measurement tool from more normal parts and than use a known current in the calibration. So like with many other meters: no accurate scale factor from the part tolerances but a measured scale factor to include the individual part variations. So one may need the accurate capacitor only for the calibration, and this may use a slightly larger one.

[Atomillo]

Yes, making seems like the easiest most accesible way. In "Whats this Teflon stuff anyhow" just twisting a wire with a teflon isolated wire works. Pease also builds capacitor in just the way Kleinsteins describes.

But then that means either buying a pico ampere current source (which seems quite expensive in eBay) or an LCR meter capable of measuring such low capacitances accurately (also not cheap). So it would mean going ever deeper in this rabbit hole (not that I would complain too loudly)

EDIT: suppose I should have said "commercial" Precision, low DA and low value capacitor in the title

[mawyatt]

Some of the various nanoVNAs flavors might prove useful for measurements, and they are not expensive!!

Best,

[Atomillo]

Some of the various nanoVNAs flavors might prove useful, and they are not expensive!!

Best,

Using a NanoVNA to measure this would be great because then I would also have a general purpose instrument useful for other things too!
I have to research the accuracy of this method but thanks for suggesting it I had not even thought about it

[bob91343]

The nanoVNA has got to be the most versatile piece of test gear, and an incredible bargain as well.  Every electronics experimenter should have one.  I can't say enough good about this little wonder.

[David Hess]

Make one with a length of RG-336 or RG-178 or similar Teflon coaxial cable, or use a twisted pair.

[Atomillo]

In the case of coax, to which terminal should I connect the shield?
I would say to the input of the op amp so that it stays at ground and thus also acts as a shield but I'm unsure

[Kleinstein]

If one would use the coax capacitance as the capacitor for a low current integrator, the input node should be the inner conductor, so that there is not extra noise pick-up. The outer conductor would be the OPs output - there a little hum current would not do much harm.

I would still prefer a mechanically defined capacitance. Teflon is relatively low DA, but still not as good as air.

[Atomillo]

The problem with a mechanical defined capacitor is actually making one 
I doubt I have neither the skills nor the materials to make a stable, low leakage air capacitor. And going with air one of course also has to worry about humidity degrading leakage which is not fun.

I've found an exaple of a Teflon wire being used as a low DA low leakage capacitor: in the AC board of the HP3458A, as the holding capacitor used in the synchronous sampling method. Of course they didn't need a stable and accurate value of capacitance, but the fact that it was good enough in terms of DA and leakage is encouraging.

[David Hess]

The problem with a mechanical defined capacitor is actually making one 
I doubt I have neither the skills nor the materials to make a stable, low leakage air capacitor. And going with air one of course also has to worry about humidity degrading leakage which is not fun.

I've found an exaple of a Teflon wire being used as a low DA low leakage capacitor: in the AC board of the HP3458A, as the holding capacitor used in the synchronous sampling method. Of course they didn't need a stable and accurate value of capacitance, but the fact that it was good enough in terms of DA and leakage is encouraging.

The large volume of an air capacitor means that they suffer from cosmic ray strikes so a Teflon capacitor may be preferred.

[magic]

I built a parallel palate capacitor to check my LC100-A meter and it turned out a spectacular fail.

The capacitor was made of 22×67mm copper clad plates (copper side inside, no worries) separated with thin 13.1mm plastic spacers. It was supposed to be 1pF, but it measures 2.5pF

This reminded me that the simple formula we learned in kindergarten is only supposed to work for plates that are large with respect to their spacing. I'm nevertheless surprised that the error can be so bad. And of course it's a big problem, because constructing or measuring a closer spacing with accuracy will be a little more difficult.

As a fallback, I stuck two parallel wires into the meter and used the balanced transmission line capacitance formula to estimate their capacitance:
C=l·π·ε/acosh(s/d)
where l is the length, ε is permittivity of the medium (air), s is the spacing between centers and d is the diameter.

This came out at 180fF vs measured 220fF. I guess there may still be some effect at the end of the line, and of course there is another problem with measuring such low capacitance: even a single conductor connected to the meter has nonzero capacitance to the meter's ground itself. Well

[magic]

Could this be made to work in practice?

If true, you could measure your pF capacitors with a single good 100nF, a few resistors and TL072.

[Terry Bites]

https://datasheets.kyocera-avx.com/ML03.pdf

Interesting read: https://www.kyocera-avx.com/docs/techinfo/RFMicrowaveThinFilm/MLO_Dielectric_Absorption.pdf

Full LT spice simand practial example from AD https://munin.uit.no/bitstream/handle/10037/6783/thesis.pdf?sequence=2

[Atomillo]

https://datasheets.kyocera-avx.com/ML03.pdf

Interesting read: https://www.kyocera-avx.com/docs/techinfo/RFMicrowaveThinFilm/MLO_Dielectric_Absorption.pdf

Full LT spice simand practial example from AD https://munin.uit.no/bitstream/handle/10037/6783/thesis.pdf?sequence=2

Many thanks for your help. Unfortunately as Kleinlein stated, with SMDs capacitors it seems difficult to eliminate all parasitic capacitances. Even more so when we consider that it will be air mounted to prevent leakage.

In the same line, it is interesting that nowhere in the datasheet do they mention leakage current.

I'm just starting to conclude that the only capacitors approaching the necessary specs are those used as low capacitance standards. Which of course are way out budget wise.

[magic]

I suspect you may encounter other problems too, like additional capacitance in wiring (THT is not entirely immune) and even between pins of the opamp (particularly in a dual).

OTOH, how hard would it be to calibrate the complete ammeter with a current source way above pA? I mean, 1pA going into 1pF is 1V/s slew rate. Clearly, you should be able to shove 1nA or maybe even 1µA into it and still be able to measure the resulting slew rate? Such currents should be much easier to generate - some voltage source, resistors, bingo.

[Kleinstein]

The problem with the parasitic capacitance does not only apply to SMD parts. THT parts are not better in this respect. For high curruracy at those small values one needs a shielded capacitor, so not just a 2 pin device, but at least a 3 contact construction with an extra shield, so that the parasitic capacitance is towards the shield and not between the 2 contacts for the measurement. The accurate capacitance is only the coupling between the 2 hot terminals, not the overall capacitance.

The integrator itself works better with a physical small part like a SMD C0G cap to reduce the effect of radiation spikes in air and keep the capacitance to ground low, as it can effect stability and noise.
Instead of using a low tolerance capacitor it may be much more practical to measure the sensitivity of the integrator afterwards to include all the parasitics. This may be relative to a larger capacitor, that is easier to get with reasonable good accuracy. Also calibration relative to an accurate high ohms resistor may be possible, though also not easy to get.

With small C0G capacitors the leakage across the cap is often less than the parasitic one via the board. It also depends a lot on cleaning. So there is little value if they would give leakage specs as in the normal use other leakage paths are more relevant and a measurement is difficult.

[Terry Bites]

You can alway phone their engineers- try that human touch.

[magic]

Humans also have parasitic capacitance to ground, they can't help you with that aspect of the circuit

[Berni]

You should NOT trust the capacitor to have the exact capacitance you want in the first place.

Even if you could buy a 0.1% tolerance capacitor for the exact thing you want, this capacitor still has to be wired into the rest of the circuit and this introduces extra parasitics, easily throwing off the original value by quite a few %.

When going for high levels of precision it tends to be best to just focus on the value being stable over time/temperature. So just get a capacitor you think will be most stable, then calibrate your DIY instrument with a known current.

Unfortunately working with picoamp things indeed get more difficult and expensive. You will need some sort of calibrated current source or an instrument capable of measuring such low currents to construct your own current source. I would recommend getting an old Keithley electometer (those in the ugly brown cases) as they can sometimes be had for a good deal and can measure bellow 1pA

[jonpaul]

Bonjour Atomillo:

Just reading  this long thread now, we have used since 1980s  high gig R and small C.

But You did not mention the source of the current or system setup. Still we can comment:

 1/ Your root goal, measurement of small currents (pA-fA) is  best handled by an electrometer, the old Kiethley 610C are designed for such use and have the appropriate gigohm R and very low leakage input connectors and amp JFET.

https://122.physics.ucdavis.edu/course/cosmology/sites/default/files/files/Ferro%20Electricity/Keithley610manual.pdf

2/ A DIY electrometer needs a special input amp or opamp, and teflon connectors. The feedback element can be a metal oxide R available from Victoreen, Caddoc, and other high R vendors. Expect 1 % accuracy at best.

3/ pF capacitors are not made in SMD nor at high precision. GenRad made some large and costly precision air cap standards, available on Ebay, ~$100...500

4/ Any pF measurement must be a 3 terminal guarded bridge or RLC meter, with no guard the measurement is very inaccurate.

5/ Slight lead position changes will dominate the test of pF C, you need a ridgid  test fixture, with guard, and you must first zero out the test setup stray capacity.

6/ We measure with vintage Tektronix 130 valve LC meter, 3 pF lower range up to 75 pF zero capability.
Another good meter is the HP 4332A. They have  the required  guard voltage capability.

7/ The capacitor is fabricated  with metal spheres (NOT PCB!) and teflon or delrin, nylon insulators as per good high voltage  technique.   One simple low capacity topology is two equal diameters spheres, like  a spark gap.

8/ The formulas for capacitance are well known, and calculators available online for parallel plates, spheres, single sphere above ground plane, etc.

9/Our calibrated HV sparkgap is a  pair of 50 mm metal sphere son  5 mm rod supports , 30 mm dia   Lucite columns supports 200 mm spacing. We read ~ 2pF guarded C between spheres with  gap is 15 mm


10/ A parallel plate capacacitor of PCB matériel  will have higher C than calculated for a metal plate due to the PCB insulation layer diélectrique, eg FR10 fiberglass.  You must account for the electric field on the back of the plates.

Hope this note is interesting,

Bon chance,

Jon

[Atomillo]

Hello:

Sorry for being slow to respond. I've just started a new semester this week and things have been a bit heptic.

There is not a specified system as such. My main target was to reliably and accurately measure down to the 10s of fAs. No need really, just a fun task I was aware this would be a challenge as I had some experience with measuring pAs.

My problem with the main idea suggested in this thread (i.e to focus on stability and calibrate the meter using a known low current) is actually generating such currents. Used, unknown state, Keithely 261 shipped to Spain are around 350 euros in eBay. That's way beyond my budget and my appetite for risk. And of course then I had to spend more money to calibrate it in order to perform meaningful measurents. With that in mind, the only option seemed to be to find an accurate method right out the gate.

Of course, high value resistors have huge TCs and high tolerances so they were out of the question. The idea I came up with is the simple circuit attached.

The reset switch is placed across the output of the op amp, along with a resistor used to avoid damage to the op amp without effect in normal operation. Normally, in the most common topology that uses this circuit (I->F converter) this is bad, because when the switch closes the op amp saturates, and then has to spend time out of saturation, which greatly damages output frequency linearity. In my case however, I would be measuring only the slope of the output signal, and doing it this way allowed me to use a common switch without having to worry about leakage or such.

At the time I assumed that capacitors with the necessary characteristics were easier to find thn high value resistors and such. This topic and the great responses by Jon Paul, Berni, Kleinstein, etc... have showed me I was wrong. After reading and following the clues provided, I also reached the conclusion that perfoming pF measurements is an art on it's own, not something to be kludged together in an evening.

After putting some though on this, I came about with an idea about a single slope current meter. And while now the absolute tolerance and TC of the capacitor is unimportant and measuring times in this scale is very easy nowadays, the problem turns into generating precise 1/10uA current pulses with 1/10/100uS widht and very low leakage when turned off. While I have some clues, that is not a matter for this thread, and to be honest, I'm not even sure if it can be accomplished.

Many thanks to all who responded for making me a lot more knowledgeable when it comes to low capacitance measurent and hurdles

[magic]

You came late to this party.

Just a few years ago you could buy 1GΩ 0.5% 25ppm/°C resistors at Mouser for ten bucks. But they stopped stocking them at about the time I got mine. Somebody snagged the last 100GΩ right before me. I now looked at the prices and availability today

[Atomillo]

I feel like that's true for a lot of TE things.
I see old threads talking about the price of used HP34401A; and then look at what I paid for mine... I was lucky to find what now is a "good deal".

It seems everything has become more expensive

[Kleinstein]

The reset at the ouput of the integrator usually does not work that way. It would only work kind of it there are protection diodes to ground at the input. It would still leave some residual charge.

[Atomillo]

Current would flow to the capacitor when the switch is closed to ground, but due to the low currents and the low time it would be turned on, such charge would be small.

And because I would be measuring the slope, a small leftover residual charge would be unimportant.

At least that's how I planned it.

[Kleinstein]

One would discharge the capacitor only if there is also a path for the current to flow also on the left side (integrator input). This could work, e.g. if the signal source is a photodiode, but not really well with a more resistive source.

[Atomillo]

Oh I think I understand.
If the switch closes, then because the op amp saturates there is no virtual ground. Thus the voltage across the capacitor reverses sign (before it was positive in the output of the op amp, and now it is the other way around) because charge conserves.

Thus unless there is a diode in the input it would not discharge.

It would work only with some op amps that include protection diodes (in the X Chapters in page 291 Chapter 4x3.7 they mention this trick)

[jonpaul]

Atomillo, a few notes:


Low current: Study JFET and valve electrometers, eg from Kiethley to see the usual techniques. You can buy old electrometers off epay for perhaps $100.
The manual has all info perhaps you can build.

 for example the excelled  KEITHLEY  600B, 602, 604  SOLID STATE ELECTROMETER 
 

Hi Value  R: We  purchased  10,000 pcs  1 Gig R from Victoreen, USA in 1980s..1990s,   OEM part t ~ $1.50 in 1 K qty.

The precision  1..1000 gig  R were used in electromenters, Radiation instruments,    special glass enclosed by Victoreen, etc.


Prices: Nowadays all components are made offshore eg China, even by USA firms, and these parts are special order and high MOQ.

The cost is following the ancient Eco 101 rule of supply and demand.

We see common parts cost increasing 20..200% per year since last 2 years, factory files and shutdown, supply chain logistic, Covid,  US admin dollar debasement policies.

Be patient and keep searching Epay for what you need eventually you may find it.

Philo:  Nothing is fast, easy or cheap! Do the work and be patient, you will be rewarded and learn a lot!


Bon Chance,

Jon

[magic]

I think at those current levels your feedback capacitor could simply be the parasitic capacitance of opamp pins and a reed switch going from OUT to IN-. Wave a magnet nearby and the capacitor discharges. Electromagnet could also work if its coil is screened electrostatically to prevent capacitive charge injection into the input node.

Any integrator resetting technique which involves shorting the output and discharging through protection diodes obviously sends a 0.7V spike to the circuit under test. I hope you are OK with that. If you are OK with even greater spikes, opamps without differential input protection diodes still have diodes clamping each input to the rails. If you short the output side to each rail in turn, the capacitor is guaranteed to hold less than ±0.7V afterwards. With an RRO opamp, such a maneuver could be performed by simply driving IN+ to each rail in turn.(It can't). It could be a good idea to include some resistance in series with the capacitor to limit peak current through the diodes. A few kΩ ought to have negligible effect on normal operation.

As for characterizing the gain of a capacitive TIA, why can't you simply connect a know value ~1000x larger capacitor to the input and drive its other end with a very low noise, low amplitude AC voltage source? Then your TIA is a normal inverting opamp stage and closed loop gain is the ratio of capacitances so the feedback capacitance including all parasitics can be calculated. A very low noise, low amplitude AC source is made by dividing down a low noise, high amplitude AC source with low value resistors.

[Atomillo]

Atomillo, a few notes:


Low current: Study JFET and valve electrometers, eg from Kiethley to see the usual techniques. You can buy old electrometers off epay for perhaps $100.
The manual has all info perhaps you can build.

 for example the excelled  KEITHLEY  600B, 602, 604  SOLID STATE ELECTROMETER 
 

Hi Value  R: We  purchased  10,000 pcs  1 Gig R from Victoreen, USA in 1980s..1990s,   OEM part t ~ $1.50 in 1 K qty.

The precision  1..1000 gig  R were used in electromenters, Radiation instruments,    special glass enclosed by Victoreen, etc.


Prices: Nowadays all components are made offshore eg China, even by USA firms, and these parts are special order and high MOQ.

The cost is following the ancient Eco 101 rule of supply and demand.

We see common parts cost increasing 20..200% per year since last 2 years, factory files and shutdown, supply chain logistic, Covid,  US admin dollar debasement policies.

Be patient and keep searching Epay for what you need eventually you may find it.

Philo:  Nothing is fast, easy or cheap! Do the work and be patient, you will be rewarded and learn a lot!


Bon Chance,

Jon

The "Nothing is fast, easy or cheap" phrase is very true. Now that I have a bit more experience with eBay I see that often the best course of action is to just wait. A lot of the times it seems, an item seems to have an extremely high price because all the ones with reasonable prices get eventually bought and only the unresonable ones remain. In that situation, the most sensible thing is to wait for another reasonable seller to appear. I've also learned you can see the prices of selled items, this gives you a much better insight.

I've printed and I'm reading the manual of K617. All the electrometers seem to use a pair of low leakage JFETs as front end. Nowadays with specialized op amps like the amaizing ADA4622 or such this seems to be mostly obsolete. The problem with buying old used electrometers is that then you also have to buy the necessary triaxial accesories. This hobby can get expensive quite fast!

[Atomillo]

I think at those current levels your feedback capacitor could simply be the parasitic capacitance of opamp pins and a reed switch going from OUT to IN-. Wave a magnet nearby and the capacitor discharges. Electromagnet could also work if its coil is screened electrostatically to prevent capacitive charge injection into the input node.

Any integrator resetting technique which involves shorting the output and discharging through protection diodes obviously sends a 0.7V spike to the circuit under test. I hope you are OK with that. If you are OK with even greater spikes, opamps without differential input protection diodes still have diodes clamping each input to the rails. If you short the output side to each rail in turn, the capacitor is guaranteed to hold less than ±0.7V afterwards. With an RRO opamp, such a maneuver could be performed by simply driving IN+ to each rail in turn.(It can't). It could be a good idea to include some resistance in series with the capacitor to limit peak current through the diodes. A few kΩ ought to have negligible effect on normal operation.

As for characterizing the gain of a capacitive TIA, why can't you simply connect a know value ~1000x larger capacitor to the input and drive its other end with a very low noise, low amplitude AC voltage source? Then your TIA is a normal inverting opamp stage and closed loop gain is the ratio of capacitances so the feedback capacitance including all parasitics can be calculated. A very low noise, low amplitude AC source is made by dividing down a low noise, high amplitude AC source with low value resistors.

I actually didn't even think about the reed switch option. Because it would be a vacuum capacitor there would be no concerns about DA or leakage currents through the inside. And the guard terminal could simply be a piece of copper tape tapep (is that the correct verb?) to the crystal body.

Also, I didn't think about that option. Accurately measuring nF is much easier than measuring pF. Thanks for this ideas they are very interesting.

I actually found an example of reed switch being used as a capacitor: https://xdevs.com/doc/_Metrology/femto_ampere_current_source.pdf by forum member Doktor Pyta. It also shows the importance of using a guard terminal.

[magic]

Leakage is still possible through contamination in the glass or on its surface

But there are switches rated for ludicrously high isolation resistance (teraohms) if you look around. Even a cheaper switch could be tested - run the integrator with open circuit input and you are measuring the sum of all leakages in the circuit. External surface can be washed with IPA to remove fingerprints and crap like that if it becomes a problem.

I'm reading that PDF. I would use a soundcard to generate and measure sinewaves instead of making a triangle generator. Note that you don't need to know anything about their absolute amplitude (within reason), only the accurate ratio of TIA output to the input into the voltage divider driving the nF capacitor.

[Kleinstein]

Reed switches can still have leakage: the glass is not a perfect isolator in a humid environment it can become relatively large leakage current. One could still get away with this with 2 switches in series and a ground link in between. So the relay / reed contact for the input discharge would see essentially zero voltage when open.

For protection there usually is a large resistor (e.g. > 100 K) right in front of the OPs input anyway. So the current during a discharge from the output and protection diodes is limited in current already.

[magic]

That's a good point and the input conducts even less current than the feedback network so it's better that way.
It has also occurred to me that with pF capacitors there isn't much energy to destroy those diodes anyway.

[Atomillo]

Leakage across the reed switch would only occur through the glass surface itselft. The guard terminal would eliminate leakage through the surface and I don't see how leakage could occur inside the evacuated enclosure

Kleinstein, could you sketch that circuit please? I'm having difficulty imagining it.

Many thanks!

[Kleinstein]

Attachted is a short drawing. The right of the 2 relays could as well be a CMOS switch.
The OP could of cause be a lower leakage one


Leakage can be on the outer surface, but also on the inner surface of the glass and even the bulk glass itself is not a perfect isolator.

[Atomillo]

I understand that the feedback capacitor would be another reed switch left always open?

[Kleinstein]

For the integration cap one has multiple options, like an air cap / the shield , a C0G or  polystyree cap.
A reed relay as capacitor would no sense in this case as than could just use 1 reed relay with nothing extra.

[Berni]

If you think that is expensive wait til you find out how much a low leakage triaxial connector costs.

But yeah you can make your own low current source by simply getting a really large value resistor and applying a fixed voltage across it