[volt-nuts] How can I make a 2000 V DC meter with an input resistance of at least 100 T ohms?

[Dr. David Kirkby]

On 23 March 2018 at 18:49, ed breya <eb at telight.com> wrote:

> I'm guessing the application relates back to your leaf electrometer
> project discussed earlier - trying to assess how the bias charge on the
> capacitor holds up from leakage and use of the instrument.


Yes it is.

If this is the case, then it's for a one-time use for design of the item,
> so shouldn't be too fancy or expensive.
>
I believe the original goal was to have the cap get charged up and then not
> need any electric support for the leaf electrometer, appearing totally
> passive, for some amount of operating time. If built-in monitoring of the
> cap voltage is now desired, that's a different story.
>

Built in monitor is not required, but if I could design something that has
a performance to allow that, I would be interested to see exactly when the
voltage drops (or rises).

>
> If the measurement is just for design, to roughly see the cap
> charge-holding time situation, then I'd recommend using methods that Chris
> described, comparing to a variable HV supply at various times and settings
> - all manual iterations, but doable. You can always say, recharge the cap,
> then guess what the voltage may be after so much time, then set the test
> supply and compare - over and over and over.
>

Part of my reason was to know if its possible to connect two electrolytic
caps in series to increase the working voltage, without any parallel
bleeder resistance. In one test, I tried charging a 600 V cap up to 1000 V,
using the power supply in my 4339B high resistance meter, which is limited
to 1 mA. The voltage would not rise above about 700 V, suggesting to me
that perhaps the leakage might increase as the voltage rises, so maybe
bleeder resistors are not required, apart for safety reasons. Safety could
be addressed other ways.


>
> If continuous, long-term, fairly accurate monitoring is desired, then
> you'd have to go with some sort of non-contact electrostatic voltmeter or
> such, as others have mentioned.
>
> Relating back to recent discussions, it's pretty clear that you're not
> going to find an actual specified resistor in the hundred T-ohm region. You
> can certainly make your own from T-ohms to infinite, but you won't be able
> to know the "exact" value. The commercial instruments that have say "200
> T-ohms" input R don't actually have that resistor value inside - it's an
> "effective" or "equivalent" derived value that depends on a real resistance
> of maybe E11-E12, multiplied by system gain.
>

So how does one make ones own resistor? I was thinking of perhaps nails in
wood, where the moisture content would control the resistance. I suspect
that idea would fail because DC would polarise the water molecules. But it
did cross my mind as a possible way.

The highest value commercial resistor I have found at a sensible price is
10 T ohms for £41 from Mouser, but that is on a 2 month lead time.

I do have the Agilent 4339B high resistance meter, so can measure high
value resistors. The basic uncertainty of that meter is 0.6%. Measuring 10
T ohm, I calculate the uncertainty would be 4.5%, so more than adequate as
a starting point. Later a DVM could calibrate a setup.

For the case of a 47 uF cap charged up, if I used a commercial 10 T ohm
resistor, then the time constant is 15 years. So a 10 T ohm input R would
be fine. For a 2.2 nF cap, which is one of which I have a 15 kV model, 10 T
ohms would give a time constant of 6 hours, which would mean the load is
not be negligible.


>
> Some electrometers like the old Keithleys have a voltage mode where the
> high-Z input amplifier is bootstrapped up as a voltage follower, but have
> less range than you want. It's conceivable that you could build the same
> thing, but with a HV amplifier follower that can reach the desired level.
> This would not be trivial.
>

Most/all the Keithleys do 200 V, which is outside the range of most
semiconductors directly.


> Again, if the purpose is just to measure the droop in bias voltage of the
> charged cap over certain time intervals, there may be another option. Since
> this is a dv/dt rather than DC measurement, you could possibly set up an
> electrometer to view the change of the bias voltage via current through
> another capacitor, and conceivably even rig it up to directly measure the
> total change in cap voltage over a given time.
>
> My main issue was to measure the voltage across two series connected
capacitors, to find out how equally it split.


> Let's say the charge storage cap is 1 uF, and you put a much smaller, less
> leaky, test cap plus some protective series R from the HV node to the input
> of the electrometer, and also clamp the input with a low leakage diode
> circuit. The test cap could be say 100 or 1000 times smaller than the main
> cap, so its effect will be small. This could be in the 10 nF or less range,
> where it should be fairly easy to find 3 kV or so rated metalized film
> plastic capacitors with suitably low leakage. Any constant DC leakage from
> the cap could be zeroed out or accounted for, at least for short-term
> measurements.
>
> The electrometer could then read the test cap current directly
> proportional to dv/dt, or integrate it back up to delta V in the charge
> mode. There are limits to the reasonable measuring ranges, of course. For
> example, 1 nF would provide 1 nA at 1V/sec - a fairly easy measurement. But
> 1V/1000 seconds could be tricky - only 1 pA to work with.
>
> Ed
>