Measuring Voltage across 10 Teraohm voltage divider

[1stimealready]

Hi everyone,

I am a very inexperienced engineer out of college and I have a problem that I'm sure this corner of the internet can help me out with. The lab that I work in has experiments that result in sources that can be approximated as high voltage (200V+), ultra high impedance (1GOhm+) sources. I can't give many more details on exactly what the experiments are, unfortunately.

We are currently using these sources to charge nanoferad range capacitors, and we would like to minimize leakage current as much as possible. We also need to measure the voltage across these capacitors repeatedly. Currently, we have an electrometer that can easily handle these measurements without loading the circuit, but our Keithley is limited to 200V max. Ideally, we could manage at least 600V. Also, we want to duplicate this testbed without buying another electrometer, so cost is a pretty limiting factor as well.

My first solution was to create a 10 Teraohm voltage divider using surface mount 500G resistors, since they are cheap compared to other options and ultimately the precision of this system doesn't need to be incredibly high. I attached a picture of the PCB below, I did not include a ground plane and maximized distance between traces to lower leakage resistance.

The problem that I'm having now is that using our electrometer at the 0.1x point on the voltage divider takes ~10 minutes to reach the value we expect. I understand that the keithley has the ability to reduce input capacitance using the guard functionality, but ideally we would be able to move away from the electrometer entirely, and instead rely on something we could ultimately read with a microcontroller. Anyways, my question to you all is whether or not this is the best approach at all, and what I can do to improve the setup.

I've seen some non-contact options that seem attractive, but they seem to mostly require very high voltages and don't seem to have good automated control, which is another requirement for us.

[nonius_]

I don't think the PCB-material (I assume it's FR4; epoxy GFRP) is suitable for these high impedances; the bulk resistance of  FR4 is much lower, IIRC.

I strongly doubt that even Teflon (PTFE) would be good enough. Possibly only dry air or an inert gas (nitrogen)?

The few times I had to deal with such high impedances I used a Teflon substrate and even then used air-insulation for the actual high-impedance parts of the circuit. (that was for a pA-meter).

[mtwieg]

10Tohm is orders of magnitude beyond what is practical with SMT components and printed circuit boards. Maybe with very special substrate material, well-controlled assembly process, and conformal coating it might be doable. But not something you can solder by hand on the benchtop.

200V isn't extremely high, so rather than make an extremely high impedance divider, it would probably be more practical to make your own high voltage electrometer front end. A good JFET-input opamp with bootstrapped supply rails could probably do it.

[natefrankie]

had that kind of issue before

[edpalmer42]

Use a bridge configuration to measure the unknown voltage.

Take a voltage source that can be adjusted to approximately the same voltage as your unknown.  Connect one terminal of a voltmeter to the output.  Connect the other terminal to the unknown voltage.  The meter will display the difference between the voltage source and the unknown.  Adjust the voltage source for zero volts on the meter.  When you reach the zero point, there is no current flow between the unknown voltage and the meter, i.e. the impedance of your measurement system is infinite.

Note that you *must* confirm that your voltmeter can have its ground terminal at that high voltage above ground.  I looked at three of my DMMs and saw numbers from 250 - 1000V depending on the model.

To create a multi-Gohm resistor, you won't be able to use surface mount resistors.  There will be too much leakage across the surface of both the board and the resistor.  Maybe glass-encased resistors could be used with Teflon standoffs or solder points.

The whole system might be wildly sensitive to noise, air currents, static electricity, people walking by, etc.  You may need to enclose the entire thing in a sealed metal box to get quiet readings.  You might also have to include a dessicant in the box to reduce humidity or flush the box with dry air.

[Smokey]

This is another one of those strange questions where it claims to be coming from a business that is doing pretty high end specialized stuff and has specific requirements, but apparently no internal engineers that can answer a first pass question about where to start?  I don't get it.

[Obsidianxenon]

I'm have no practical experience in ultra-high impedance work, but I feel like it would actually be more cost effective to buy another electrometer or make a high voltage front end like mtwieg said. If the lab you are working in can afford to have a bunch of 500G resistors laying around, I really don't understand why they didn't go and get the proper equipment for their experiments. Of course, I don't work there, so I can't judge.

I don't think working on reading this with a microcontroller is what you should be focusing on right now. Why complicate things further with having to find/design an accurate and suitable ADC for it, when you can put half the effort in to make a good analogue front end that would work for the electrometer? Then again I don't know how many measurements you need to make, but it would seem that there would have to be a lot to make it necessary to automate?

Someone correct me if I'm wrong.

[xvr]

Just an idea: connect (using a switch) a discharged capacitor (let call it C2) of a larger capacity to the original one (let call it C1). Then measure the voltage that results after the charge is distributed between the capacitors.
The voltage will drop: V will be equal to Vin*C1/(C1+C2)

[ejeffrey]

The standard technique for ultra high impedances is to use pcb standoffs and to pont to point wiring for the high impedance nodes.  That and hyper vigilant cleanliness of all parts   At the impedances you are talking about you might need dry purge gas.

But also don't design for teraohms when gigaohms will work.  It sounds likely that you can fix your design to not need such high impedances.

Designing your own electrometer front end is not hard but you can also multiplex with reed switches which will have very high isolation resistance.

[Alex Nikitin]

The idea with a Teraohm divider is not really workable. While it is possible to create such a divider and even do it using SMD resistors (not on a FR4 board, certainly, but using something like the Rogers 4350B laminate), the time constants involved and all potential parasitic capacitances and leakages if everything is not perfectly clean would render the experience rather frustrating, IMHO (as you from the look of it already found). And what for? 10Teraohm is not that much, it would give you a 100pA current load at 1kV, far greater than a good electrometer would. One of my current pet projects is a 1kV electrometer buffer circuit for any multimeter, working either as a direct 1kV capable follower, or as an active divider, producing 10V output for 1kV input, in both cases providing the input current well below 1pA for 1kV input. I like the idea of an active divider more from the safety perspective, as it won't produce any HV on the output while a direct follower obviously would. On the other hand the divider option would require an actual precision divider. Well, you might be able to buy such a buffer from me when it is ready  .

Cheers

Alex

P.S. - with your current contraption you might try to use your electrometer as a picoammeter and your chain of resistors in series with the input, that way the speed should improve considerably.

P.P.S. It will introduce an additional non-linearity in your voltage measurements compared to a voltage divider configuration, as the SMD resistors you use should have an enormous voltage coefficient or resistance, which in a divider is compensated and in a voltage to current conversion is not.

[amyk]

wildly sensitive to noise, air currents, static electricity, people walking by, etc.

The currents and impedances here are basically in the realm of static electricity and electrostatics. Even ambient RF will have visible effects.

[Zero999]

The circuit board layout is no good. There should be a slot under each resistor to minimise tracking. The PCB must be well-cleaned and covered in a conformal coating.

Why take the output from the 0.1 point on the divider? Add a 10G resistor to the bottom, to form a 1000:1 divider. Now a decent low-bias current J-FET/MOSFET input op-amp can be used to buffer a standard multimeter, giving a range of +/-200V on the 200mV range.