Coaxial guard voltage to measure very low currents

[NaxFM]

Hi everyone.
For a university project I need to be able to measure very low currents (less than 1uA) with maximum accuracy and stability possible using only what i have, and i have a 7.5 digit DMM, a bunch of opamps and coaxial cable.
I know that for very low current a triaxial cable with very careful guarding is required, but those cost a lot and I can't buy them.

I thought of a cheap method to apply a guard voltage and it involves two coaxial cables, however it's the first time I need to do measurements with such high accuracy and before i build everything i wanted to ask you if this is a valid idea and how I can improve it.

I have a constant current source which uses a differential amplifier to maintain a constant output, my idea was to tap the voltage at the sense resistor and buffer it to create a guard voltage to apply to the shied of a coaxial cable. For the return path another coaxial cable but this time with the shield connected to ground.

What do you think? Do you have any sugestion?

[bsw_m]

I do not know of any DMM with a current range of 1uA. And this means that the device will measure at the limit of sensitivity, with all the negative consequences for the measurement accuracy.
Why don't you consider using a transimpedance current converter?
As for cable leakage, the potentials between the braid and the central core will be no more than 100 μV, I think it’s easy to calculate what kind of leakage will be along the cable.
A more important issue is the noise generated by the cable dielectric. And cable capacitance. Therefore, here is a simple recommendation - the cable is as short as possible.
Sorry for the short answer. But at the moment I don't have the opportunity to describe in more detail.

[jonpaul]

Bonjour NaxFM, What are the voltages involved?

A "very low" current...1 uA....

Rather than a DVM, an electrometer like the old Kiethly 610, 621,  are low cost ($100) and much better instrument than a DVM.

Triax is very costly, hard to terminate and and may not even  be needed.

Coax cables vary widely in dielectric, thickness, etc.

eg RG174/U thin diameter polyester, vs RG6-U very large diameter

The lowest leakage dielectric can be a coax of Teflon.


Bon chance,

Jon

[NaxFM]

I do not know of any DMM with a current range of 1uA. And this means that the device will measure at the limit of sensitivity, with all the negative consequences for the measurement accuracy.
Why don't you consider using a transimpedance current converter?
As for cable leakage, the potentials between the braid and the central core will be no more than 100 μV, I think it’s easy to calculate what kind of leakage will be along the cable.
A more important issue is the noise generated by the cable dielectric. And cable capacitance. Therefore, here is a simple recommendation - the cable is as short as possible.
Sorry for the short answer. But at the moment I don't have the opportunity to describe in more detail.

Well, the keysight 34470A has a 1uA current range with 0.05% + 0.005% accuracy, and the Keithley DMM7500 has a 10uA range with impressive 0.0075% + 0.0030% accuracy, they are both perfectly capable of measuring currents down to the nanoAmp region. Especially for the DMM7500 this is a big selling and marketing point when paired with the 1MS/s digitizer function.
I can't use a transimpedance converter because one of the fundamental requirements for this project is measuring the current with a multimeter. I can't explain in detail what we are doing but we need to measure current directly.
I'm asking this question because i saw Shahriar video about the DMM7510 rewiew and when he tried to measure a 100pA current with a simple coaxial cable with no guarding the reading was all over the place.
I know it's a ridiculously low current and i also know i can't pretend to perform metrology grade measurements with my equipment, i just need to perform the best possible measurement i can with what I have

[garrettm]

Assuming the DMM's ammeter is internally connected to the HI terminal (i.e., high-side sensing), then no guarding of the LO terminal is needed. You can of course shield the LO connection using coax, but it's unlikely to make much of a difference.

As for guarding the cable to the DMM's HI terminal, an electrometer grade op amp (e.g., ADA4530-1 (probably overkill for your application)) can be wired as a voltage follower and used as an active guard to drive the outer shield of the coaxial cable. The non-inverting input connects to the HI terminal of the current source and its output to the coax shield.

Alternatively, an old electrometer like a Keithley 616 or 617 can be used as the active guard. I assume you need the extra resolution/accuracy your DMM provides as opposed to using an electrometer directly.

For reference, see Analog Devices' application note AN-347. It has information on how properly apply guarding when using op amps. In addition, reading through the user manual for an electrometer like the Keithley 617 can help with understanding how guarding works in high impedance circuits.

[garrettm]

I'm asking this question because i saw Shahriar video about the DMM7510 rewiew and when he tried to measure a 100pA current with a simple coaxial cable with no guarding the reading was all over the place.

When measuring below 2nA, you will want to avoid bumping or moving the coaxial cable since large amounts of charge (relative to what is being measured) can be generated from flexing or hitting the cable. Note that not all coax, or even triax, are created equal. Some are worse than others at generating charge under physical stress. Beldin 9222 is some of the worst of the worst when it comes to charge generation. To check if your cable is satisfactory, connect it to an oscilloscope with at least 1 or 2 mV per division sensitivity and then flex or hit the cable with a screw driver. Triggering is tricky, but it isn't very hard to get everything figured out for testing. Some RG58 can be good, others not so good.

Below is an example of Pomona 4964 SS "low triboelectric" coax when tapped with a screw driver.

[NaxFM]

Assuming the DMM's ammeter is internally connected to the HI terminal (i.e., high-side sensing), then no guarding of the LO terminal is needed. You can of course shield the LO connection using coax, but it's unlikely to make much of a difference.

As for guarding the cable to the DMM's HI terminal, an electrometer grade op amp (e.g., ADA4530-1 (probably overkill for your application)) can be wired as a voltage follower and used as an active guard to drive the outer shield of the coaxial cable. The non-inverting input connects to the HI terminal of the current source and its output to the coax shield.

Alternatively, an old electrometer like a Keithley 616 or 617 can be used as the active guard. I assume you need the extra resolution/accuracy your DMM provides as opposed to using an electrometer directly.

For reference, see Analog Devices' application note AN-347. It has information on how properly apply guarding when using op amps. In addition, reading through the user manual for an electrometer like the Keithley 617 can help with understanding how guarding works in high impedance circuits.

Thank you! I'll definitely read it, just like I'm already reading the Keithley low level measurement handbook.
And yes, we need the high resolution of the DMM, so we can't use an electrometer.
I also had doubts about the need for the coaxial on the Low side, but meh, since it doesn't cost nothing I might as well leave it there. A simple cable or a coaxial has no real cost difference, they will be soldered anyway, so no connectors needed.
Also thank you for that opamp model. It's a very pricey but due to its bias current (which we can't even measure) we could use it like a reference to see how much different opamps impact the reading

[NaxFM]

Below is an example of Pomona 4964 SS "low triboelectric" coax when tapped with a screw driver.

Wow, thank you again!
We didn't think about this. Of course the setup will be very stable with no movement at all, but it's something to be very aware of

[MegaVolt]

"best possible measurement" is a very poor criterion. We need some numbers to understand which efforts are useful and which ones will be a waste of time and money.

To measure low current, two requirements must be met:
1. Low leakage current (PTFE coated wires or bare wires. Air is an excellent insulator.)
2.Shielding. If point 1 is fulfilled, then any stable potential, for example, GND, is sufficient. There is no need for an additional protective amplifier. But better is a separate chamber made of conductive material.

A protective teacher is added when the insulating properties of the material are not enough. For example, the DMM7510 promises a shunt drop of no more than 15mV, i.e. if the outer conductor is connected to GND then the inner conductor differs by only 15mV. This is more than enough for your application.

[MegaVolt]

I almost forgot:

3. Immobility. All wires must be at rest. Any movement will be visible on the device.

And of course, I highly recommend https://download.tek.com/document/LowLevelHandbook_7Ed.pdf

[fcb]

Active guarding with low current measurements isn't necessary. Shielding is.

Add to what others have said about stoping any physical movement being very important I would also say thermal stability of the whole setup.

[guenthert]

[..]
And yes, we need the high resolution of the DMM, so we can't use an electrometer.
[..]

(what distinguishes a DMM from a electrometer?)
High resolution w/o stability is of very little value, but the old Keithley 617 has an analog output taken from just before its ADC.  So if the 4.5 digits it shows aren't enough you can add as many as you can afford by connecting a DMM there.

[David Hess]

I do not know of any DMM with a current range of 1uA. And this means that the device will measure at the limit of sensitivity, with all the negative consequences for the measurement accuracy.

The 2 volt range of a common 3.5 digit 10 megohm input multimeter in voltage mode can be used as a 200 nanoamp full scale current meter, with a burden voltage of 2 volts and a resolution of 100 picoamps.

[garrettm]

Active guarding with low current measurements isn't necessary. Shielding is.

I would argue that it depends on the ammeter's burden voltage. A DMM usually has a large (>>100uV) burden voltage, and thus would benefit from active guarding when measuring >= 6.5 digits at 1uA (or there abouts). If done correctly, stability of the LSD should increase with an active guard as temperature dependent cable leakage would decrease (I_leak ≈ V_burden/R_leak) as would HI side capacitance (and hence dielectric absorption). At any rate, it would speed up settling time of the measurement, which often has the greatest impact on accuracy of low current measurements.

If the burden voltage was negligible (100uV or less) then simple twinax cabling (using fluoropolymer insulation for inner conductors) may be sufficient, where the shield is connected to DMM LO guard.

[DeltaSigmaD]

A burden voltage causes many problems at low currents. If the burden voltage is kept low by using a low shunt resistor value, you are adding significant current noise to the input signal. To measure in the nA range and below, a virtual ground measurement input (inverting OP input) is the superior solution, as with the K617.
You must be also aware that a DMM can source unwanted signals at its input connectors, since it is not specialised to measure low currents <1nA. This might be a problem when measuring directly at a sensor. For instance, the K34470A itself generates about 0.25 uVrms at 50 Hz and 0.7 uVrms at 150 Hz in the 1 uA range, please see attached spectrum which was measured with my high resolution ADC (HRADC 5.5.7). This line hum may sound extremely weak, but it corresponds to 700 pArms or 700 ppm of full range (1 uA). The spectrum of the HRADC is free of any peaks within 0 to 500 Hz when disconnected from K34470A current input, since it is battery-operated (good shielding is prerequisite).

[Xandinator]

Modern day electrometers often come with 6.5d resolution and quite good digitizing speeds (take into account that the 1 MS/s and 7.5d in conjunction are going to be utopian anyways, so why not use the TIA tap off an older/cheaper electrometer). Shielding (and mechanical fixation) is the solution to the noise problem, guarding addresses leakage (which primarily comes with proper shielding). Eliminate noise first, then leakage - your initial sketch contrives to do it in reverse. Maybe you can fix both by simply wrapping it in Al foil or placing in a Teflon padded pot w/ lid? Shielding bags from EMI testing may also prove useful?
Also, as MegaVolt pointed out, a protective teacher is always a valuable asset

[NaxFM]

Thank you eveyone! You all gave me very valuable informations.
I didn't think it could be so much complicated to get reliable low current measurement. We will try to apply and compare all the techniques you explained me and we will also try to take into consideration all the possible uncertainty contributions.
Really, thank you again!

[garrettm]

Best test equipment for low noise coax-triax is sex-shop toys
https://ampnuts.com/avk-6/

LOL, that was quite entertaining!

I wouldn't have thought to use a vibrator to test the cables. Now that I'm thinking about this, a speaker connected to a signal generator/power amplifier would be an interesting test stimulus.

Back when I tested my cables (Keithley, HP/Agilent, and Beldin triax), I made a simple pendulum to hit them, tapped on my desk next to the cable and then gently flexed the cables by hand. Pretty boring in comparison to the vibrator.

I've attached some photos of my test setup at the time.