AC leakage issue with high impedance measurement setup

Question

I am having an AC leakage current problem with my measurement setup that I typically use for lock-in measurements.
I employ a 100 M\$\Omega\$ resistor as a voltage-current converter, and in series, a 50 k\$\Omega\$ resistor serves as a dummy load (only for testing purposes), as illustrated in the schematic diagram below. Normally, instead of the dummy load, I would have the DUT, which is basically the channel of a FET transistor.

The signals in the setup are both generated and acquired by a signal conversion unit that provides both analog inputs and outputs. The voltage drop across the 100 M\$\Omega\$ resistor is measured using a separate low-noise differential amplifier unit. All the connections are made with coaxial cables with BNC connectors and BNC Y-splitters.
For testing purposes, I apply both DC and AC voltages to measure the current (the target current in normal condition is 50 nA). The DC signal amplitude is 5V, and the AC signal applied is 5 Vpk at 20 Hz.

The issue arises when I disconnect one end of the load resistor, leaving it floating. In theory, this setup should result in no return path for the current, and therefore, there should be no current flow (also the input impedance to GND @ DC of the differential amplifier is >10T\$\Omega\$). DC measurements work as expected (near zero current measured). However, when I perform (lock-in) AC measurements, I still observe a current reading of approximately 38 nA. If I further remove the load resistor, leaving one end of the 100 M\$\Omega\$ resistor partially open (though it remains connected to the differential amplifier via the BNC Y-splitter), I measure around 27 nA.

I suspect capacitive coupling causing this issue and I’m wondering how can I fix this problem.

Answer 1

By my calculation 27nA at 5V, equates to a leakage impedance of 185M\$\Omega\$ impedance. And at 20Hz this equates to a capacitance of just 40pF.

Coax capacitance varies, but 60-100pF per m is quite typical, so depending on the length of cable you are using, this could well account for the current flows.

In terms of "fixing", if the reading is stable (which it should be for constant cable length and physical setup) then perhaps you could just calibrate out by subtracting the current flow due to stray capacitance from the final reading?

An alternative "trick" which I've seen used for low value capacitance measurement is to "guard" the feed signal, and to make the measurement on the return side.

Instead of connecting AO1 direct to a single piece of coax, you move the sense to the return path, and connect the feed to its own piece of coax, where both the shield and core are driven with the same signal.

This should remove the offset with no load, but there will be a small shunting effect on the AC measurement, with some of the current through the load coupling down to ground through capacitance instead of via Rm. This will appear as a gain error, and again could be calibrated out with a reference measurement and scaling.

(Depending on the range of measurements you need to take, and the importance of zero accuracy vs FSD accuracy, you may find either the zero offset or gain calibration more attractive.)

Reducing the size of Rm to say 10M\$\Omega\$ would significantly reduce the impact of stray capacitance in both setups (though with reduction of sensitivity). Alternatively, if the load is purely resistive and you can reference the phase of the signal relative to the excitation signal, you could extract the capacitive vs resistive elements.

(In the capacitive measurement case, there are even better solutions which use differential measurement and two signals 180degree out of phase, both guarded. This may or may not be applicable in your application, though it could be that the AD7745/6 device could be directly used to make the measurement you are seeking.)

The most complete solution (at the expense of additional complexity, and possible ringing) is to guard the excitation signal as suggested above, but also to isolate the shields on the coax of the cables connecting to the Rm and Rdummy midpoint, and drive them with a suitably damped unity gain buffer connected to the signal line. This effectively reduces the stray capacitance to zero as there is no voltage difference between the shield and core.

Some instrumentation amps such as the ADA4530 incorporate a guard buffer amp for exactly this purpose (though with slightly different guard topology), and using one of these for the differential pre-amp may be your best option.

The linked datasheet has many more details, example circuits and additional suggestions such as the use of triax cables.

Answer 2

It is leakage from the coax cables likely.

For such high impedances, you must use active guarding of the coax shields, i.e. not connect them to ground but to a buffered version of the inner contact voltage.