I need to measure the electrical resistance of a volume of ground.
To do this I need to cause a current to flow between two metal electrodes pushed into the soil (let's call them the "current" electrodes) and measure the potential difference created by this flow using a second set of electrodes connected to a voltmeter (lets call them the "voltage" electrodes).
Since the charge between the current electrodes causes ions in the soil-water to accumulate around the electrodes I need to use an alternating square-wave current source (in the 50-150Hz range - low enough so we don't get problems with complex impedance). And since I'm interested in the way in which the voltage between my measurement electrodes changes over time I will use an oscilloscope to make my measurements - which must therefore be voltages in a reasonable range (1mV to 10V).
The ratio of the current flowing between the injecting electrodes to the voltage between the measurement electrodes gives me a "resistance" value using Ohms law and a simple geometric modification. And that solves my original problem.
I can use an off-the-shelf 12vDC to 110V AC square-wave "mains" converter to supply the voltage to drive the square-wave alternating current powered by a simple 12v battery. 110v is high, I know, but the contact resistance of the electrodes with the soil is in the 1kohm to 50kohm range and to get a current flow high enough to measure with precision (at least 1mA) I need to drive the current with a voltage of tens to hundreds of volts - one commercial system I own uses voltages as high as 800v to measure ground resistance, though 100v maximum is more common.
The current will still be too low to measure precisely using a Hall-effect current sensor so I need an alternative.
So here's my problem: The off the shelf circuits I can buy to measure small current accurately and precisely, by conversion to a voltage of reasonable range, are DC only but the current flowing into the ground must be square-wave AC. So what simple circuit, perhaps a version of a shunt-plus-amplifier, can I use to convert the AC current to an equivalent (zero-crossing) AC voltage measurement in the <+/-10v range my oscilloscope can accept, without significantly affecting the current itself?