Mistake in the schematic! R5 and R7 are 22k for availability!
Somewhere in this forum I read about the AD8421, and I thought I could build a probe around this device without a pre-amplifying-stage with JFETs or so. Sure, performance wouldn't be phenomenal, but it would stay small and affordable. You may correct me regarding this early decision, as it may be a bad one and I based much of this design on this choice.
I started wit Daves teardown of the LeCroy differential probe and thought I'll copy the input impedance and main passive input architecture. I use the AD8421 and I want to power this device with two 9V batteries, which should be allowed to get as low as 7V. I decided for about 700V allowed input voltage (DC or AC-peak). The 7V batteries left me with a maximum of 4.5V at the input (see AD8421 datasheet, min input voltage is negative supply plus 2.5V) I would go for about 150 times attenuation. I decided for a bit more and chose 25k as attenuation resistor to ground. With 1% resistors, a 1k pot would suffice to calibrate for symmetry. As 25k is not as easy obtainable as I thought, I later switched to 22k which left me with an attenuation of 1/178,7.
Then there were long calculations regarding the capacitors, but in the end I chose to use 10pF ones as these are easier to obtain in 1% accuracy which really was necessary to be able to tune the HF path under worst circumstances. With the 3 10pF+-1% capacitors and an attenuation of 178,7 I ended up with a parallel resistance range of 587,4...599,26pF. The chosen capacitors net up to 588(+1%!)pF worst case, but I chose to include the 10pF here nonetheless because I did not account for stray capacitance loading the input yet and figured it would be better to have some headroom in the other direction. Also, usually it should work when the caps null out their tolerances a bit.
The effect of stray resistance, especially with shielding around the input, has yet to be discovered, but this is my first guess, which might or might not work (I hope and think it does though). In the rare occasion that the tolerances add up too much, I can just leave out C5 or C12 respectively.
The strange device S1 is a switch to set the Gain of the amplifier. I seem to have miscalculated the attenuation here as I calculated with 1/177,7 instead of 1/178,7, but oh well. This might still be more exact than the tolerances, which is why I deem it reasonable. The switch sets the Gain to 1,77; 17,7 and 177 respectively to yield a final attenuation of 1/1, 1/10 or 1/100 of the differential signal. This should in theory allow to measure a 1V drop over a shunt riding on 230V no problem.
On the output I added 47 Ohms before the signal feeds into an attached cable with BNC-plug to sorta match cable impedance. Overkill? Not enough?
Regarding construction:
Input cables shall be simple banana plugs to allow attachment of probes. This should be fine as bandwidth is quite low and source impedance should be low as well. (correct me if I am wrong, but it should work this way)
Output cable is directly attached BNC cable, say 1m length.
Case will be 3d printed with strain reliefs for the cables and a place for the batteries. Mentioning batteries, I should add a switch for these.
The complete front end shall be shielded. I think of doing that with a solderable can, but I do not know what impact they have on stray resistance. Input regarding this topic would be welcome! They are also quite expensive and small. A ground plane would shield the bottom side, adding yet more stray capacitance.
I have seen spark gaps in some designs, but I am hesitate to include them as the ground (which is provided by the BNC) may be unplugged and I think 3 2kV caps in series or 4 500V resistors should be safe enough - probably even safer than PCB spark gaps. Feel free to correct me here as well.