[Radio Wrangler]

Any value will do as far as getting directional sensing goes.

If you don't have enough inductance, it will be a difficult load on whatever is driving it. If you go for too much inductance you'll run into problems with self resonant frequency due to capacitance between the turns. These are exactly the same issues as with designing a simple transformer.

40uH is going to have a reactance of 452 Ohms at 1.8MHz. If you have amplifiers between the two antennae and the goniometer primary coils, this is almost ten times 50 Ohms. In transformer terms it sets the magnetising current and this factor at the LF end is plenty. So the next question is whether you can make a 40uH winding of the physical size required by your mechanism and get the self resonant frequency to be well above your upper frequency goal of 30MHz?

So 40uH is a reasonable figure if the goniometer is driven from 50 Ohm-ish amplifiers or directly from 50 Ohm-ish antennae.

Some (Classic Tektronix) colour TV test equipment had goniometer transformers to allow a front panel knob to rotate the phase of a subcarrier frequency signal through a full 360 degrees. The stator coils were driven with a 90 degree phase shift to make this work.

Marconi made a number of ship's direction finding receivers which worked with Faraday-screened crossed-loop antennae. A motor drove the goniometer sense coil as it looked for the nulls.

Aircraft carry an ADF Automatic Direction Finder. Essentially a square block of ferrite with two coils at right angles to each other... think of it as a 2-dimensional ferrite rod antenna. The goniometer it feeds is simulated electronically. Coverage is LF-MF where the beacon transmitters are plus long and medium wave broadcasters. Pilots are required to know how to use them to get their instrument ratings, but in use they've been supplanted by GPS. They are still officially seen as a fallback. So planes carry multiple GPS receivers, so there are plenty of satellites.... the risk comes from interference problems.

So goniometers are still in use, though the people using them are unaware of the name. They'd probably think it was something quite rude if they heard the word.

David