Here is my attempt at calculating a Hoop Loop. I would be very appreciative if you would look it over.
Thanks for the heads-up in the Solid State Radios forum. Somehow I missed this post.
The Hoop Loop was designed to replace
the built-in antenna. So the transformer secondary (the high inductance) is in place of the radio's loopstick antenna, not in parallel.
If you put any inductance in parallel with the loopstick the total inductance seen by the tuning cap will be less than it should be, ruining the tuning range. There's no reasonable way to get around this.
What you need to do is determine the inductance of the internal antenna, remove it, and replace it with a transformer of the same inductance. If the internal antenna winding is tapped, as in my Zenith Royal 705, you'll have to accommodate that, but it probably isn't.
You can't calculate the primary until you've set the secondary inductance. Divide the secondary inductance by the inductance of the antenna and take the square root, to determine the end-to-end inductance of the primary. Add a turn or two to each end until you test it.
Testing is easy if you have a second portable radio that will sit inside the Hoop Loop. As close to either end of the band as possible, tune in a station on the radio that's directly connected to the Hoop Loop. Then tune the second radio to the same station. Rock the Hoop-Loop radio's tuning back and forth. The signal on the second radio should peak at exactly the same place as it peaks on the Hoop-Loop radio. If it doesn't, try pruning the primary evenly from both ends. Because of the high turns ratio, a couple of turns makes a big difference.
This whole experiment was made much easier in the Tecsun PL-380 because the chip will tune inductances from around 250-450 uH across the entire band, giving manufacturers some slack when designing the loopstick. With an analog radio it's harder because the inductance can't vary much from the design value.
When I use the Hoop Loop with a communications receiver, there is no internal antenna. I wound a transformer that would resonate the Hoop Loop across the band with a 365-pF cap (using a second, portable radio as above to prove to myself I really was tuning the antenna). Then I used a third winding of only a few turns to couple the transformer to the receiver antenna connector.
I don't think you need the ESD diodes. The impedance there is very low and as the loop gives a dc short circuit there isn't likely to be any static build-up. Plus, their capacitance is going to be multiplied by the turns ratio and appear across the secondary.
For others' reference, here's the Hoop Loop article: http://kr1s.kearman.com/html/hooploop.html