For your reference, here are some Electronics calculators, just in case you don't want to do all that messy math-stuff.
LC Resonance Calculator
Air Core Inductor Calculator
In my adventures in Theremin Design, the LH and I went in the basement and began to plug random stuff into the Proto-board, just trying to get a nice sine wave from a fixed Colpitts oscillator. We didn't have too much luck; we had used the above calculators, figured out some values, but are having problems with the inductors. The coils we have pre-wound just were not "big" enough.
So I am winding a couple of coils this afternoon. We have a pair of these:
A-848032-2 MPP TOROID (this is a little donut of material called Molypermally. It's made of 79% nickel, 17% iron and 4% molybdenum alloy powder.)
The magnetic permeability of the material is 60 mu. The LH believes that 30 turns will give me 15 mH.
Yes, we calculated correctly. I wound some spare wire around the blue donut and we were good. But that was with a capacitor that is 1000 pF. However, the capacitance between a human hand and the Budgie antenna is not going to be very good -- so we decided to reduce the capacitance to 100 puff. That's going to take more like 60 turns. Soooo.... I'm winding. I am using some nice copper wire from a deflection yoke from an old TV set. Nothing like recycling.
They worked. It took 65 turns. One has a impedance of 112 mH and the other 116 mH. Yeah. Now I'm tired. I received a nice diagram from a reader -- I was going to play with transistors. But I didn't have the right ones. I may have to actually BUY something.
The project so far: two inductors.