Hi Itsu and all,
In the meantime I did some simulations in LTspice. I have found that the needed 50:1 transformation ratio comes out only as being around 22:1, using the measured primary inductance of 55 uH and single turn secondary of 136 nH on the T520-2 core.
If we use this data sheet
https://alexsradioshop.de/wp-content/uploads/2023/01/AmidonAMI.pdf and we use the formulas included in page 1, we can reverse calculate the number of turns for the measured primary and secondary inductances
(using AL = 207 uH/100 turns from data sheet for that core).
So the calculated number of turns is 51.5 for the measured 55 uH primary coil (which sounds reasonably close for your 50 turns, see note below).
However, the calculated number of turns comes out as 2.5 for the 136 nH secondary coil. The formula predicts 20.7 nH inductance for a single turn on this core.
The simulations show a 50:1 ratio if I use 28.1 nH inductance for the secondary coil, see attached screenshot. The 28.1 nH is much closer to the predicted 20.7 nH than the
136 nH. With the 28.1 nH secondary the Q of the LC circuit comes out as very nearly 370 at 2166 kHz.
Checking your 40 turns on the T200-2 core for your measured 18.8 uH inductance by reverse calculation, it gives 39.5 turns, very close to 40. (AL for T200-2 is 120 uH/100 turns.)
For consideration only: known rule of thumb for a 1 cm long wire inductance (OD = 1 mm) is about 10 nH and the T520-2 core has a permeability of 10.
I attach a simulation of the transformer with 28.1 nH secondary coil driving the LC circuit at resonance. For the total loss resistance in the LC circuit I used 0.69 Ohm.
Note: The little higher inductance of 28.1 nH I had to use (versus the reverse calculated 20.7 nH) to get the 50:1 ratio may come from the 50 turn primary coil which gave the 55 uH
primary inductance as you measured, probably a little high. If I use 52 uH instead of 55 uH to reverse calculate the number of turns, I get 50.1 i.e. 50 turns you have.
Using 52 uH in the simulation and using the 20.7 nH inductance for the secondary coil, I got V3 / V2 = Q = 45 Vrms / 0.1218 Vrms = 369.4 i.e. the same Q result, just the voltage levels are lower.
Gyula