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vac tube TC secondary design question

Hi coilers,

I want to design a good secondary for my tube coil.

My primary is 9" diameter and 5" high. The LC of the primary circuit
resonates at 650kHz. I cannot really change this much - in particular I cant
make it much lower.

I believe the problem is to design a secondary that resonates at this
frequency, has the highest number of turns and has the largest diameter
possible so that the coupling is high. I was thinking of between 5" and 6"
diameter, but this is difficult without building numerous prototypes.

Has anyone wound a secondary that resonates at around 650kHz? What were the

Is there a good way of estimating the resonant frequency of the secondary
without building it?
I tried using the formula
f (MHz)= (1175 * (h/d)^0.2)/(d*N)
but it always overestimates the frequency when I build and test coils.

Do you think it is more important to have a higher number of turns, or a
higher coupling factor for a tube coil?

I was thinking of using 16" length of #18 on 5" diameter, approx 380 turns.
Does this seem about right?


BTW: My tube coil now uses a pair of 572Bs, a 4kv supply, one huge 1nF 15KV
doorknob primary C, and a 16 turn copper tube primary L.