New formula for secondary resonant frequency

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>" <paul-at-abelian.demon.co.uk>

Hi All,

Calculator fiends may like to try out the following formula for
estimation of secondary resonant frequency. Applies to bare coils
(ie no top-load and no primary) in normal grounded-base configuration,
when situated over a reasonably well defined ground, with the coil
base not more than half the coil length above ground.

Starting with:

 turns;
 h = length of secondary winding, metres;
 d = diameter of secondary - metres;
 b = height of winding start above ground - metres;
 awg = wire gauge, AWG;

 (metres = inches * 0.0254)

Compute:
 
 x = h/d                                  (form factor)
 wd = 7.348e-3/pow(1.122932, awg-1)       (wire diameter - metres)
 sr = turns * wd/h                        (spacing ratio)

 fa = -94.6683*awg*awg*awg + 9000.55*awg*awg - 301175*awg + 3.64056e+6
 fs = 3.50662*sr*sr - 7.90171*sr + 5.83019
 fx = -0.000211179*x*x*x + 0.00557568*x*x + 0.0664809*x - 0.0153254
 t = fa * fs * fx/h/h
 s = -3.85188e-15*t*t*t + 1.17176e-8*t*t + 0.631829*t + 482.463

and finally,

 fb = log( b/h/0.2)                       (use the natural logarithm)
 Fres = s * (1.02 + fb/98.9065);          (Hertz)

Accuracy is around 2% average, with a peak error of around 4%.

Some examples:

My big CW coil: b=0.15, h=1.6, turns=725, awg=12, d=0.58;
                Measured 90.9 kHz, formula 90.2 kHz, -0.8% error

My half-coil:   b=0.15, h=0.8, turns=365, awg=12, d=0.58;
                Measured 150.7 kHz, formula 151.4 kHz, +0.5% error

Terry's big coil: b=0.025, h=0.762, awg=24, d=0.2606, turns=1001;
                Measured 148.4 kHz, formula 146.1 kHz, -1.5% error

Marc Metlicka's 
large h/d coil: b=0.3302, h=1.07696, awg=24, d=0.1081, turns=1700;
                Measured 276.9 kHz, formula 276.9 kHz, 0.0% error

The formula was derived by curve fitting to a database of around
1700 simulated secondary coils, and is expected to be more accurate
than estimates based on Medhurst capacitance.

Regards,
--
Paul Nicholson,
Manchester, UK.
--