# Re: New formula for secondary resonant frequency

```Original poster: "Terry Fritz" <twftesla-at-uswest-dot-net>

Hi Paul,

Fantastic formula for us computer type folks!! :-))

I also wanted to point out the dramatic affect Sonotube can have on such
calculations.

I inserted a Sonotube type form into my regular big coil form to see the
differences it would make.

http://hot-streamer-dot-com/TeslaCoils/Misc/SonoQ/SonoQ.jpg

Using many toys,

http://hot-streamer-dot-com/TeslaCoils/Misc/SonoQ/Stuff.jpg

I scanned the coil's frequency response with and without the extra tube
inserted.  I swept the frequency linearly from 140 kHz to 150 kHz and
measured the response with a whip antenna connected to the scope.  The
differences are shown at:

http://hot-streamer-dot-com/TeslaCoils/Misc/SonoQ/SonoQ1.jpg

With the second tube inserted into the center of the big coil tube, the
frequency dropped from 147.2kHz to 146.68kHz.  The Q dropped to 69.5% of
the original.  Although Sonotube is fairly good for coil forms, its loss
can affect such details...

Cheers,

Terry

At 10:55 AM 2/2/2001 +0000, you wrote:
>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.
>--
>

```