Re: New formula for secondary resonant frequency

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

Original poster: "Kurt Schraner by way of Terry Fritz <twftesla-at-uswest-dot-net>" <k.schraner-at-datacomm.ch>

Hi Paul,

your developpment of a secondary calculation formula, on a sound
theoretical basis, realized by a huge amount of simulations and
fitting a set of engineering formulas to the results, is very
much appreciated and welcome! With my limited means, and small
number of coils, I tried to evaluate your new formula, by
introducing it in Excel (...sorry: I know it's a Microsoft
program ;o)). First was a test for the implementation in Excel,
with your data:
						
Coil      Pauls big CW	Pauls half-coil	Terry's big	Marc
Metlicka's 	
turns     725		365		1001		1700	
h         1.6		0.8		0.762		1.07696	m
d         0.58		0.58		0.2606		0.1081	m
b         0.15		0.15		0.025		0.3302	m
awg       12		12		24		24	

Fres,cal  91.1		152.9		147.6		279.6	kHz
Fres,exp  90.9		150.7		148.4		276.9	kHz
Diff      0.2%		1.4%		-0.5%		1.0%	cal-exp

As obvious, there is a difference in the results, relative to
yours, however it's not too big. I guess, it might be the
rounding of the equation coefficients in the last digits. As a
next, 4 of my own coils are compared:
						
Coil      Sk B&W	Sk Long Coil	Sk 12cm Coil	Sk 20cm Coil
turns     821		1950		921		979
h         1.768	1.41		0.585		0.68
d         0.4013	0.1633		0.1207		0.2
b         0.7		0.5		0.2		0.5
awg       17.162	22.053		22		22

Fres,cal  131.4	157.3		409.0		209.3 Paul's formula
Fres,exp  119		147.7		368		202.7
Diff      10.4%	6.5%		11.2%		3.2%  cal-exp

Fres,cal  123.1	139.6		372.9		200.0 Wheeler/Medhurst
Diff      3.4%		-5.5%		1.3%		-1.3% cal-exp

It seems, my coils are yet more happy with Wheeler/Medhurst,
however the precision of the experimental data have to be
considered. Regarding the instruments, I believe to be quite
precise (specifics can be supplied). The most of error probably
stems from the spacial situation, present, when measuring the
coils: capacitive influence of the surroundings! The B&W coil,
i.e., was tested in my living room, which is one floor above
ground level, and the top of my big coil only ~0.4m from the
ceiling.

BTW: Would you have perhaps at hand, a version of your function 
fa = -94.6683*awg*awg*awg + 9000.55*awg*awg - 301175*awg +
3.64056e+6
beeing currently a function of awg, made a function of wire
diameter instead, like f(wd[m])? Measured values of wire diameter
could more easyly be introduced that way.

Hope,the tables will arrive in a well readable condition!

Greets
Kurt Schraner





Tesla list wrote:
> 
> 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.
> --