Re: New formula for secondary resonant frequency

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

Original poster: "harvey norris by way of Terry Fritz <twftesla-at-uswest-dot-net>" <harvich-at-yahoo-dot-com>


--- Tesla list <tesla-at-pupman-dot-com> 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)
I do not understand this here, or the formulas. You
start with 4 variables: h,d,b,awg
and then somehow conclude that only 2 are necessary by
the finished assumption
fb = log( b/h/0.2) 
I dont know what f(b) is supposed to indicate but
taking the ln  or log(e)symbol as then natural log as
you indicate, there still seems the problem of whether
you are indicating whether the quantity equals 
ln([b/h]/0.2) or ln(b/[h/0.2]) which I think can be
different quantities.       
   Also the finished equation demanding another
variable s
Fres = s * (1.02 + fb/98.9065);    Can you be more
specific as to what the quantity s is? The wire
diameter divided by the height of the coil is already
a small number but when we in turn multiply that by
the turns we are only reaching the value of h again? I
am truly confused here, are the rest of the numbers
some kind of computer coil program?  
Confused In Ohio HDN
           
> 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.
> --
> 
> 
> 


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