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*To*: tesla-at-pupman-dot-com*Subject*: New formula for secondary resonant frequency*From*: "Tesla list" <tesla-at-pupman-dot-com>*Date*: Fri, 02 Feb 2001 08:05:41 -0700*Resent-Date*: Fri, 2 Feb 2001 08:12:07 -0700*Resent-From*: tesla-at-pupman-dot-com*Resent-Message-ID*: <T35J_C.A.78D.D5se6-at-poodle>*Resent-Sender*: tesla-request-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. --

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