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*To*: tesla-at-pupman-dot-com*Subject*: Optimum toroid size*From*: paul-at-abelian.demon.co.uk (by way of Terry Fritz <twftesla-at-uswest-dot-net>)*Date*: Sun, 01 Oct 2000 20:27:38 -0600*Delivered-To*: fixup-tesla-at-pupman-dot-com-at-fixme

John H. Couture <couturejh-at-worldnet.att-dot-net> wrote: (in RE: Resonant wire length issues) > What are your recommendations for finding the optimum toroid > size for any secondary coil other than using the 1/4 wavelength > as Tesla did? I thought Tesla had a clever answer for coilers > asking how to find the optimum toroid. I'm afraid I don't know of any theoretical formula for selecting an optimum toroid size for a given coil. Very generally, if you wish to optimise for maximum output voltage, you would seek to use the minimum possible topload capacitance consistent with achieving sufficient control over the field strength to prevent breakout. I don't see a direct way to calculate that. Lets explore the difficulties. The tesla coil will try to attain an RMS voltage of around Vt = sqrt( Eff * Q * Pin * sqrt( L/C) / D) where Q, L, C have their usual definitions, Pin is the mean RMS input power, D the effective duty cycle, and Eff the overall power efficiency of the exciter. (Those using capacitor discharge excitation will prefer a different formula). This voltage rise will be frustrated if the toroid size is smaller than optimum, due to breakout. I'm unable to comment on how the breakout potential for a given topload and coil geometry is predicted, so I'll just pretend that a function Vb = Fb( S...) exists which gives the maximum sustainable potential Vb for a given coil as a function of a set S of numbers which describe the toroid geometry options. More certainly, a function C = Fc( S...) also exists which gives the total equivalent capacitance of the given resonator as a function of the same set of toroid options. We can reasonably suppose that both Fb and Fc increase with the overall toroid dimensions S. If so then Vt will decrease with toroid size while Vb will increase, and thus there is a point of intersection. We get something like | Vt | -_ . Vb volts | - _ . | X _ | . - _ | . - _ | . - _ ------------------------------------------ small Dimensions S large The point of intersection X represents the optimum toroid size for maximum voltage from the given coil. To the left of X, the voltage is limited to the dotted Vb curve by breakout. To the right of X the voltage is limited to the dashed Vt curve by the reduced frequency and the need to charge up the higher capacitance. Some applications might trade output voltage for higher stored energy to achieve better regulation and would therefore use a larger than optimum topload. A smaller topload may be appropriate if spectacular corona displays are the aim. The difficulty of calculating the position of X is seen by setting Vt = Vb, to get sqrt( Eff * Q * Pin * sqrt( L/Fc( S...)) / D) = Fb( S...) which would need to be solved for S. Neither Fc nor Fb are likely to be trivial functions, and moreover, it can be seen that the solution depends not only on the coil parameters L and Q, but also on the exciter efficiency power level, and mode of operation. Thus, most coilers will try to experiment with a range of toroid sizes and heights to find the best performance, which is (apparently) a lot more fun than solving equations. Regards, -- Paul Nicholson, Manchester, UK. Secondary modeling project http://www.abelian.demon.co.uk/tssp/ --

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