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Re: [TCML] Primary Generated Field and Coupling Coefficient



Andrew Robinson wrote:
<div class="moz-text-flowed" style="font-family: -moz-fixed">Has anyone ever mapped out the fields produced by the three different primary coils? Is so could you PLEASE send me a link to some images or results. What factors determine the primary geometry thats best suited for a coil. It seems there are a lot of helical primaries on big coils, and flat pancake primaries on medium coils. Do inverse conical primaries achieve better efficiency? Ultimately the transfer between coils is dependent on the change of flux, but it seems situating the secondary in a region of closer field lines will ultimately achieve better efficiency. Helical primaries tend to produce vertical field lines much like an ideal solenoid, whereas flat pancake primaries produce a more torus shaped field (Just off top of my head) The inverse primary seems to be a good middle man between the two. Finally, can someone point me towards the formula to determine coupling coefficient? I've heard ideal is between .05 and .2. I need a formula to determine where I sit currently in order to make adjustments. Thanks
The coupling coefficient determines in how many cycles the energy transfer from primary to secondary occurs. With too few cycles, quenching at the primary spark gap is problematic, and the primary coil is too close to the secondary coil, inducing the "racing sparks" problem. With too many cycles, losses increase and tuning becomes too critical. The range around 0.1 is a good choice, resulting in energy transfer in about 5 cycles. There is no simple formula for the coupling coefficient. The general formula is a complicated integral, and approximations are quite complicated too. Several programs are available to evaluate the inductances and coupling coefficients in a Tesla coil. My version is the program Inca, available at http://www.coe.ufrj.br/~acmq/programs.

A list of the ideal coupling values. The numbers a:b in the "mode" indicate the ratio of the two resonance frequencies of the complete system.

Mode 1:2, energy transfer in  1.0 cycles: k= 0.6000000000
Mode 2:3, energy transfer in  1.5 cycles: k= 0.3846153846
Mode 3:4, energy transfer in  2.0 cycles: k= 0.2800000000
Mode 4:5, energy transfer in  2.5 cycles: k= 0.2195121951
Mode 5:6, energy transfer in  3.0 cycles: k= 0.1803278689
Mode 6:7, energy transfer in  3.5 cycles: k= 0.1529411765
Mode 7:8, energy transfer in  4.0 cycles: k= 0.1327433628
Mode 8:9, energy transfer in  4.5 cycles: k= 0.1172413793
Mode 9:10, energy transfer in  5.0 cycles: k= 0.1049723757
Mode 10:11, energy transfer in  5.5 cycles: k= 0.0950226244
Mode 11:12, energy transfer in  6.0 cycles: k= 0.0867924528
Mode 12:13, energy transfer in  6.5 cycles: k= 0.0798722045
Mode 13:14, energy transfer in  7.0 cycles: k= 0.0739726027
Mode 14:15, energy transfer in  7.5 cycles: k= 0.0688836105
Mode 15:16, energy transfer in  8.0 cycles: k= 0.0644490644

Antonio Carlos M. de Queiroz

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