Re: mini coil primary coupling ?

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
 >
 > Original poster: "Laurence Davis by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <meknar-at-hotmail-dot-com>

 > === I am curious how you came up with mode that it would be running from 
just
 > the coupling factor.  Is this from experience or calculations that show
 > that mode most efficient
 > with 0.18k?

During the energy transfer from primary to secondary, the transformer
and its two capacitances oscilates at two frequencies at the same time
(the "frequency splitting" phenomenon when two identical oscillators
are coupled). These frequencies are in a ratio a:b, that is what I
call the "mode". Usually a=b-1. An analysis of the system reveals that
if the mode is a:b then the coupling coefficient is:
k=(b^2-a^2)/(b^2+a^2). For mode 5:6, k=0.1803278689.
Two cosinusoids with the same amplitude with frequencies in the
ratio 5:6 add to zero, forming the "first notch" after 3 full
oscillation
cycles (always b/2 cycles for any mode). You can observe the waveforms
using the programs at:
http://www.coe.ufrj.br/~acmq/programs
Try the mrn4 program, or the teslasim program.

 > Perhaps I am not understanding coupling.  when I try to envision the energy
 > transfer...
 > I look at it as light.  waveform peaks would be a point source of light.
 > the light emits in all directions.

Just magnetic fields.

 > In a vacuum, these wavefronts move at the speed of light.  When they move
 > through matter, they are delayed.  I'm stretching here, but as the distance
 > from a em source is increased by X, the field drops by 1/X.  I learned that
 > from playing with spools of wire and increasing the distance and measuring
 > voltage output. (500ft spools of 12awg connected to 120vac, with a 1/2
 > steel square channel as a lossy 'core').
 > Does this effect slow the wavefront this much?

In this case, there is no core, and so the field disperses more easily.

 > Is coupling a percentage of energy received?  is it unitless? does a
 > coupling of 0.5 mean that complete energy transfer is in 2 cycles? ...
 > 0.33k in 3 cycles? (light goes on)  so .18 means complete energy xfer in 6
 > cycles? (oh wait you said 3 cycles for complete transfer).

The coupling is related to the fraction of the magnetic field generated
by one coil that crosses the core of the other coil. It varies from 0
for uncoupled coils to 1 for practically coincident bifilar coils.
The coupling coefficient is k=M/((L1 L2)^(0.5)), where M is the
mutual inductance between the coils. M is the ratio between the
voltage in one coil and the ratio of variation of the current in the
other. Curiously, it's the same for input in L1 or L2.

If both coils are tuned to the same frequency (when separated), then
even with k<1 it's possible to transfer energy from one capacitor to
the other, but after a few oscillations. How many is determinated by
the coupling coefficient only, if the tuning is correct. The minimum
is one cycle for mode 1:2, that results in k=0.6. Tesla coils with
usual structures result in k<0.2, what places the mode above 4:5.

Antonio Carlos M. de Queiroz