Re: mini coil primary coupling ?

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

Original poster: "Peter Lawrence by way of Terry Fritz <teslalist-at-qwest-dot-net>" <Peter.Lawrence-at-Sun.COM>

Antonio,
         I was starting to wonder if ETesla6 had problems until I read your
post. My primary F-res is 158 KHz, and ETesla6 predicts a secondary F-res
of 204 KHz, when I have everything tuned for "best" (subjective...) sparks.
I was expecting the F-res's to be equal, but are you saying that, in isolation,
the primary and secondary should be tuned to different frequencies, in
a:b ratio where typically a = b-1.

In my case these Fs are pretty close to 5:4 ratio, and then we get desired
K = 0.2195 from your formula, but in reality my K (according to ACMI) is
around 0.1

My precise questions are:
1. should the primary and secondary be tuned (separately, in isolation) to
    the same frequency,
    and adjust the K (by varying coil proximity) to get a K of 0.180,
    and then expect to observe at run-time the coils oscillating at the 5:6
    ratio,
-or-???
2. should the primary and secondary be tuned (separately, in isolation) to
    be in the ratio of 5:6 (and if so, is it sec=5 and pri=6, or vice-versa),
    and adjust the K (by varying coil proximity) to get a K of 0.180,
    and then expect to observe at run-time the coils oscillating at the 5:6
    ratio they were tuned for


3. of the a, b, which is the primary and which is the secondary. if the
    "first notch" is always at (b/2) then b has to be even, and we only
    have 5:6, 7:8, 9:10,... modes available (not 6:7, 8:9,...). Am I
    understanding this correctly?


Since I don't have an O-scope, it would be nice to have theory predict what
to build, and then have it come out working (or to put it another way,
experimenting is nice, but after a while you want to understand why it
works the way it does).

thanks,
Pete Lawrence.


 >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
 >
 >