Re: A new Tesla coil and k measurements

["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: "Paul Nicholson by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>
 >
 > Hi Antonio,

 > Yes, providing h/d is not too small. You should see k at Fres tend
 > towards the low frequency k.

Ok. I will try.

 >  > Maybe a cosinusoidal distribution, ending at an angle that is
 >  > function of the coil self-capacitance and of the top load
 >  > capacitance may give a better result.
 >
 > Yes, just make an estimate of the number of degrees at which
 > to end the profile.  It's easy to put in the current profile
 > into Neumann's integral - just weight each elementary source
 > with the current at that point.  I usually use a base current
 > of unity, which means that the resulting effective L is referred
 > to the coil base.

I tested this. The integral computes a mutual inductance that
agrees with your numbers below. But I would have to compute the
inductance L2 with the same profile to get the correct k. I
don't have yet an adequate method for inductance calculations.

The final angle can be found be considering that the current
that feeds the top load is ibase*cos(final_angle), while the
remaining part of ibase goes to the "self-capacitance".
We find then that cos(final_angle)=ctop/(ctop+cself).

 >...(skipping interesting calculations)

 >       pri.L|     sec.L| pri-sec.M| sec-pri.M|pri-sec.K|sec-pri.K
 >    57.22 uH|  28.57 mH| 138.15 uH| 138.15 uH|    0.108|    0.108

Ok.

 > Now commenting back in the special current profile of the secondary,
 > we get instead:
 >
 >      pri.L|     sec.L| pri-sec.M| sec-pri.M|pri-sec.K|sec-pri.K
 >    57.22 uH|  18.37 mH| 124.03 uH| 138.15 uH|    0.121|    0.135
 >
 > Note that now we've messed with the current profile, the pri-sec
 > and sec-pri mutual L and k are no longer the same.  The value we
 > need is the pri-sec M and k, which are consistent with your HF
 > observations.    The pri-sec M is based on the voltage induced in
 > the primary from the specified secondary current, which is the one
 > you're looking for.

The different mutual inductances is something strange. Neumann's
formula would continue to be symmetrical. The calculation for sec-pri.M
appears to assume uniform currents in both coils, since the result
is the same of the first case, but L2 is being calculated with
nonuniform
current.

 > Thanks for providing the dimensions, I'll run them through the tssp
 > software to get some waveforms, and these should match pretty
 > closely your system.  We should be able to model the antenna length,
 > etc, and come up with the same tuning.  Lack of a well defined
 > ground plane and nearby objects could mess things up a little, but
 > we should still get more or less the correct mode numbers.

My "ground" in the measurements was the power line ground. The coils
were 3.5 cm above a wooden table, that was enough of "ground".
Objects at more than ~50 cm away didn't cause differences
in the waveforms.
I took these pictures with my low-power test setup, looking at the
primary voltage. The first with the bare secondary coil, and the
others with 40 cm and 80 cm of antenna:
http://www.coe.ufrj.br/~acmq/tesla/no_top_load.jpg
http://www.coe.ufrj.br/~acmq/tesla/mid_top_load.jpg
http://www.coe.ufrj.br/~acmq/tesla/full_top_load.jpg
Time scale: 5 us/div. Vertical scale: 1 V/div.
(I didn't annotate the values (nF) of the primary capacitors used...)
Note what appears to be an inconsistency between the number of
cycles to the first notch and the number of cycles in the first
full beat. Maybe caused by some nonlinearity in my test setup, or
a not fast enough step.
The first beat starts from about +4V. The start of the first
cycle is not visible in the pictures.

Antonio Carlos M. de Queiroz