Re: A new Tesla coil and k measurements

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

Original poster: "Paul Nicholson by way of Terry Fritz <teslalist-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Hi Antonio,

 >  With a larger capacitance, maybe I can see the low-frequency k.

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

 > 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.

 > How can a current profile be specified in Acmi? The documentation
 > doesn't mention this (I have the version 0.7b).

Ah, this feature is in the current version, 0.8b 1st March 2002,
but it is not mentioned in the documentation.  I'll attend to this
and upload a new version.  But for now you specify the current by
an expression in the parameter 'S'.

For example, your secondary might be


  secondary {

    radius   0.044

    height1 0
    height2  0.319

    current cos( S * pi/2)   ; S runs 0..1 along the coil
    conductor 32 awg
    turns 1152
  }

which gives the output

     SCNY.L| SCNY.R
   18.37 mH| 174.02

in which the L is the equivalent series inductance referred to the
coil base.  Commenting out the current statement

    ;;;;; current cos( S * pi/2)

then gives the normal output for low frequency behaviour:

     SCNY.L| SCNY.R
   28.57 mH| 174.02

which is close to your DC measurement.

Adding in the primary coil...

  primary {
     radius1 0.07
     radius2 0.124
     height 0-0.025    ; Er, no unary minus in acmi
     conductor 18 awg
     turns 14.7
   }

and throwing in some output commands:

  show self( primary) as "pri.L" with inductance
  show self( secondary) as "sec.L" with inductance
  show mutual( primary,secondary) as "pri-sec.M" with inductance
  show mutual( secondary,primary) as "sec-pri.M" with inductance
  show coupling( primary,secondary) as "pri-sec.K"
  show coupling( secondary,primary) as "sec-pri.K"

gives the result (still with uniform secondary current)

      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

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.

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.
--
Paul Nicholson
--