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>

 > You can expect a difference in the high frequency coupling
 > coefficient when the secondary is lightly loaded.
 >
 > The calculated k and M should agree well with measurements made
 > using line frequency currents.  But as you say, the secondary
 > current at resonance will be non-uniform so the effective k will
 > likely differ.

I made a measurement in my coil, without top load and with a maximum
top load. There is really a difference in k. I get mode 7:8
without top load (k=0.133) and mode 8:9 with full top load (k=0.117).
My full top load is still quite small compared with the self-
capacitance of the coil, however (cself=5.55 pF cmax=~12 pF). With a
larger capacitance, maybe I can see the low-frequency k. Maybe the
presence of the shorted turn made by the top load also adds a
small error factor.

 > In section 6 of
 >
 >   http://www.abelian.demon.co.uk/tssp/pn1401.html
 >
 > the coupling is treated as a distributed quantity, and as such is
 > represented by an integral operator.  The effective k is taken to be
 > the square root of the determinant of this operator.  Actual beat
 > waveforms are accurately described by this model.

A numerical example of the application of those calculations
would be useful. I am trying to adapt Neumann's formula to account
for a current profile in the secondary. 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.

 >  > Do programs as Fantc, Acmi, and Mandk take the current profile
 >  > into account?
 >
 > Acmi and Mandk assume uniform current. Although acmi can be told to
 > use a given current profile, it will not compute what that current
 > profile actually is.  Fantc does compute the current profile (when
 > doing a resonance analysis), and will report the effective secondary
 > self inductance based on that computed current as 'Les'.

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

 > At present fantc doesn't do a distributed analysis of the joint
 > primary-secondary resonance, which it would need to do to report
 > the actual mode frequencies and k-factor.  Some of section 6 would
 > need to be implemented in the geotc library.
 >
 > If you're going to do some accurate measurements it would be nice
 > to run the tssp model on the system.

The precise geometry of my present system is:
Secondary: Length=0.319 m; radius=0.044 m; turns=1152, #32 wire.
Primary (flat): rmin=0.07 m; rmax=0.124 m; turns=14.7, #18 wire.
The primary is 2.5 cm below the secondary. Wire center.
The top load is a disk with 0.074 m of radius, 0.012 m of thickness,
0.014 m above the secondary, with an antenna above it that adds
about 6 pF when fully extended (0.8 m, maximum thickness 1 cm,
minimum 0.002 m).
With 5.07 nF of primary capacitance, the system is in tune with
the antenna at 0.401 m (there is a small difference, depending on
if I extend the thinner or the thicker segments).
Measured inductances: L2=28.2 mH. L1=59.82 uH (L1 at high frequency).
I get a high-frequency k of about 0.12. The low-frequency prediction
is k=0.109. 10% off.
http://www.coe.ufrj.br/~acmq/tesla/tefp.html

Antonio Carlos M. de Queiroz