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>
 >
 > Antonio,
 >
 > Putting in your dimensions to tssp gives:
 >
 >   Fpri: (with secondary removed) 295.5 kHz;
 >   Fsec: (with pri gap open) 293.0 kHz (1/4 wave);   861.7 kHz (3/4 wave);
 >
 >   Coupled resonant modes:  278.3 kHz and 313.1 kHz;

I get:
Fpri: 290 kHz. Fsec the same (assuming that complete beats are a
consequence of this).
Coupled resonant modes: 272 kHz, 307 kHz
The 3/4 wave mode appears to be around 840 kHz (see below).

 > I reckon that gives a k just under 0.12 and mode 8:9 operation.
 > The secondary current is pretty uniform, with the top current
 > coming out at just under 70% of the base current.
 >
 >   Secondary:
 >     C_disc:   2.7pF   (in situ)
 >     C_whip:   4.1pF   (in situ)
 >     C_coil:   4.4pF   (effective at Fres)

Medhurst gives 5.55 pF.

 >     C_total: 11.2pF   (aka Ces of the resonator)
 >
 >     Ldc: 28.3 mH
 >     Les: 26.5 mH      (effective at Fres)
 >
 > I used a whip length of 0.401m, that's length of whip, not the
 > height of its top.

I observed that with the thinnest segments of the antenna extended
I need 41.1 cm. With the thickest segments extended, 36.3 cm.

 > I would say we have reasonable agreement with your system, but the
 > waveforms don't quite match the scope trace in
 >
 >   http://www.coe.ufrj.br/~acmq/tesla/tefp.html
 >
 > I have an extra RF cycle in each beat.  Does this graph
 > represent the system as documented, or was this taken with the
 > coil base connected to the primary?

The waveform there is correct. The mode is something between 7:8
and 8:9. The ideal waveform is somewhat distorted by losses.
Before the first notch, it looks as mode 7:8, but there is an
extra cycle before the second notch. I can get that same waveform
simulating a lumped system with k=0.121, Rprim=3 Ohms (mostly due
to my square wave generator), and Rsec=180 Ohms (skin losses only).

 > Do you have something with which to measure the two actual mode
 > frequencies to see how close we are?  If so, can you look for the
 > 3/4 wave resonance too and check that?  The 3/4 wave should be at
 >
 >      primary gap open: 861.7 kHz
 >   primary gap shorted: 866.6 kHz

I measure 272 kHz and 307 kHz, corresponding to:
k=((f2/f1)^2-1)/((f2/f1)^2+1)=0.1205.
Your values correspond to k=0.1183.
To see the higher resonances, the easiest method that I found was
to tune the primary an look for complete beats with the usual square
wave excitation at the spark gap. For this coil I can
easily see many resonances, before losses eat everything.
This is what I see (1 us/div):
3/4 wave: http://www.coe.ufrj.br/~acmq/tesla/normal34.jpg
5/4 wave: (missing...)
7/4 wave: http://www.coe.ufrj.br/~acmq/tesla/normal74.jpg
9/4 wave: http://www.coe.ufrj.br/~acmq/tesla/normal94.jpg
11/4 wave: http://www.coe.ufrj.br/~acmq/tesla/normal114.jpg
Frequencies:
1/4: 290 kHz
3/4: 840 kHz
5/4: ---
7/4: 1600 kHz
9/4: 1960 kHz
11/4: 2300 kHz
All this with the regular top load. Note that the energy transfer
time is practically fixed, with the coupling coefficient decreasing.

Antonio Carlos M. de Queiroz