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>

Comparing measured with modelled frequencies,

        Measured        Modelled
   1/4:   290 kHz        293 kHz    +1.0%
   3/4:   840 kHz        862 kHz    +2.6%
   5/4:   ---           1314 kHz
   7/4:   1600 kHz      1716 kHz    +7.3%
   9/4:   1960 kHz      2162 kHz   +10.3%
  11/4:   2300 kHz      2574 kHz   +11.9%

This characteristic of increasing +ve error with higher modes tends
to occur with coils where the wall thickness of the coil former is
significant.  The extra dielectric of the tube wall increases the
internal capacitance over the value calc'd by tssp.  The increase
affects the higher modes more because the effect is proportionally
greater for short range Cint than for long range, so the higher
modes see a greater capacitance increase over the modelled values.

I don't think there's anything wrong with any of the given
dimensions, and we'll just have to live with these Fsec offsets.

Antonio wrote:
 > Coupled resonant modes...

      Measured    Modelled     Error
  F1:  272 kHz     278.3 kHz   +5.6%
  F2:  307 kHz     313.1 kHz   +2.0%

Yes, that highlights the major discrepancy with the modelling, which
I'm sure accounts for the remaining error in k:

 > k=((f2/f1)^2-1)/((f2/f1)^2+1)

      Measured    Modelled     Error
   k:  0.1205      0.1173      -2.7%

I suspect we haven't got the primary resonance modelled correctly,

      Measured    Modelled     Error
  Fpri: 290 kHz    295.5 kHz    +1.9%
  Lpri:  59.82 uH   57.2 uH     -4.4%

Your L1 measurement was at HF, so I guess 59.82uH is the total
primary circuit inductance, rather than just Lpri?

If I cheat and use 15.05 turns instead of 14.7 (thus changing Lpri
but expecting k to remain the same because the overall dimensions
stay fixed), I get mode frequencies: 274.9 kHz and 309.6 kHz, and
a coupling of 0.1183.  The 'geometric k' will have stayed the same
but the change to Lpri seems to have altered the 'effective k' when
the coupled resonance is modelled.

So much for cheating. It moved k the right way, but I think in
reality some of the extra Lpri must be coming from primary circuit
inductance.  Depending on just where this is, it could increase or
decrease k.   For example if the primary circuit actually loops
around the secondary 15 times, with 14.7 turns in L1 and the
remaining 0.3 of a turn as an extra wide radius arc, it might
actually increase the geometric coupling, rather than reduce it as
an 'off-axis' extra inductance would do.

I think to resolve this 3% discrepancy on k, it will be necessary
to measure parameters of the primary circuit in a little more
detail.

For me, I'm interested to see whether how the three types of
coupling coefficient relate.  We have:

  a) The geometric k, computed by Neumann and acmi, measurable at low
  frequency.  Measured/modelled = 0.108/0.108;

  b) The modified geometric k, modified by applying Neumann with a
  predicted or estimated secondary current profile. Un-measurable.
  Modelled = 0.112;  (*)

  c) The effective k, calculated by the full model, measured by beat
  waveform examination, or dipping the mode frequencies.
  Measured/modelled = 0.1205/0.1173;

I'm interested to see how close (b) comes to (c).  I think they
should agree if the correct current profile is used.  However, I'm
sure that the secondary current profile accounts for the major 10%
difference between (a) and (c).

(*) I say unmeasurable, but perhaps if the sec base was driven with
CW at the sec Fres, with primary o/c, the induced primary voltage
could then be measured and compared with secondary base current to
obtain M.  Vtop of the secondary would also have to be measured to
obtain Les, and then k = M/sqrt(L1*Les).  But with a percent or so
error in each measurement, the overall result may not be accurate
enough to determine the quality of (b) as an estimator of (c).
--
Paul Nicholson,
Manchester, UK
--