Overtones and velocity factors

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Gerry wrote:
> The boundary conditions allow a voltage max at the top and
> voltage min at the bottom.

Yes.  And in between, alternating voltage maxima and minima
at 1/4 wave intervals.

> The corresponding frequencies (proportional to 1/lamda) dont
> scale the same, as you say, because the velocity factors are
> different.

Yes, both frequency and wavelength must be measured or
calculated (for each mode the numbers will be different) in
order to characterise the behaviour.  To make matters even more
interesting, the velocity (and therefore lambda) varies a little
along the coil, depending on the particular distribution of
reactance in any given setup.   For example, added shunt C, such
as that due to the proximity of a primary winding or a strike
ring, causes a reduction of velocity in that region, shortening
the wavelength a little, but these are small effects that only
show up in precision measurements and models.

> What causes the velocity factor to get less than one???

My guess is the dominant factor is turn-to-turn capacitance,
which is rather high in a closewound coil.  As frequency goes
up, the series inductance reduces to something more like the
self-L of the wire as the mutual inductance contributions
coming in from other turns begin to cancel out.  The velocity
values begin to depend more on wire diameter and the pitch and
much less on h/d.  The calculations for velocity and Z would
be similar to those for a twin wire feeder but because of the
close proximity of the wires, I would guess the velocity factor
might go as low as that of a coax cable.  I've never pursued
this in any detail because the frequencies where these factors
become significant are very much higher than TC operating
frequencies.

> when others in the group use the 3rd harmonic terminology are
> they speaking loosely about the 3/4 wave overtone or the 3rd
> harmonic in the primary waveform??

If they talk of '3rd harmonic' they should mean three times the
fundamental drive frequency, not an overtone of the resonator,
but - the terms are often used carelessly.

> Lastly, in terms of measurements, is the only data you are
> seeking the resonant modes of a coil??? or are you also after
> the spectral content of a racing spark???

The spectral content of a racing spark is what we're after (in
the other thread).  The 'racing' frequencies will correspond with
one or a bunch of resonant modes of the system.

> Maybe if we capture the fields using Terry's antenna and
> digital scope to store a one shot capture, one can post
> process that waveform to get the spectral contents.  Would
> this work...

Might do ok, but not so good.  I asked for base current capture
because the high frequency content is more easily seen in that
waveform.   In the top voltage, or in a distant E-field probe,
the HF content will be rather harder to see and extract.  The
reason for that is the lower in-coil impedance of the higher
overtones.   Those signals propagate with a smaller V/I ratio
than the lower modes, so appear in a smaller proportion in a
voltage or E-field probing.  By measuring currents instead, the
opposite applies - the HF stuff is easier to see.

The E-field probe is worse than a direct voltage probe because
it is taking a kind of average of the E flux emanating from the
resonator.  Higher modes have several voltage maxima, each with
opposite polarity of instantaneous voltage to the next, so
tending to cancel one another out at a distant E-field probe.
This is the same 'averaging' effect that I mentioned in the
previous post which causes reduction of long range mutual
capacitance.

So, there are good fundamental reasons for choosing base
current capture.   In addition, it is also easy to calibrate
and easy to screen.

Dest wrote:
> Marco Denicolai`s first coil (h:d = 4.58) for comparison
> http://www.pupman.com/listarchives/1998/June/msg00181.html

>     Freq         Mode    Ratio    |   Freq       Mode    Ratio
> a.  148.4kHz    1/4 wave   1.0    |  324 KHz      1/4     1.00
> b.  353.4kHz    3/4 wave   2.38   |  813 KHz      3/4     2.51
> c.  513.8kHz    5/4 wave   3.46   |  1475 KHz     5/4     4.55
> d.  666.4kHz    7/4 wave   4.49   |  1766 KHz     7/4     5.45
> e.  819.8kHz    9/4 wave   5.52   |  2053 KHz     9/4     6.34

Yes, something suspicious about Marco's results there.

>     Freq        Mode         Owvf  |   Freq       Mode    Owvf
> a.  61.9kHz     1/4 wave     1.72  |   324 KHz     1/4    1.84
> b.  157.9kHz    3/4 wave     1.46  |   813 KHz     3/4    1.54
> c.  229.7kHz    5/4 wave     1.27  |   1475 KHz    5/4    1.67
> d.  294.4kHz    7/4 wave     1.17  |   1766 KHz    7/4    1.43
> e.  355.6kHz    9/4 wave     1.09  |   2053 KHz    9/4    1.29

The owvf reveals it nicely, since it should change monotonically,
but doesn't: surely a mode has been missed.

>     Freq      Mode  Ratio  Owvf  |  Freq      Mode  Ratio  Owvf
> a.  61.9kHz   1/4   1.00   1.72  |  324 KHz   1/4   1.00   1.84
> b.  157.9kHz  3/4   2.55   1.46  |  813 KHz   3/4   2.51   1.54
> c.  229.7kHz  5/4   3.71   1.27  |  1166 KHz  5/4   3.60   1.32
> d.  294.4kHz  7/4   4.76   1.17  |  1475 KHz  7/4   4.55   1.19
> e.  355.6kHz  9/4   5.75   1.09  |  1766 KHz  9/4   5.45   1.11

> like it?

Yup. Nice job - that fits well.  But something is still wrong,
the owvf numbers above are too large for h/d=4.58;  For that
geometry, 1/4 wave should be 1.78;  3/4 should be 1.40;
5/4 should be 1.19; all give or take 5%.   This error is because we
don't know how many turns Marco used, so the wire length is unknown.

We can estimate it, though:- Let W = unknown wire length.  Using
the frequency measurements and the known dependence of velocity
factor on h/d, we have:-

   W/1 * 4 * 324/300e3 = 1.78, so W = 412 metres;

   W/3 * 4 * 813/300e3 = 1.40, so W = 387 metres;

So he must have used 400m of wire, = 1165 turns, give or take
a few percent.

I put Marco's dimensions, with 1165 turns, and some guesses of
the experimental arrangement, into our tssp model, to get

 Mode  Measured   Model     Error
 1/4   324 kHz   328 kHz    +1.2%
 3/4   813 kHz   809 kHz    -0.5%
 5/4   n/a      1179 kHz
 7/4  1475 kHz  1502 kHz    +1.8%
 9/4  1766 kHz  1854 kHz    +5.0%
11/4  2053 kHz  2175 kHz    +5.9%

The high +ve error of the model at the 1/4 wave suggests that
some stray top C was present, say a few of cm of trailing
wire: 1pF would be enough.  That estimate of 1166 kHz for 5/4 mode
looks like a pretty good one.   The +ve error at the higher modes
is quite common with this model - it doesn't allow for some E flux
passing vertically through the coil former material.

> you must be extremely careful when reading archives and must
> constantly do the reality check on all info

Yes, and not just archives, but current posts, theories, results...

You can see from the question that Marco posed, and some of the other
posts from that era, that nobody knew then how to work out the mode
frequencies properly and the naive expectation was that they would
be harmonic.
--
Paul Nicholson
--