Re: Resonance, and now magnifiers

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

Original poster: Terry Fritz <teslalist-at-twfpowerelectronics-dot-com>

Hi,

At 05:26 PM 7/19/2004, you wrote:
> >From another thread:
> > Using a large top load capacitance ... helps force the
> > best resonant point near the 1/4 lamda point.
>
>This doesn't make any sense, although something along these
>lines is often heard from experienced coilers.  It sounds as
>if we're supposed to choose the topload C so as to make the
>resonance a 1/4 wave.  Larges toploads are certainly good,
>but the justification in terms of tuning to some quarter-wave
>point is faulty.
>
>It's a 1/4 wave resonance regardless of how much extra C,
>if any, is added. We can list some of the changes that occur
>as top C is added:-

All the 1/4 wave stuff comes from folks trying to use 1/4 wave antenna 
models to predict Tesla coil parameters.  It sort of works a little...  But 
Tesla coils are not at all 1/4 wave antennas...  Lumped LC models with 
Medhurst and a little fudging work very well for the needs of tuning a 
coil.  Tesla coils are not true LC lumped networks either, but the models 
there work vastly better for day-to-day needs.  Tesla coils with arcs have 
pretty substantial power dissipative top loading too...


>* All the mode frequencies move down.  The fundamental (1/4
>wave) moves down more than the overtones.
>
>The remaining points all refer to the 1/4 wave mode...
>
>* The coil current becomes more uniform.
>* As a consequence, the effective inductance becomes closer
>to the low-frequency inductance, Ldc.   For coils with h/d
>more than about 1.5, this means the effective inductance
>increases.
>* Because Les moves closer to Ldc, the coil's effective
>capacitance becomes closer to the Medhurst value, so the
>calculation Fres = 1/(2*pi*sqrt(Ldc *(C_med + C_top)) gives
>a more accurate prediction of Fres as top C is increased.
>
>The benefits to the coiler of the heavily toploaded coil
>are, possibly:-
>
>* Now the fundamental is much lower than the overtones, so
>we may find less of the bang energy is going into these higher
>modes.
>* The large top C makes plenty of charge and energy available
>for streamer formation.

Yes!! ;-))

>* The frequency is more accurately predicted by a simple
>calculation involving C_medhurst.

The large C dominates, and makes the simple models work better.

>* The topload controls the E-field gradient around the coil,
>protecting the top turns from breakout, but also shapes the
>wider field to that breakout tends to develop horizontally
>outwards from the toroid, as opposed to taking the shortest
>distance (vertically downwards) to earth, or looping back
>into the coil itself.

Yes!!


>The secondary resonance itself offers no meaningful target by
>way of a specific value for top loading.  It will happily
>display quarter-wave behaviour with any top C.   I think the
>choice of a large topload is made purely to obtain a favourable,
>or even optimum, coupling between the secondary and the
>discharge/streamer load.

It appears that any top C, regardless of secondary wire length, works fine 
if tuned.


>Perhaps I can throw in a few words about magnifiers?
>For these comments I'll treat the joint secondary-tertiary
>as a single resonator.
>
>I've described how end-loading pulls down the fundamental much
>more than the higher modes.  With the magnifier, we exploit
>the next higher mode of the resonator - the 3/4 wave, as well
>as the fundamental.  The idea is to tune the 3/4 wave mode so
>that it will reach the voltage peak of its alternating cycle
>at the same instant as does the fundamental. This will increase
>the output voltage beyond that of a similar coil whose 3/4 wave
>mode is just left to some random tuning.
>
>To tune the 3/4 mode, we must pull its frequency down from
>the unloaded value so that it has the correct frequency
>relationship to the fundamental.   Applying end loading pulls
>both modes down and gets us part of the way.  But obviously
>we need to control the 3/4 wave frequency independantly of
>the 1/4 wave.  We do this by applying more external capacitance,
>but this time attaching it near the other voltage maxima of
>the 3/4 wave mode - say about 1/3rd the way up the resonator.
>
>This 'middle' capacitance affects the 3/4 wave mode more than
>the 1/4 wave mode, so we now have the means of tuning each mode
>with some independence of the other.  This tends to be done by
>splitting the coil at the appropriate point and maintaining the
>connection with a piece of wire (the 'transmission line' of
>magnifier terminology).  The resonator now finds extra
>capacitive loading near its 3/4 wave voltage maxima: the top
>end-effect C of the secondary, plus the transmission line C,
>plus the lower end-effect C of the tertiary.
>
>If done correctly, the 3/4 wave mode is now timed to reach
>a voltage peak simultaneously with the fundamental after a
>certain (design choice) number of RF cycles have elapsed.
>
>Why bother going to all this trouble?  Well the 3/4 wave
>mode is excited anyway, to some extent, whether we like it
>or not.  So rather than waste that energy, we might as well
>try to use it.   The extent to which higher modes are excited
>in any coil depends on how the primary induction is distributed
>along the coil.  If we want to achieve high coupling (for what-
>ever reason) we cannot do so by spreading the primary along
>the secondary, for reasons of voltage breakdown.  So we have
>to apply strong coupling to just a short region of the
>secondary at its cold end.  It's this highly end-concentrated
>coupling which tends to put a greater proportion of the bang
>energy into the higher resonances of the secondary.  Therefore
>it's a natural evolution of the TC to try to tame and exploit
>these.[*]

I do wonder how much useful extra energy is there and if we will waste 
energy trying to get at the 3/4 wave's energy?  Big magnifier's do well 
since they are so big a two coil system just does not "fit".  So breaking 
the coil up into smaller parts has a big physical advantage.


>I've described all this to show how a bit of 'distributed'
>theory can be applied to understand the motivation for
>constructing magnifiers. (I must point out that when coilers
>think about magnifiers, they don't usually think about them in
>the kind of terms that I've used above).  Antonio has
>thoroughly documented this tuning of multiple resonance
>networks using the lumped model,
>
>  http://www.coe.ufrj.br/~acmq/tesla/magnifier.html
>
>(There are of course 3 modes in operation in the magnifier,
>not just the two I mentioned above.  The primary coil adds
>adds another relevant degree of freedom and when this is
>coupled to the secondary we find an additional 1/2 wave mode
>at work along the secondary-tertiary.   This too is tuned to
>reach a top-volts peak simultaneously with the other two.) [+]
>
>You can see some modelled results for the mode spectrum of
>Thor, in the last two graphs in
>
>  http://www.abelian.demon.co.uk/tssp/tmod.html
>
>This isn't a magnifier, just a heavily toploaded TC, but it
>shows the predicted levels and current distributions of each
>of the resonances.

I think we need to consider streamer loading too.  The lossless models are 
neat, but streamer loading and losses changes things from the easy to 
calculate world...


>Coiler's don't tend to take much notice of the higher order
>resonances of either primary or secondary.  Many perhaps don't
>even realise they are there - mistaking the behaviour of the LC
>model for that of the real coil.  Some coilers will admit that
>the secondary has lots of resonances, but will insist that
>the primary has only one, thinking perhaps that because it is
>more 'lumped' it is working in some basically different way.
>
>I should think most of the time this lack of awareness isn't
>any problem, after all the coils work.  But I think it's
>useful to build up a mental picture of the distributed
>resonance, if only for the coiler's satisfaction of having a
>deeper understanding of the coil's behaviour.
>
>And there's always the hypothesis that some of this HF
>activity may contribute to the racing arc phenomena.
>If for example, one of the primary resonances happens to
>be similar in frequency to one of the secondary resonances.
>Say the first primary overtone collided with, say, the
>5th overtone of the secondary, there's nothing to prevent
>the two coils transferring energy back and forth at these
>high frequencies.

The higher order stuff "may" dramatically affect spark gap quenching and 
streamer propagation!!!


>Admittedly the various overtone amplitudes are small compared
>with fundamental.  But set against this is the fact that
>the peak-trough distance of the overtone standing waves
>spans fewer turns along the coil than does the fundamental -
>fewer in inverse proportion to the number of quarter-waves.
>
>Plus they sit atop the pedestal of the large 1/4 wave voltage,
>so at the very least they will eat into the coil's breakdown
>'headroom'.
>
>Racing arcs tend to be cured by small adjustments to topload
>height or coupling, eg raising the secondary or lowering the
>primary.   When we model these kind of changes, we don't see
>any great change in the voltage gradients reached.  Nor do
>models show any real gradient problems under out of tune
>conditions.  One wonders then why the real coils seem to show
>such sensitivity to coupling and topload height with respect
>to racing arcs.   One thing our models *dont* account for is
>the effect of primary overtones.  It may be conceivable that
>the small adjustments mentioned are having the side effect
>of shifting the mode spectra of one or both coils with the
>unwitting consequence of removing a nasty collision of HF
>resonances.

Racing arcs and super powerful primary to secondary arcing just are not 
well explained now....  I have watched primary to secondary arcs blow 
through 1/4 inch G-10 I am just stunned that they can exist and do 
that!!!  The energy concentration in those arcs is doing something 
"odd"!!!  I have always turned to "transformer action", but the models 
don't seem to support that well...  Suppose 1 foot up the coil, there was 
suddenly a 6 inch low R path to ground?....  Would the arc energy be "BIG"?


>Finally, returning to the issue of large toploads.  A point
>not mentioned earlier is that the higher overtones of the
>secondary are available at the top of the coil at a rather
>low impedance, thanks largely to the top-C.  It might be the
>case that this low impedance HF energy contributes to streamer
>heating during breakout, helping to keep things cooking nicely
>in between the rather lower frequency ebbs and flows of the
>quarter-wave current.  Magnifiers, for example, are likely to
>have higher overtone amplitudes than regular TCs, and so might
>be predicted to give brighter streamers for a given streamer
>length.
>
>Anyway, there must be some food for thought and experiment in
>there somewhere.
>
>[*]  This phenomena of 'concentrated induction near at the end
>of the coil' leading to 'greater proportion of energy in the
>higher overtones' is a fairly general phenomena.  I like to
>demonstrate it with an effect familiar to guitar players. As
>the string is plucked closer to the bridge, the tone becomes
>brighter as the overtones (almost harmonics in this case) take
>up a greater proportion in the mix of string vibrations that
>give the guitar its tone.  The guitarist is changing the shape
>of the initial (triangular) displacement of the string. The
>essential physics is that the mix of mode amplitudes (and phases)
>must be such that the superposition of all the modes at t=0 along
>the string (or coil) equals the initial displacement distribution.
>This is a Fourier-like synthesis in the spatial domain, with the
>normal modes of the string as basis functions.
>
>[+] As Antonio shows, the idea extends to include many overtones.
>As more and more overtones are tuned into coherence at the
>voltage peak, the TC operation becomes more pulse-like compared
>with the leisurely sinusoidal energy transfer of the normal TC.
>--
>Paul Nicholson
>--

Cheers,

         Terry