Re: Resonance, and now magnifiers

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

Original poster: "Dr. Resonance" <resonance-at-jvlnet-dot-com> 


Perhaps I should say it another way:  A large topload helps to reduce
unwanted small resonances at frequencies higher than the fundamental
frequency.  Even though these resonances may be small they effectively
"steal energy" that should go towards the fundamental resonance point in the
sec coil.

Also, all resonances, however small or large, can begin "beating" against
each other and form small standing waves which can interfere (destructive &
constructive interference) with the lower fundamental resonance.  These
unwanted frequencies can produce unequal potentials across the sec coil, and
specifically in the case of small toploaded resonators, along with too much
coupling, can produce the dreaded "racing sparks".

Dr. Resonance

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