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Re: Magnifier system
Malcolm,
Well thought out post as usual! Comments are inserted below...
Tesla List wrote:
>
> >From MALCOLM-at-directorate.wnp.ac.nzSun Nov 17 22:55:20 1996
> Date: Mon, 18 Nov 1996 12:54:42 +1200
> From: Malcolm Watts <MALCOLM-at-directorate.wnp.ac.nz>
> To: tesla-at-pupman-dot-com
> Subject: Re: Magnifier system
>
> Hello Jeff,
> You ask....
>
> > From what I have read, I thought the secondary coil could be
> > electrically modelled as a series RLC circuit in some sense because
> > of the way it behaves when driven at different frequencies.
>
> Adding a large topload is lumping capacitance at one end so the
> system does tend to a series RLC. It wouldn't be pure RLC series
> unless all secondary Cself was eliminated (impossible). Also, since
> the primary couples mostly into the bottom end of the resonator,
> waves propagate up and down the structure.
>
> > And to
> > get maximum output voltage at the terminal, we should drive it at
> > the 1/4 wavelength frequency to produce a voltage maximum at the
> > terminal, but you pointed out that this is the electrical length of
> > the wire (not physical) when we wind up the coil. So how exactly is
> > electrical length mathematically determined?
>
> As a matter of convenience I use the quantities that appear to us as
> inductance and capacitance to predict the fundamental vibrational mode
> of the coil. They work well in practice. However, as the Corum's
> have shown, these things can be shown even more convincingly by
> examining the structure as a waveguide. I have serious doubts whether
> their predicted voltages for cap discharge systems are correct though.
> After all the discussion on conservation of energy recently I don't
> think you can ignore the fact that there is real measurable
> capacitance in the system and there is a fundamental limit on the
> voltage that can be obtained with a given amount of energy. Here's
> an interesting one to consider: We can measure the coil inductance
> with a fair degree of accuracy as a lump, and lo and behold, when we
> apply Medhurst's Cself formula, we find that the lumped L and Cself
> tell us with a good degree of accuracy what the fundamental resonant
> frequency will be. BUT, the inductance is not all effective in
> practice for a resonator with no topload. Consider: current in the top
> turns is all but zero, so not all the L is effectively there. What is
> the actual Cself then that makes the coil resonate as though our
> calculations suggest it is? I think this is where the Corum's view of
> things departs from the recipe approach and more accurately describes
> resonator action (more said below).
>
Comment:
At the 1/4 wave frequency, a base-excited resonator's input impedance
appears
to behave _identically_ to a series RLC with C=(Ctoroid + Cself). From a
theoretical standpoint, a the Corums' helical resonator model may more
accurately predict behavior at other frequencies as well. Woever, from a
practical standpoint, the fact that a base-driven resonator "looks" like
a simple RLC makes things a WHOLE lot simpler when designing or
measuring a system.
> You mention: > > >Mutual inductance
> > >between turns gives uo a multiplier and the huge drop in physical
> > >length of the coil (winding height) over the longwire considerably
> > >reduces the capacitance of the structure, so much so in fact that
> > >the increase in inductance is insufficient to compensate for the drop
> > >in capacitance for the actual wirelength to resonate as though it were
> > >an isolated longwire.
> >
> > How is uo multiplied?
>
> By mutual inductance between turns. No significant equivalent coupling
> exists for a longwire between portions of its length.
>
> > And isn't the capacitance due to the effect of the
> > wire or loops of the wire above ground?
>
> Experiments I and others have done suggest the coil self-C is that of
> a (not-so-well) isolated cylinder - i.e. inter-turn capacitance
> doesn't count. What I read in the Colorado Springs Notes suggests
> Tesla didn't understand this, at least initially. He thought of
> various schemes to reduce Cself which, had interturn capacitance been
> the culprit should have worked. If you look up the coil, each turn is
> shielded from all but its immediate neighbors above and below so you
> have a stack of tiny capacitances in series. The bottom turn appears
> to have quite significant coupling with ground as it has no effective
> shielding below it.
>
> > And for the magnifier system, how exactly does this system multiply
> > the base fed input voltage to produce a higher output voltage?
>
> NOTE TO ALL: What I'm about to say here is my opinion, is not fixed
> in concrete (yet), and is open to any other opinion that explains
> things better. It's a bit wordy since I use such opportunites to get
> get my own thoughts in order and also submit these to peer review for
> critical examination. I am not afraid of being found incorrect so all
> views welcomed.
>
> It is important first to note that what is presented to the base
> of the resonator is not just voltage but current as well.
> Both the resonator used as a TC secondary and magnifier are the
> same and accumulate whatever energy is imparted by the
> primary/oscillator by wave action.
> The bottom turn in each has the highest current of all turns
> since it subjected to the greatest capacitive loading of all turns.
> As you travel up the winding, the loading becomes progressively less
> and if you have no terminal, the top turns pass virtually no current
> at all (under no spark conditions). Each turn is inducing a current in
> its neighbours and hence voltage across its neighbours. IMO the
> volts/turn should be rather high at the base and virtually nil at the
> top, but the sum of the voltages is great, and there is a volt/turn
> gradient that tapers off as one reaches the top of the winding i.e.
> the top turn barely contributes. I should note here that an analysis
> by Greg Leyh suggests that mutual inductance between the turns does
> not greatly contribute though and I'd be very interested to hear what
> he has to say about this.
Comment:
With no top-loading and no breakout, the above argument is reasonable.
The Corums' open-circuit helical resonator model probably comes closest
to modelling actual behavior. An unloaded helical resonator behaves very
much like an open-circuit high-impedance transmission line driven at its
1/4 wave frequency. The amplitude of the voltage as we progress up the
coil should increase approximately as the sine of the phase distance
from the bottom, rising to a maximum at the top (90 degrees). Fully 50%
of the output voltage is reached only 1/3 of the way up the coil! This
certainly agrees with your statement that the maximum volts/turn
gradient is at the base of the resonator. Similarly, the current
amplitude should vary approximately as the cosine, with the maximum at
the bottom, decreasing to 0 at the very top. However, fully 50% of the
coil base current would still be present 2/3 of the way up the coil.
The actual behavior inside an unterminated resonator is a little more
complex, since self-C is greater at the bottom of the coil, and the
resonator's transmission line impedance is thus not constant with
respect to height above the base. As a result, the actual voltage and
current
distributions will differ from the sinusoids in a uniform line. The
practical
impact of this effect for simple constant-diameter helical resonators is
reduced secondary "Q" (broader 1/4 wave peak, lower voltage
multiplication).
Some speculation:
Once we heavily topload the system, the series RLC model should become
more accurate in describing internal resonator behavior. As heavy
top-loading begins to overshadow the effects of coil self-C, the
resonator begins to behave more as a lumped L. This should more evenly
distribute the secondary current through the entire length of the
secondary, resulting in a more linear distribution of voltage from
bottom to top, and reducing, somewhat, the inter-turn voltage gradient
at the base.
> It is my opinion that the magnifier and standard two coil system
> should show equal outputs *if* they can be coupled to their driving
> systems by the same degree. The reason for that contention is that
> in each system with the same bang energy and gap losses (all other
> losses being minimized), gap losses are reduced for tight coupling by
> virtue of the fact that it takes fewer cycles for the energy to be
> transferred to the resonator. I also assume that we are talking equal
> capacitance in the resonator systems. A smaller resonator is going to
> have a smaller Cself than a large one so should develop higher
> voltages for a given lump of transferred energy. This could be part of
> the reason for MAG #11- E's amazing performance.
Comment:
Right on! Elevating the tertiary coil will reduce self-C somewhat.
Turning it upside down (as Richard has done) will _significantly_ reduce
self-C due to "shading" by the relatively large toroid underneath.
Excellent insights into both theory and practice!
> I suspect that there are also considerable differences in
> resonator behaviour in the two systems. The classic 2-coil system
> exhibits all the characteristics of any double-tuned circuit system,
> namely side frequency generation and the upper frequency can excite
> the resonator to a voltage maximum part way down. I think it possible
> that choosing k carefully may minimize the chance of this happening
> because some resonator vibrational modes are favoured over others, the
> determining factor being reflections from the top end. This something
> that begs a serious investigation.
> However, an end-fed resonator should not produce this frequency
> split since it is not e.m. coupled so winding flashovers should be
> less of a problem for a given rate of energy transfer. Another one to
> check out with the scope.
> In practice, mag drivers can use very tight coupling because
> the driver prim/sec is fundamentally a transformer and built to
> withstand the strain of a high volt/turn gradient over the whole
> winding whereas the close turns in the resonator won't permit this
> without seriously bolstered insulation. K's of 0.65 have been reached
> in specially built accelerator coils however so it can be done.
> It is also important to remember that in the magnifier system,
> the base of the resonator is already at a very high voltage so less
> of a voltage across the resonator itself needs to be developed for
> the same total output voltage.
Comment:
Good points! There should be another benefit as well. Most coilers wind
their resonators using a single uniform wire gauge. This results in a
tradeoff: ideally the bottom-most (heavy current) portion of the coil
should be wound with larger diameter wire to minimize skin-effect
losses, while the lower-current upper portion could benefit from higher
inductance via more turns of finer gauge wire. By splitting the driver
and resonator into two optimal pieces, a magnifier provides the best of
both, while also offering the benefits outlined above.
> Spark output from any system is not dependent on voltage alone.
> Channel heating (current) and duty cycle (average power throughput)
> also play an important role in generating long sparks.
> I must try the following too (IMO it should work): charging a
> capacitor with one end connected to ground and discharging the other
> end through a gap to the bottom of the resonator should do similar
> things to a transformer driver circuit (don't try this with a
> normal Tesla power supply - there is *NO* isolation between the
> resonator and the 60 Hz circuitry).
Comment:
I'm not sure I understand the circuit you're describing. Could you
elaborate a little, Malcolm?
> Finally, I welcome comments on this analogy. Imagine
> the resonator as being like a beach. As one moves from bottom to top
> (deep to shallow), wave tops get higher and higher as the energy
> moves from the deep to the shallows. Unlike the resonator, the
> distance from deep to the shallows is considerably greater than a
> wavelength for a beach so the beach behaves more like a transmissive
> medium than a resonator (where energy is being bounced between two
> ends). It might go some way to showing how wave amplitude builds as
> energy travels from bottom to top though.
Comments:
Interesting analogy! About 5 miles from my home we have a "wave pool"
which consists of a large swimming pool and artifical "beach". The pool
has large movable plates (hydraulically driven) along one edge of a
pool. By timing very small movements of the plates to coincide with the
natural resonant frequency of waves in the pool, large artificial
breakers can be created at will. These plates would sort of be analogous
to the high current end of the resonator, and the beach the top end.
I also envision the resonator as behaving sort of like a fiberglass whip
antenna. With nothing on the far end, we can move the base back and
forth slightly at the natural 1/4 wave rate while otherwise holding it
rigid, thereby building up large oscillations at the far end of the
whip. By adding a
substantial weight (capacitance) to the far end of the whip, the
resonant frequency is now lowered. As we get the top swinging at the
lower 1/4 wave length, the relative amount of energy focused at the end
of the whip is much higher for a given amplitude.
>
> Jeff, thanks for asking some very interesting questions.
>
> Leaving the field wide open for comment, criticism and experimental
> evidence,
> Malcolm
>
> PS - I will be measuring spectral characteristics of mag systems
> before the year is out so hope to answer some of the questions above.
I look forward to the results! Thanks again for an interesting and
informative post!
Safe coilin' to ya!
-- Bert --