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Re: Secondary Theory (Was Bipolar Coil)




  Malcolm, Terry, All-

  I agree when Malcolm and Terry say only measurements can solve this
problem. With the JHCTES program I show how the exact frequency, total
secondary capacitance, and toroid capacitance can be determined. For the
preliminary TC design a graph is provided to find the approximate toroid
capacity. This is entered as an input in the program. The program output
gives the approximate frequency for building the coil.

  After the coil is built a test is made to find the exact frequency. The
program toroid capacitance (input) is then adjusted to show this exact
frequency in the output. When the adjustments are complete you will now also
have in the outputs the exact total secondary circuit capacitance and the
actual capacitance of the toroid when placed on the secondary coil. Even if
the toroid is an inner tube covered with foil. What a fantastic program! (:>)

  John Couture

----------------------------------

At 01:30 AM 5/7/99 -0600, you wrote:
>Original Poster: "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz> 
>
>Hi Terry,
>
>> Original Poster: Terry Fritz <twftesla-at-uswest-dot-net>
>> 
>> Hi Malcolm and All,
>> 
>> 
>> At 10:07 AM 5/3/99 +1200, you wrote:
>
><snip>
>> >      In attempting to apply purely classical lumped values to the 
>> >coil the analysis will come unstuck because it misses the electrical 
>> >behaviour at different frequencies.
>> 
>> 
>> My God Malcolm!!  Still quoting from the Corum's on 1/4 wave helical
>> resonator theory!! :-))
>
>Just trying to give the armchair analysts their dues ;)
>  
>>     The secondary does act like a lumped parameter model with a
different set
>> of rules.  I have shown directly that there are no current phase shifts in
>> the secondary as would be predicted by the Corum's 1/4 wave theory.  I
>> directly disproved their coherence theory too :-)).  In fact, their 1/4
>> wave theory does really hold, but when one plugs the "right" numbers into
>> their complex equations, you end up pretty much back at the lumped
>> parameter model.  The Corum's used values that they took from some radio
>> inductor theory that does not apply to our coils.  This caused them to
>> develop their rather complex theory based on none real data.  The rest is
>> history...  Your observation that they assume steady state conditions, is a
>> major flaw in their analysis...
>
>And not the only one either. I don't for a moment think that a 
>uniform transmission line models the secondary accurately. I am of 
>the opinion that it looks like an inductor at the base trending to a 
>capacitor at the top. I once modelled this with real life components 
>to find the grading that worked. However, I thought it might be 
>interesting to see what a different group of academics makes of the 
>model. I have to admit that the lack of phase shift in current from 
>bottom to top has been difficult to make sense of unless the real 
>electrical wavelength of the coil matches the physical one. The 
>measurements suggest that this is indeed the case.
>
>>     Today, lumped parameter models have shown to be exceptionally accurate.
>> In fact, even some very subtle harmonic effects seen in real life can be
>> predicted using advanced computer models (the ones I don't tell anybody
>> about ;>)).  The theory and real data agree very well.  The old 1/4 wave
>> stuff, just like the old wire length stuff (sorry Nikola), simply has no
>> basis and cannot be demonstrated in real life.  Today, we have the tools to
>> actually see voltage and currents in operating coils with excellent
>> accuracy.  The results have been modeled and the whole thing makes sense
>> and works.
>> 
>>     However, make no mistake.  The secondary is not simply and inductor
and a
>> capacitor.  Even though it "acts" like a lumped system, it is really a
>> complex combination of electromagnetic fields.  However, these effects are
>> not related to the old 1/4 wave theory at all.  The E-Tesla program of mine
>> really proved a lot of the new theory in that it relies on being able to
>> predict inductances, capacitances, and field distributions on the secondary
>> system.  If it used the wrong theory, that program would fall apart like a
>> house of cards.
>> 
>
><snip>
>>     Wheeler arrived at his famous (and very accurate) formula by
methodically
>> testing many many coils and fitting his results to an equation with a set
>> of constants.  As John would say, "empirically".  Unfortunately, there is
>> not and will not be a simple equation for this that is based on none
>> empirical results unless somebody changes the present state of mathematics
>> radically.  Only by computers crunching trillions of calculations and
>> simulating physical fields, can we now predict what is going on.
>> Theoretically it is not complex, but to actually come up with the numbers
>> is far beyond simple equations other than the empirical ones (I'm starting
>> to sound just like John aren't I :-)).
>
>I don't have the slightest problem with Wheeler's equation. I am 
>completely satisfied that it works. I think Medhurst arrived at his 
>theory retrospective to a large number of measurements which did
>something similar to our measurement of the resonant frequency 
>in order to deduce Cself.
>
>>     Your observation that the current lessens along the length of the
coil is
>> valid but this has nothing to do with 1/4 wave theory as defined by the
>> Corum's work.  Current is simply absorbed into the surrounding area around
>> the coil in the form of stored potential energy as a charged capacitance.
>
>IMHO that can only happen without phase shift if the line is really 
>very much shorter electrically than the 1/4 wavelength. Right?
>
>> There are basic equations for this distribution but I forgot what I called
>> them at the moment (delayed cosine distribution ??).  It is odd that this
>> lessening current does not seem to change the secondary's inductance.  The
>> real results seem to demonstrate this very firmly...  This should be
>> studied more, preferably with the help of the heavy theoretical folks (I
>> hope Mark is listening :-)).
>
>I don't expect the inductance to change because of the uneven current 
>distribution. It is fixed I would say.
>
>> >    In short, the formula gives utterly reliable results for 
>> >predicting the resonant frequency but I question its accuracy as a 
>> >description of the real electrical behaviour of the coil. I also 
>have 
>> >reason to suspect its accuracy at extreme (e.g. 20) h/d ratios 
>> >although it does show a capacitance minimum at an h/d of 1 (a result 
>> >which corresponds with highest unloaded coil Q) and a tendency for 
>> >the L/C ratio to degrade towards what one would expect that of a 
>> >longwire to be either side of h/d=1.
>> 
>>     The big problem with the Medhurst equation predicting a coil's resonant
>> frequency, is that Tesla coils like big top loads.  When a top terminal is
>> added, the capacitance distribution changes radically and no simple
>> equation can predict what it will be given the wide variety of top loads we
>> use today.  I don't think we are going to see the "Tesla coil with an inner
>> tube covered with aluminum foil equation" for resonant frequency any time
>> soon :-))
>
>I think that the fact that the total apparent capacitance is less than 
>Ctop + Cself when summed individually suggests that there is 
>something wrong with Medhurst's picture of Cself. However, it is 
>demonstrably true that there is shading by one of the other going on 
>also. Testament to that fact is that a given terminal when put atop 
>one coil has a measured capacitance completely different to that
>which it has when put on top of a secondary of a different diameter.
>I still think an equation can be arrived at for a given pairing by 
>considering the geometries.
>
>>     As far as I know, E-Tesla (and it's converted forms) is the only program
>> that can predict a secondary's resonant frequency, given only a set of
>> dimensions, from pure field theory.  It does not use lookup tables or any
>> experimental data other than basic electromagnetic constants.  It certainly
>> does not use any 1/4 wave theory, in fact, it only serves to disprove it...
>> 
>> This is obviously a big subject that could go on and on.  If it is of
>> interest, we can start a new thread an go for it...
>> 
>> Cheers,
>> 
>>     Terry
>
>Always interested. As you rightly point out, measurement must be the 
>final arbiter of theory.
>
>Regards,
>Malcolm
>
>
>