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Re: bi-polar (center-fed) TC

Hi Malcolm and All,


At 10:07 AM 5/3/99 +1200, you wrote:
>Hi Brent,
>           Very interesting read:
>
>> Original Poster: Brent L Caldwell <stretchmonster-at-juno-dot-com> 
>> 
>> 
>> 
>> Ralph:
>> 
>>     In your post you mentioned your calculations of the inductance and of
>> the coupling constant.  
>>     Here at Texas Tech, several professors and post-doc's were trying to
>> create a mathmatical model of a tesla coil's behavior, to use as a
>> starting ground for a math model of another, similar pulsed power
>> project.  Anyway, one thing that everyone quickly realised was that the
>> classical, physics II formulas for calculating solenoid inductances don't
>> work well for inductors operating at high frequencies.  It seems that
>> inductance is frequency dependent, too.  
>
>There are a a few frequency dependencies, most notably the ESR of 
>the coil. The model they need has been produced by the Corums some 
>time ago. It is a 1/4 wave transmission line model with a low 
>impedance termination at the driven end and open circuit/capacitively 
>loaded termination at the output end. Note that the Corum's output 
>voltage projections have conditions attached: steady state sinusoidal 
>drive and no terminal breakout. These conditions do not apply to gap 
>excited coils. They take no cognisance of the fact that a shot of 
>finite energy can only do so much voltage-wise with a defined 
>terminal capacitance.
> 
>      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!! :-))

	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...

	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.

>
>>     I haven't done a great deal of investigation of any of the wheeler
>> equations, to see how they measure up, so I can't speak for them. 
>> Furthermore, I don't know how programs like WinTesla do their
>> calculations, and I have never used any of them, so I can't say anything
>> about them either.
>>     At any rate, most of the highly mathmatical professors and post-docs and
>> engineers here at Tech did not like the idea of trial and error tuning,
>> because it wasn't "sophisticated" enough for them.  They all tried to
>> calculate the inductance using formulas mentioned above, and NONE of the
>> numerous Ph.D's in physics and electrical engineering, who worked on our
>> tesla coil, ever got it to work.  
>>     The only person here that could ever get the coil to resonate was a lab
>> technician self taught amateur scientist with only and eighth grade
>> education, (kind of reminds me of Maxwell).  This technician knew very
>> little math, needless to say, and was not distracted by all the fancy
>> stuff, and wasn't afraid to tune by trial and error.
>>     On this list you may find people who rely heavily on theoretical
>> calculations, and I imagine this post will stir up some dirty looks and
>> comments from those who do, but I can tell you that I have personally
>> observed that equations, as sophisticated and complicated as they may be,
>> do not always produce useful results, especially with tesla coils.  
>>     If you do use equations and fancy math stuff, I know that you must be
>> very careful to use them right, as they can be quite deceptive and
>> misleading sometimes.
>
>   In the days when I knew nothing of the real electrical behaviour I 
>regarded the secondary as a lumped inductance and hunted for a 
>formula to give a figure for self-capacitance of a single layer helix 
>connected to ground at one end. My goal was to find a formula that 
>gave a predictable and reliable means of calculating a capacitance 
>value that would enable a secondary to be *designed* to resonate at a 
>specific frequency and eliminate a plethora of formulae that failed 
>to work for most if not all cases. The only formula I found that 
>worked was arrived at by Medhurst. I have found that for the typical 
>range of h/d ratios we work with, this formula taken together with 
>Wheeler's inductance formula does give the result desired. However, I 
>now regard this formula as something of a kludge because the whole 
>inductance does not come into play in a coil without a topload due to 
>the uneven current distribution in the coil.

	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 :-)).

	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.
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 :-)).

>    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 :-))

	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

>
>Malcolm
>