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Re: bi-polar (center-fed) TC

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.

>     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.
    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.

Malcolm