RE: Calculating secondary resonance of bipolar coils

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

Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>" <free0076-at-flinders.edu.au>



On Mon, 8 Jan 2001, Tesla list wrote:

> Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>"
<paul-at-abelian.demon.co.uk>
> 
> Darren Freeman wrote:
> 
> > I would have expected the two halves to be rather well magnetically
> > coupled leading to a much greater inductance (looking at only half
> > of the coil) by nearly a factor of two. I can't see how calculating
> > the thing with half of the coil is going to give the correct answer.
> 
> That's right. As you say, mutual inductance (and capacitance) between
> the two halves prevents accurate analysis as two quarter wave
> sections, unless the coil is split and the parts separated so that
> their fields do not significantly overlap.
> 
> The half wave, or bipolar coil, is quite easy to model in free space,
> the difficulty comes when you want to calculate the frequency for 
> operation horizontal above a ground plane. Determining the external
> capacitance distribution is a time consuming process with this
> geometry, although far from impossible.

I am very interested in TC modeling on computer. I have checked out your
website (very briefly) and I think that it is going to keep me going for a
while. I can recommend to every avid coiler to at least have a skim of it
since there's some interesting stuff there (I won't spoil it for you - go
check it out!).

> 
> The 'half-wave' is the simplest possible mode of resonance of a
> solenoid, and is the natural 'ground state' of an open circuit coil
> in free space, or placed horizontally above a ground plane. In this

By this are you implying multiple modes of oscillation as in quantum
mechanics? Would it then be possible to achieve multimode oscillation?
Can the system be considered to be linear or is the dielectric of the 
enabel going to saturate and result in some interesting coupling between
various modes of oscillation?

> mode the current maximum is exactly at the center. As the coil is
> tilted towards the vertical (wrt the ground plane) the nice symmetric
> shape of the current profile is altered as the external capacitance
> becomes asymmetric. The position of the current maximum moves away
> from the center towards the end with greatest external C. Eventually
> when the base of the coil comes close to the ground, or is connected
> to ground, the current peak ends up at about 5 or 10% of the way up
> from the base of the coil. This is now the familiar 'quarter-wave'
> resonance, although it can be seen from the above description that we
> haven't actually changed modes, it's just a continuous deformation of
> the shape of the lowest resonance from the case of perfect symmetry of
> the balanced bipolar to that of the completely unbalanced monopolar
> coil, with a gradual reduction of Fres of the order of 30% in the
> process.

Once again I'm listening with interest. Well, reading with interest at
least =)

> 
> > I am assuming that the 1/4 wave theory is a myth and that the
> > circuit acts as a lumped inductance and capacitance, both of which
> > are demonstrated at:
> >
> > hot-streamer-dot-com/TeslaCoils/MyPapers/MyPapers.htm
> 
> No, its the lumped inductor which is an idealisation which doesn't
> occur in nature. A 'lumped inductor' does not display the spectrum of
> resonances present in a real inductor. In the past some have
> erroneously argued that there is a choice to be made between operating
> a coil in 'lumped' or 'transmission line' modes, which is a very silly
> debate.

The only source of knowledge that I had previously been inclined to
believe was Terry's phase measurements and his voltage profile
measurements. I was quite convinced that the lumped inductor model was
appropriate for explaining the profile he obtained, since the mutual
inductance between turns is greater in the middle and he found a minor
increase in volts/turns towards the middle but no '1/4 wave' effect, which
would be a sinusoidal profile wouldn't it? As you say the lumped
inductance model is only an approximation, but it did look like it worked.
Not to worry though, I'm happier with your more complete explanations
anyway.


> 
> See 
>  http://www.pupman-dot-com/listarchives/2000/August/msg01119.html
> 

I did. It was interesting. Some of it was stuff that you keep in the back
of your mind but never think about normally, thanks for reminding me about
the significance of transmission line theory in coiling!

> Terry's paper demonstrates the phase equality between top and bottom
> of a quarter-wave transmission line very nicely.
> 
> See Terry's more recent comments on this topic at
> 
>  http://www.pupman-dot-com/listarchives/2000/August/msg01116.html

I read the copy attached. Thanks. (I refer the reader to the message I am
replying to if the link above fails, since I didn't repost it)

> [Terry, this seems to be the correct URL for your comments on
>  topsync.html, but it does not show any text, is there a problem with
>  the archives?]**
> 
> Cheers
> --
> Paul Nicholson,
> Manchester, UK.
> Secondary modelling project http://www.abelian.demon.co.uk/tssp/
> --

Visit that site!!

> 
> ** Aparently there was some sort of problem with this post in the archives.
>  I put the original post below:
> -----------------------------------------



Thanks for the informative reply.

Darren Freeman