Re: bipolar coil design

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>

Hi Lee, All,

Some comments on bipolars...

Lee Kohlman wrote:

> I am planning to build a bipolar coil.

> Secondary- 20 Awg wound 56" on a 6.25" pvc form,
> approx 1700 turns

> Secondary frequency- 112.76kHz

> Topload- 2x 6" aluminum dryer duct 30" diameter toroid,
> 1 on each end 4" from secondary windings.

The bipolar is a bit tricky because none of the available
design programs will handle them properly - they all expect
one end of the coil to be grounded, with the coil upright
and the topload on top.   In the bipolar coil, high voltages
appear at both ends, and the middle is roughly at ground
potential - and this alters the way the capacitance and
inductance is calculated.

The electrical resonance in the bipolar coil is what we call
a 'half wave',  which means that the oscillation is like a
see-saw: no motion (zero voltage) in the middle, but a large
movement (high voltage) at the ends.  This is a little
different to the traditional arrangement which vibrates more
like a ruler clamped to the edge of a table, so that only the
free end has a large movement/voltage, with the other end being
clamped to earth potential by the ground connection.  This
is called a quarter wave resonance.

But as you probably realise, the bipolar coil can be thought
of as two traditional quarter wave coils fitted back to back.
If you look at the see-saw from the pivot to one end, it looks
just like the quarter wave vibration of a ruler.  Hence a
reasonable procedure might be to run the calculations as if
you were building a quarter wave coil, but using only half the
length and turns of your full secondary.

This is reasonably valid because the bipolar coil, its voltages,
and the electric fields around it, are symmetrical about the
plane running through the middle of the coil.  This plane of
symmetry is at zero potential, and the result is that each half
of the system sees a 'virtual' ground plane occupying the place
where the real ground would be if that half of the coil was
working by itself as a quarter wave resonator.

If I calculate the quarter wave resonance of a 28" coil, using
850 turns, with the base 1.5" above ground (so as to leave a 3"
gap in the bipolar, as Dr. Resonance suggests), fitted with
one of your toroids, I get around 168 kHz.  Two of these, placed
back to back would (to an approximation) give a half wave
resonance, also at 168kHz.

Lee, this is rather higher than the one you calculated with
JavaTC.  I get about 118kHz if I use the full length coil for the
calculation, but this is incorrect - you must use half the length
and half the turns if you are running a program intended for a
quarter wave, for the reason given above.

The actual frequency is likely to be lower than predicted, by
some difficult to calculate amount.  This is because the two
toploads are probably going to be closer to ground than they
would have been when perched on top of a vertical coil.
Therefore there will be more end capacitance present in the
actual system than the calculations allow for.

To mitigate this and other effects, it's a good idea to design
in more than the normal amount of tuning range in the primary
coil, especially on the low side.  The 168kHz is likely to be
an upper limit because all the well understood but hard to
calculate effects act to pull the frequency down from this
ideal value.

Lee wrote:
> Primary- 6 turns .25" copper tube flat spiral 4.5" id, 8" od
> at center of secondary
> Cap- .03uF

This design will resonate at a frequency much too high for the
secondary resonance.  The coupling coefficient to the secondary
is also quite high.

I think the primary coil design must be the most tricky bit of
the whole project.   Not least of which because that nice symmetry
of the voltages, with zero in the middle, is only an ideal case.
In practice the secondary voltage will find its own balance - at
a point dependent on how well matched the end capacitances are,
and on how evenly the streamers are formed at each end.  The zero,
therefore, may be drawn away from the center of the coil by
any asymmetry present - such as drawing an arc from one end to
ground.

This is not good news for the primary, and to cope with this
inevitability, it would be a good idea to build in a lot more
voltage breakdown capability than normal.  If the inner diameter
of the primary was raised to say 12-14", the inductance increases,
the coupling reduces, and the voltage breakdown tolerance is
raised.    Putting in the 3" gap is a good move - it reduces the
otherwise excessive coupling and increases breakdown tolerance.

BTW, a convenient side effect of the fairly large length/diameter
ratio of this coil, and also the 3" gap, is that the inductance of
each half can be taken to be half that of the complete coil, with
only about 2% error (or 6% error without the 3" gap).  As a result
the half wave frequency of this bipolar is very close to sqrt(2)
times the quarter wave frequency of the whole coil.  This is less
true of smaller h/d ratios, unless a gap is used.
--
Paul Nicholson
--