Re: Flat secondary measurements

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

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Hi Terry,

When it comes to analysing flat spiral configurations, the only
tricky bit facing us is dealing with the large amount of distributed
mutual capacitance between primary and secondary.  Negligible effect
in a flat-primary/helical-solenoid TC, but for flat-pri/flat-sec we
will need an additional coupling matrix in the equations for the
dual resonator.  This is a non-trivial change, so can we focus on
just the solitary flat secondary for now?

> I have tried changing the Guassean surface before and have always
> gone back to the sphere!  If it works, computer time is of zero
> concern there.

Fair enough.  The physics is OK either way.

John Tomacic wrote:
> Surprisingly, the inductance of the flat spiral coil is 60% higher
> for the same length of wire. In this case the length of wire is
> 1478 feet.

Interesting.  I've always assumed that a flat spiral would have less
inductance than the same length of wire wound into a solenoid. But
I've just run some numbers through acmi,

flat {
   radius1 0.01 
   radius2 0.50 
   height 0
   conductor 0.5 mm ; radius
   turns 392
}

helix {
   radius 0.25
   height1 0
   height2 0.49 
   conductor 0.5 mm ; radius
   turns 392
}

(the 392 turns chosen to give 0.8 spacing ratio with 1mm diam wire
 over a 49cm winding)

Both require about 25cm x 2 pi x 392 centimetres of wire, but
we get

  Flat           Helical

L 55.7 mH        52.9 mH 
R 13.99 ohms     13.72 ohms.

So not as much as your 60%, but still an increase, which is not what
I would have guessed.   John, can you let us know your coil
dimensions and measurements that lead you to that amazing 60% ?

> Since the wire resistance is the same for both coils,
> is it safe to conclude that the Q of the spiral would be 60% higher
> seeing that Q is proportional to XL/R?

That would be nice!  But the proximity effect will interfere with
that increase, in a way that I don't know how to calculate.

Could the experts with the inductance formulae please check my flat
spiral calcs for sanity?

Cheers, 
--
Paul Nicholson
--