Re: eddy current with secondary coil

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

Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk> 

Chris Swinson wrote:

 > Is there a program which will calculate secondary coils with
 > space windings? and maybe even further do the math to work
 > out various resistance and current effects of litz wire also

Further to earlier informative answers,

Skin effect is fairly easy to calculate, but the extra proximity
effect is difficult.  There's a nice method for the case where
wire radius is less than the normal skin depth,

  http://thayer.dartmouth.edu/inductor/sfdj.pdf

but this doesn't really apply to normal TC secondaries.  Last I
heared the professionals were still working on proximity loss...

Tssp has never been able to predict coil losses and Q factors
partly because of the above.  Best we can do is get to within
a factor of two either way on the coil's AC resistance.

Following a series of experiments by Terry,

  http://www.abelian.demon.co.uk/tssp/qvar070402/

it became clear that precise calculation of the coil's
contribution to the overall resonator loss was not so important,
because

  a) the overall loss has so many other (often quite variable)
     factors.
  b) the operation of TCs is not much affected by Q factor, until
     the Q factor goes below a few tens or so.

On secondary effective inductances, there are two values of
interest:

  Les: equivalent series inductance, which you can determine
       by simultaneous measurement of base current and top volts.

and

  Lee: equivalent energy storage inductance, determined by
       simultaneous measurement of base input impedance and
       Q factor.

which are both frequency dependent and differ from Ldc.

Les is used in the formula f=1/(2*pi*sqrt(LC)) and Lee is
used in the formula Vout = Vin * sqrt(Ls/Lp).

Both values can be calculated quite accurately from the geometry
of the coils, by first solving for the current distribution,
and then calculating the total induced voltage and total
stored energy (respectively) by the usual integrals, but with the
current weighted by the known distribution.

(For many TC's the difference between Les and Lee is not worth
loosing sleep over - the Medhurst C will approximate both to 5%
or so. But the difference becomes important with small h/d or flat
coils, and is interesting theoretically.)

In my limited experience, the secondary coil contributes only a
modest proportion to the total loss.  Eg my big coil ought to
have a Q somewhere between 700 and 1200, depending on proximity
loss guestimates.  But in reality the Q is usually between 100
and 300.  Thus slight improvements in secondary Q produced by
say, space winding, are diluted by the other system losses and
may not be very noticeable.  Indeed, if the space winding is
achieved by reducing the overall number of turns, the inductance
may reduce by a greater factor than the AC resistance, thus
actually reducing the Q!

Ed wrote:
 > Has anyone ever worked out the complete solution including
 > effect of capacitance on current distribution?

Tssp looked at this a while ago.  Cap between neighbouring
turns contributes little (1%) to the total effective capacitance,
instead it is the overall shape and size of the coil which is
the main determinant.

  http://www.abelian.demon.co.uk/tssp/pn2511.html

gives an intro to the physics of the distributed reactances,
and calculation of voltage and current profiles.
Tssp gives the differential equations for a general solenoid,
and these are solved for the V/I distributions by first turning
them into matrices, and then finding the eigenvectors.

See Terry's key experiments in

  http://www.abelian.demon.co.uk/tssp/tfcp260302/
  http://www.abelian.demon.co.uk/tssp/pn2510/

for comparisons of predicted with measured current and
voltage distributions, respectively.

On the topic of eddy currents, earlier answers are correct in
their assessment of the impact on low frequency inductance -
the secondary inductance will go down very slightly.

Bart also described the effect on the HF inductance, which will
increase when the toroid is added, but as Bart explained, this
is the consequence of the extra loading capacitance making the
current distribution more uniform and is not an eddy current
effect.

The effect of eddy loops (in the topload, ground, strike ring,
whatever) is to reduce the low frequency inductance of the
secondary, usually by only a small amount, say 1% or less.
Whether this is accompanied by extra loss depends on the
resistance and inductance of the eddy loop(s).  But in view
of the small coupling the eddy losses cannot be very great.

Chris Swinson wrote:
 > I do want to maximize RF power is anyone has got any ideas
 > on this ?

Yes, but you have to tell us what load the RF power is to be
delivered to.  From that we can tell the load impedance and how
it couples to the coil.  Then if it's a CW coil, you have to
let us know the RF source output impedance.  Then we can select
a secondary with the correct characteristics to match the two,
for a specified operating frequency.

Dimensions and turns of the secondary would be chosen so that
source matches to load at a loaded Q of say 10 or 20, against
an unloaded Q of say 100-200, to give about 90% efficiency.

Antonio wrote:
 > The exact effect on the coupling coefficient of a Tesla
 > transformer of the nonuniform current distribution in the
 > secondary (and maybe in the primary too) could be predicted.

Tssp software computes the coupling coefficient taking into
account all the nonuniform currents and voltages. It does so
by first computing the inductance and capacitance matrices,
then solving for the normal modes, then k is computed from the
two beat frequencies in the normal way. I see no hope of closed
solutions for these things but the numerical models are good
enough to demonstrate that we understand the physics.  Even at
modest spatial resolution (such as implemented in GeoTC), the
accuracy is probably better than all other available models.

--
Paul Nicholson
--