# Re: [TSSP] Measured vs. Operating coil coupling?

```Original poster: "Paul by way of \"Terrell W. Fritz\" <terrellf-at-qwest-dot-net> by way of Terry Fritz <twftesla-at-uswest-dot-net>" <paul-at-abelian.demon.co.uk>

Terry,

4. With a large toroid, the top current can be a large proportion of
the base current, eg 70%, so that there can be a sizeable current
available for induction at the top.

5. The induced currents in a shorted turn, toroid, or ground sheet
are not in themselves a bad thing - in fact they can be quite useful
if carefully managed. Its the I^2R loss in the shorted loop that
really counts, and whether or not the shorted loop destroys the Q of
the coil depends on the impedance match between the loop resistance
and the rest of the system.  For any shorted loop there will be a
worst possible loop resistance that will have,  for the particular k
factor involved, the max impact on system Q, and that worst resistance
will be the matched resistance.  If the loop R is below or above this,
the impact on Q will be reduced accordingly. Thus a shorted loop which
has a very low R will only have a tiny effect on Q,  even though the
induced current can be quite high,  as seen by the apparent reduction
of the secondary inductance. To demonstrate this qualitatively I've
generated a set of response curves for a resonating solenoid coupled
to a shorted turn:

http://www.abelian.demon.co.uk/tssp/tmp/eddy-coupling.gif

The green curve is the worst-case scenario - the resonator is well
matched to the shorted loop resistance of 1K ohms and the Q is very
low. The blue and red traces show the response with a loop resistance
of 100K ohms and 10 ohms respectively, and you can see that, when we
are well away from the 'matched' resistance, the effect of the
shorted turn on the Q is much reduced.

So the moral is - if you're going to have a shorted turn, make it a
good one, eg the nice wide conductor of the toroid. There is an

6. The regime in which shorted loop R is well below the 'matched' R
is commonly used for screening in RF circuits, eg the screening cans
around an RF coil, or the silver plated inner surface of a cavity
resonator. The beauty of this is that the big currents stirred up in
the screen emit their own mag field, of a polarity which tends to
cancel out the total mag field outside of the screen, in other words,
although the screen material is non-magnetic, the eddy currents that
it carries do in effect act as a magnetic shield, preventing the mag
field from extending beyond the screen.

7. I'm currently exploring the controlled use of eddy currents in a
ground sheet - you may recall that I layed out some 30m^2 of sheet
Ali under my coil, in a pattern which avoided induction of circulating
currents, in an attempt to raise the Q by more efficiently catching
the external displacement currents of the coil. Well the rise of Q
was small - certainly not the vast improvement I hoped for. I have a
coil with an AC resistance of around 40 ohms, which forms a resonator
with an effective loss of around 150 ohms. I can account for another
50 of those, so there are still around 50 ohms unaccounted for in the
loss budget. I'm assuming now that this missing loss is due to eddy
currents stirred up in the soil beneath the coil. My next experiment
will be to lay out the ground sheet as a continuous conductor, to see
if the 'screening can' effect will noticeably improve the system Q by
cancelling out the mag field extending down into the ground.

> the current profile along the secondary at 60Hz AC may be different
> than the operating profile

Yes, I've prepared two graphs showing the V/I profiles of Marco's
Thor system when driven by a CW voltage applied to the (untuned)
primary terminals, as modeled by tssp:

http://www.abelian.demon.co.uk/tssp/tmp/tviplot.thor-p.60.gif
http://www.abelian.demon.co.uk/tssp/tmp/tviplot.thor-p.66030.gif

for drive at 60Hz and at 66.03kHz respectively. Clearly we can expect
the k factor at the operating frequency to differ from that measured
with low frequency currents, although of course the mutual inductance
is the same in both cases since that is frequency-independent and is
fixed by the geometry of the coils.

As you know, tssp's time domain simulator is currently under test, so
hopefully over the next few months we can turn up some reliable
statements about how the effective operating k relates to the mutual
inductance M. Note that the familiar formula k=M/sqrt(LpLs) only
applies to coupled resonant circuits where the two separate coils are
tuned to the same frequency, and when the system is driven near to
that frequency. Away from resonance, or with mis-matched resonators,
the k is a more complicated expression, so we are on shaky ground if
we try to talk about k at 60Hz - better to stick with M.

On the whole, I'd expect a modest Fres shift - say of order 1% down,
on making a radial cut through the toroid, but no noticeable
difference in performance. I believe this has been reported by those
who have taken the trouble to test this.

Just to add one final piece of speculation, there is some possibility
that the shorted turn of the toroid may be of some slight benefit, in
that it's resistance may dampen the higher resonant modes rather more
than the two desired operational modes either side of Fres, thus
perhaps usefully suppressing the unpleasant consequences of higher
mode excitation, eg racing arcs and difficult quenching.  Plenty of
research to be done on this topic.

By all means forward these comments to the pupman list if you wish.

Cheers,
--
Paul Nicholson,
Manchester, UK.
--

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