Re: Measuring self-capacitance directly (Re: flat secondary)

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

Hi Bart, All,

Many thanks for taking the trouble to put the formulas to such a
fair test.  Your setup of the coil above a ground plane under an
open sky reproduces the modeled conditions just about perfectly.

The size and h/d of your coil places it pretty well central in the
landscape of coils covered by the formula, so we would expect it
to do well.  The formulas will work noticeably less well with small
coils and short h/d, my guess is they will over-estimate the Fres.

>  Ldc=133.78mH, Les=112.52mH.

The utilisation factor of this inductance, by which I mean the ratio
Les/Ldc, is 113/134 = 0.84, which is typical of this middling h/d. 
This ratio gets bigger with smaller h/d, and with short coils, the
ratio can exceed unity, sometimes by 10 or 20%.  Interestingly, the
flat spiral coils are coming out with a very high Les/Ldc, eg 140%,
but only if they are driven from the rim, ie center hot.  See some
modeled data for Marc's 20" flat coil,
http://www.abelian.demon.co.uk/tssp/mm250202/
which compares rim feed with center feed.  

The rim feed arrangement has a very high transfer impedance of 132kV
per amp of base (err, rim) current, which is around double the value
typically found in TC solenoid secondaries.

Note the current maximum in the rim-fed occurs around 12% of the
way in from the rim, and the current at this point is double that of
the base current - which is the cause of the high Les.  In turn, the
high current maximum is due to the strong effect of internal
capacitance (the C between distant turns) acting radially in the
outer half of the winding.  The rim-fed flat coil behaves a lot like
a short h/d solenoid.

Plenty of interesting experiments to do here: A direct measurement
of Les would be a good and easy start, to demonstrate that it really
is that much higher than Ldc.  For a more challenging experiment:
Measure the current profile of a rim-fed flat spiral, to see if it
matches the predicted curve.  This would require a specially
constructed coil, with about 10 or so series tapping points, through
which small resistors can be inserted in series with the coil.

Oh, and finally, much of the error seen when applying Medhurst C to
find Fres, comes from using Ldc instead of Les.  A calculated Les 
together with the Medhurst C should do a better job.
--
Paul Nicholson
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