From: Paul
Date: Thu, 28 Sep 2000 11:52:34 +0100
Subject: [TSSP] Progress report 28th Sep 2000
New Version
-----------
A new version 0.3c of software and documentation is available,
although the programs are probably still not worth attempting to
download and run.
Reference Measurements
----------------------
Thanks to Terry Fritz, Mark Rzeszotarski, and Malcolm Watts, we
now have a valuable database of reference measurements. So far
only samples have been run through the model, which is enough
to reveal some software problems. More later on this.
Mutual inductance estimates
---------------------------
Mark Rzeszotarski thoughtfully provided formulae and tables from
F.W. Grover, 'Inductance Calculations', 1946, which just happened to
be exactly what was needed to fix a problem with Mpt, the mutual
inductance matrix estimate. The program was using a formula based
on Grover's tables taken from an electrical engineering handbook.
Unfortunately the handbook author had had some troubles converting
cgs to SI units, plus a few other things, so the results were a
little out. I've incorporated Grover's tables directly and the
mutual inductance estimates are much improved. The normalising
factor sigma now differs from unity by only a couple of percent at
the most. This is a great improvement - it allows Mpt to be
computed for any solenoid shape so long as all the turns are
concentric. Not only that, but it also opens the door to detailed
modelling of the coupling due to a primary winding.
The most prominent result of this fix is a slight increase in the
strength of mutual inductive coupling at long range along the coil,
resulting in higher propagation velocity at the higher overtones and
positive errors of a few percent in the estimate of f5.
Internal capacitance
--------------------
The above fix highlights the weakness of the interpolation of
internal capacitance along the coil. At long range the capacitance
is slightly overestimated and at short range, the estimate breaks
down completely. Previously this was being worked around by leaving
out the short range capacitance altogether, which more or less
compensated the long range overestimate. A slight code change now
includes more of the short range capacitance which provides a little
extra dispersion to compensate for the mutual inductance increase.
Frequency estimate errors
-------------------------
The net effect of the two changes described has altered all the
frequency estimates. Comparing average errors of toroided and
unloaded coils before and after the changes:
Toroided No toroid
before after before after
f1 -0.7% -1.2% +1.9% +0.5%
f5 -0.2% -1.9% +1.6% -1.0%
The model on average predicts frequencies slightly lower than
measured, and predicts a little too much dispersion.
Series resistance, input impedance and Q factor
-----------------------------------------------
The crude assumption that all the current is confined to a surface
layer of depth equal to the standard skin depth has been replaced
by an integrated loss based on exponential decay of current with
depth. The resulting AC resistances now agree quite well with
tables taken from Grover.
Some errors were found in the Q factor calculations - a factor of
sqrt(2) was missing from the stored energy calculations (converting
from phasor values to instantaneous V and I) and also the stored
energy of the internal capacitance was being counted twice.
With these two errors fixed, the program is beginning to show some
agreement on Q factor at f1. Comparing Q factor estimates with
measurements supplied by Malcolm Watts:
Q meas Q model (adjusted for source impedance)
f1 393 395 coil 1, h/d = 4, spacing ratio 0.92
f1 329 239 coil 2, h/d = 4, spacing ratio 0.49
The predicted Q factors agree quite well with calculations based on
Medhurst's table, yet for some reason fall well short of the
measured Q in the case of coil two.
Coils at high elevation
-----------------------
Data supplied by Mark Rzeszotarski and Malcolm Watts both provide
reference measurements for coils at high elevation. When compared
with the model, the frequency estimates are a long way out, eg:
Measured Model Error
f1 885 kHz 1081 kHz +22% MZ small28a
f1 600 kHz 708 kHz +18% MW coil 1, h/d=1
The hope was that high elevation would emphasize the contribution
of internal capacitance but instead, the external capacitance is
proving hard to determine, partly due to ambiguity of the external
field in the absence of a well defined ground plane, and partly due
to some problems with the laplace solver. It is not clear at this
stage whether further work on the laplace solver can fix this.
Meanwhile the only option is to confine the model to coils with
base less than one coil height above a definite ground plane.
Ground plane eddy current losses
--------------------------------
On hold, while I'm still waiting to receive a heap of papers on this
subject - our wonderful antiquated underfunded library system here
in the UK takes weeks to obtain journal articles.
Software Changes
----------------
Right now the laplace solver tlap.c is undergoing a complete
re-write. The existing version is so slow that gaussian
elimination would produce a quicker solution for the field!
Essentialy the nested iteration multigrid will be replaced by
a V-cycle coarse grid correction multigrid. Hopefully this
will produce a more accurate estimate of the lower spatial
frequency modes of the field (these are more important at high
elevation), as well as a giving big improvement in run time.
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------------
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Regards All,
--
Paul Nicholson,
Manchester, UK.
--
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.