NEC-LIST: Small Loop Antenna Close to the Ground

The results reported by Chris Teixeira for a loop at varying height
over Sommerfeld ground are a good way of testing NEC for this problem,
and it sounds like the results are what I would expect. In fact, I am
surprised that the results for the loop with ka=0.1 were good, but
don't know how close that got to the ground. I would run these tests
for varying height for any loop, even with ka approaching 1.0. For
perfectly conducting ground the problem is no worse than in free
space, but the limited accuracy of the Sommerfeld integral evaluation
means that you cannot get accurate results in many cases for loops
close to real ground.

Dick Adler says that NEC can be used with the Sommerfeld integral
solution for receiving antennas over real ground, but I have not tried
this.

The basic problem with small loops is that the Moment Method matrix
becomes ill-conditioned when the current has been expanded in
localized basis functions, as in NEC. Each basis function has a lot
of + and - charge, and this charge must add up to nearly zero on a
small loop, resulting in numerical cancellation. Similar problems
occur in matching the field. Without ground, you can run the double
precision code, and starting with 14 place accuracy you can have a
fairly small loop and still have a few places of precision left. The
Sommerfeld integrals for ground are typically evaluated to no more
than about five places of accuracy for the single or double precision
code to avoid too much computation time. In NEC these values are
stored in tables and the actual values for the solution are obtained
by interpolation. The result of this table lookup is accurate to
about four places. This works well for most structures, but it does
not take much cancellation in the solution until there is no accuracy
left.

The way to fix the small loop problem is to include one basis function
that is a constant current around the loop (with no charge.) Then
this basis function dominates when the loop is electrically small, and
the ill-conditioning is eliminated. We have done this with good
results in a version of NEC for loops in free space, but not over
ground. One problem in doing this is tracing all possible loops in
various complicated structures. Since we did not get a good algorithm
going for tracing loops, the loop basis function is not in NEC-4.

Jerry Burke
LLNL
Received on Wed Mar 15 2000 - 17:31:21 EST