NEC-LIST: axial-mode helix

Re: Axial-mode helices

> ... They suffer from the well-known problems of loops coupling with
> free ends ... parallel wires ... Transverse currents can also be
> significant.

I have not seen any evidence of loop problems with single-wire NEC
helix models. There are no loops unless the turns are shorted
somewhere. There can be problems with helix models due to parallel
wires in the point-matched NEC solution. A Galerkin code such as that of
Harrington, Popovic...(?) may give better results. However, NEC seems to
give reasonable results for typical single-conductor helices. For the
axial-mode helix on page 268 of Stutzman and Thiele's "Antenna Theory
and Design" the NEC pattern was in reasonable agreement with the
measurements of Maclean and Kouyoumjian. Their helix was on a finite
back plane (not specified in the book) and the NEC helix was on an
infinite PEC plane. Also, the NEC pattern was slightly different in the
plane containing the source and helix end, and in the plane normal to
that. A better average gain (~2.0) was obtained by including a short
vertical wire between ground and the helix for the source (2 segments
and 0.1 wavelengths) rather than connecting the helix directly to the
ground plane. This source wire had an effect on the sidelobes but not
the main beam. The pattern comparison will be in the November ACES
Newsletter "Modeler's Notes".

A while back we used NEC and the Rao, Wilton, Glisson PATCH code to
study the propagation constant on helices in the pass band of ka from
about 0 to 0.8. One technique was to model a long helix with a 1 volt
source a few segments from one end. The current was saved on a file.
Then a post processor combined the original current and the current
reversed end-to-end and multiplied by a complex constant that
represented a terminating impedance. The complex constant was adjusted
with an optimization program to minimize the standing wave, and thus
determine a matched load. The remaining traveling wave was then matched
with a linear fit in magnitude and phase to determine the propagation
constant. The result for propagation constant in the pass band of the
helix was in close agreement with the solution of the tape-helix
determinantal equation for a tape with width equivalent to the wire
radius (radius = width/4). The typical characteristic of normalized
propagation constant --

----------------
Bn = beta*a/(k*a*sin(pitch angle))
   = (vel. of light/vel. of current along axis)/sin(pitch angle)
   = 1.0 for current at velocity of light along the wire path
----------------

versus ka is a broad inverted U, with Bn slightly less than 1.0
in the center of the pass band, and decreasing (faster wave vel.) at
the low and high ends. This very close agreement with the tape-helix
equation held for pitch angles from 2 to 10 degrees and wire
diameter/pitch from 1.e-8 up to 0.25. However, for diameter/pitch=0.25
it was necessary to use 80 to 160 segments per turn to get close
agreement (on an expanded scale) with the tape-helix result. With
"only" 40 segments per turn Bn at the center of the inverted U was too
low by about 0.3% -- relatively small error, but big compared to the
thinner helices. With 160 segments per turn the NEC segments far
exceeded the normal radius/length limit, but the result for propagation
constant seemed to hold up. Probably could not trust the input impedance
though.

The PATCH code, also gave very close agreement with the tape-helix
equation for thin tape widths, but for tape width/pitch=0.5 the Bn vs k
characteristic developed a rounded M shape with errors also a few tenths
of a percent. We tried modeling the tape with a strip of pairs of
right or isosceles triangles with the same result. Increasing the
number of patches per turn increased the M-shaped error, rather than
decreasing it as in NEC. However, as the number of strips (of pairs
of triangles) in width was increased from 1 to 6 the Bn characteristic
converged to the tape-helix result. With multiple strips in width the
patch model showed loop-current problems, blowing up by many orders of
magnitude at the helix ends. However, these loop currents decayed
rapidly away from the ends, and did not present a problem in determining
the propagation constant. With a single strip in width the loop
currents could not flow, as in the NEC single-wire model.

The tape-helix determinantal equation assumes that phase is constant
in planes normal to the helix axis and ignores transverse currents.
The single-strip PATCH helix puts some constraint on phase, but am not
sure just what. Also, there is no transverse current. The
multiple-strip PATCH helix allows the phase to do what it wants, and
also allows transverse currents. The NEC wire model did not allow
transverse currents. Many uncertainties here, including the accuracy
of the tape-helix determinantal equation for large tape width.

While this technique could not be used in the stop band, where an
axial-mode antenna operates, it did provide a validation of the NEC and
PATCH solutions. The errors seen in propagation constant were very
small for antenna purposes. In the stop band the NEC current showed the
expected multiple decaying modes. I did not try comparing with the
tape-helix solution (and had trouble finding solutions of the
determinantal equation.) Also tried a Prony analysis of the near fields
along the axis of the helix that showed forward and backward waves and
a velocity-of-light mode that increased toward the upper end of the
pass band, and apparently became the radiating mode.

It would be interesting to hear whether people who have problems with
helix models get bad pattern shape, impedance and absolute gain, or
everything.

Jerry Burke
LLNL
Received on Thu Nov 14 1996 - 20:23:00 EST