NEC-LIST: Some responses to comments received on "How does a wire antenna radiate?"

Dear fellow NEC-lister,

The responses to my posting on NEC-list of my version of how a wire
antenna radiates have been several and all rather thought provoking. I
don't have answers or suggestions for answers for all (and perhaps may
never) but lest silence imply bafflement, I have thought it prudent to
try to offer some kind of response, no matter how tentative, to at
least some of the comments.

Let me deal with those of Jos Bergervoet first.

Jos asserts that in making the statement that there is no NET charge
acceleration when an impulsive current passes along the antenna, I am
assuming that the derivative of delta function is zero. This is not
so. I certainly agree that charge acceleration is the derivative of
current and so I do need be looking for the derivative of delta
function. This, of course, is the double delta function (see, for
example, M J Lighthill, "Fourier Theory and Generalised Functions",
Cambridge University Press, 1964), two delta functions of equal weight
but opposite sign, the one following instantaneously upon the heels of
the other. It is for this reason that I say that two equal and
opposite and therefore cancellatory kinks are produced in the line of
force, so that no radiation results. Again I recommend a reading of
the paper of Glen Smith's to which I referred in my original NEC-list
contribution which deals with a finite difference version of this
problem in a way that's easy to follow.

With Jos's other point, my reply has to be this. The response of any
linear system to any excitation is the convolution of its impulse
response with the excitation. Hence once the impulse response is
known, one can say something about any other case, time harmonic or
what else. If the impulse response permits no other possibility than
radiation from the end of the wire, then that must always be so.

At this point I might also comment that due partly to time and
equipment deficiencies, I have not yet seen Jos's movies, but from the
favourable reception which they seem to have had, very much look
forward to doing so.

Let me now turn to Radios Toys. Let me first disclaim enough knowledge
of QED to be able to discuss the problem from this point of view, but
I don't think that we need to. An antenna with spikes would certainly
radiate all along its length and not simply at its ends; this follows
because it would present a constantly varying characteristic impedance
to the guided wave progressing along it. However the ability of the
antenna to couple to the modes of free space is determined solely by
its overall length, by how many of these modes have their cutoff radii
within its circumscribing sphere. And remember, it is coupling into
more than the normally excited number of these modes which produces
supergain. A hedgehog antenna (to coin a term) might have interesting
properties but it would not exhibit supergain.

This leaves me with Ed Miller, the last of those whom I'm going to
include in this response. The points that Ed raises are puzzling ones
and I can't pretend to have more than tentative answers, answers which
at Ed's hands may soon be demolished..

Let me begin by saying that I going to assume that the SCF can be
treated as a limiting case of the biconical antenna where the cone
angle has simply gone to zero, and certainly the biconical antenna, in
that it has a uniform spherical TEM mode characteristic impedance, is
capable of supporting a current distribution sinusoidal with
radius. First of all I'm going to advance what on Schelkunoff's
classification is a field theoretic argument (as opposed to the
circuit theory argument I used before) to attempt to show that
radiation along the length of the filamentary bicone is not to be
expected. It has defied me to state this in a way that I find
convincing in other than rather anthropomorphic terms, which may
offend some purists, but here it is.

Consider an impulsive primal disturbance. As the wavefront produced by
that disturbance expands, guided by the arms of the antenna, it cannot
"know" that it is going to be called on to radiate until it is
"surprised" by suddenly reaching the discontinuity produced by the
truncation of the guiding structure. It could not have been "expected"
to have "anticipated" the discontinuity about which it did not "know"
and to have started to radiate in advance of reaching it. If we close
off the possibility of other than end of structure radiation (or what
is equivalent in field terms, say that radiation starts at the
aperture, the boundary between the antenna's circumscribing sphere and
free space, something that would seem to make sense in the context of
Huygens Principle), then we are left to find some other way than
radiation along the length of the antenna to account for Ed's finding
that the total radiated power is bounded by log(kL).

I'm going to suggest that it's because, as the antenna becomes longer,
its aperture surface is moved further out so that an ever growing
number of the free space modes have their cutoff radii within it,
remembering that Parseval's theorem (or whatever its equivalent is for
the free space modes) tells us that the total power is the sum of the
powers in the individual modes. As more are are excited, is it
possible that more power can be conveyed away from the antenna, that
it becomes easier for it to radiate? I think that Ed himself helps me
a bit when he notes (if I read him correctly) that the charge at the
filament ends is independent of L. This is consistent with the current
pulse argument that I advanced in my initial contribution.

My last comment is on the constant radius cylinder dipole. I don't
think that Ed and I disagree that in this case there will be some
radiation from along its length as well as its ends. Whether I was
fair in describing it as second order is less clear, although in doing
so, I did say that I was referring to "slender antennas". We agree, of
course, because we both recognise that such an antenna will exhibit a
guided mode characteristic impedance which varies along its length,
actually increasing logarithmically if we assume it locally to be that
of a bicone having the same base (rod diameter) and height (distance
from the terminals) as the corresponding bicone. Note that this
agreement is intact whether or not one accepts the idea that for a SCF
radiation is solely an end phenomenon.

>From a circuit theory point of view, trying to pass a charge wave
along such a structure is to be compared with trying impulsively to
ram water into the big end of a tapered tube; only some of the impulse
will get to the end and the rest will be decelerated and reflected
continuously as the impulsive wave progresses along the tube. And, as
we've said, where there's charge acceleration (positive or negative),
there will be radiation. Since taper and therefore reflection is most
rapid nearer the terminals, this would account for the early time
relected current pulse which I understand Ed has observed when a
Gaussian pulse is applied to such an antenna.

As I have noted, other points have been raised that I have not yet
addressed. I will try to do this as time and the evolution of my
thinking permits. I work at the Institute only two days a week,
normally Mondays and Tuesdays, and there are a lot of other things to
do when I'm not here, including trying to convince my wife that I've
actually retired.

Harry E Green,
Adjunct Research Professor,
Institute for Telecommunications Resaech,
University of South Australia.

7 March 2000 @ 10.47 am (local time)
Received on Tue Mar 07 2000 - 04:27:44 EST