NEC-LIST: How does a wire antenna radiate?

Dear fellow NEC-lister,

I have followed the recent discussion in NEC-list on how an antenna
radiates with some interest and, at the risk of adding further
confusion, have decided to record a point of view which I hope will
prove useful.

A good place to start is to read the first chapter of Schelkunoff's
"Advanced Antenna Theory", published in 1952 by John Wiley. Although
the passage of time has seen him largely fall from fashion,
Schelkunoff is an author from whose clear insight much is to be
learned.

Schelkunoff classifies antenna theories into two broad types. These
are (1) circuit theories in which the emphasis is on the current and
charge on the conductors and (2) field theories in which the emphasis
is on the fields and the conductors appear only as boundaries. He
subdivides the latter class into two further subclasses which he
identifies respectively as resonator theories and mode theories, a
distinction which however is not too important for the purposes of
this discussion.

To date the NEC-list discussion has focussed on what in terms of this
classification are circuit theories. It is interesting therefore to
start by looking at the problem a little more closely from this point
of view. Here it is most useful to go to the time domain and to
consider radiation which results from the propagation of a current
impulse along the antenna conductors.

Radiation from accelerated charge can be interpreted physically as a
"flicking" of the lines of force in which the radiation field
propagates out along the line in much the same fashion as does a kink
on a rope flicked at one end. This idea is said to be due to J J
Thomson, discoverer of the electron and a colleague of Maxwell. It is
described at length in R M Eisberg & L M Lerner, "Physics, Foundations
and Applications", McGraw Hill, 1981 (without attribution to source)
and more succinctly (with attribution to Thomson) in S G Starling & A
J Woodall, "Physics", Longmans Green, 1950. I have also used it in a
paper which I have recently published (H E Green, "Antennas without
Maxwell?", Journal of Electrical & Electronic Engineering, Australia,
Vol.19, No. 4, December 1999, pp 157-163) in which I am able to deduce
the Green's function for a radiating current element without explicit
recourse to the field equations.

As the impulse passes along the conductor, the charges are first
accelerated in one direction and then immediately equally and
oppositely in the other, so there is no NET acceleration. Two mutually
cancellatory kinks are produced and there is therefore no net
radiation field. This will be true everywhere except at the ends where
the impulse comes to a halt and is reversed (reflected). Here there is
net acceleration and therefore radiation. The travelling impulse
therefore radiates only from the end of the wire.

This is essentially the point of view put forward by G S Smith in the
latter part of his APS Magazine feature article (G S Smith, "On the
Interpretation for Radiation from Simple Current Distributions", APS
Magazine, Vol. 14, No. 4, August 1998, pp 39-44), although he doesn't
explicitly develop his argument in terms of kinks in the
field. Inasmuch as a time harmonic travelling wave can be written as a
superposition of impulses, it follows that a wire subject to time
harmonic excitation will radiate only from its ends. Moreover, as the
supposedly sinusoidal current distribution on a wire excited at its
centre can be resolved as a pair of travelling waves (W Scott Bennett,
"A Basic Theorem that Simplifies the Analysis of Wire Antennas", APS
Magazine, Vol. 40, No. 1, February 1998, pp 22-30), it must be equally
true that radiation from it occurs at its ends and, if the presence of
the generator there leads to a further discontinuity at which net
acceleration of charge is possible, at its centre as well. Well
almost!

It is useful to pause for a moment to consider what antenna geometry
is needed to support a uniform travelling wave of current. It turns
out that a biconical antenna will do this as it has a characteristic
impedance which is constant along its length. When we have a pair of
uniform cylinders rather than co-apecial, coaxial cones, this will not
be so and characteristic impedance will vary with distance from the
centre of the antenna.

Under these circumstances the current standing wave cannot be purely
sinusoidal and it is to be expected that there will be some radiation
along the length of the antenna instead of merely at its ends and
centre (That we should then expect radiation at intermediate points
would seem also to follow from the work of Simon and Biggi - I do not
have this reference to hand but am sure that it can be found in C H
Walter's "Traveling Wave Antennas", for example). However for slender
antennas this is likely to be second order compared with end
radiation.

As Abraham showed in 1898 (the reference is given at the foot of p.165
of Schelkunoff's book, referred to earlier), a purely sinusoidal
current distribution will exist only when the cylinders have become
filamentary and any theory which assumes such a distribution will not
and cannot reveal anything other than end radiation. This is why the
customarily published formula for the radiation pattern of a
centre-fed dipole, when suitably dissected, appears to show that
radiation has come only from its ends and centre (see Jordan &
Balmain, for example).

Viewed in the alternative field theoretic framework, i.e. considering
the antenna as a waveguide, the picture is different though
complementary. In this view, some kind of primal electromagnetic
disturbance at the centre of the antenna gives rise to a wave which is
guided by the conductors of the antenna to its aperture, the boundary
of its minimum circumscribing sphere with free space, from where it is
radiated. If the antenna is biconical, for example, the waveguide
mode will be a spherical TEM wave.

The primal disturbance may of of any of a number of forms, e.g. actual
acceleration of physical charge in the immediate neighbourhood of the
terminals or by mode conversion from a plane wave on the feeding
transmission line into the spherical mode needed on the
antenna,. However, beyond supposing it to be confined to a small
region near the terminals, we need not be too concerned with the exact
nature of this primal disturbance.

On this theory, radiation of energy occurs by mode conversion at the
boundary sphere from the bound waveguide mode into a superposition of
the modes of free space. Free space modes are discussed in Chapter 6
of Harrington's "Time Harmonic Electromagnetic Waves". Harrington
makes it clear that for each free space mode, there is a "cutoff"
radius about which there is a relatively rapid change in the mode
impedance from primarily reactive to primarily real. Modes for which
the boundary sphere lies within their cutoff radius will not be
excited or excited only with difficulty.

This accounts for the increasing complexity of the radiation pattern
of a centre-fed dipole as it becomes longer. A longer dipole has
access to a "richer" set of free space modes , detail in the pattern
being developed by the presence of the higher order basis functions in
much the same way as the fine structure of a Fourier series is
contributed by the higher order harmonics.

The mode theory also serves to answer some questions about antenna
action which are not obvious from the circuit theory point of
view. One is why the current wave propagates at the velocity of
light. Seen as a waveguide, the current is no longer primary but
simply the response of the charges on the conductors to the wave in
the waveguide, serving simply as a termination for the lines of force
necessary for the presence of a TEM mode on the bicone.

The situation is perhaps to be compared with standing on the bank of a
channel down which a wave is passing. As the wave interacts with the
shore, it rustles the detritus on the shoreline. The rustling of the
detritus is not the cause f the wave but a manifestation of its
presence. However from the rustling we might expect to be able to
infer the nature of the wave in the channel which caused it, much as
accident assessors are able to use skid marks to infer something about
the motion of the vehicles involved. The skid marks didn't cause the
accident but are a lasting response to it. It may be for some reason
like this that integrating over the current distribution gives a
correct account of the radiation field.

Another advantage of the wavegiuide theory is its immediate connection
with Huygens Principle in which each successive wavefront is seen as
having been begat by its immediate predecessor as the wave travels
from the region of primal disturbance to the aperture and beyond. Even
so, the mode theory does not seem to give a clear quantitive
description of the conversion of the guided into the radiation
field. To be sure, one can write each field as a set of modes and mode
match them across the aperture, but this is a mathematical rather than
a physical procedure.

The point that I'm finally making is this. If one is looking for
physical explanation, there are differing and complementary
standpoints from which to view radiation from an antenna. Neither
contradicts the other but rather the one fills out the picture where
the other is more obscure.

I've been thinking about this problem for some time as part of my aim
to try to make antennas more easily understandable to undergraduates
who must feel comfortable with them but no longer have the time to
persevere down the traditional road to enlightenment. My thoughts owe
much to considerable e-mail correspondence with Ed Miller and Scott
Bennett (not, I believe, a member of NEC-list) but it is to be
emphasised that they my own and I do not ask either to take any
responsibilty for what they may regard as misinterpretations on my
part,

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

Tuesday 29 February 2000 @ 4.15 pm (local time)
Received on Wed Mar 01 2000 - 06:12:24 EST