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

Hello Harry,

> 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.

Actually, I've made some NEC runs of wires 10 wavelengths long while
letting the radius approach zero, or at least to 10^-20 wavelengths,
which is pretty close. The current distribution does appear to
approach a sinusoid in the limit, as I think has been previously
concluded, perhaps first by Pocklington. I should add that it's the
imaginary component that approaches a sinusoid while the real part
tends towards zero.

> 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 should acknowledge that the Log(kL) trend is not my finding;
Balanis' antenna book derives a formula for the total power coming
from a SCF. Perhaps this result has been presented earlier elsewhere;
I suspect that it has.

> 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.

The modal argument may be one that provides an alternative for
explaining the growth in radiated power. But, it doesn't address the
question of where that radiation comes from, at least not that I can
see. It's probably worth mentioning again that if the total radiated
power of the unit-amplitude SCF is plotted versus length and compared
with that radiated by a fixed-radius dipole modeled using NEC the
length of which is systematically increased and whose maximum current
magnitude is set to unity, the two results overlap except in the
region of their maxima. It's also worth mentioning that while the
Log(kL) trend is not in dispute for either the SCF or the NEC dipole,
what causes that behavior is not so clear. There are several things
about these two simple problems that I still don't understand.

Best wishes,

Ed

--
Dr. Edmund K. Miller
3225 Calle Celestial
Santa Fe, NM 87501-9613
505-820-7371 (Voice & FAX)
e.miller_at_ieee.org