On Aug 8, 1:13 pm, Roy Lewallen wrote:
Joel Koltner wrote:
"Roy Lewallen" wrote in message
streetonline...
Not by a long shot! Here's a simple example from the EZNEC demo program,
using example file Cardioid.EZ. It's a two element array of quarter
wavelength vertical elements spaced a quarter wavelength apart and fed with
equal currents in quadrature to produce a cardioid pattern. The impedance of
a single isolated element is 36.7 + j1.2 ohms. In the array, the impedances
are 21.0 - j18.7 and 51.6 + j20.9 ohms, and the elements require 29 and 71
percent of the applied power respectively in order to produce equal fields.
The deviation is due to mutual coupling.

That's a much, much greater difference than I would have guessed. Wow...

Isn't the input impedance of one element affected not only by the relative
position of the other element, but also how it's driven? I.e., element #1
"sees" element #2 and couples to it, but how much coupling occurs depends on
whether the input of element #2 is coming from a 50 ohm generator vs. a 1 ohm
power amplifier (close to a voltage source), etc.? (Essentially viewing the
antennas as loosely coupled transformers, where the transformer terminations
get reflected back to the "primary.")

Not directly. What counts (considering the simple case of two elements)
is the magnitude and phase of the current in the other element, and
their spacing, orientation, and lengths. A good way to look at the
effect of mutual coupling is as "mutual impedance", i.e., the amount of
impedance change caused by mutual coupling. (Johnson/Jasik covers this
concept well.) If you were to feed two elements with constant current
sources (as in the Cardioid.EZ EZNEC example), mutual coupling doesn't
change the element currents, but only the feedpoint impedances. With any
other kind of feed system, the impedance change causes the currents to
change, which in turn affects the impedances. So the feed method
certainly does have an effect on the currents you get, which affects
both mutual coupling and pattern.

There's a lot more about this, and how to design feed systems which will
effect the desired currents, in the _ARRL Antenna Book_.

Thanks for the book links. Do you happen to have a copy of "Small Antenna
Design" by Douglas Miron? And have an opinion about it? Or some other book
on electrically small antennas? (Not phased arrays, though :-) -- more like
octave bandwidth VHF or UHF antennas that are typically 1/10-1/40 lambda in
physical size.)

I just recently purchased Miron's book but haven't yet looked at it in
any depth. It appears to be most interesting to anyone wanting a better
understanding of method of moments numerical methods. If you can read
German, you might be interested in _Kurze Antennen_ by Gerd Janzen. But
your search for small, broadband antennas puts you bump-up against the
principle "small - broadband - efficient, choose any two". They'll be
inefficient, which will hurt you both receiving and transmitting at VHF
and above. The book I'd go to for researching the possibilities would be
Lo & Lee's _Antenna Handbook_. You might also get some ideas from
Bailey, _TV and Other Receiving Antennas_, since TV antennas have to be
pretty broadband.

Roy Lewallen, W7EL

Simply in an effort to provide a bit more insight, or perhaps I should
better say to suggest a math tool that may lead you to more insight,
consider what "mutual impedance" means. In a simple circuit where
there's a current through an impedance, the voltage drop across it is
given by V = Z * I. If you expand this idea to include mutual
impedances, the Z becomes a matrix, and I and V are vectors. So in an
antenna system with, say, four feedpoints, V becomes a vector of four
voltages, one for each feedpoint, and I similarly is a vector of four
currents, one for each feedpoint. Z is then a four-by-four matrix
with self-impedances along the diagonal and mutual impedances off the
diagonal. It is clear that if you know the four currents, you can
find the voltages. Further, if you can invert the Z matrix, then you
can calculate the currents if you know the voltages. That also
suggests how to find the mutual impedances: if you excite one
feedpoint with a known current and leave all the rest open, you can
measure the voltages at each (including phase) and that immediately
gives you the mutual impedance from the excited feedpoint to each of
the others: your I vector has only one non-zero component. Repeat
for each feedpoint.

You can use the same sort of analysis with other systems which have
interaction among components. For example, a system of inductors
which share magnetic fields can easily be characterized by a matrix of
self-inductances and mutual inductances. For a single inductor, V =
L*di/dt; if you have two coupled inductors, V1 = L1 * di1/dt + M12 *
di2/dt, and V2 = M21 * di1/dt + L2 * di2/dt -- or in matrix notation,
V = L * d/dt(I). That can expand to as many inductors as you care to
consider.

(If this is confusing, it's probably best to just ignore this
suggestion...)

Cheers,
Tom