Joel Koltner wrote:
Hi Roy,

"Roy Lewallen" wrote in message
treetonline...
There are two errors in your analysis. The first is that you've neglected
mutual coupling between the elements.

Yes, I assumed it was negligible. When we analyzed arrays in class some years
ago, the starting point was always, "assume each antenna has the pattern of a
single dipole in isolation, is matched to the transmission lines, with input
current 1A @ angle whatever." We did analyze the patterns for a couple of
local Oregon TV & radio stations, BTW, including whichever radio? station it
is up in Portland (very roughly) near you off of I-205 as you drive past
Oregon City.

But that happens only in special cases and not by any means all cases.

The phased arrays I had in mind were those that were usually separated by a
"significant" fraction of a wavelength, e.g., lambda/8 or more. That's
probably not far enough apart to neglect coupling?

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.
This particular array is a special case of another kind -- there is no
net effect of the mutual coupling on the array gain, so it has 3.0 dB
gain over a single element. This isn't true in the general case, however.

Neglecting the mutual coupling is convenient for the professors because
it simplifies the problem and allows them to illustrate the simple
addition of fields. The problem is that it leads some students to think
they have the whole story.

In very large arrays such as those used for radar, the vast majority of
elements are in essentially the same environment relative to each other
so the mutual coupling has the same effect on all except the outer few
elements. But it simply can't be ignored in arrays of a few elements.

Your correct value of 1.414 mV/m is correct, but it represents a 3, not 6,
dB gain relative to a single element (which produced 1 mV/m).

6dB vs. 3dB is a rather embarassing outright brain fart on my part. :-) (The
usual case of confusing "twice the power = 3dB" with "twice the voltage =
6dB").

For a much more detailed explanation of these phenomena, I recommend reading
the treatment of phased arrays in Chapter 8 of the _ARRL Antenna Book_. I'm
admittedly a bit partial to this particular treatment, since I wrote it.

Thanks Roy, I'll take a look!

Another source which has a good discussion of the topic is Johnson's
_Antenna Engineering Handbook_, or earlier editions edited by Jasik. Be
wary of amateur and hobbyist publications (other than the _ARRL Antenna
Book_ -- very few authors understand the topic, and pass along their
misconceptions.

Roy Lewallen, W7EL