I don't think that's a valid excuse. The 3 dB rule applies to phased
arrays only when mutual coupling is ignored or in a few special cases.
Mutual coupling had to have been known at least at the time of the
invention of the Yagi-Uda antenna in 1926, and probably long before
that. It was being calculated for geometrically simple antennas at least
as early as 1943 (cf. R. King, Proc. IRE). Work proceeded rapidly
through the '40s, with papers describing increasingly accurate
techniques with antennas of increasing complexity.

We now have the means to calculate mutual coupling much more easily than
before, and for geometries which were impossible to deal with before we
had computers to do the work, but I don't think we've modified our
understanding of the phenomenon for many decades (some notable antenna
charlatans notwithstanding). Anyone measuring the gain of a short Yagi,
the gain of which routinely exceeds 3 dB per doubling of elements by a
considerable margin, must have become aware of the shortcoming of the 3
dB rule.

I suspect that if we were to read the cited quotations very carefully,
we'd see qualifications that explain neglecting mutual coupling.

Roy Lewallen, W7EL

Ian White GM3SEK wrote:
+3dB is a valid generalization, based on sound physics - but it is only
a generalization.

At the time those Grand Old Men were writing their textbooks, such
generalizations were the best that anybody could manage. But they had no
way of checking their accuracy - or more important, why and when they
start to become INaccurate.

50 years on, we do have a way, and we now know much more than they did.
That makes it very dangerous to quote those Grand Old Generalizations as
accurate and universal truths. Richard was quite correct to describe the
"+3dB rule" as "naive" - because, at today's level of knowledge, it is.

But we still need to know that the +3dB generalization exists; and
understand the fundamental reasons for it. That fundamental
understanding is what protects us against stupid mistakes.

Roy Lewallen, W7EL wrote:
"I don`t think that`s a valid excuse."

That old authors were satisfied with approximations may have less to do
with ignorance than with not having computers and programs to make
analysis fast and easy. The computer gurus have done well. A seconndary
effect of a paucity of computer power is a requirement for more
measurements. As the title of this thread is:"Accuracy of Antenna
Testing Ranges". measurement is still a concern.

As one who was doing plenty of tests and measurements 50 years ago, I`d
like to testify that if I could get 1-dB accuracy, I was satisfied.
Bailey may not have thought that was good enough accuracy, but I think
it was realistic for the period in the field. I`m sure the NBS did
better. But for ordinary purposes. 1 dB is probably good enough for
graphs and tables to be comparable in accuracy to the measurements you
can make. Of course, everyone wants complete accuracy.

Richard Fry`s and Arnold Bailey`s tables were within 1-dB. I think it`s
satisfactory.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
1 dB is probably good enough for
graphs and tables to be comparable in accuracy to the measurements you
can make. Of course, everyone wants complete accuracy.

I remember asking my college prof back in the '50's:
How can we trust a graph where none of the measured
values actually fall *on* the graph line?
--
73, Cecil http://www.qsl.net/w5dxp

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