Richard Harrison wrote:
My original comment was in support of Arnold B. Bailey who said
something about increasing antenna gain by 3 dB every time you double
its size. Precisely, that`s not true, but I gave an example from Kraus
where he did much the same thing.

+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.


--
73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek

"Ian White GM3SEK" wrote
Richard Harrison wrote:
My original comment was in support of Arnold B. Bailey who said something
about increasing antenna gain by 3 dB every time you double its size.
Precisely, that`s not true, but I gave an example from Kraus where he did
much the same thing.

+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.
_______________

No doubt the 'GOM' knew the exact gain changes from successive doublings of
an antenna aperture, or could calculate them if they wished to. The
difference between the two isn't very important except when it is part of
the equation to arrive at some legally required ERP, such as in commercial
broadcasting.

Below are the gains of a series of commercial FM broadcast transmit arrays
to illustrate the point. The elements (bays) in these arrays all are one
wavelength apart, and driven with equal power and phase.

# Elements C-pol Gain (dBd)
1 -3.55
2 -0.21
4 3.09
8 6.34

Starting with the gain of the 1-bay and adding exactly 3 dB per doubled
aperture in this example would result in 5.45 dBd gain for the 8-bay,
meaning that FM ERP when using this approach would be more than 18% below
its licensed value (illegal).

RF

Richard Fry wrote:
"The elements (bays) in these arrays all are one wavelength apart, and
driven with equal power and phase.

# Elements C-pol Gain (dBd)
1 -3.55
2 -0.21
4 3.09
8 6.34"

Bailey`s Table 10-I, which Richard Clark referred to as "naive", appears
on page 484 of "TV and Other Receiving Antennas".
The heading is Array Gain (approximate rule).

Nunber( of Half-Wave Rods (N) and
Numeric PowerRatio Gain (dB) 1
0
2 3
4 6
8 9

First difference from Richard Fry`s table is the loss of 3.55 dB as the
result of circular polarization (mostly) as half of the power which a
linearly polarized reference dipole would
use is cross-polarized.

The steps between doubling the number of elements in Richard Fry`s table
are all nearly 3 dB. Bailey says "approximate rule". He is vindicated.

Best regards, Richard Harrison, KB5WZI

"Richard Harrison" wrote
First difference from Richard Fry`s table is the loss of 3.55 dB
as the result of circular polarization (mostly) as half of the power
which a linearly polarized reference dipole would use is
cross-polarized.

That, and the fact that the radiation pattern from each element is not the
pure cosine function assumed for a 1/2-wave dipole. It has slightly less
gain peak gain.

The steps between doubling the number of elements
in Richard Fry`s table are all nearly 3 dB.

"Nearly" is right, but the difference is not uniform for successive doubling
of apertures.

A small variation in the bay-bay spacing (departing from 1 wavelength) is
needed as a function of the number of bays, to maximize the peak gain from
this type of an array. The arrays in my table all have exactly 1-wavelength
element spacing, and the peak gain from arrays of them is lower than
expected for lower numbers of elements, and higher than expected for higher
numbers of elements -- which stretches/compresses that nominal 3 dB delta.

Fine points, to be sure.

RF

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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