"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