Richard Fry wrote:

... which supports my contention earlier in this thread: The peak gain
increase between a 1/4-wave and a 1/2-wave or 5/8-wave vertical is 3dB
above the gain differences of those antennas as dipoles of _twice_ that
length in free space.

Things seem to be getting a little confused here.

When you replace a free space environment with a perfect ground plane,
the *average* field strength of *all antennas* increases by 3 dB for a
given power input because of the reduced volume. This shows up as a 3 dB
gain increase when the gain is referenced to a free-space antenna such
as an isotropic source. No antenna is given any additional advantage
over any other - they all get the same amount of increase. So if I read
the above statement correctly, it's not true. The gain increase between
a 1/4 and 1/2 or 5/8 wave antenna over a perfect ground is the *same* as
the gain increase between a 1/2 and 1 or 5/4 wave dipole in free space.
Not 3 dB greater. If you'll look at the patterns of the antennas, you'll
find that the pattern of a 1/4 wave vertical over perfect ground is
identical in shape to half the pattern of a 1/2 wave free space dipole,
but 3 dB stronger. Likewise for any other vertical and its twice-as-long
free space dipole counterpart.

When the perfect ground is replaced by real ground, an attenuation
factor is introduced which actually changes the pattern shape. This
pattern shape change is different for each height of vertical because it
depends on the angle at which the radiation from each part of the
antenna strikes the ground. The different antenna heights have different
current distributions and so different fractions of the total radiation
hits the ground at different angles. The effect of the attenuation at
each elevation angle depends on the ground constants and the frequency.

You're probably more used to looking at surface wave attenuation, where
this ground reflection effect doesn't exist. Instead, there's a single
frequency and ground dependent attenuation that's essentially the same
for all antenna heights. What I'm talking about here is sky wave
radiation which consists of both a directly radiated "ray" (which
undergoes no attenuation other than that caused by its expanding volume
with distance) and a "ray" reflected from the ground. It's the
attenuation and phase shift of this second "ray", which depends on the
elevation angle, ground constants, and frequency, which causes the
pattern shape modification and attenuation of low angle signals. If you
look into the way NEC-2 operates you'll see that it does just this
calculation. The relationship of the reflected ray before and after
striking the ground is described by a fairly simple reflection
coefficient, which is quite different for horizontally and vertically
polarized waves. If you assume a current distribution, it's not
difficult to calculate the pattern manually. The reflection coefficients
can be found in Kraus.


Repeating the reasons for this...

* the electrical length of the vertical is doubled by its image below the
ground plane (a 1/4-wave vertical monopole becomes an electrical
1/2-wave dipole)

I don't think that's a good use of the term "electrical length". It is
true that the radiation pattern of a 1/4 wave vertical over perfect
ground (but not imperfectly conducting ground) is the same as that of a
half wave dipole in free space. Also, its feedpoint impedance assuming
no loss is exactly 1/2 that of a 1/2 wave dipole in free space.


* the peak "free space" gain of the monopole and its image is increas-
ed 3dB, because all radiation from it is confined to one hemisphere
(above the ground).

Yes, but this is altered if the ground isn't perfect. When the ground
isn't perfect, the shape of the pattern of the monople is no longer the
same as half a free space dipole, so the gain difference is no longer a
constant 3 dB at all angles. Some of the radiated energy is lost in the
ground reflection, and the fraction which is, depends on the angle at
which it strikes the ground.

Roy Lewallen, W7EL