Hi Richard,

My previous posting didn't reach the group, so I made a new one.
On 8 jun, 16:25, "Richard Fry" wrote:
[deleted}

No matter the relative value of its h-plane radiation, the resulting ground
wave field from an AM broadcast station is subject to losses not only by
1/distance, but also as a function of earth conductivity and the frequency.
Only for free space paths does the field decay by 1/distance, alone.

I fully agree with this. It is the reason that an AM broadcast
transmitter has its main lobe (Take of Angle) at non zero elevation.
When you would measure the field strength at, for example, 30 degr
elevation, you would find the 1/distance decay.

When you would measure the field strength of an AM broadcast
transmitter over seawater, the 1/distance decay holds to about 100km.
Above that you have to correct for earth curvature.

If the h-plane ERP of an AM monopole did not match the peak ERP of a
1/2-wave dipole when driven with the same tx power, then the monopole could
not generate the same field as the peak, free-space field of that dipole,
when the monopole is measured in its far field, but close enough to it for
groundwave propagation loss due to the conductivity of the path to be small.

You should distinguish between transition region and far field
(Fraunhofer) region. Close to the transmitter the field generated by
the ground current coincide with the field from the vertical radiator
therefore 3 dB gain increase in field strength occurs. Further away
from the antenna, both amplitude and phase of ground current will
change with respect to the field from the radiator, partly destructive
interference occurs.

Only a surface with infinite conductivity will support the surface
wave up to infinity, hence giving main lobe at zero elevation (for
vertical radiators up to 5/8 lambda). Even a vertical radiator (for
example 1/2 wave dipole) not touching ground will show max radiation
at zero elevation for perfect conducting ground plane (there is no
(pseudo)Brewster angle for surface with infinite conductivity).

This was proven in the Brown, Lewis and Epstein study in 1937, where at 0.3
miles for 60-90 degree verticals they measured an equivalent field strength
of better than 190 mV/m at 1 mile for 1 kW of radiated power. The peak,
free-space field from a 1/2-wave dipole for those conditions is about 195
mV/m.

The objective of the Brown, Lewis and Epstein study was to get as much
as power radiated instead of dissipated in the ground, especially with
relative small antennas (financial aspect). They did not investigate
Take of Angle.

BTW, they did a good job as the field strength from a 1/2-wave dipole,
free space, 1kW input is about 138mV/m (rms) at 1 mile. Their
measurements show 190mV/m (almost 3 dB gain).

If you have access to a full wave EM simulator that supports
dielectric layers, you could run a simulation of the far field pattern
for a vertical radiator.

Best regards,

Wim
PA3DJS