I don't know the answers here, but I have been following this discussion
trying to make sense of it. I am beginning to get a dim view of how
this may work. The definitions of reciprocity given, or implied, so far
have been causing me some confusion. I have seen two or three
definitions so far along with some implied definitions and they are not
the same, however all of these definitions seem to have something in common.
For example K1MK wrote:
.."Suppose I send a plane wave at some complicated diffractive surface.
Let's say this plane wave was initially moving from left-to-right in one
direction with a uniform amplitude. Upon encountering the surface, the
wave gets diffracted and ends up going off to the right in a bunch of
different directions with differing amplitudes and phases.
What reciprocity says is if I send in a bunch of waves from the right
from different directions with differing amplitudes and phases such that
they replicate the output seen above, I'll get a copy of the original
wave moving to the left."...
Assuming no energy dissipated in the object, that kinda makes sense,
however this doesn't completely explain the question at hand. If you
apply that to a radio example you also don't have the complete set of
incoming rays to do the combining.
N3OX wrote:
..."The demonstration of reciprocity ends in equation 9, showing that
the wave coming in from the left (1) and exiting the right (t) gives the
same fraction of transmission across the barrier the as the wave
entering the right (1) and leaving the left (t'). If you transmit 1 and
the DX station gets t, reciprocity says that if the DX station transmits
1, you get t. You transmit 100W they get, say, 20 microwatts... they
transmit 100W, you get 20 microwatts."...
This is a little different from the first statement, but it doesn't
contradict it.
K1MK previously made a statement that agrees with the previous one by N3OX:
..." All reciprocity says is that for any one of the multiple diffracted
rays, the amplitude of that diffracted ray depends only on the included
angle between the incident ray and the diffracted ray and not on the
direction of the incident ray."....
Hmmm. That would imply that the shape of the object that is doing the
diffracting is not important. Maybe this statement is too simplified or
maybe I'm not intrepreting it properly.
However from these comments, the one thing in common is that the
transmitted path loss, in either direction, has to be the same for any
angle pairs you pick regardless of the shape of the object. At first I
though that required an identical diffraction pattern for both
directions, but maybe not. I had to draw a few diagrams to convince
myself that this was possible. I drew an incident received waveform and
split in into several diffracted waves. Then from the transmit side I
looked at a wave hitting the object at one of these same angles. As
long as you make the angle pair (one side to the other) the same loss,
the rest of the pattern can be anything.
Let me do a bit of rambling and maybe someone will tell me how far off
base I am. For an incident wave, there would be a completely different
diffraction pattern for each angle and direction, but for any particular
angle pair, the path loss in both directions would have to be the same
(according to these definitions). A practical radio example, of course,
would consist of more than one wave. For a radio wave (ignoring
ionosphere effects) looking at an object near a source, there will be an
infinite number of incident waves hitting the object and these will
produce an infinite number of diffraction patterns, but they will
combine with some attenuation to produce a signal at a desired angle on
the other side. To simplify, let's assume only one angle is used for
this path and all signal for the path came from diffraction by the
object. In the reverse direction, a single incoming wave at the path
angle, will produce a diffraction pattern consisting of the same number
of waves that were used to produce the signal from the other direction
(excluding any waves which did not hit the object and those that
contributed zero to the path).
I'm not sure I understand exactly why this happens, but it does seem
possible, and it agrees with the definitions presented so far, unless I
have gone astray somewhere. It also doesn't contradict HFTA, which says
that the attenuation produced by a path object is different for
different shapes. Unfortunately it is not possible to turn the path
around in HFTA to prove the point. You would need to be able to
generate a single wave of selectable angle to do it. Turning the object
and using the same source isn't the same thing.
It was also interesting to see some examples listed where reciprocity
does not apply, but these are due to some special cases, mostly
associated with polarization.
Comments, either way, appreciated.
Jerry, K4SAV
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