"Owen Duffy" wrote in message
...

There has been much discussion about wave cancellation, anihalation,
interaction etc. The discussion was initially about waves confined to a
transmission line (but would apply also to a waveguide in a sense) and
then progressed to radiation in free space.

Let me initially explore the case of radiation in free space. I am
talking about radio waves and the radiation far field.

If we have two widely separated antennas radiating coherent radio waves
don't they each radiate waves that travel independently through space. (I
have specified wide separation so as to make the effect of one antenna on
the other insignificant.

If we were to place a receiving antenna at a point in space to couple
energy from the waves, the amount of energy available from the antenna is
the superposition of the response of the antenna to the wave from each
source. This is quite different to saying that the electric field (or the
magnetic field) at that point is the superposition of the field resulting
from each antenna as is demonstrated by considering the response of
another recieving antenna with different directivity (relative to the two
sources) to the first receiving antenna.

A practical example of this is that an omni directional receiving antenna
may be located at a point where a direct wave and a reflected wave result
in very low received power at the antenna, whereas a directional antenna
that favours one or other of the waves will result in higher received
power. This indicates that both waves are independent and available to
the receiving antenna, the waves do not cancel in space, but rather the
superposition occurs in the antenna.

Though we frequently visualise nodes and antinodes in space, or talk of
nulls in space (eg have you ever noticed that when you stop a car at
traffic lights, you are smack in the middle of a null), whereas it seems
to me that the realisation of a null involves the response of the
receiving antenna.

This explanation IMHO is more consistent with the way antennas behave
than the concept that waves superpose in space, it allows waves to
radiate outwards from a source, passing through each other without
affecting each other. Whilst we routinely look at plots of the
directivity of an antenna, and assume that the plotted directivity is
merely a function of polar angle, we overlook that the plotted pattern
assumes an isotropic probe at a distance very large compared to the
dimensions of the antenna (array). Tracing the position of a pattern
minimum in towards the array may well yield a curved path rather than a
straight line, and a curved path is inconsistent with waves anihalating
each other or redistributing energy near the antenna and radiating
outwards in true radial direction from some virtual antenna centre.

So, it seems to me that coherent waves from separated sources travel
independently, and the response of the probe used to observe the waves is
the superposition of the probe's response to each wave. (A further
complication is that the probe (a receiving antenna) will "re-radiate"
energy based on its (net) response to the incoming waves.)

Now, considering transmission lines, do the same principles apply?

A significant difference with uniform TEM transmission lines is that
waves are constrained to travel in only two different directions.

Considering the steady state:

If at some point two or more coherent waves travelling a one direction,
those waves will undergo the same phase change and attenuation with
distance as each other and they must continue in the same direction
(relative to the line), and the combined response in some circuit element
on which they are incident where superposition is valid (eg a circuit
node) will always be as if the two waves had been superposed... but the
response is not due to wave superposition but superposition of the
responses of the circuit element to the waves. It is however convenient,
if not strictly correct to think of the waves as having superposed.

That convenience extends to ignoring independent coherent waves that
would net to a zero response. For example, if we were to consider a
single stub matching scheme, though one there might consider that
multiple reflected waves arrive at the source, if they net to zero
response, then it is convenient to regard that in the steady state there
are no reflected waves, the source response is as if there were no
reflected waves. An alternative view of that configuration is that
superposition in the circuit node that joins the stub, the line to the
load and the line to the source results in conditions at that end of the
source line that do not require a reflected wave to satisfy boundary
conditions at that point, and there really is no reflected wave.

Steady state analysis is sufficiently accurate and appropriate to
analysis of many scenarios, and the convenience extends to simplified
mathematics. It seems that the loose superposition of waves is part of
that convenience, but it is important to remember the underlying
principles and to consciously assess the validity of model
approximations.

Comments?

Owen


its too well considered and sensible... i predict this thread will die a
quick and quiet death, there is no fodder for arguments.