Re: Independence of waves

Owen Duffy wrote:
But is it possible to inject two coherent waves travelling independently in the same direction? Could I not legitimately resolve the attempt at a circuit node (line end node) of two coherent sources to drive the line to be the superposition of the voltages and curents of each to effectively resolve to a single phasor voltage and associated phasor current at that node, and then the conditions on the line would be such as to comply with the boundary conditions at that line end node. Though I have mentioned phasors which implies the steady state, this should be true in general using v(t) and i(t), just the maths is more complex.

Two coherent waves traveling independently in the same
direction in a transmission line are collinear and
interfere in a permanent manner, i.e. they interact. Why
this is so is easy to understand when one superposes the
two E-fields and the two H-fields. The total E-field changes
by the same percentage as does the H-field. In an EM wave,
ExB is proportional to the joules/sec associated with the
wave.

When two coherent EM
waves are superposed while traveling in the same direction
in a transmission line, the total ExB magnitude decreases
if the interference is destructive and increases if the
interference is constructive. A destructive interference
event gives up energy to a constructive interference event
somewhere else. That is what changes the direction and
magnitude of the reflected wave at a Z0-match point. If
the interference is destructive toward the source, the
"extra" energy will be redistributed in the direction of
the load as constructive interference energy.

I can see that we can deal mathematicly with two or more coherent components thought of as travelling in the same direction on a line (by adding their voltages or currents algebraicly), but it seems to me that there is no way to isolate the components, and that questions whether they actually exist separately.

Thanks Owen, you have just described coherent wave interaction
in a transmission line.

So, whilst it may be held by some that there is re-reflected energy at the source end of a transmission line in certain scenarios, a second independent forward wave component to track, has not the forward wave just changed to a new value to comply with boundary conditions in response to a change in the source V/I characteristic when the reflection arrived at the source end of the line?

Yes, wave interaction is permanent. Canceled waves cease to
exist in their original direction of travel in the transmission
line.

And we haven't mentioned power, not once!

Every EM wave possesses an E-field and an H-field. The cross
product of the RMS value of those fields is proportional to
average power. One can avoid mentioning power, but one cannot
run away from the fact that the power associated with each EM
wave is ExB. If Vref and Iref exist, then the joules/sec in
Eref x Href has to exist. The fields cannot be separated from
the energy necessary for them to exist. Such is the basic
nature of EM waves.
--
73, Cecil http://www.w5dxp.com
.

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