Thoughts on voltage vs power, reflection vs interference:

What most RF people do is deal exclusively with voltages. Power is
considered only at the beginning and end of a voltage analysis, NOT
during the voltage analysis. If joules/second are to be tracked
seamlessly throughout the analysis, a working knowledge of the effects
of superposition/interference is absolutely necessary. Optical
physicists do not have the luxury of working exclusively with
voltages, as we do in RF, so they must necessarily understand
superposition/interference and be able to track every component of
irradiance (power density).

I took a look at Johnson and he is dealing with voltage, not power,
and certainly not with dissipationless resistances as part of the
generator source impedance. He uses 'k' sub-script 'g' as the symbol
for the voltage reflection coefficient. I'm going to use 'rho' for his
'k' with braces {g} indicating subscripts. His *voltage* reflection
coefficient at the generator is:

rho{g} = (Zg-Z0)/(Zg+Z0)

which is just standard *voltage* wave reflection mechanics. What
happens to the energy (power) in superposed waves is completely
transparent when superposing voltages. For instance, let's say we have
two 200 watt waves in a 50 ohm environment which makes each of their
voltage magnitudes equal to 100 volts RMS. The electric fields of the
two waves are 120 degrees apart. What happens when we superpose 100
volts at +60 degrees with 100 volts at -60 degrees?

Every student of three-phase power systems knows the result will be
100 volts at zero degrees. All is well until we take a look at the
energy in those two superposed waves. Each wave is associated with an
ExH amount of power, V^2/Z0=200w, for a total of 400 watts in the two
waves. The resultant (total?) superposed wave contains 200 watts of
ExH power. Most people don't give this idea a second thought but where
did the other 200 watts go? To answer the question, one must
understand destructive/constructive interference. In the above
example, there is 200 watts of destructive interference present so the
resulting "total" voltage is not the only component of superposition.

If the above occurs in a transmission line, the amount of destructive
interference energy that is lost in the direction of superposition,
e.g. toward the load, is redistributed in the only other direction
possible, i.e. toward the source. There is a second 200w wave
generated that travels toward the source but that fact is not covered
when voltage superposition is involved. Note that it is a reverse-
traveling wave but it is technically not a reflection of a single wave
as it is the result of superposition of two waves.

Voltage superposition takes care of itself and everyone believes in
the conservation of energy principle which is probably why very few
people ask, "Where does the power go?" It is only when we are trying
to track energy throughout the system that we are forced to understand
the effects associated with interference.

Thoughts on one-port analysis vs two-port analysis.

Sources are necessarily treated as single-port devices. We know we
often get completely different reflection coefficients when treating
something as a single-port device vs as a dual-port device. For
instance, most of us treat a dipole feedpoint as a single-port device
when it is actually far from being a single-port device. In reality,
many other things besides a single reflection, are happening at a
dipole's feedpoint. The actual physical reflection coefficient at the
feedpoint of a "50 ohm" dipole fed with 50 ohm coax is around 0.845
because the characteristic impedance of a #14 wire 30 feet above
ground is around 600 ohms. Proof: Eliminate the reflections from the
ends of the dipole by terminating the ends of the inv-V dipole to
ground through 600 ohm resistors and the SWR on the 50 ohm feedline
goes to 12:1.

Because of reflections from the ends of the dipole, a lot of
interference is happening at the feedpoint which results in a
*virtual* reflection coefficient of 0.0 only because of the single-
port analysis that is ordinarily used. IMO, a virtual reflection
coefficient is a *result* and cannot cause anything including
reflections. IMO, only physical reflection coefficients, i.e. physical
impedance discontinuities, can *cause* reflections. Much of what we
consider to be reflections are the result of interference.

Seems that something similar, but more complicated, is happening
inside a source where there is an active-source component in the mix.
IMO, what is happening to the energy inside a source cannot possibly
be understood without taking the effects associated with interference
into account.
--
73, Cecil, w5dxp.com