Cecil Moore wrote:
Gene Fuller wrote:
For future reference, however, just remember: Fields first, then power
or energy. That's the way superposition really works.

Way back before optical physicists could measure light
wave fields, they were dealing with reflectance,
transmittance, and irradiance - all involving power
or energy. They are still using those concepts today
proven valid over the past centuries. Optical physicists
calculate the fields *AFTER* measuring the power density
and they get correct consistent answers.

"Way back" is irrelevant. One only needs to open a serious text book on
Optics, such as Born and Wolf, to see how optical physicists perform
analysis today.


Quoting HP AN 95-1: "The previous four equations show that
s-parameters are simply related to power gain and mismatch
loss, quantities which are often of more interest than the
corresponding voltage functions."

I agree with this statement completely (surprised??). S-parameter
analysis is very useful. However, the "corresponding voltage functions"
are equally valid, even if not as "interesting". What you might also
notice in AN 95-1 is that there is no mention of incident and reflected
waves on a transmission line, each carrying energy (or power or whatever
you prefer), and passing like ships in the night.

You like to talk about conservation of energy, implying that your
"powerful" reflected wave model is essential to meeting the conservation
of energy requirement. In fact, your model is a poster child for the
violation of energy conservation. Electromagnetic energy, like any
energy, is a scalar quantity, and it is only positive. It is not
possible to "net" the non-zero energy contributed from your
counter-traveling waves to zero. The direction of the wave propagation
does not change the sign of the energy. Be careful here; energy is *not*
the same as the energy flux or Poynting vector. Don't mix terms that
have totally different units. What *can* be assigned negative values are
the fields. (Voltage and current are not exactly "fields", but they will
work for these transmission line examples.) A "net" of zero volts or
current is exactly what happens at the standing wave nodes resulting
from the counter-traveling waves. After you have done the superposition
correctly, using fields, not energy or power, then you can easily
determine the energy and power state as needed. Conservation of energy
will be automatically satisfied, assuming no mathematical blunders. The
Maxwell equations would be pretty useless if they did not provide
conservation of energy.

For future reference, just remember: Fields first, then power
or energy. That's the way superposition really works.

73,
Gene
W4SZ