On Jun 24, 5:27*am, Keith Dysart wrote:
This equation is problematic. Firstly, it mixes power with voltage
since theta is the angle between the voltage waveforms.

You apparently don't understand what happens when one takes the dot
product of two voltage phasors (and divides by Z0). The result is
watts but the math involves the cosine of the angle between the two
voltage phasors. All competent EEs should already know that.

As K1TTT said, "why not just do the whole thing with voltages?"

Because the title of this thread is: "What happens to reflected
energy?", not what happens to reflected voltages? Doing the whole
thing with voltages allows the obfuscation of interference to be swept
under the rug.

Because some of you guys don't recognize interference when it is
staring you in face? I was taught to recognize interference between
voltage phasors at Texas A&M in the 1950s. What happened to you guys?
Here's a short lesson about dot products of voltage phasors and the
resulting interference between the two voltages.

Vtot = V1*V2

Vtot^2 = (V1*V2)^2

Vtot^2/Z0 watts = (V1*V2)^2/Z0 watts

There will be the two obvious power terms, V1^2/Z0 and V2^2/Z0,
representing the powers in the individual waves before superposition.
There will be a third, additional interference term whose dimension is
watts that *requires the dot product* between the two phasor voltages.
Therefore, your objection is apparently just based on ignorance of the
dot product of two voltage phasors.

This mixing is bad form and
clearly demonstrates the incompleteness of the power based analysis.

Good grief! This "bad form" has been honored in the field of optical
physics for at least a century. It was taught in EE courses 60 years
ago. I don't know what has happened in the meantime. Walter Maxwell
explains interference in section 4.3 in "Reflections" and obviously
understands the role of interference in the redistribution of energy.

The second is that there are two solutions depending on whether the
positive or negative root is used? Why is one discarded? Is this
numerology at work?

Negative power is just a convention for "negative" direction of energy
flow. All EEs are taught in our engineering courses to ignore the
imiginary root when calculating resistance, energy, or power.

For instance, the Z0 for the 1/4WL matching section between R1 and R2
needs to be SQRT(R1*R2). When you perform that math function, do you
really go on a world-wide search demanding a transmssion line with a
negative Z0? Please get real.

Thirdly, it only produces the correct answer for average energy flows.
If the instantaneous energy flows are examined, the results using
this equation do not align with observations.

You forgot to add that instantaneous energy is as useless as tits on a
boar hog, or as Hecht said, putting it mildly: "of limited utility".
It appears to me that instantaneous energy is just a mathematical
artifact inside a process requiring integration in order to bear any
resemblence to reality. Omit the integration and the process loses
touch with reality. Instantaneous energy has zero area under the curve
until the intergration process has been performed. A zero area
represents zero energy. Otherwise, when you integrate from zero to
infinity, the result would be infinite energy.

Do you have any kind of reference for your treatment of instantaneous
power?
--
73, Cecil, w5dxp.com