Keith Dysart wrote:
But you need to clearly state your limitations and stop
flip flopping.
What you are calling "flip flopping" is me correcting
my errors. Once I correct an error, I don't flip-flop
back. My error was in assuming that the power-density
(irradiance) equation only works on average powers.
K7ITM convinced me that it works on instantaneous powers
also.
I am surprised, this being 2008, that I could actually be
offering a new way to study the question, but if you insist,
I accept the accolade.
I'm sure you are not the first, just the first to think
there is anything valid to be learned by considering
instantaneous power to be important. Everyone except
you discarded that notion a long time ago.
Analysis has shown that when examined with fine granularity,
that for the circuit of Fig 1-1, the energy in the reflected
wave is not always dissipated in the source resistor.
Yes, yes, yes, now you are starting to get it. When
interference is present, the energy in the reflected
wave is NOT dissipated in the source resistor. Those
facts will be covered in Part 2 & 3 of my web article.
Ptot = P1 + P2 + 2*SQRT(P1*P2)cos(A)
Which of the two needs the 'cos' term?
Ps(t) = Prs(t) + Pg(t)
or
Pg(t) = Pf.g(t) + Pr.g(t)
In fact neither do.
For instantaneous values of voltage, the phase angle is
either 0 or 180 degrees so the cosine term is either +1
or -1. The math is perfectly consistent. That you don't
recognize the sign of the instantaneous interference term
as the cosine of 0 or 180 is amazing.
Non-the-less do feel free to offer corrected expression that include
the 'cos(A)' term.
I did and you ignored it. There is no negative sign in the
power equation yet you come up with negative signs. That
you don't recognize your negative sign as cos(180) is
unbelievable.
The math holds as it is. But I invite you to offer an alternative
analysis that includes cos(A) terms. We can see how it holds up.
It it unfortunate that you don't comprehend that the cos(0) is
+1 and the cos(180) is -1. The sign of the instantaneous
interference term is the cosine term. The math certainly does
hold as it is - you are just ignorant of the "is" part.
--
73, Cecil
http://www.w5dxp.com