Jim Kelley wrote:
Joules per second doesn't have phase, Cecil. Your claim was the value
was 1 joule/sec. And the equation is stated pretty clearly in AN-95-1
as the sum of the terms. It doesn't have a minus sign, and it there
isn't a cosine term in it. a1 and a2 are complex voltages, and their
relative phase take care of itself - unless of course you square the
equation. That's how you end up with nonsense like 0=4.

As you know, I have repeated all this to you before so
you cannot possibly still be confused. Why you continue
your obfuscation of the truth is really strange.

b1 = s11(a1@0deg) + s12(a2@180deg) = 0

1. When we square both sides of the equation, the
product of 2*s11(a1@0deg)*s12(a2@180deg) is at 180
degrees so the sign of the term is negative. (but you
already knew that)

2. Joules per second doesn't have phase. I have said that
over and over. The phase term in the power density
equation is the relative phase between the two associated
voltages. (but you already knew that)

3. The equation stated in AN-95-1 is a normalized voltage
equation which is the sum of phasors - no negative sign
required for phasor addition. (but you already knew that)

4. Phasor symbols don't have minus signs and the real value
of a phasor is understood to include a cosine term even
though it is omitted by convention. (but you already knew that)

5. The general case of the squared equation is the same
as the intensity (power density) equations from Hecht
and Born & Wolf. It doesn't contain a minus sign.

Ptot = P1 + P2 + 2*SQRT(P1*P2)cos(A)

A is the angle between the two associated normalized
phasor voltages, a1 and a2, and its cosine is sometimes
negative. (but you already knew that)

I did not end up with nonsense like 0=4. You ended up
with nonsense like 0=4 by engaging in deliberate
irrational obfuscation. Why you feel the need to
act that way is really strange.
--
73, Cecil http://www.w5dxp.com