Jim Kelley wrote:
Perhaps we just misunderstand each other, but I don't know of another
way to interpret what you have written.

Yes, you do, Jim. You know that I agree with you on almost
every technical point yet you incessantly try to erect
straw men so you can knock them down. You are almost
always trying to discredit someone who agrees with you.
To that unfair tactic my response is:

From: "An Energy Analysis at an Impedance Discontinuity in
an RF Transmission Line", by W5DXP, WorldRadio, Oct. 2005

"Single-source RF energy in a transmission line and laser
light are both coherent electromagnetic energy waves that
obey the laws of superposition, interference, conservation
of energy, and conservation of momentum."

"The term 'power flow' has been avoided in favor of 'energy
flow'. Power is a measure of that energy flow per unit time
through a plane. Likewise, the EM fields in the waves do the
interfering. Powers, treated as scalars, are incapable of
interference. Any sign associated with a power in this paper
is the sign of the cosine of the phase angle between two
voltage phasors."

If you don't believe that power
interferes, then why else would you continually write interference
equations in terms of power?

Because that's what Dr. Best, Hecht, and Born and Wolf do.
Intensity, irradiance, and Poynting vectors are *power*
densities. Multiply the following intensity-irradiance
equation by unit-area and what do you get? Why, you get
WATTS of power!

Itot = I1 + I2 + 2*SQRT(I1*I2)cos(A) in watts/unit-area

Multiplying both sides of the equation by unit-area

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

I assume that's how Dr. Best came up with the equation.

Or don't even multiply by unit area - just use Poynting
vectors instead where each P above is a Poynting vector.
The dimensions of a Poynting vector are identical to
the dimensions of irradiance and intensity.

You can't just arbitrarily throw
quantities with any units you like into equations, and then claim
authoritative references as your source, Cecil.

I have not done that, Jim. The Poynting vector has exactly
the same units as intensity and irradiance. Multiply both
sides of the equation by unit-area and the result is WATTS,
the unit of power and that's fully consistent with the
rules of mathematics.

Is it your contention
that interference is not a validating pre-requisite for use in an
interference equation?

The question appears to have a trivial answer so it must
be just another straw man. Yes, interference exists if
interference exists and interference doesn't exist if
interference doesn't exist. Satisfied?

I'm pretty sure somebody using the name Cecil Moore posted Ptot = P1 +
P2 +2*SQRT(P1*P2), and used the equation to show how two 100 watt
generators generate 400 watts. Help me out. Where did I mess up here?

False so just another straw man. I said two 100 watt generators
do *NOT* generate 400 watts because there is no interference
between the generators. Maybe you need your glasses changed?
I did follow that posting up showing how two 100 watt *waves*
can engage in total constructive interference and obtain a total
of 400 watts.

Even you should be able to figure out how two 100 watt generators
can be made to produce a forward power of 400 watts in a
transmission line with an SWR of 5.83:1 and that is perfectly
consistent with Hecht, and Born & Wolf's intensity equations.

************************************************** ****************
HECHT AND BORN & WOLF'S TOTAL CONSTRUCTIVE INTERFERENCE EQUATIONS
ASSUME THERE IS AN EQUAL MAGNITUDE OF TOTAL DESTRUCTIVE INTERFERENCE
OCCURRING SOMEWHERE ELSE TO SATISFY THE REQUIREMENTS OF THE
CONSERVATION OF ENERGY PRINCIPLE. For every total constructive
interference equation I1 + I2 + 2*SQRT(I1*I2), there exists a
total destructive interference equation I1 + I2 - 2*SQRT(I1*I2)
The destructive interference and constructive interference
always sum to a net power density of ZERO such that the AVERAGE
power always remains the same.
************************************************** ****************

Let's say we have two light waves of 100 watts/cm^2 intensity
and we cause them to interfere constructively. Here's the
intensity equation for total constructive interference.

I1 + I2 + 2*SQRT(I1*I2) = 100 + 100 + 2*SQRT(100*100) = 400 watts/cm^2

Multiply both sides of the equation by cm^2 and you get
400 watts of power and indeed that square cm would be
getting very warm. Somewhere else exists a square cm
with zero intensity.

That is Born and Wolf's equation (16a) on page 259 of the 4th
edition of "Principles of Optics). The equation is correct
and the dimensions are correct. It is also Hecht's equation (9.15)
on page 388 of the 4th edition of "Optics". Those authors all label
the 2*SQRT(I1*I2) term as the *interference term*.

Let's say we have two RF waves or 100 watts/cm^2 intensity and
we cause them to interfere constructively in a coax transmission
line with a cross sectional area of one square cm.

P1 + P2 + 2*SQRT(P1*P2) = 100 + 100 + 2*SQRT(100*100) = 400 watts/cm^2.

With those dimensions, the intensity equation and the Poynting
vector equation are EXACTLY the same. This is equation 12 from
Dr. Best's QEX article, "Wave Mechanics of Transmission Lines,
Part 3: ..." in the Nov/Dec 2001 edition. The fixed cross sectional
area of the coax is redundant and we can choose to deal entirely
with watts.
--
73, Cecil http://www.w5dxp.com