Cecil,

I think you are conflating models with nature, and trying to champion
one correct model over another correct model! It's confusing to
onlookers and boring.

There is NO inconsistency between saying "there's only one
electromagnetic field in a transmission line" and "a circulator
seperates the forward wave from the reflected wave" if you've suitably
defined what all those terms mean and you do the correct math.

The electromagnetic field as a function of space and time in the
coaxial transmission line is a three-dimensional time dependent field.
There's a description wherein one single vector valued function
E(r,phi,z, t) describes the electric field and another describes the
magnetic field, and of course, you can get one from the other, so in
some sense, all you need to describe what's going on is E(r,phi,z,t).

Now, in the coaxial TEM mode the radial and azimuthal dependence of the
fields becomes trivial, and you're just left with some function E'(z,t)
to describe the electric field, and one B'(z,t) for the magnetic field
(once again, you can of course, get one from the other) It turns out
that mathematically you can represent this function as a superposition
of other functions, forward and reverse traveling waves. It's just a
DIFFERENT WAY OF WRITING IT DOWN.

A circulator *doesn't know math*. Its operation may have a simple
description in the language of forward and reverse waves, but it does
what it does no matter what model you use to describe it. If you get
different answers using a forward and reflected wave description than
some other description, then one or both of your descriptions are
wrong. The conversion of one mathematical description of the
electromagnetic field into a series of statements in English and the
argument based on those words never gets you anywhere on this topic.
Why not pick up a copy of Jackson's Electrodynamics and write down what
you're trying to say mathematically. If you're right, everyone will
have to be convinced.

73,
Dan

wrote:
I think you are conflating models with nature, and trying to champion
one correct model over another correct model!

Nope, the mainstream wave reflection model is being attacked
as incorrect.

I'm trying to correct some misconceptions concerning
violations of the conservation of energy principle
by simplified model shortcuts. Modern RF EM textbooks don't
deal with conservation of energy. There's no equations to
quote because the textbooks ignore the problem.

For instance, it can be shown that a one-second long lossless
transmission line with a measured forward power of 200 watts
and a measured reflected power of 100 watts does indeed in
reality contain 300 joules of RF energy traveling at the speed
of light. Is there really any more logical location for those
300 joules than in the forward and reflected waves which are
necessary for standing waves to exist?

Einstein said a math model of reality should be as simple as
possible but not too simple.
--
73, Cecil, http://www.qsl.net/w5dxp

Hey Cecil,

Can you sum up the problem with conservation of energy that modern RF
textbooks get wrong?

Dan

wrote:
Can you sum up the problem with conservation of energy that modern RF
textbooks get wrong?

They don't get it wrong - they just don't discuss it at all.
But here is an example of the problem:

http://eznec.com/misc/food_for_thought/

First article - last paragraph. W7EL considers
steady-state conditions while ignoring the previous
transient state conditions. He implies that the
energy in the reflected wave cannot be recovered but
it is indeed dissipated as power in the system after
power is removed from the source. The source supplies
exactly the amount of energy during the transient power
up conditions needed to support the forward and reflected
waves during steady-state. This is easy to prove. But
W7EL's Ivory Tower protects Him from peons like me.
--
73, Cecil http://www.qsl.net/w5dxp

The net power flux in the line gets smaller as the reflected wave gets
stronger while maintaining a constant electric field (constant voltage
as in Roy's example). If you can match to the new impedance at the
line input; that is, make the electric fields both stronger, you can
get a larger net power flux even in the presence of some elevated SWR.

See LaTeX formatted math at
http://en.wikipedia.org/wiki/Useran_Zimmerman/Sandbox

The flux of stored power in the line, interestingly enough, is a
sinusoidal function of position.

I'm still thinking what to make of it, but I thought I'd post the math
for people to look at (and check, please!!!!)

... I'll be back later.

73,
Dan

wrote:
I'm still thinking what to make of it, but I thought I'd post the math
for people to look at (and check, please!!!!)

Thanks, Dan.

If I understand correctly, Roy's argument is that since
the source is not supplying any steady-state energy to
the lossless stub, there is no energy in the reflected
wave within the stub.

If we make Roy's lossless stub one second long, the
picture becomes clearer. For the first two seconds,
the 100 watt source pours 200 joules of RF energy
into the stub. After that, during steady-state, the
source supplies zero energy. But those 200 joules
are still in the stub, 100 joules in the forward
wave and 100 joules in the reflected wave, and they must
obey the conservation of energy principle.

There is *always* the exact amount of energy in the
forward and reflected waves as required to achieve
the forward and reflected power readings in a Z0
calibrated environment.
--
73, Cecil, W5DXP

Cecil Moore wrote:

If I understand correctly, Roy's argument is that since
the source is not supplying any steady-state energy to
the lossless stub, there is no energy in the reflected
wave within the stub.

That sounds right... if the reflection coefficient is 1 then there's no
net power flux into/through the line in steady state, and this can be
described if you like by counterpropagating waves each carrying the
same amount of energy.

The problem is, in your other example where you say 200 joules in the
forward wave + 100 joules in the reflected wave = 300 joules in the
line total, you're neglecting the vector character of the power flux.

Yes, the waves carry energy, but they carry it in different directions.
The net power flux in the line with 200W forward power and 100W
reflected power is 100W net power flowing to the load from the source.
The real part of the Poynting vector of the reflected wave opposes that
of the forward wave, as long as I got all the signs right.

I don't think we can neglect the imaginary part of the Poynting vector,
though. It's not zero and I think it represents the flow of the power
in the stored fields in the line, and if we want to get the total
energy in the line, we have to include the stored fields.


Dan