Cecil,

You've set up a false dichotomy here. When I, and others, write "The
electric field is the superposition of a forward and reverse traveling
wave" maybe it would be better to say "The electric field has two
terms, one that appears to be a forward traveling wave and one that
appears to be a reverse traveling wave." or something like that.
There's one electric field vector and one Poynting vector. Or there
are two. The structure of the electric field and the structure of the
real part of the Poynting vector both admit BOTH explanations of what's
happening.

You're not gonna get 300J in your one second line.... the stored energy
flux in the line depends on the wavelength of the incident RF, and in
retrospect, you might expect this from the fact that a misterminated
line goes through cyclical impedance variations as you change its
length (something that I know you're quite familiar with :-) )

I think the energy density per unit length in the line is proportional
to the Poynting vector (or it's integral over the cable cross section,
and the proportionality constant is the group velocity of the waves, I
think) I left Jackson at work, so I'm not certain right now. What I
am certain of is that you can't take the energy in the forward wave and
add it to the energy of the reflected wave and get that there are 300J
in a 1 second line carrying a 200W forward wave and a 100W reverse
wave. Rather, there's a 100W net forward power flux and THAT will give
you the energy contained in the part of the field that's actually
moving from source to load. The energy contained in the reactive part
has an integral that's going to cyclically vary with the length of the
line, and sometimes goes through zero (kL or kL - phi equal to an
integer multiple of Pi... or any integer multiple of a half wavelength,
which happens to be the length of an impedance repeating line, eh?)



Dan

wrote:
When I, and others, write "The
electric field is the superposition of a forward and reverse traveling
wave" maybe it would be better to say "The electric field has two
terms, one that appears to be a forward traveling wave and one that
appears to be a reverse traveling wave." or something like that.
There's one electric field vector and one Poynting vector. Or there
are two. The structure of the electric field and the structure of the
real part of the Poynting vector both admit BOTH explanations of what's
happening.

I know and accept both explanations. The problem is the other side
refuses to acknowledge the validity of the wave reflection model.
If you have gotten the idea that I reject the superposed wave model,
you are mistaken. I fully accept both models. The problem is that
others have rejected the non-superposed component wave model.

I contend that one gets the same results using the components of
superposition, i.e. the forward wave and the reflected wave, that
one obtains after the superposition of those two waves. Others say
that is an invalid treatment because superposition causes the
reflected wave to cease to exist and the energy just "sloshes"
around inside the transmission line. (Never mind that RF energy
must necessarily travel at the speed of light and only reverses
direction at an impedance discontinuity.)

Rather, there's a 100W net forward power flux and THAT will give
you the energy contained in the part of the field that's actually
moving from source to load. The energy contained in the reactive part
has an integral that's going to cyclically vary with the length of the
line, and sometimes goes through zero (kL or kL - phi equal to an
integer multiple of Pi... or any integer multiple of a half wavelength,
which happens to be the length of an impedance repeating line, eh?)

That's one model. The other model is, assuming a purely resistive Z0,
the forward voltage is in phase with the forward current and therefore
there are no reactive vars in the forward wave. The reflected voltage
is in phase with the reflected current and therefore there are no
reactive vars in the reflected wave. This model works just as well as
the one above, sometimes better because of simplicity. It has the
advantage of being easily able to track the real energy because there
is no "unreal" energy in the model. :-)

If the forward wave component is analyzed separately, there are no vars
because the forward voltage is in zero phase with the forward current
(assuming a perfectly resistive Z0). The same is true for the reflected
wave. So we are easily able to calculate how much energy is contained
in those two waves devoid of any calculation of vars.

Assume that we have a one megahertz signal into a transmission line
that is electrically 360 degrees long, near lossless, the forward
power is 200W, and the reflected power is 100W. I am willing to bet
the energy contained in the feedline during steady-state is very
close to 300 microjoules no matter how complicated the math used to
get the answer that I just came up with off the top of my head.

Note that the transmission line is one millionth of a second long
and therefore contains one millionth of the energy of a one
second long line.
--
73, Cecil http://www.qsl.net/w5dxp

I say it's 100 microjoules.

200W forward - 100W reverse = 100W net forward power. The percieved
issue of some people not believing in the seperate forward and
reflected waves just doesn't come in here... it's that the real part of
the Poynting vector is REDUCED by reflections. If you want to contest
this point then you need to tell me where the sign error is.

If you have a constant voltage (constant electric field) output on your
radio then this effect actually causes LOSS of power transfer through
even a lossless line.

You've got a 200W matched condition, power flux is 200W. You have 100W
reflected wave, you get a net power flux of 200W - 100W = 100W. You
can see this from the Poynting vector which is proportional to the
difference of the squares of the electric field amplitudes of the
forward and reflected waves. You can also do this with lumped circut
impedance analysis too.

If you can't bump Ef up by using an impedance matching network, the net
power flux is REDUCED by the reflected wave, and as such, the stored
energy in the fields in the line is ALSO reduced. If you can increase
the forward electric field in the face of mismatch, you can push the
200W into the load.

The reflected wave makes it so you need more voltage to push RF down
the coax.

Not 300 microjoules. 100 microjoules. The energy per unit length in
the line is proportional to the Poynting vector.



Dan

wrote:
I say it's 100 microjoules.
200W forward - 100W reverse = 100W net forward power.

Sorry Dan, you are right about the power and wrong
about the energy. There are indeed 100 watts of *net*
power. But we are not talking about the net energy
delivered to the load. We are talking about the total
energy in the transmission line and there's no such
thing (to the best of my knowledge) as negative energy.
Forward traveling energy is positive energy. Reverse
traveling energy is positive energy. The energy rejected
by the load is NOT negative energy. Forward traveling
energy and reverse traveling energy add, not subtract.

Hint: Two energy components cannot superpose to a zero
scalar value. The result is always a scalar sum.

If we have 200 microjoules in the forward wave and we
have 100 microjoules in the reflected wave, the total
energy in the transmission line is 300 microjoules. If
the standing wave model differs from that amount, it
is wrong.

You
can see this from the Poynting vector which is proportional to the
difference of the squares of the electric field amplitudes of the
forward and reflected waves.

True for net watts, not true for joules. In the standing wave
model, there's 100 watts of net power containing 100 microjoules.
The other 200 microjoules are stored in the (virtual) reactances.
If you calculate the energy necessarily stored in the L and C of
the line, you will find the other 200 microjoules. I would have
to hit the books to refresh my memory on that calculation but
any other result would violate the conservation of energy principle.

If you can't bump Ef up by using an impedance matching network, the net
power flux is REDUCED by the reflected wave, and as such, the stored
energy in the fields in the line is ALSO reduced.

That applies to the watts. It doesn't apply to the vars. The actual
voltages and currents are increased by the standing waves while the
phase angle goes non-zero. Vars require real energy. That real energy
can be calculated by knowing the current through a perfect inductor
and/or the voltage across a real capacitor.

Not 300 microjoules. 100 microjoules. The energy per unit length in
the line is proportional to the Poynting vector.

The energy per unit length is not proportional to the net Poynting
vector which is (Pz+ - Pz-) (using Ramo/Whinnery conventions). The
energy per unit length is actually (Pz+ + Pz-). Why that has to be
true is contained in the conservation of energy principle and is
the source of confusion for many posters on this newsgroup.

Hint: Has anyone ever seen a quart of negative water?
--
73, Cecil http://www.qsl.net/w5dxp

I'll find the book.

I see what you're saying, but I'd like to work through in detail. What
page should I be looking on?... I'll get back to you on Monday; Ramo
and Whinnery's "Fields and Waves..." is in the UMCP library.

Dan

wrote:
I see what you're saying, but I'd like to work through in detail. What
page should I be looking on?... I'll get back to you on Monday; Ramo
and Whinnery's "Fields and Waves..." is in the UMCP library.

You won't find exactly what I am saying in Ramo/Whinnery.
I'm pre-assuming that you accept the conservation of energy
principle. :-)

My 1950's Texas A&M college textbook was, "Fields and Waves
in Modern Radio", by Ramo/Whinnery, 2nd edition pp 284-296.
--
73, Cecil http://www.qsl.net/w5dxp

I've come around to that conservation of energy stuff ;-)

I understand that your argument involves the energy that enters the
line before it knows anything about the load, the energy that enters in
an initial transient, but unless you can show that nothing happens
during the initial transient to deliver some or all of that initial
energy to the load, your argument has a hole.

You're presupposing that there is some energy that enters the line
during an initial transient that cannot leave until you shut the source
off, so you get the 100J related to the 100W net power flow and 100J
that went into the line before the source knew about the load.. and
then there's another 100J that enters somehow? I guess to set up the
reflected wave?

The argument is circular. The initial transient supplies 200J of
stored energy to the line so there must be 300J in a one second line if
there's 100J in the steady-state fields associated with power flow.
Since there's 300J in the line, the initial transient must have
supplied 200J in stored energy. It's just not working for me.


Dan