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

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

I'm glad - most folks here ignore it. :-)

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.

Let's return to the one second long lossless transmission line.
From a 100 watt transmitter, at the end of second number one,
the line will contain 100 joules and the load will have accepted
zero joules. Since the load is rejecting 1/2 of the incident energy,
at the end of the 2nd second, the source will have supplied 200 joules,
there will be 150 joules of energy in the line, and 50 joules will have
been accepted by the load. If the source is equipped with a
circulator+load, this is steady-state with 150 joules of energy stored
in the transmission line.

At t=0:
zero joules zero joules
100w--------one-second long feedline------load rho^2=0.5
Pfor=0-- --Pref=0 Pload=0

At t=1:
100 joules zero joules
100w--------one-second long feedline------load
Pfor=100w-- --Pref=0 Pload=0

At t=2:
150 joules 50 joules
100w--------one-second long feedline------load
Pfor=100w-- --Pref=50w Pload=50w

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?

Yes, at the end of the 2nd second, the source has supplied 200 joules
and the load has accepted 50 joules. That leaves 150 joules left over
that cannot be any place except in the line according to the
conservation of energy principle. In a circulator+load system, we
have reached steady state with 150 joules in the transmission line
that will not reach the load until after the source is powered down.

The argument is circular.

Proving that confusion exists. It's actually not circular. It's
based on cause, effect, and the conservation of energy principle.
I apologize if I have not explained it in a way that is easy to
understand. Please bear with me.

It's all linear cause and effect. With an ideal auto-tuner
at the source, none of the reflected energy is accepted back by
the source. Half the energy incident upon the load is rejected. There
is no other place for the extra energy to be except inside the
transmission line. I have an EXCEL spreadsheet that might help you
sort all of this out. A copy of its output is available at:

http://www.qsl.net/w5dxp/1secsgat.gif
--
73, Cecil http://www.qsl.net/w5dxp

Cecil Moore wrote:
I have an EXCEL spreadsheet that might help you
sort all of this out. A copy of its output is available at:

http://www.qsl.net/w5dxp/1secsgat.gif

The EXCEL spreadsheet corresponding to the above can be
downloaded from: http://www.qsl.net/w5dxp/1secTline.xls
It includes a graph of forward power, reflected power,
and joules stored in the transmission line.
--
73, Cecil http://www.qsl.net/w5dxp