Error correction
 

Reg Edwards wrote:
A correction - insert dt instead of dz.

Another correction is in order. The resistive term should be i(z) * R
and the conductance term should be v(z) * G.


The fundamental partial differential equations of transmission lines
are -

- dv/dz = R + L*di/dt

- di/dz = G + C*dv/dt

where volts v and current i are incremental functions of distance and
time, and z is incremental distance along line.

bart

Mismatched Zo Connectors
 

On Sat, 26 Aug 2006 12:02:14 GMT, Cecil Moore
wrote:

the newcomer
assumes that Cecil is there without ever having to swing
a bat.

The "newcomer" must be defined in the IEEE dictionary as "dolt" given
there are many possible solutions, and only a dolt (obviously not a
fan) would come to only ONE conclusion and that one being the least
likely in baseball experience.

The fan sitting next to him, hearing this exclamation is undoubtedly
squirming in his seat. That dolt has left unexpressed how, without
swinging a bat, that the runner was advanced to third, or worse, that
he got there on the basis of not swinging a bat alone - clearly a
violation of laws of baseball.

Let's consider another conundrum. The dolt, having arrived late, now
perceives:
1. the returned, fielded ball held by the catcher standing on home;
2. three bases loaded with runners;
3. a runner on the base line;
4. the scoreboard reveals this is the bottom of the ninth with two
outs.

Are there 4 men in the transmission line, or only three with the
mismatched termination at the load of home base?

The dolt would tell the fan next to him four (using specious math);
the fan would say none (using the laws of baseball). Solution = the
umpire would agree with the fan - and the side retires, the game is
over.

In the transient end-of-state, it takes a few minutes before the dolt
realizes
1. the solution;
2. he has no beer;
3. there are 75000 fans in the exits between him and his car;
4. Luigi is going to be waiting for him to cover his lost sucker bet;
5. he has no beer.

Mismatched Zo Connectors
 

Cecil Moore wrote:

[snip]

Some people on this newsgroup say that the wave reflection
model is invalid, that forward and reflected waves don't
have a separate existence. From QEX: "Contrary to popular
views, the forward and reverse waves on a transmission line
are not separate fields." It would follow that a laser beam
normally incident upon an ideal mirror results in a beam of
light not superposed from separate forward and reverse fields.

I have challenged people holding those concepts to create a
standing wave without superposing separate forward and
reverse waves and have gotten zero responses.

Cecil,

I believe Dan has addressed this issue, and I am sure that I have on
many occasions.

When superposition applies, as it does in this linear, non-pathological
case, there is no difference between the reality of the components vs.
the reality of the sum. In other words, there is no more information
from your separation of a standing wave into forward and reverse
components than there is in the standing wave itself.

The standing wave is a perfectly good and complete solution to the wave
equations applicable to this steady-state problem. It is possible to
sub-divide in many ways, but there is no new information in doing so.

If you want to specifically address transients then another set of
equations will be needed.


ad hominem

You have railed against seduction by math models on many occasions.
However, that is exactly what you are doing here. Trying to create some
new physical reality by manipulating the numbers.

/ad hominem

73,
Gene
W4SZ

Mismatched Zo Connectors
 

Cecil Moore wrote:
Gene Fuller wrote:
Try writing the appropriate equations for your puzzler, in steady state
conditions, and then figure out where to insert the transient behavior.

I have already provided the equations, Gene. In a one second long
lossless transmission line, 200 watts of forward power equals 200
joules of energy in the forward wave. 100 watts of reflected power
equals 100 joules in the reflected wave. Total joules in the
transmission line equals 200 + 100 = 300 joules. The equations
are trivial.
--
73, Cecil, W5DXP


Cecil,

Gee, somehow I can't quite pull the wave equations out of your "trivial"
response.

73,
Gene
W4SZ

Mismatched Zo Connectors
 

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

Mismatched Zo Connectors
 

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

Mismatched Zo Connectors
 

Gene Fuller wrote:
When superposition applies, as it does in this linear, non-pathological
case, there is no difference between the reality of the components vs.
the reality of the sum.

I accept both methods of analysis. What I object to is people
rejecting the wave reflection model. e.g. "Reflected waves
don't really exist and don't really contain any energy."
As in the earlier discussion about standing wave phase, you
and I wind up on the same side of the argument.

What I object to is the irrational conclusions drawn by proponents
of the standing wave analysis. Here are some of the past assertions:

Forward waves and reflected waves cease to exist after they have
been superposed. The standing wave is all that is left.

Question: If the components of superposition cease to exist,
doesn't that mean the products of superposition also cease to
exist? (No answer)

Standing waves don't require a forward wave and a reflected wave.

Question: How does one obtain a standing wave without a forward
traveling wave and a reverse traveling wave? (No answer)

You have railed against seduction by math models on many occasions.

I have railed against the assertions that superposition destroys
forward and reflected waves such that they cease to exist in reality.
From a recent QEX article: "I wish to emphasize the fact that the
forward and reverse waves really do not exist separately, ..."

So I ask you, Gene, if forward waves and reverse waves do not
exist separately, how can they possibly be superposed? Seems to me,
the above statement from QEX is a violation of cause and effect.

If forward waves and reverse waves do not exist separately, how
can they possibly be separated by a circulator?
--
73, Cecil http://www.qsl.net/w5dxp

Mismatched Zo Connectors
 

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

Mismatched Zo Connectors
 

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

Mismatched Zo Connectors
 

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