Revisiting the Power Explanation
 

Walter Maxwell wrote in
:

....
voltage and current values of rho at the matching point which produces
either a virtual short or a virtual open circuit that causes the
re-reflection. I have shown this to be true in my QEX article of
....

Walt,

I am talking about the steady state.

I see discussion about this need for total re-reflection at the source,
and some even describing the function of an ATU as a "total re-
reflector", and it makes me wonder why we are grappling with re-
reflection at the source end of the line in the steady state.

My understanding is that:
1. The ratio of elecric field to magnetic field per unit length (or V/I)
in an infinite transmission line is constrained by the geometry of the
line and the permeability and permittivity of the components carrying the
two fields. That ratio is expressed as Zo.
2. If a wave with V/I=Zo reaches the end of the line, and the load does
not permit V/I to be Zo (ie a mismatch), a reflected wave is launched,
and it is of magnitude and phase such that (Vf+Vr)/If-Ir)=Zl (all complex
values).

In the steady state, after all has settled (ie converged), the
transmission line reaches an equilibrium where the source V/I
characteristic is consistent with (Vf+Vr)/If-Ir) at the input end of the
line.

Why is it necessary to complicate the analysis with tracking multiple re-
reflections, potentially an infinite number of reflections of diminishing
significance, an analysis that converges in the limit on the answer given
by the solution of the source V/I characteristic and (Vf+Vr)/If-Ir) at
the input end of the line (which is the equivalent input impedance). Note
that (Vf+Vr)/If-Ir) at the input end of the line is determined solely by
the tranmission line propagation constant, length, Zo and the far end
load impedance, for avoidance of doubt, source impedance is not
relevant.

Such an approach does not require invention of virtual re-reflectors or
virtual s/c or o/c, or ATUs or pi couplers with virtual properties.

Owen

PS: Before someone brings up TV ghosts, they are not steady state
phenomena. If significant distortion of modulation is caused by
reflections, then clearly the scenario is not sufficiently steady state
to allow steady state analysis.

Revisiting the Power Explanation
 

Keith Dysart wrote:
Have you computed the correct result then?

Yes, the results are identical with or without
the 1WL of 75 ohm lossless line, exactly as the
theory predicts it should be.

Have you read w2du's web page yet?

I am not sure where you are going with this. As you map
the system for s parameter evaluation, which is the two
port network that you are evaluating?

The generator's connection to the 450 ohm ladder-line.

An ideal source, as
used in this example, must be able to both source and sink
current. You will need to specify more for us to determine
whether the circuit you propose will achieve that to a
sufficient degree.

Actually, as the one asserting it is possible, the
onus of proof is upon you to come up with a real-
world design (besides the one in your dreams). I
predict you will need something like a circulator
to actually dissipate the reflected energy. Your
violation of the conservation of energy principle
just won't fly.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Owen Duffy wrote:
Why is it necessary to complicate the analysis with tracking multiple re-
reflections, potentially an infinite number of reflections of diminishing
significance, an analysis that converges in the limit on the answer given
by the solution of the source V/I characteristic and (Vf+Vr)/If-Ir) at
the input end of the line (which is the equivalent input impedance). Note
that (Vf+Vr)/If-Ir) at the input end of the line is determined solely by
the tranmission line propagation constant, length, Zo and the far end
load impedance, for avoidance of doubt, source impedance is not
relevant.

The answer is subtle. Consider the following lossless example.

XMTR--x--1WL 450 ohm line--y--1WL 450 ohm line--50 ohm load

The SWR is 9:1 everywhere on the 450 ohm line.
(Vf+Vr)/(If+Ir) = 50 ohms at points x and y. There are reflections
to the left of y but no reflections to the left of x. Why?

The answer is the interference
pattern set up by the 50 ohm environment left of x and the
450 ohm environment to the right of x. Total destructive
interference is occurring to the left of x and total constructive
interference is occurring to the right of x. That cannot be said
of point y yet the V/I ratio is identical to x. The physical rho
at point y is zero. The physical rho at point x is 0.8. That's
the difference. Reflections occur only at physical impedance
discontinuities.

In S-parameter terms at x: b1 = (s11)(a1) + (s12)(a2)

In RF terms at x: Vref1 = rho1(Vfor1) + tau2(Vref2)

The two terms to the right of the equals sign are the voltages
that engage in wave cancellation resulting in a Z0-match at x.

So to answer your question: The 50 ohm virtual impedance at point
y is incapable of causing reflections even though it has an identical
V/I ratio to point x. The physical impedance discontinuity at x is
fully capable of causing reflections along with the ensuing
interference.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Walter Maxwell wrote:

Sorry Jim, but I take exception to your statement, "If redirection of energy takes place,
it takes place by reflection - not interference."

Hi Walt -

I am preparing a more lengthy response, and in the interim let me say
that I'm sorry you take exception. But my statement is nevertheless
honest, truthful, and factual. What part of it do you feel is
contradicted by physical laws?

I am familiar with your chapter 23. You sent me a copy of it quite
some time ago. I had hoped that our work together might have changed
your point of view about this.

73, Jim AC6XG

It is the interference between the forward and reflected voltages and beween the forward and reflected
currents that yields the resultant voltage and current values of rho at the matching point which produces
either a virtual short or a virtual open circuit that causes the re-reflection. I have shown this to be true
in my QEX article of Mar/Apr 1998, entitled, "Examining the Mechanics of Wave Interference in Impedance
Matching. It is also Chapter 23 in Reflections 2.

Using the complex values of rho I have shown the magnitude and phase relationships of the aforementioned
voltages and currents at the stub point that result in a virtual open circuit at the stub point to waves
reflected from a 3:1 mismatched load. The result is no reflections on the line between the stub and the
source, but a 3:1 SWR on the line between the mismatched load and the stub. If you don't have a copy of this
article please let me know and I'll send you one via email.

Walt, W2DU

Revisiting the Power Explanation
 

Jim Kelley wrote:
But my statement is nevertheless
honest, truthful, and factual. What part of it do you feel is
contradicted by physical laws?

I find it strange that Hecht's definition of "interference"
doesn't even mention your alleged cause of the interference,
i.e. superposition. From "Optics", by Hecht in his own
bold italics:

"Optical interference corresponds to the interaction of
two or more light waves yielding a resultant irradiance
that deviates from the sum of the component irradiances."

One might argue that "the interaction of two or more light
waves" is superposition but why didn't Hecht choose
"superposition" instead of "interaction"? And a
"correspondence" of interference to the interaction of
the waves certainly doesn't imply cause and effect. It
seems instead to imply an inseparability between the
interference and the interaction of the waves which
is of course obvious.

Hecht seems to treat the superposition principle as more
of a set of rules to be followed by the interfering waves
than an actual act. FYI, the definition of "superpose"
doesn't mention EM waves at all.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Cecil Moore wrote in
et:

....
So to answer your question: The 50 ohm virtual impedance at point
y is incapable of causing reflections even though it has an identical
V/I ratio to point x. The physical impedance discontinuity at x is
fully capable of causing reflections along with the ensuing
interference.

....

Cecil, I don't understand what you mean by 'virtual impedance', why and how
it differs from equivalent impedance (being the complex ratio of V/I at a
point), and why it has these magical relection properties. Perhaps it is
just an invention to support your proposition.

Given that my statement was qualified to the steady state, your inisistence
that point x is different in behaviour to point y says to me you are
silently changing scope to transient conditions to confuse the reader.

Owen

Revisiting the Power Explanation
 

Owen Duffy wrote:
Cecil, I don't understand what you mean by 'virtual impedance', why and how
it differs from equivalent impedance (being the complex ratio of V/I at a
point), and why it has these magical relection properties. Perhaps it is
just an invention to support your proposition.

The IEEE Dictionary seemingly goes out of its way to
try to emphasize the difference between a virtual
impedance and a physical impedor. Obviously, there is
a difference between a physical resistor and the ratio
of voltage to current called resistance where no physical
resistor exists. One is the (A) definition and the other
is the (B) definition. A virtual resistance does not
dissipate power. What? A dissipationless resistance?

If no physical impedance discontinuity exists, there can
be no reflections. V/I ratios, by themselves, with no
associated physical impedances, are a result, and not the
cause of anything. (The exception to that statement is a
source.)

The impedance looking into a transmission line is a virtual
impedance caused by system parameters. It is a result -
incapable of causing anything. Unless it is located at a
physical impedance discontinuity, absolutely nothing happens
because of the V/I ratio.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

On Mar 29, 6:41 pm, Cecil Moore wrote:
Keith Dysart wrote:
Have you computed the correct result then?

Yes, the results are identical with or without
the 1WL of 75 ohm lossless line, exactly as the
theory predicts it should be.

This is clearly not correct. Without the 75 Ohm line the first
reflection does not arrive back at the generator for 62 cycles.
With the 75 Ohm line, the first reflection arrives back at the
generator after only two cycles. The response is not at all
the same, though I agree, they do arrive at the same steady
state condition.

The discontinuity between the 450 Ohm line and the 75 Ohm line
produces a re-reflection back towards the load, which is one of
the two sources of ghosts in your experiment, the other being
the 75 Ohm line connection to the 450 Ohm generator. Remember
that any impedance discontinuity produces a reflection. Without
the 75 Ohm line, there are no reflections back towards the load
and no ghosts (i.e. for the original experiment).

So the two experiments are clearly different. For the experiment
without the 75 Ohm line (i.e. the original example), can you
derive the magnitude of the re-reflected voltage that reaches
the load and creates a ghost?

If so, please let us know the magnitude and how to derive it.

Have you read w2du's web page yet?

Yes, but it is discussing, as its title clearly states, "Additional
Experimental Evidence Proving Existence of Conjugate Match and
Non-Dissipative Source Resistance In RF Power Amplifiers".
I find it not applicable to the experiment at hand since we
are neither discussing a reasonable implementation of an
RF Power Amplifier nor is there a conjugate match.

Regardless, the real question is can you compute the magnitude
of the re-reflection when it reaches the load and what is the
methodology? (And please do not modify the experiment to do so.)

....Keith

Revisiting the Power Explanation
 

On Mar 29, 7:17 pm, Cecil Moore wrote:
Owen Duffy wrote:
Why is it necessary to complicate the analysis with tracking multiple re-
reflections, potentially an infinite number of reflections of diminishing
significance, an analysis that converges in the limit on the answer given
by the solution of the source V/I characteristic and (Vf+Vr)/If-Ir) at
the input end of the line (which is the equivalent input impedance). Note
that (Vf+Vr)/If-Ir) at the input end of the line is determined solely by
the tranmission line propagation constant, length, Zo and the far end
load impedance, for avoidance of doubt, source impedance is not
relevant.

The answer is subtle. Consider the following lossless example.

XMTR--x--1WL 450 ohm line--y--1WL 450 ohm line--50 ohm load

The SWR is 9:1 everywhere on the 450 ohm line.
(Vf+Vr)/(If+Ir) = 50 ohms at points x and y. There are reflections
to the left of y but no reflections to the left of x. Why?

Did you swap x and y in the second last sentence and really mean
"There are reflections to the left of x but no reflections to
the left of y"?

....Keith

Revisiting the Power Explanation
 

Keith Dysart wrote:
Cecil Moore wrote:
Keith Dysart wrote:
Have you computed the correct result then?
Yes, the results are identical with or without
the 1WL of 75 ohm lossless line, exactly as the
theory predicts it should be.

This is clearly not correct. Without the 75 Ohm line the first
reflection does not arrive back at the generator for 62 cycles.
With the 75 Ohm line, the first reflection arrives back at the
generator after only two cycles. The response is not at all
the same, though I agree, they do arrive at the same steady
state condition.

I am only talking about steady-state so the conditions are
indeed identical, as I stated.

So the two experiments are clearly different.

No, technical theory says they have to be the same in the
steady-state condition. Saying they are different violates
the laws of physics.

Yes, but it is discussing, as its title clearly states, "Additional
Experimental Evidence Proving Existence of Conjugate Match and
Non-Dissipative Source Resistance In RF Power Amplifiers".
I find it not applicable to the experiment at hand since we
are neither discussing a reasonable implementation of an
RF Power Amplifier nor is there a conjugate match.

That you find it "not applicable" is part of your problem.
You ignore reality in favor of your wet dreams. That's your
choice but please don't try to convince the rest of the
world to join you. The impedance seen by the reflections is
NOT the 450 ohm resistor. The impedance seen by the reflections
is the V/I ratio of the source.

Regardless, the real question is can you compute the magnitude
of the re-reflection when it reaches the load and what is the
methodology? (And please do not modify the experiment to do so.)

I have asked you before - please provide me a math model of the
source and I will be more than glad to do so. Hint: Handwaving
the existence of a source is not acceptable. Where's the beef?
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Keith Dysart wrote:
Did you swap x and y in the second last sentence and really mean
"There are reflections to the left of x but no reflections to
the left of y"?

No, a properly calibrated Bird wattmeter will measure
some reflected power to the left of y but zero
reflected power to the left of x. Hint: Point x achieves
a Z0-match which re-reflects all reflected energy back
toward the load. That is a result of total destructive
interference toward the source and total constructive
interference toward the load, a concept that presently
seems to be beyond your comprehension.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

On Fri, 30 Mar 2007 02:59:38 GMT, Cecil Moore
wrote:

XMTR--x--1WL 450 ohm line--y--1WL 450 ohm line--50 ohm load

Keith Dysart wrote:
Did you swap x and y in the second last sentence and really mean
"There are reflections to the left of x but no reflections to
the left of y"?

No, a properly calibrated Bird wattmeter will measure
some reflected power to the left of y but zero
reflected power to the left of x.

You clearly have never calibrated a Bird Wattmeter for a 450 Ohm Line
(or any line).

As for this "some" power. "Some" power can be "measured" by any of a
half dozen ways to improperly use instrumentation. It doesn't lift
the gravitas of a "hint" to proof.

Hint: Point x achieves
.... yadda yadda yadda ...
a concept that presently
seems to be beyond your comprehension.

This must be the 80% of correct that is moot.

73's
Richard Clark, KB7QHC

Revisiting the Power Explanation
 

On Mar 29, 10:55 pm, Cecil Moore wrote:
Keith Dysart wrote:
Cecil Moore wrote:
Keith Dysart wrote:
Have you computed the correct result then?
Yes, the results are identical with or without
the 1WL of 75 ohm lossless line, exactly as the
theory predicts it should be.

This is clearly not correct. Without the 75 Ohm line the first
reflection does not arrive back at the generator for 62 cycles.
With the 75 Ohm line, the first reflection arrives back at the
generator after only two cycles. The response is not at all
the same, though I agree, they do arrive at the same steady
state condition.

I am only talking about steady-state so the conditions are
indeed identical, as I stated.

That does cause some difficulties since we are discussing ghosts,
clearly a transient phenomenom. Remember the question: What is
the magnitude of the first re-reflection to reach the load?

So the two experiments are clearly different.

No, technical theory says they have to be the same in the
steady-state condition. Saying they are different violates
the laws of physics.

Thank you for agreeing that they are different for the non-steady
state situation under discussion.

Yes, but it is discussing, as its title clearly states, "Additional
Experimental Evidence Proving Existence of Conjugate Match and
Non-Dissipative Source Resistance In RF Power Amplifiers".
I find it not applicable to the experiment at hand since we
are neither discussing a reasonable implementation of an
RF Power Amplifier nor is there a conjugate match.

That you find it "not applicable" is part of your problem.
You ignore reality in favor of your wet dreams. That's your
choice but please don't try to convince the rest of the
world to join you. The impedance seen by the reflections is
NOT the 450 ohm resistor. The impedance seen by the reflections
is the V/I ratio of the source.

But what a surprise, that is 450 Ohms. Try plotting it. Compute
the slope.

Regardless, the real question is can you compute the magnitude
of the re-reflection when it reaches the load and what is the
methodology? (And please do not modify the experiment to do so.)

I have asked you before - please provide me a math model of the
source and I will be more than glad to do so. Hint: Handwaving
the existence of a source is not acceptable. Where's the beef?

Sure, why not? Just for fun let's do the Norton model for the
generator. A 2 Amp ideal current source in parallel with a
450 Ohm resistor. Recall that an ideal current source has an
infinite impedance and adjusts its voltage to whatever is necessary
to cause 2 Amps to flow. This is quite a simple model and
EXACTLY models the generator because it is the same as the
definition of the generator used in the experiment. It is
quite amenable to analysis.

Remember that the question to be answered is: What is the
magnitude of the first re-reflection to reach the load?

Use the methodology of your choice, but you can't make any
changes to the circuit since such changes might alter the
transient behaviour. Hints:
- steady state analysis is unlikely to work since the
question is about the transient behaviour.
- for a methodology that works try googling lattice diagrams.
These are specifically applicable to the transient behaviour
of a system.

And to get any marks at all, show your work along with the answer.

Good luck.

....Keith

Revisiting the Power Explanation
 

On Mar 29, 7:17 pm, Cecil Moore wrote:
The answer is subtle. Consider the following lossless example.

XMTR--x--1WL 450 ohm line--y--1WL 450 ohm line--50 ohm load

The SWR is 9:1 everywhere on the 450 ohm line.
(Vf+Vr)/(If+Ir) = 50 ohms at points x and y. There are reflections
to the left of y but no reflections to the left of x. Why?

The physical rho
at point y is zero. The physical rho at point x is 0.8. That's
the difference. Reflections occur only at physical impedance
discontinuities.

Certainly true. To be somewhat more complete there is another
rho at x. You have correctly computed rho from the generator
to the line, but there is also a rho from the line to the
generator: -0.8. This can handily be used to compute the
magnitude of the reflected signal that is re-reflected
towards the load. And when dealing with transients, will
permit you to compute the magnitude of the ghosts, of
which there are an infinite number for each change in
the signal, though of declining magnitude. In a sense,
the ghosts show how the system settles to its
'steady-state'.

....Keith

Revisiting the Power Explanation
 

Keith Dysart wrote:

w5dxp wrote:
The impedance seen by the reflections
is the V/I ratio of the source.

But what a surprise, that is 450 Ohms. Try plotting it. Compute
the slope.

It is 450 ohms under no load conditions. It drops when
one adds the load. Please read w2du's web page to find
out why the reflections do not see 450 ohms and so are
re-reflected.

http://www.w2du.com/r3ch19a.pdf

Sure, why not? Just for fun let's do the Norton model for the
generator.

Please choose a real world source.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Keith Dysart wrote:
Cecil Moore wrote:
The physical rho
at point y is zero. The physical rho at point x is 0.8. That's
the difference. Reflections occur only at physical impedance
discontinuities.

Certainly true. To be somewhat more complete there is another
rho at x. You have correctly computed rho from the generator
to the line, but there is also a rho from the line to the
generator: -0.8.

Not exactly correct. Rho is calculated at a point
of discontinuity, not from-to along a line. The
reverse rho at point x is -0.8. There could
exist another point of discontinuity inside the
source but unless reflections are allowed to reach
the source, we have no clue what it might be. If
100 volts is supplied at point x in the example,
we have no way of knowing what the source impedance
might be.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

On Thu, 29 Mar 2007 16:32:31 -0700, Jim Kelley wrote:



Walter Maxwell wrote:

Sorry Jim, but I take exception to your statement, "If redirection of energy takes place,
it takes place by reflection - not interference."

Hi Walt -

I am preparing a more lengthy response, and in the interim let me say
that I'm sorry you take exception. But my statement is nevertheless
honest, truthful, and factual. What part of it do you feel is
contradicted by physical laws?

Hi Jim,

It's been a long time since we discussed this point, so I've forgotten how we ended up on it. The part I feel
is contradicted is that when total re-reflection is caused without a total discontinuity such as a physical
short or open circuit, it is caused by resultant of the interference between the forward and reflected
voltages and the interference between the forward and reflected currents. When the phase relationships between
the respective voltages and currents are correctly adjusted to achieve an impedance match, the resultant is
either a virtual short circuit or a virtual open circuit, which causes total re-reflection of the waves
reflected from the mismatched load terminating the line. Consequently, the interferences cause the
re-reflection.

Are you saying that this explanation of the re-reflection concept is incorrect?

Walt

I am familiar with your chapter 23. You sent me a copy of it quite
some time ago. I had hoped that our work together might have changed
your point of view about this.

73, Jim AC6XG

It is the interference between the forward and reflected voltages and beween the forward and reflected
currents that yields the resultant voltage and current values of rho at the matching point which produces
either a virtual short or a virtual open circuit that causes the re-reflection. I have shown this to be true
in my QEX article of Mar/Apr 1998, entitled, "Examining the Mechanics of Wave Interference in Impedance
Matching. It is also Chapter 23 in Reflections 2.

Using the complex values of rho I have shown the magnitude and phase relationships of the aforementioned
voltages and currents at the stub point that result in a virtual open circuit at the stub point to waves
reflected from a 3:1 mismatched load. The result is no reflections on the line between the stub and the
source, but a 3:1 SWR on the line between the mismatched load and the stub. If you don't have a copy of this
article please let me know and I'll send you one via email.

Walt, W2DU

Revisiting the Power Explanation
 

On Thu, 29 Mar 2007 22:20:48 GMT, Owen Duffy wrote:

Walter Maxwell wrote in
:

...
voltage and current values of rho at the matching point which produces
either a virtual short or a virtual open circuit that causes the
re-reflection. I have shown this to be true in my QEX article of
...

Walt,

I am talking about the steady state.

Hi Owen, so am I. The value of (Vf+Vr)/(If-Ir)= Zi is the result of the convergence of all reflected waves.

I see discussion about this need for total re-reflection at the source,
and some even describing the function of an ATU as a "total re-
reflector", and it makes me wonder why we are grappling with re-
reflection at the source end of the line in the steady state.

If we don't consider re-reflected waves at the source end of the line the source is never going to deliver all
of its available power.

My understanding is that:
1. The ratio of elecric field to magnetic field per unit length (or V/I)
in an infinite transmission line is constrained by the geometry of the
line and the permeability and permittivity of the components carrying the
two fields. That ratio is expressed as Zo.
2. If a wave with V/I=Zo reaches the end of the line, and the load does
not permit V/I to be Zo (ie a mismatch), a reflected wave is launched,
and it is of magnitude and phase such that (Vf+Vr)/If-Ir)=Zl (all complex
values).

This is true.

In the steady state, after all has settled (ie converged), the
transmission line reaches an equilibrium where the source V/I
characteristic is consistent with (Vf+Vr)/If-Ir) at the input end of the
line.

Not yet. There is more to be done.

Why is it necessary to complicate the analysis with tracking multiple re-
reflections, potentially an infinite number of reflections of diminishing
significance, an analysis that converges in the limit on the answer given
by the solution of the source V/I characteristic and (Vf+Vr)/If-Ir) at
the input end of the line (which is the equivalent input impedance). Note
that (Vf+Vr)/If-Ir) at the input end of the line is determined solely by
the tranmission line propagation constant, length, Zo and the far end
load impedance, for avoidance of doubt, source impedance is not
relevant.

Without inserting some sort of matching device between the source and the line input for causing re-reflection
of Vr and Ir, (Vf+Vr)/(If-Ir) will not equal source V/I, and consequently the source will not deliver all its
available power. When Vr and Ir are caused to be re-reflected in phase with Vf and If, respectively, the
source will deliver all its available power, because the line-input Z will now equal source Z = V/I.
Therefore, the source impedance is totally relevant.

The matching device that causes Vr and Ir to be re-reflected is either a virtual oc or a virtual sc, which is
produced by adjustment of the device that orients the appropriate relationship between the forward and
reflected voltages and between the forward and reflected currents.

Such an approach does not require invention of virtual re-reflectors or
virtual s/c or o/c, or ATUs or pi couplers with virtual properties.

Well Owen, then how do you explain re-reflection at the souce in the absence of z virtual sc or oc?

Walt

Revisiting the Power Explanation
 

Walter Maxwell wrote:
Well Owen, then how do you explain re-reflection at the souce in the absence of z virtual sc or oc?

I'm not Owen but in S-Parameter terms it is explained by:

b1 = (s11)(a1) + (s12)(a2) = 0

When (s11)(a1) equals -(s12)(a2), there is total destructive
interference in the direction of b1 toward the source. That's
the wave cancellation that is associated with your sc and oc.
As the Florida State web page says:

http://micro.magnet.fsu.edu/primer/j...ons/index.html

"... when two waves of equal amplitude and wavelength that are
180-degrees ... out of phase with each other meet, they are not
actually annihilated, ... All of the photon energy present in
these waves must somehow be recovered or redistributed in a
new direction, according to the law of energy conservation ...
Instead, upon meeting, the photons are redistributed to regions
that permit constructive interference, so the effect should be
considered as a redistribution of light waves and photon energy
rather than the spontaneous construction or destruction of light."

In a transmission line with only two directions, a "redistribution"
certainly implies a reversal in direction of the wave energy
involved in the wave cancellation, i.e. a re-reflection.

On the above Florida State web page, one can set the two waves
to the same frequency, same magnitude, and opposite phase and
observe the wave cancellation. Question is: What happens to
the energy in the canceled waves in a transmission line?
Answer: re-reflection in the opposite direction.
--
73, Cecil, w5dxp.com

Revisiting the Power Explanation
 

Richard Clark wrote:
Unfortunately, to raise the prospects of interference requires that
load, and requiring that load immediately violates the first condition
above - no physical manifestation.

If the impedance discontinuity between two different Z0s
of transmission lines is not a "load/physical manifestation",
then we can toss out an S-Parameter analysis as invalid.
--
73, Cecil, w5dxp.com

Revisiting the Power Explanation
 

On Fri, 30 Mar 2007 14:45:56 GMT, Walter Maxwell
wrote:

The part I feel
is contradicted is that when total re-reflection

Hi Walt,

Here I read the subject - reflection.

is caused without a total discontinuity such as a physical
short or open circuit,

Here I read a first condition - no physical manifestation.

it is caused by resultant of the interference between the forward and reflected
voltages and the interference between the forward and reflected currents.

Here I read the causal connection between the subject and the
condition.

However, waves do not mix in a linear space. The proof is the lack of
heterodyning of the RF soup we live in. Further, interference is the
mixing product of at least two sources (waves, what-have-you) in a
load. No load, then no interference.

Unfortunately, to raise the prospects of interference requires that
load, and requiring that load immediately violates the first condition
above - no physical manifestation.

When the phase relationships between
the respective voltages and currents are correctly adjusted to achieve an impedance match, the resultant is
either a virtual short circuit or a virtual open circuit, which causes total re-reflection of the waves
reflected from the mismatched load terminating the line. Consequently, the interferences cause the
re-reflection.

All of this is true in isolation, in fact it describes the actions of
a physical load called an ATR/TR Tube in a RADAR waveguide. When the
right wavelength conditions of a wave and environment meet in the
tube, formerly an open it now conducts to create:
1. A literal short;
2. A short that is found at even quarterwave intervals;
3. An open that is found at odd quarterwave intervals.
The physical and literal short was first necessary as the initiator.
Without the tube, the co-mixing of waves would not have done the job
in isolation.

Are you saying that this explanation of the re-reflection concept is incorrect?

I'm afraid so.

73's
Richard Clark, KB7QHC

Revisiting the Power Explanation
 

Richard Clark wrote:
Cecil Moore wrote:
If the impedance discontinuity between two different Z0s
of transmission lines is not a "load/physical manifestation",
then we can toss out an S-Parameter analysis as invalid.

If frogs had wings, they wouldn't bump their assess a-hoppin'

Well, does the impedance discontinuity between two different
Z0s of transmission line meet your requirement of a "load/
physical manifestation"? Is a characteristic impedance
physical enough for you?
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

On Fri, 30 Mar 2007 16:33:30 GMT, Cecil Moore wrote:

Walter Maxwell wrote:
Well Owen, then how do you explain re-reflection at the souce in the absence of z virtual sc or oc?

I'm not Owen but in S-Parameter terms it is explained by:

b1 = (s11)(a1) + (s12)(a2) = 0

When (s11)(a1) equals -(s12)(a2), there is total destructive
interference in the direction of b1 toward the source. That's
the wave cancellation that is associated with your sc and oc.

Cecil, I know you're not Owen, but my statement to him was a challenge for him to explain in HIS words why he
believes my explanation of the concept is wrong.

When you recite chaper and verse to me you're preaching to the choir, but you knew that.

Walt

Revisiting the Power Explanation
 

On Fri, 30 Mar 2007 16:51:36 GMT, Cecil Moore
wrote:

Richard Clark wrote:
Unfortunately, to raise the prospects of interference requires that
load, and requiring that load immediately violates the first condition
above - no physical manifestation.

If the impedance discontinuity between two different Z0s
of transmission lines is not a "load/physical manifestation",
then we can toss out an S-Parameter analysis as invalid.

If frogs had wings, they wouldn't bump their assess a-hoppin'

Revisiting the Power Explanation
 

Walter Maxwell wrote:
When you recite chaper and verse to me you're preaching to the choir, but you knew that.

Just wanted to provide some support from HP's Ap-Note 95-1
available on the web from:

http://www.sss-mag.com/pdf/hpan95-1.pdf
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

On Fri, 30 Mar 2007 09:38:20 -0800, Richard Clark wrote:

On Fri, 30 Mar 2007 14:45:56 GMT, Walter Maxwell
wrote:

The part I feel
is contradicted is that when total re-reflection

Hi Walt,

Here I read the subject - reflection.

is caused without a total discontinuity such as a physical
short or open circuit,

Here I read a first condition - no physical manifestation.

it is caused by resultant of the interference between the forward and reflected
voltages and the interference between the forward and reflected currents.

Here I read the causal connection between the subject and the
condition.

However, waves do not mix in a linear space. The proof is the lack of
heterodyning of the RF soup we live in. Further, interference is the
mixing product of at least two sources (waves, what-have-you) in a
load. No load, then no interference.

Unfortunately, to raise the prospects of interference requires that
load, and requiring that load immediately violates the first condition
above - no physical manifestation.

When the phase relationships between
the respective voltages and currents are correctly adjusted to achieve an impedance match, the resultant is
either a virtual short circuit or a virtual open circuit, which causes total re-reflection of the waves
reflected from the mismatched load terminating the line. Consequently, the interferences cause the
re-reflection.

All of this is true in isolation, in fact it describes the actions of
a physical load called an ATR/TR Tube in a RADAR waveguide. When the
right wavelength conditions of a wave and environment meet in the
tube, formerly an open it now conducts to create:
1. A literal short;
2. A short that is found at even quarterwave intervals;
3. An open that is found at odd quarterwave intervals.
The physical and literal short was first necessary as the initiator.
Without the tube, the co-mixing of waves would not have done the job
in isolation.

Are you saying that this explanation of the re-reflection concept is incorrect?

I'm afraid so.

73's
Richard Clark, KB7QHC

Oh, 'cmon Richard, are you saying that if a load reflected wave incident on the source wave doesn't result in
an interference between the two waves? If this is what you're really saying, then it is equal to saying that
the principal thrust of my book Reflections is wrong. Is this what you mean? And are you saying that the
report of the Fl State professors that Cecil referred to is also wrong?

In addition, when the radiation from two dipoles fed from the same source is of the same magnitude and
opposite phase at a point in space, resulting in a null in the radiation pattern at that point, are you saying
that the radiation from the two dipoles is not in interference at that point? If this is what you're saying,
then how is the null in the pattern created?

Walt

Revisiting the Power Explanation
 

Cecil Moore wrote:
Jim Kelley wrote:
But my statement is nevertheless honest, truthful, and factual. What
part of it do you feel is contradicted by physical laws?

I find it strange that Hecht's definition of "interference"
doesn't even mention your alleged cause of the interference,
i.e. superposition. From "Optics", by Hecht in his own
bold italics:

"Optical interference corresponds to the interaction of
two or more light waves yielding a resultant irradiance
that deviates from the sum of the component irradiances."

One might argue that "the interaction of two or more light
waves" is superposition but why didn't Hecht choose
"superposition" instead of "interaction"? And a
"correspondence" of interference to the interaction of
the waves certainly doesn't imply cause and effect. It
seems instead to imply an inseparability between the
interference and the interaction of the waves which
is of course obvious.

Hecht seems to treat the superposition principle as more
of a set of rules to be followed by the interfering waves
than an actual act. FYI, the definition of "superpose"
doesn't mention EM waves at all.

Cecil,

You seem to misinterpret the significance of the "weasel words" used by
your various author-gurus.

An expression such as, "Optical interference corresponds to the
interaction . . .", without any accompanying equations is intended to
give the reader a general feeling for what is going on. Such words do
not imply cause and effect. Nor should those fuzzy expressions be taken
to imply "inseparability" as a rigid requirement.

Interference is merely a convenient description of what happens when
waves meet. There are no equations for "interference"; there are no
units for "interference"; there are no standard symbols for
"interference". Interference is an observation, not a physical law.

Stick to the standard field equations and you will not be misled. I am
confident that somewhere Hecht goes though the standard treatment of
setting up field functions with boundary conditions and then solves the
equations to show what happens at interfaces. Interference can be seen
in the solutions to that problem. I'll bet he does not start with
interference and then proceed to determine the E-fields and H-fields.

Superposition is a basic mathematical concept that applies to linear
systems. It is not necessary to catalog every possible application for
superposition. The fact that your definition of "superpose" does not
mention EM waves is of zero importance in the world. Superposition still
applies even if your dictionary does not know about it.

73,
Gene
W4SZ

Revisiting the Power Explanation
 

Gene Fuller wrote:
There are no equations for "interference";

On the contrary, quoting from "Optics", by Hecht,
page 283, 4th edition: "It follows from Eq.(7.9)
that the resultant flux density is not simply the
sum of the component flux densities; there is an
additional contribution, 2*E01*E02*cos(A1-A2), known
as the *interference term*. The emphasis is Hecht's,
not mine.

Later on page 388: "The interference term becomes

I12 = 2*SQRT(I1*I2)cos(Gamma)"

What does it take to make that look like an equation
to you? Have you ever taken time to read and understand
"Optics", by Hecht?
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Richard Clark wrote:
There is absolutely no example of interference that does not rely on a
load to reveal it.

I suspect you would consider blowing smoke through
a region of interference or any other means of detection
to be a "load"? (It is left to the readers to conclude
what it is a load of.)

So the real question is metaphysical: Does undetected
interference exist and if so, how does one prove it?
Reminds me of some of the steady-state arguments.

The students of Aristotle would argue that the interference
exists whether it is detected or not. (A thing is what it
is.)

The students of Plato would argue that the interference
doesn't exist unless it is detected. (A thing is not
necessarily what it appears to be.)
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

On Fri, 30 Mar 2007 18:19:20 GMT, Walter Maxwell
wrote:

Oh, 'cmon Richard, are you saying that if a load reflected wave

Is not the same statement as your earlier one:
On Fri, 30 Mar 2007 14:45:56 GMT, Walter Maxwell wrote:

The part I feel is contradicted is that when total re-reflection
is caused without a total discontinuity such as a physical
short or open circuit

What is in your "without a total discontinuity" that is now found in
your "load reflected wave?"

Are we to now parse "total discontinuity" as being wholly different
from "partial discontinuity" such that waves suddenly mix from that
difference?

My example of the classic AT/ATR tube evidences EVERY observation you
offer, except it is a necessary load without which those observations
would never appear. If I were to replace its "total discontinuity"
with a weak tube (it exhibits less than total short); it too would
exhibit EVERY observation you offer EXCEPT they would be imperfect or
"partial discontinuities" repeated every quarter wave. It is obvious
that the effect follows the physical load, not the waves (they haven't
changed when the tube went bad). The physical load is the principle
in the process of interference.

There is absolutely no example of interference that does not rely on a
load to reveal it.

73's
Richard Clark, KB7QHC

Revisiting the Power Explanation
 

On Mar 30, 11:11 am, Walter Maxwell wrote:
The matching device that causes Vr and Ir to be re-reflected is either a virtual oc or a virtual sc, which is
produced by adjustment of the device that orients the appropriate relationship between the forward and
reflected voltages and between the forward and reflected currents.

Such an approach does not require invention of virtual re-reflectors or
virtual s/c or o/c, or ATUs or pi couplers with virtual properties.

Well Owen, then how do you explain re-reflection at the souce in
the absence of z virtual sc or oc?

There is no need for complete re-reflection and therefore no need
to invent a virtual sc or oc.

It is easier to explain outside of a generator so let us consider
two transmission lines of different characteristic impedance
joined in the centre of our page. For convenience assume the
generator is on the left and the load is on the right.

Further, the forward voltage on the left line (Vlf) exists, while
the reverse voltage (Vlr) is zero.

On the right section of the line there is both a non-zero forward
voltage (Vrf) and reverse voltage (Vrr).

(The above could be physically achieved when the section of the line
on the right is being used as a quarter-wave matching transformer.)

Now how can it be that Vlr is 0 unless Vrr is completely
reflected?

Easy. Two things happen to the Vlf, part of it is reflected
and part of it goes through; the amounts controlled by RC.

Two things also happen to Vrr, part of it is reflected and
part of it goes through; the amounts controlled by -RC.

The conditions to satisfy that Vlr be 0 is simply that
the contribution to Vlr from the reflected Vlf is equal and
opposite in sign to the contribution from the part of Vrr
that goes through.

Doing a little algebra will reveal that when the above condition
is satisfied, Vrf is equal to Vlf minus Vrr, but this is purely
numerology and should not be take to mean that all of Vrr is
re-reflected. Once this is understood there is no need for
complete re-reflection or virtual short or open circuits.

A little mental exercise will show that the conditions
described above for the connection of two transmision lines
is isomorphic to the conditions at the generator output
terminals so the same explanation can be applied there.

....Keith

Revisiting the Power Explanation
 

On Mar 30, 8:35 am, Cecil Moore wrote:
Keith Dysart wrote:

Sure, why not? Just for fun let's do the Norton model for the
generator.

Please choose a real world source.

Well I guess that settles it. You clearly are not aware of the
methodologies. Even ones that work on the simplest of examples.

But this is positive. Once you know what you don't know, you
can move forward with education.

The question is answerable with the information provided. All
that is needed is to know the methodology.

I suggest again, google '"lattice diagrams" reflection'.

Alternatively, just ask and there are many here who would
be willing to assist you (or anyone else) with learning the
techniques.

....Keith

Revisiting the Power Explanation
 

Walter Maxwell wrote in
:

On Thu, 29 Mar 2007 22:20:48 GMT, Owen Duffy wrote:
....
I am talking about the steady state.

Hi Owen, so am I. ...
....
Why is it necessary to complicate the analysis with tracking multiple
re- reflections, potentially an infinite number of reflections of
diminishing significance, an analysis that converges in the limit on
the answer given by the solution of the source V/I characteristic and
(Vf+Vr)/If-Ir) at the input end of the line (which is the equivalent
input impedance). Note that (Vf+Vr)/If-Ir) at the input end of the
line is determined solely by the tranmission line propagation
constant, length, Zo and the far end load impedance, for avoidance of
doubt, source impedance is not relevant.

Walt, it seems to me from your comments that fundamentally you disagree
with the above statement.

Let me work a simple, but practical example. Apologies for the example
being two cascaded transmission line sections to demonstrate that you do
not need S parameters to solve the problem.

We have a G5RV with a feed point impedance (Z1) of say 90+j10 at 14.2MHz.

The feed point is connected to 9.85m of Wireman 554 ladder line. The
propagation constant (gamma) for the line is 6.80e-4+j3.20e-1 and Zo is
360.00-j0.56. Using gamma, Zo and Z1, the input impedance to this section
of line (Z2) is 92.37+j15.06. Due to line losses, only 97.2% of the input
power passes into the load.

The ladder line is connected to 11m of Belden 8267 (RG213) to the
transmitter. The propagation constant (gamma) for the line is 2.71e-3
+j4.51e-1 and Zo is 50.00-j0.27. Using gamma, Zo and Z2, the input
impedance to this section of line (Z3) is 27.44+j4.18. This input
impedance is not dependent on the transmitter, it does not matter whether
the transmitter contains a pi coupler, an ATU, a broadband coupled output
with or without low pass filters, or any kind of "total re-reflector"
invention. Due to line losses, only 93.1% of the input power is passes
into the second line section, and therefore only 93.1% of 97.2% or 90.5%
of the input power passes into the load.

The amount of RF power from the transmitter will be the power that the
transmitter delivers to a load of *any* kind of load of that same
impedance (27.44+j4.18). If you adjust a valve transmitter's pi coupler
to optimise power output into this load, you a merely adjusting the
transformation of the external load to suit the valve's available voltage
swing, current swing and conduction angle (within linearity, dissipation
and drive constraints). The optimal values of the pi coupler components
are readily calculated for the the valve's available voltage swing,
current swing and conduction angle, and such is routinely done in
engineering design of PAs.

There is no need to resort to the invention of a "total re-reflector" to
describe how this works.

Owen

PS: the solution of the tranmission line segments using load impedance,
characteristic impedance, and propagation constant uses the transmission
line formula that can be found in any good transmission line text. The
values given for gamma above are for length units of a metre.

I hope the maths was correct above, it is unchecked and I may have
embedded some errors, but the method is correct, the line sections were
solved using the calculator at http://www.vk1od.net/tl/tllc.php .

Revisiting the Power Explanation
 

Cecil Moore wrote:
Gene Fuller wrote:
There are no equations for "interference";

On the contrary, quoting from "Optics", by Hecht,
page 283, 4th edition: "It follows from Eq.(7.9)
that the resultant flux density is not simply the
sum of the component flux densities; there is an
additional contribution, 2*E01*E02*cos(A1-A2), known
as the *interference term*. The emphasis is Hecht's,
not mine.

Later on page 388: "The interference term becomes

I12 = 2*SQRT(I1*I2)cos(Gamma)"

What does it take to make that look like an equation
to you? Have you ever taken time to read and understand
"Optics", by Hecht?

Cecil,

That quote agrees completely with what I said. Interference is a
description of the equations. It is not a part of the equations per se.
Do you see anything in the quoted equations that looks like a symbol for
"interference"? I see E, A, I, and Gamma, but nothing that would seem
to represent "interference". Is there a hidden variable in there somewhere?

You keep trying to make interference act as some sort of primary
physical law rather than merely a convenient observation and
description. No wonder these threads go on forever.

Nobody denies the existence of interference. However, interference is
the result of all the equations and calculations, not the source.

73,
Gene
W4SZ

Revisiting the Power Explanation
 

Keith Dysart wrote:
Doing a little algebra will reveal that when the above condition
is satisfied, Vrf is equal to Vlf minus Vrr, but this is purely
numerology and should not be take to mean that all of Vrr is
re-reflected.

What happens to the energy in those voltage waves?
(1) EM Voltages exist without energy
(2) The conservation of energy principle is invalid
(3) Keith is prone to wet dreams
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Keith Dysart wrote:
Well I guess that settles it. You clearly are not aware of the
methodologies. Even ones that work on the simplest of examples.

Perhaps you could educate me. Please provide an
S-Parameter analysis of the math model of the
source that you have refused to provide.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Owen Duffy wrote:
There is no need to resort to the invention of a "total re-reflector" to
describe how this works.

Do you deny that the principle of superposition allows
Walt to evaluate the effects of the separate forward
and reflected waves and then superpose the results?
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Gene Fuller wrote in
:

That quote agrees completely with what I said. Interference is a
description of the equations. It is not a part of the equations per

Gene, IMHO the terms "constructive interference" and "destructive
interference" are poor terms. If "interference" describes essentially the
phasor result of summation of two (or more) phasor (ie coherent)
quantities, then there is no need for the constructive and destructive
qualifiers if the phase relationship is given (and it must be to perform
the summation).

The two terms are often used to mean total reinforcement (0 deg phase
difference) or total cancellation (180 deg phase difference and equal
amplitude). I note the Wikipeadia page at
http://en.wikipedia.org/wiki/Destructive_interference infers that usage.

To my mind, there is so much loose usage of the terms to consider that a
reader will reliably understand what the writer meant, and so in the
interest of better communication, I don't use them.

The in-phase and out-of phase, equal amplitude cases are a very small
subset of the real world cases that are of interest in solving
transmission line problems, yet they dominate, possibly cause, the
simplistic discussions in this place.

The usage here appears to derive from a certain person's need to use
terminolgy and examples from other electromagnetic radiation applications
to describe transmission lines. So far, it seems that when the
alternative explanation disagrees with the direct explanation, the flaw
has been in adaptation of the alternative explanation to the problem.

Owen

Revisiting the Power Explanation
 

Gene Fuller wrote:
That quote agrees completely with what I said.

Gene, you remind me of an ex-friend of mine who when
asked what would happen if he were caught by his wife
in bed with his girlfriend, said, "I would just
deny it."

You said there is no equation for interference.

Hecht in "Optics" provided the equation that you
said didn't exist. I12 is the symbol for interference
between the I1 and I2 waves.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Owen Duffy wrote:
Gene, IMHO the terms "constructive interference" and "destructive
interference" are poor terms.

They are accepted well-defined terms in the field of antenna
radiation. NEC antenna simulations calculate the amount of
constructive and destructive interference before presenting
the radiation patterns.

Quoting Hecht of "Optics" fame: "The principle of Conservation
of Energy makes it clear that if there is constructive interference
at one point, the 'extra' energy at that location must have come
from elsewhere. There must therefore be destructive interference
somewhere else."

You seem not to understand that the constructive interference that
results in the gain of a Yagi antenna, must obtain that energy from
an equal amount of destructive interference in another direction.
If constructive and destructive interference didn't exist, all
antennas would be isotropic. Think about that.

You already no doubt understand constructive and destructive
interference in the radiated fields of antennas. Just broaden
that understanding to transmission lines. The destructive
interference toward the source in a Z0-matched system is
identical to the destructive interference off the back of
a Yagi antenna. The constructive interference toward the load
in a Z0-matched system is identical to the constructive
interference off the front of a Yagi antenna.

The in-phase and out-of phase, equal amplitude cases are a very small
subset of the real world cases ...

Absolutely not true for amateur radio systems with antenna
tuners. The function of the antenna tuner is to bring the
forward and reflected waves into phase (or 180 degrees out
of phase). All matched amateur radio antenna systems fall
under the category of in-phase (or 180 degree out of phase).
In either case, the cosine of the angle between the two
voltages is zero, reactance is neutralized, and V*I*cos(0)
is 100% in watts, 0% in vars.

The usage here appears to derive from a certain person's need to use
terminolgy and examples from other electromagnetic radiation applications
to describe transmission lines.

No matter what your opinion, Owen, EM waves *are* EM waves.
They all obey the laws of physics. I suspect you know a lot
more about constructive and destructive interference than
you realize at the moment. Antenna gain depends on it.
--
73, Cecil http://www.w5dxp.com