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