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