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