Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Gene Fuller wrote:
* Does your IEEE dictionary have an entry for "stationary"?

I'm afraid you have been taken in by my devil's
advocate argument based on Keith's faulty concepts.
If what he says is true about standing waves, then
the same concepts apply to traveling waves. If there
are no traveling wave energy components being transferred
when two traveling waves are flowing in opposite
directions, then it logically follows that there can
be no traveling wave energy component being transferred
when one traveling wave is flowing in one direction.

The *NET* energy flow is zero in a standing wave.
But the component energy flow in the underlying EM
waves is alive and well and flowing right through
those current and voltage nodes without even knowing
that they are there. The illusion of zero energy flow
in EM traveling waves is one of the problems with
shortcuts. EM waves have a set of boundary conditions
that must be satisfied for them to exist. One of
those conditions is that they must necessarily
travel at c(VF). "Stationary" is not possible for
any single EM wave. Nobody has been able to provide
an example of a standing wave without the underlying
forward and reverse EM traveling wave components
(not even you) :-). Another condition for the existence
of an EM traveling wave is that it has an associated
energy level without which it cannot exist.

A stationary EM wave is a contradiction in terms,
an oxymoron. EM waves cannot stand still
and exist only as a concept in the human mind.
It is an illusionary temporarily superposed profile
of two waves that, in reality, are moving in opposite
directions at c(VF) and have absolutely *NO* effect on
each other. The forward EM wave possesses direction
and momentum that doesn't change until it encounters
a physical impedance discontinuity. The reverse EM
wave possesses direction and momentum that doesn't
change until it encounters a physical impedance
discontinuity. Anything else would violate the laws
of physics.
--
73, Cecil, w5dxp.com

Cecil,

Nobody said the "wave" was stationary, only the point of zero energy is
stationary. You have again demonstrated that you are not reading and
understanding.

The *NET* paragraph above is simply unmitigated nonsense. It appears
that mistaken notion is one of the root causes of your continuing
confusion. Until you get over this bogus idea of colliding energy flows
there is no hope for further enlightenment.

73,
Gene
W4SZ

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Gene Fuller wrote:
I did not say the graphic was incorrect, but rather that it is
irrelevant. It correctly shows the addition of two sine waves.

OK, if it is irrelevant, why did they publish it?
Why do they talk about "redistribution" of energy
in other directions during a destructive interference
event? Doesn't changing the direction and momentum of
a wave qualify as "interaction"?

And when those two sine waves are coherent, of equal
amplitude, and opposite phase, they permanently *CANCEL*
each other. Doesn't that satisfy the definition of
"interacting"?

I see you have been strangely silent on my example of
s11(a1) originating and flowing away from the impedance
discontinuity only to be canceled by s12(a2) when it
flows through the impedance discontinuity and encounters
the s11(a1) wave flowing away from the impedance
discontinuity. How can the effect of one wave on the
other not be interaction when both are flowing away
from the impedance discontinuity and are *NEVER*
incident upon any impedance discontinuity?


Cecil,

I did respond to your example. I referred you to the message from K7ITM.
The answer is contained in his quote. Since you seemed to have missed
that one, here is the conclusion.

The waves you are trying to create and then quickly cancel, in delta-t,
simply never existed. Problem solved.

73,
Gene
W4SZ

Analyzing Stub Matching with Reflection Coefficients
 

On Apr 23, 7:56 am, Cecil Moore wrote:
Gene Fuller wrote:
* Does your IEEE dictionary have an entry for "stationary"?

I'm afraid you have been taken in by my devil's
advocate argument based on Keith's faulty concepts.
If what he says is true about standing waves, then
the same concepts apply to traveling waves.

It becomes clear from your posts that you have a wave
centric view of these behaviours. It is often valuable to
have more than one way to view a situation. Let me offer
you another.

While I will describe this view only for transmission
lines, its equivalent in free space would be the Maxwell
equations, so, knowing your support for Maxwell, you
should find it attractive.

The voltages and currents on a transmission line can
be described with a collection of differential equations.
When these differential eqations are solved for a set of
boundary conditions, the results describe the voltage
and current on the line as a function of time and
location along the line.

Were one to set up an ideal line (for simplicity),
terminated in its characteristic impedance, the functions
that describe the voltage and current on the line can
be derived. Plugging in the time and location one can
determine the voltage at that place and instance. The
curious investigator will be tempted to plot the voltage
for a particular time as a function of location. The
resulting plot will be nicely sinusoidal. Were one to
plot the result for deltaT later, one finds a plot with
exactly the same shape, but slightly shifted. A movie
would show this nice sinusoid shifting its location at
a constant velocity. And our intrepid investigator
names this a travelling wave, a convenient moniker.

Let us consider another line. This one is open circuited.
Solving the diffential equations that describe the line
for these new boundary conditions produces a different
set of functions of time and location. Plotting the
function of voltage with respect to location again
produces a sinusoid, but the amplitude depends on the
selected time. This plot, when played as a movie, shows
no sign of moving and our intrepid investigator names
it a standing wave, another convenient moniker.

But just because they are both called waves does not
make them the same. One always has the same shape and
amplitude and appears to move. The other shares the shape,
does not move and has an amplitude that varies.
Fundamentally, they are both just convenient visualizations
of solutions from the same set of differential equations
with different boundary conditions.

For the standing wave, further arithmetic reveals that the
function that expresses the voltage as a function of time
and location can be simplified and made more useful if
it is expressed in terms of two travelling waves, one
from the left and one from the right. But this is just
an alternate expression of the function that resulted
from the solution of a set of differential equations.

While the initial differential equations express voltage
and current, one could certainly derive equations that
expressed power, or energy storage, or whatever happened
to be of interest. One could then solve these and the
expression that results would be a function of time and
location.

Were one to solve the differential equation for power
on the open circuited line at a location of a voltage
null, the answer would be zero. And all computed without
the need for forward and backward waves.

---

So which is the truth? The differential equations or
the forward and backward waves? Which analysis technique
is more complete? And which is the alternative view that
makes the problems solvable in reasonable time?

It is clear to me that the differential equations rule,
much as Maxwell's equations are considered the root for
electric and magnetic fields.

Travelling and standing waves are mere visualizations,
though that visualization simplifies solving many
problems. But forward and reverse waves are definitely
not the foundation on which all else rests.

....Keith

Analyzing Stub Matching with Reflection Coefficients
 

On Apr 23, 8:54 am, Gene Fuller wrote:
Cecil Moore wrote:
Gene Fuller wrote:
* Does your IEEE dictionary have an entry for "stationary"?

I'm afraid you have been taken in by my devil's
advocate argument based on Keith's faulty concepts.
If what he says is true about standing waves, then
the same concepts apply to traveling waves. If there
are no traveling wave energy components being transferred
when two traveling waves are flowing in opposite
directions, then it logically follows that there can
be no traveling wave energy component being transferred
when one traveling wave is flowing in one direction.

The *NET* energy flow is zero in a standing wave.
But the component energy flow in the underlying EM
waves is alive and well and flowing right through
those current and voltage nodes without even knowing
that they are there. The illusion of zero energy flow
in EM traveling waves is one of the problems with
shortcuts. EM waves have a set of boundary conditions
that must be satisfied for them to exist. One of
those conditions is that they must necessarily
travel at c(VF). "Stationary" is not possible for
any single EM wave. Nobody has been able to provide
an example of a standing wave without the underlying
forward and reverse EM traveling wave components
(not even you) :-). Another condition for the existence
of an EM traveling wave is that it has an associated
energy level without which it cannot exist.

A stationary EM wave is a contradiction in terms,
an oxymoron. EM waves cannot stand still
and exist only as a concept in the human mind.
It is an illusionary temporarily superposed profile
of two waves that, in reality, are moving in opposite
directions at c(VF) and have absolutely *NO* effect on
each other. The forward EM wave possesses direction
and momentum that doesn't change until it encounters
a physical impedance discontinuity. The reverse EM
wave possesses direction and momentum that doesn't
change until it encounters a physical impedance
discontinuity. Anything else would violate the laws
of physics.
--
73, Cecil, w5dxp.com

Cecil,

Nobody said the "wave" was stationary, only the point of zero energy is
stationary. You have again demonstrated that you are not reading and
understanding.

I think he may be too busy having that strange kind of dream he talked
about when he implicitly threw out at least 90% of all S-parameter
analysis by saying that "reality requires complete reflection of the
return wave at the interface between the [matched] source and the
line." Either you believe in the superposition principle in linear
systems, or you don't. He obviously doesn't.

From the lab,
Bunsen

Analyzing Stub Matching with Reflection Coefficients
 

Gene Fuller wrote:
The *NET* paragraph above is simply unmitigated nonsense. It appears
that mistaken notion is one of the root causes of your continuing
confusion. Until you get over this bogus idea of colliding energy flows
there is no hope for further enlightenment.

If colliding energy doesn't flow, then waves interact
away from an impedance discontinuity since the colliding
energy components are in separate EM waves traveling in
opposite directions. Which will it be? You cannot have
it both ways.

1. The ExB joules/sec components in the forward wave and the
reflected wave pass through each other with no interaction
such that the *NET* energy flow is zero.

2. The ExB joules/sec components flowing in each direction
cause all energy to stop flowing because of wave interaction.

Please tell us which one is true and which one is false.
--
73, Cecil, http://www.qsl.net/w5dxp

Analyzing Stub Matching with Reflection Coefficients
 

Gene Fuller wrote:
The waves you are trying to create and then quickly cancel, in delta-t,
simply never existed. Problem solved.

Problem solved by rendering an s-parameter analysis
invalid?

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

So s11(a1) and s12(a2) in the s-parameter equations don't
exist and never existed. Don't you think you should tell
HP so they can change their Ap Notes?
--
73, Cecil, http://www.qsl.net/w5dxp

Analyzing Stub Matching with Reflection Coefficients
 

Keith Dysart wrote:
Were one to solve the differential equation for power
on the open circuited line at a location of a voltage
null, the answer would be zero. And all computed without
the need for forward and backward waves.

The *NET* power at any point on a lossless stub is
zero so that is no big deal. The standing wave
current is always 90 degrees out of phase with
the standing wave current so cos(90) = 0. At a
voltage node, all of the energy has simply moved
into the magnetic field.

Calculate the number of electromagnetic joules in
the line and get back to us on how they are reflected
from your above purely virtual impedance at a
voltage "null" and how they can even exist without
a velocity of c(VF).
--
73, Cecil, http://www.qsl.net/w5dxp

Analyzing Stub Matching with Reflection Coefficients
 

Dr. Honeydew wrote:
Either you believe in the superposition principle in linear
systems, or you don't. He obviously doesn't.

Superposition is known to fail in nonlinear systems.
A source is obviously not linear. The V/I of an active
dynamic source resists any attempt at linear
superposition. How does your superposition work
when you try to spit up a fire hose?
--
73, Cecil, http://www.qsl.net/w5dxp

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
The *NET* power at any point on a lossless stub is
zero so that is no big deal. The standing wave
current is always 90 degrees out of phase with
the standing wave current so cos(90) = 0. At a
voltage node, all of the energy has simply moved
into the magnetic field.

With 4 amps of RF current at that voltage "null",
how could zero joules/sec possibly exist at that
point? Methinks there are some I^2*Z0 joules/sec
in that 4 amps of RF EM current that necessarily
must be traveling at c(VF).
--
73, Cecil, http://www.qsl.net/w5dxp

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Dr. Honeydew wrote:

Either you believe in the superposition principle in linear
systems, or you don't. He obviously doesn't.


Superposition is known to fail in nonlinear systems.
A source is obviously not linear.

Sources are linear. Consider the classic voltage source.. it has zero
impedance. You can stack as many voltage sources as you like, and the
voltage at the top of the stack is the same as the sum of the individual
voltages.



The V/I of an active
dynamic source resists any attempt at linear
superposition.

- a practical RF source, perhaps, might be nonlinear, although it's
pretty easy to come close.. Consider an oscillator isolated by an
isolator or a big pad.

How does your superposition work
when you try to spit up a fire hose?

Just fine. No different than receiving a faint signal superimposed on a
large interfering signal at a different frequency.