Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
x
a1=10----|
|----s21(a1)=5 toward the load
s11(a1)=5----|

For those of you who are unfamiliar with the way s-parameter
voltages are normalized, here are the *actual measured*
voltages at the impedance discontinuity at t=0 + delta-t.
All three voltages can easily be seen on an o'scope a
short time after t=0. During the buildup to steady-
state Vref1 goes from 50V to 0V. How that is possible
without interaction is the question for ac6xg.

x
Vfor1=70.7V----|
|----120.7V=Vfor2 toward the load
Vref1=50V----|
rho1-- | --tau2(Vref2)=0

The corresponding equation used by RF engineers is:

Vref1 = rho1(Vfor1) + tau2(Vref2)

In this t=0 case, Vref2=0, so

Vref1 = rho1(Vfor1) at t=0
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Gene Fuller wrote:
You don't believe in superposition, do you? It is discussed in lots of
books if you want to understand.

Do you believe Jim's argument that two coherent EM
waves of equal magnitudes and opposite phases traveling
collinearly in the same direction in a transmission line
can never be canceled? If Jim is right, we can toss the
s-parameter analysis in the garbage can and join Roy in
calling it gobbledigook (sic).

Cecil,

Never is a long time. And I am sure you would slip away from free space
or a linear medium to provide some counter example as soon as I agreed.

I agree with Jim and Roy, and most of the rest of the world.
Electromagnetic waves, or photons if you prefer, simply do not interact
without the assistance of interfaces, discontinuities, or a non-linear
medium. Interference is a result from linear superposition. No waves are
harmed in the process.

At interfaces and discontinuities lots of things can happen. There are
well-established techniques for analyzing those things. There is no law
of "conservation of waves", however. There is also no law that says all
of the individual component waves you may choose to create need to have
some sort of detailed energy balance. I have explained several times how
the conservation of energy law works, but you seem to disbelieve me.
(Hint: I did not make this stuff up. I gave you direct quotes from very
reliable sources.)

Since you keep bringing up s-parameters, with the implication that they
provide some new truth, perhaps you might go back and re-read AN-95-1.

From page 7 of the slide version:

"If other independent and dependent variables had been chosen, the
network would have been described, as before, by two linear equations
similar to equations 1 and 2, except that the variables and the
parameters describing their relationships would be different. However,
all parameter sets contain the same information about a network, and it
is always possible to calculate any set in terms of any other set."

The other variables described earlier in the note include voltage and
current. Again, we come to my old standby, mathematical convenience.
S-parameters are very useful, but they bring nothing new to the physical
reality.

73,
Gene
W4SZ

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Cecil Moore wrote:
x
a1=10----|
|----s21(a1)=5 toward the load
s11(a1)=5----|

For those of you who are unfamiliar with the way s-parameter
voltages are normalized, here are the *actual measured*
voltages at the impedance discontinuity at t=0 + delta-t.
All three voltages can easily be seen on an o'scope a
short time after t=0. During the buildup to steady-
state Vref1 goes from 50V to 0V. How that is possible
without interaction is the question for ac6xg.

x
Vfor1=70.7V----|
|----120.7V=Vfor2 toward the load
Vref1=50V----|
rho1-- | --tau2(Vref2)=0

The corresponding equation used by RF engineers is:

Vref1 = rho1(Vfor1) + tau2(Vref2)

In this t=0 case, Vref2=0, so

Vref1 = rho1(Vfor1) at t=0


Cecil,

I am impressed! That's a pretty fancy o'scope you got. Measurement of
voltages to four significant digits at t = 0 + delta-t is definitely
world-class. That 291.4 ohm line is pretty special as well.

Is there some non-standard definition of *actual measured* that we
should consider to help interpret your results?

8-)

73,
Gene
W4SZ

Analyzing Stub Matching with Reflection Coefficients
 

Gene Fuller wrote:
Never is a long time.

Waves never interact *is* a long time.

I agree with Jim and Roy, and most of the rest of the world.
Electromagnetic waves, or photons if you prefer, simply do not interact
without the assistance of interfaces, discontinuities, or a non-linear
medium. Interference is a result from linear superposition. No waves are
harmed in the process.

"No waves are harmed in the process" implies that waves can
never be canceled. Yet, all the textbooks and all the web
pages say that when two coherent collinear waves of equal
magnitudes and opposite phases meet, they only appear to
be destroyed but their energy components are actually
"redistributed" in different directions.

That's exactly what happens to reflected waves toward the
source when a Z0-match is achieved. The energy components
in the reflected waves, s11(a1) and s12(a2), are redistributed
back toward the load. How does b1 ever go permanently to
zero without s11(a1) and s12(a2) canceling each other?

There is also no law that says all
of the individual component waves you may choose to create need to have
some sort of detailed energy balance.

Yes, there is, Gene. It is called the conservation of
energy principle. You cannot create energy in one place,
have it destroyed in another place, and then argue that
everything is all right because the net energy balance
remains the same.

"If other independent and dependent variables had been chosen, the
network would have been described, as before, by two linear equations
similar to equations 1 and 2, except that the variables and the
parameters describing their relationships would be different. However,
all parameter sets contain the same information about a network, and it
is always possible to calculate any set in terms of any other set."

The other variables described earlier in the note include voltage and
current. Again, we come to my old standby, mathematical convenience.
S-parameters are very useful, but they bring nothing new to the physical
reality.

Then why are you so afraid to discuss an s-parameter
analysis? Please respond to my example posting. How
does s11(a1) go from 5 to 0 without interacting with
something?
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

On Apr 16, 8:35 pm, Cecil Moore wrote:

No they don't. If the waves themselves changed, then their resultant
superposition would also change. It's a completely unfounded notion,

If what you say is true, then if we measure field strengths
far enough away from an antenna to get outside the range
of interference, then all antennas are isotropic.

"Outside the range of interference"? Yes, please call NASA and tell
them about that. :-)

ac6xg

Analyzing Stub Matching with Reflection Coefficients
 

Gene Fuller wrote:
I am impressed! That's a pretty fancy o'scope you got. Measurement of
voltages to four significant digits at t = 0 + delta-t is definitely
world-class. That 291.4 ohm line is pretty special as well.

Your non-technical diversions are noted. How about discussing
the technical question that was posed?

The voltages can be viewed on an o'scope. Their magnitudes
agree with the above calculated magnitudes. Do you know
of any reason that those voltages would not obey the
rules of the reflection model? When does a reflection
coefficient of 0.707 not reflect 0.707 of the incident
voltage?

The 291.4 ohm line is chosen to make rho=s11=0.707. My "450"
ohm ladder-line measures to be actually 380 ohms. Nothing
special about 291.4 ohms except that:

(291.4-50)/(291.4+50) = 0.707

We could actually design a feedline with Z0 = 291.4 ohms.
Want me to show you how? :-)

If you don't like that value, use 300 ohms and 51.5 ohms
for the coax. I'm sure between the choices of 50 ohm
coax and 52 ohm coax, there must be a 51.5 ohm coax in
there somewhere.
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

Jim Kelley wrote:
"Outside the range of interference"? Yes, please call NASA and tell
them about that. :-)

You said that EM waves cannot be perfectly collinear.
Therefore, there has to exist a distance where they
diverge and stop interfering. Your words, not mine.
--
73, Cecil http://www.w5dxp.com

Analyzing Stub Matching with Reflection Coefficients
 

On Apr 16, 9:20 pm, Cecil Moore wrote:

Do you believe Jim's argument that two coherent EM
waves of equal magnitudes and opposite phases traveling
collinearly in the same direction in a transmission line
can never be canceled?

I asked you to show me the two waves of equal magnitude and opposite
phase travelling in the same direction in a transmission line. Show
me the waves, Cecil.

AC6XG

Analyzing Stub Matching with Reflection Coefficients
 

On Apr 17, 8:30 am, Cecil Moore wrote:

You said that EM waves cannot be perfectly collinear.
Therefore, there has to exist a distance where they
diverge and stop interfering. Your words, not mine.

You are mistaken. In order to prevent errors of this sort in the
future, please quote the words you intend to refer to.

ac6xg

Analyzing Stub Matching with Reflection Coefficients
 

Cecil Moore wrote:
Gene Fuller wrote:
I am impressed! That's a pretty fancy o'scope you got. Measurement of
voltages to four significant digits at t = 0 + delta-t is definitely
world-class. That 291.4 ohm line is pretty special as well.

Your non-technical diversions are noted. How about discussing
the technical question that was posed?

The voltages can be viewed on an o'scope. Their magnitudes
agree with the above calculated magnitudes. Do you know
of any reason that those voltages would not obey the
rules of the reflection model? When does a reflection
coefficient of 0.707 not reflect 0.707 of the incident
voltage?

The 291.4 ohm line is chosen to make rho=s11=0.707. My "450"
ohm ladder-line measures to be actually 380 ohms. Nothing
special about 291.4 ohms except that:

(291.4-50)/(291.4+50) = 0.707

We could actually design a feedline with Z0 = 291.4 ohms.
Want me to show you how? :-)

If you don't like that value, use 300 ohms and 51.5 ohms
for the coax. I'm sure between the choices of 50 ohm
coax and 52 ohm coax, there must be a 51.5 ohm coax in
there somewhere.


Cecil,

You rarely reply directly to anything, and this is no exception. I was
commenting on the *actual measurement* that you claimed. You added the
emphasis, not me. Perhaps it was a *virtual measurement* instead? Do you
find that you can achieve the desired results more often with such
measurements?

8-)

73,
Gene
W4SZ