Roy:

[snip]
"Roy Lewallen" wrote in message
...
I'm sorry I'm having such a hard time communicating, and maybe the
trouble is that I've been misunderstanding what has been said. Here's
how it looks to me.
[snip]

Heh, heh... don't feel bad, that is common in any discourse using the medium
of USENET Newsgroup postings!

[snip]
So what's bothering me is that I'm completely unable to start with what
I believe to be true about the relationships between voltages, currents,
and characteristic impedance of a transmission line (itemized as three
assumptions in a recent posting), and arrive at anything but the
classical equation which is universally used for transmission line
analysis.
[snip]

I'm with you man! I like and, only use, the classical definitions of rho
and
the Scattering Matrix wich correspond to the "actual" waves supported by
the wave equation [The Telegraphist's Equations] on passive transmission
lines.

I simply don't like the version of rho/Scattering matrix which uses the
complex
conjugate of the "reference impedance" or what ever else you wish to call
the charateristic or surge impedance simply because the transition between
Z and conj(Z) represents an impedance discontinuity, a big one in fact, and
physical intuition tells me that there will alwasy be some effect on waves
which
have to transit such a discontinuity.

I am not a bigot about this use of the conj(Z) and I can quote several
excellent
authoritative references that do so. I don't however agree with Slick's use
of
conj(Z) in the numerator and just Z in the denominator, I believe that to be
the result of some typographical error or complete errors in
misunderstanding.

I do understand that for special kinds of problems it may be convenient to
adopt
different definitions for rho and the Scattering Matrix, and that is fine
just as long
as the definers remain consistent thereafter and indicate their departure
from the
more common usual definitions. Confusion sets in when there are proponents
of
the different definitions discussing/arguing about results without first
agreeing on
the definitions.

[snip]
I've posted both a detailed derivation of the formula for reflection
coefficient and a numerical example of a terminated transmission line
with complex Z0.
[snip]

You do good work Roy.

[snip]
elements or "semi-infinite" transmission lines -- or no derivation at
all. The alternate dervivations, it seems, can't for some reason
withstand the condition that a simple, finite length transmission line
be involved. Rather than presenting a simple analysis of a system with a
transmission line (as I did), all I've seen in response is lumped
element or "semi-infinite" transmission line analyses with indignant
protestations if I question the possibility that the presented models
don't accurately represent a finite transmission line.
[snip]

Because Roy, the use of semi-infinite transmission lines in a simple
"theoretical"
derivation is easier to communicate in short NG postings and easier to
understand
and manipulate than complex long "arithmetical" developments, no matter how
practical.

I too can give the group numerous practical Engineering design calculations
of real
problems that many have solved over the years in the communications
industry, not
made up problems like yours, but real ones involving complex Zo transmission
lines
with highly variable Zo's of lengths up to 18,000 feet operating with very
little
"talker echo" [reflection coefficient] over frequency ranges of a handful of
decades,
using very economical lumped approximations to Zo in the balancing networks.
There
are several patents issued in this area. But I am sure that most would get
glassy eyed
with those detailed Engineering calculations.

Which would you rather have, some detailed long drawn out Engineering
calculations
or a simple two line theoretical proof that using Zo and not conj(Zo)
results in no talker
echo only for an image matched line.

The theory of "image matching" was developed by Campbell and Zobel in the
time
frame of the early 1920's, why are we trying to prove it again now using
arithmetic?

[snip]
I really think that by now, anyone who is able to benefit from the
discussion has done so, and those who remain will continue to hold their
views no matter what. So I won't further waste the time of either group
by continuing to question the issue. I hope that the derivations I've
posted are helpful to those people who are interested in seeing where
the common formulas and equations come from.
[snip]

Thanks for all of your efforts Roy. As you know I agree completely with
your
results and conclusions.

But I must re-iterate I don't agree with your methods. The use of
arithmetic where
a little algebra and mathematical theory of trasmission lines will suffice.
is not my ideal of good communications.

Kraus, Balmain and all of your "other heros" make use of semi-infinite lines
in their
developments and descriptions of the meaning of Zo, I just don't see what
*your*
problem is with that approach. I can assure you that Maxwell did not use
"arithmetic"
in the development of his equations, nor did the first person to "define" a
reflection
coefficient!

I am perplexed by your approach to say the least, but perhaps I just don't
understand...

--
Peter K1PO
Indialantic By-the-Sea, FL.

Slick:

[snip]
If you believe that there are theoretically no
reflections in a conjugate match, then with

Zl=50+j10 and Zo=50-j10,

the conjugate equation correctly cancels the reactances
giving no reflections, while the non-conjugate still
incorrectly gives a magitude (non zero) for rho.

Slick
[snip]

Oh yes here are voltage reflections at a conjugate match!

Simply put as waves pass across the transition from an impedance
of Zo to an impedance of conj(Zo) they are crossing a boundary
with an impedance discontinuity. Zo on one side and conj(Zo)
on the other side is definitely discontinuous! Unless of course,
Zo = conj(Zo) which occurs only when Zo is real.

There will always reflections at such an impedance
discontinuity where an impedance faces its' conjugate.

If an impedance Zo faces itself Zo there will be no "voltage
reflections", this phenomena was called an "image match" by
Campbell and Zobel way back around 1920 or so, it represents
the basis for the image match design of filters and transmission
systems. Do any reader's here recall image parameter filter
design? I designed more than a few that way myself.

If an impedance Zo faces its' conjugate conj(Zo) then there will be
no "power reflections", but there will in general be voltage reflections,
and this is called a "conjugate match" and represents the basis
for "insertion loss" design of filters and transmission systems.
Darlington and Cauer introduced the insertion loss design
of filters which eventually supplanted the older Campbell,
Zobel image parameter design.

The "classical definition of voltage reflection coefficient from
theoretical physics and the solutions to the wave equations is
the one that does not use the conjugate. This classical
definition corresponds to the calculations made by a reflectometer
configured to measure the reflected voltage at the boundary
between Z and Zo such that if Z=Zo the reflected voltage
(often called the "talker echo") will be zero. This will not
correspond to maximum power transfer in the general case.

i.e. "classical" rho = (Z - Zo)/(Z + Zo) is not zero at a conjugate match.

I also believe that this is "Mother Nature's" reflection coefficient
for it is exactly what she uses as she lets the waves propagate
down her lines of surge impedance Zo following her partial differential
equations at every point along the way. At every infinitesimal
length of line all along it's length the waves are passing from a
infinitesimal region of surge impedance Zo to the next infinitesimal
region of surge impedance Zo and there are no voltage reflections
anywhere along that [uniform] line, although if the line is not lossless
there will be energy lost as the wave progresses.

Slick... On another whole level it simply does not matter which defiinition
of the reflection coefficient one uses to make design calculations though,
as
long as the definition is used consistently throughout any calculations.

One can convert any results based on the non-conjugate version of rho to
results based on the conjugate version of rho and vice versa.

In other words, neither version is "RIGHT" or "WRONG" as long
as the results from using that particular definition are interperted
correctly in terms of the original definition.

In fact one can cook up an [almost] completely ficticious reference
impedance, one which has no relation whatsoever to the Zo of the line.

Just call the ficticious, perhaps complex reference impedance R
[I like to use R since in my mind it stands for "Reference", and it need
not be a pure resistance.] and use this R in a defintition of rho and/or a
Scattering Matrix and then any and all subsequent calculations afterwords
will be correct as long as this ficticious R is used consistently with the
definitions in terms of the electrical port vectors the voltage v, current i
and
wave vector comprising the "waves" a and b.

rho = (Z - R)/(Z + R) = b/a = (v - Ri)/(v + Ri)

This is true simply because the "waves" a and b are mathematically
just simple linear combinations of the voltage v and current i! Look
at how simple the relationship is...

[a, b] and [i, v] are simply related by a simple transformation
matrix as follows:

a = v + Ri
b = v - Ri

or

wave vector = matrix * electrical vector

And the matrix, in this case is:

| 1 R |
| 1 -R|

As long as you choose a reference impedance R such that the transformation
matrix is non-singular then you can go back and forth from a, and b to
v and i any time, any where, etc...

So... who gives a damm about the defintion of rho as long as you are
consistent.

Unless of course, like Roy and others, you insist that the "waves"
correspond to
some preconceived notion of what waves really are... ;-)

Thoughts, comments,
--
Peter K1PO
Indialantic By-the-Sea, FL

"Peter O. Brackett" wrote in message thlink.net...
Slick:

[snip]
If you believe that there are theoretically no
reflections in a conjugate match, then with

Zl=50+j10 and Zo=50-j10,

the conjugate equation correctly cancels the reactances
giving no reflections, while the non-conjugate still
incorrectly gives a magitude (non zero) for rho.

Slick
[snip]

Oh yes here are voltage reflections at a conjugate match!

Simply put as waves pass across the transition from an impedance
of Zo to an impedance of conj(Zo) they are crossing a boundary
with an impedance discontinuity. Zo on one side and conj(Zo)
on the other side is definitely discontinuous! Unless of course,
Zo = conj(Zo) which occurs only when Zo is real.

There will always reflections at such an impedance
discontinuity where an impedance faces its' conjugate.



I disagree completely. The theoretical impedance of a resonant
series L and C (which is lossless) is zero. So in a conjugate
match, where they cancel out, in an ideal loss-less world, it
would be equivalent to the series C and L not being there at all,
with the source and load 50 ohms free to pass max. power delivered to
the load.




If an impedance Zo faces its' conjugate conj(Zo) then there will be
no "power reflections", but there will in general be voltage reflections,


??? if the square of the magnitude of the voltage RC is the power RC,
then your statement is incorrect. And rho (magnitude of Voltage RC) is the
square root of the Power RC.




i.e. "classical" rho = (Z - Zo)/(Z + Zo) is not zero at a conjugate match.


That's why it is incorrect for complex Zo.



I also believe that this is "Mother Nature's" reflection coefficient
for it is exactly what she uses as she lets the waves propagate
down her lines of surge impedance Zo following her partial differential
equations at every point along the way. At every infinitesimal
length of line all along it's length the waves are passing from a
infinitesimal region of surge impedance Zo to the next infinitesimal
region of surge impedance Zo and there are no voltage reflections
anywhere along that [uniform] line, although if the line is not lossless
there will be energy lost as the wave progresses.


Maybe "Mother Nature" should take a Les Besser course...


Slick... On another whole level it simply does not matter which defiinition
of the reflection coefficient one uses to make design calculations though,
as
long as the definition is used consistently throughout any calculations.


I totally disagree again:

Did you read Williams' data?


The data follows:

Note: |rho1*| is conjugated rho1, SWR1 is for
|rho1*|, |rho2| is not conjugated and SWR2 applies
to |rho2|

X0.......|rho1*|..SWR1.....|rho2|..SWR2
-250..... 0.935...30.0.....1.865...-3.30
-200..... 0.937...30.8.....1.705...-3.80
-150..... 0.942...33.3.....1.517...-4.87
-100..... 0.948...37.5.....1.320...-7.25
-050..... 0.955...43.3.....1.131...-16.3
-020..... 0.959...47.6.....1.030...-76.5
-015..... 0.960...48.4.....1.010...-204
-012..... 0.960...48.9.....0.997....+/- infinity
-010..... 0.960...49.2.....0.990....+305
-004..... 0.961...76.3.....0.974....+76.3
0000..... 0.961...50.9.....0.961....+50.9

The numbers for not-conjugate rho are all over the
place and lead to ridiculous numbers for SWR. It
is also obvious that for a low-loss line it
doesn't matter much. But values of rho greater
than 1.0, on a Smith chart correspond to negative
values of resistance (see the data).



Excellent work William. You are also showing how
a rho1 leads to ridiculous numbers for the equation:

SWR = (1 + rho)/(1 - rho)

The non-conjugate equation simply cannot handle
complex Zo.

Some people think we should throw out the SWR formula
completely, but this is complete nonsense, of course.

SWR = (1 + rho)/(1 - rho) works for 0=rho=1,
for very good reason, as it applies to passive networks only.

And the conjugate will always give 0=rho=1,
even with a complex Zo.


Slick

Slick:

[snip]
I disagree completely. The theoretical impedance of a resonant
series L and C (which is lossless) is zero. So in a conjugate
match, where they cancel out, in an ideal loss-less world, it
would be equivalent to the series C and L not being there at all,
with the source and load 50 ohms free to pass max. power delivered to
the load.
[snip]

Which is exactly what happens for all energy passing through at
the resonant frequency of the series LC!

And for instance if you are testing with a sinusoidal generator at
that frequency that is exactly what you will observe.

Of course if you are testing with a broad band signal rather
than a sinusoidal signal lots of much more interesting stuff
happens. That all can be calculated simply by using the
full functional descriptions of the network/transmission
system, i.e. assuming Z = Z(p) where p = s + jw, etc, etc...

[snip]
??? if the square of the magnitude of the voltage RC is the power RC,
then your statement is incorrect.
[snip]

To which voltage reflection coefficient do you refer? :-)

No! The square of the magnitude of the voltage reflection coefficient is
not,
in general, equal to the power reflection coefficient.

[snip]
That's why it is incorrect for complex Zo.
[snip]

Slick, no "correctly" defined reflection coefficient is "incorrect".

There can easily be an infinity of different "correct" reflection
coefficients so defined,
and none is "incorrect" so long as no incorrect conclusions are drawn from
their use.

The only "incorrect" ones are the reflection coefficients that are not
defined based upon simple non-singular linear combinations of the electrical
variables i and v.

Slick, your view of the reflection coefficient world is far too narrow!

Widen your horizons, there is more than one way to go to hell, and
chosing a particular definition of a reflection coefficient and forcing
all others to believe in it is nothing short of bigotry!

[snip]
Maybe "Mother Nature" should take a Les Besser course...
[snip]

I am sure that Dr. Besser is an honorable and accomplished man despite
his obviously narrow views of "waves".

[snip]
I totally disagree again:

Did you read Williams' data?
[snip]

Yes I "scanned" it and lost interest quickly, because of the gratuitous
use of mind boggling numerical tables in ASCII text on a newsgroup
posting!

I am sure that William did a lot of work whilst typing in those long
strings of numbers without error. Good work William!

Hey I'll scan in and post a listing of a couple of thousand lines of the Zo
versus frequency of 18,000 feet of plastic insulated AWG 24 wire if that
will help. I've got hundreds and hundreds of pages of such data! :-)

[snip]
Excellent work William. You are also showing how
a rho1 leads to ridiculous numbers for the equation:

SWR = (1 + rho)/(1 - rho)

The non-conjugate equation simply cannot handle
complex Zo.

Some people think we should throw out the SWR formula
completely, but this is complete nonsense, of course.

SWR = (1 + rho)/(1 - rho) works for 0=rho=1,
for very good reason, as it applies to passive networks only.

And the conjugate will always give 0=rho=1,
even with a complex Zo.
[snip]

Hey, again your view of rho and VSWR is too narrow.

Ask yourself what is the meaning of SWR in that formula
when rho is complex and SWR is complex!

Actually if you let your mind expand a little beyond your
narrow view of things you will find that complex SWR can
have a physical and useful meaning as well.

--
Peter K1PO
Indialantic By-the-Sea, FL

"Peter O. Brackett" wrote in message
link.net...
Slick:

Hey, again your view of rho and VSWR is too narrow.

Ask yourself what is the meaning of SWR in that formula
when rho is complex and SWR is complex!


how can swr be complex... in my book it is:

SWR=(1+|rho|)/(1-|rho|)

so swr can't be complex.

Dr. Slick wrote:

"Peter O. Brackett" wrote:
There will always reflections at such an impedance
discontinuity where an impedance faces its' conjugate.

I disagree completely. The theoretical impedance of a resonant
series L and C (which is lossless) is zero. So in a conjugate
match, where they cancel out, in an ideal loss-less world, it
would be equivalent to the series C and L not being there at all,
with the source and load 50 ohms free to pass max. power delivered to
the load.

Better be careful. Did you just assert that you can change
the SWR on a feedline by forming a conjugate match at the source?
All Peter is saying is that the VSWR on the feedline will not be 1:1
if Z-complex-load differs from the purely resistive Z0 of a lossless
line. For a lossless line, there is nothing you can do at the source
to change the SWR at the load.

However, if the line is lossless, you can achieve maximum power
transfer anyway even in the face of a high SWR.
--
73, Cecil http://www.qsl.net/w5dxp



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"Peter O. Brackett" wrote in message hlink.net...
Slick:

[snip]
I disagree completely. The theoretical impedance of a resonant
series L and C (which is lossless) is zero. So in a conjugate
match, where they cancel out, in an ideal loss-less world, it
would be equivalent to the series C and L not being there at all,
with the source and load 50 ohms free to pass max. power delivered to
the load.
[snip]

Which is exactly what happens for all energy passing through at
the resonant frequency of the series LC!

And for instance if you are testing with a sinusoidal generator at
that frequency that is exactly what you will observe.

Of course if you are testing with a broad band signal rather
than a sinusoidal signal lots of much more interesting stuff
happens. That all can be calculated simply by using the
full functional descriptions of the network/transmission
system, i.e. assuming Z = Z(p) where p = s + jw, etc, etc...



Well, of course i assume the conjugate match to occur at ONE frequency,
and with a small signal sine wave.




[snip]
??? if the square of the magnitude of the voltage RC is the power RC,
then your statement is incorrect.
[snip]

To which voltage reflection coefficient do you refer? :-)

No! The square of the magnitude of the voltage reflection coefficient is
not,
in general, equal to the power reflection coefficient.



Nope! Page 16-2 of the 1993 ARRL: rho=sqrt(Preflected/Pforward)

Look it up yourself, don't take my word for it.





The only "incorrect" ones are the reflection coefficients that are not
defined based upon simple non-singular linear combinations of the electrical
variables i and v.


I don't think you know what you are typing about here..



Slick, your view of the reflection coefficient world is far too narrow!

Widen your horizons, there is more than one way to go to hell, and
chosing a particular definition of a reflection coefficient and forcing
all others to believe in it is nothing short of bigotry!



Believe what you will... I ain't forcing anyone to accept anything!
I will tell you what respected authorities have written, though.

Jesus, dude. Do you want me to agree with you even when i think you
are incorrect?

Or would you prefer me to be honest?


[snip]
Maybe "Mother Nature" should take a Les Besser course...
[snip]

I am sure that Dr. Besser is an honorable and accomplished man despite
his obviously narrow views of "waves".



YOU are the one with the narrow views. Besser's courses are like
$1,200 a head. Do you think companies would pay him to steer them wrong?

Please!




Yes I "scanned" it and lost interest quickly, because of the gratuitous
use of mind boggling numerical tables in ASCII text on a newsgroup
posting!

I am sure that William did a lot of work whilst typing in those long
strings of numbers without error. Good work William!



Lost interest, or don't want to look at information that you disagree
with?



[snip]
Excellent work William. You are also showing how
a rho1 leads to ridiculous numbers for the equation:

SWR = (1 + rho)/(1 - rho)

The non-conjugate equation simply cannot handle
complex Zo.

Some people think we should throw out the SWR formula
completely, but this is complete nonsense, of course.

SWR = (1 + rho)/(1 - rho) works for 0=rho=1,
for very good reason, as it applies to passive networks only.

And the conjugate will always give 0=rho=1,
even with a complex Zo.
[snip]

Hey, again your view of rho and VSWR is too narrow.

Ask yourself what is the meaning of SWR in that formula
when rho is complex and SWR is complex!



Sigh... rho is the MAGNITUDE of the RC, so it isn't complex.

And SWR is never complex! And a negative SWR is pretty
meaningless!

If you want to rewrite the RF books, good luck.


Cheers,

Slick

Cecil Moore wrote in message ...

I disagree completely. The theoretical impedance of a resonant
series L and C (which is lossless) is zero. So in a conjugate
match, where they cancel out, in an ideal loss-less world, it
would be equivalent to the series C and L not being there at all,
with the source and load 50 ohms free to pass max. power delivered to
the load.

Better be careful. Did you just assert that you can change
the SWR on a feedline by forming a conjugate match at the source?
All Peter is saying is that the VSWR on the feedline will not be 1:1
if Z-complex-load differs from the purely resistive Z0 of a lossless
line. For a lossless line, there is nothing you can do at the source
to change the SWR at the load.


As usual, your sentences don't make too much sense, which is probably
why you go one with your record-breaking threads.
Maybe you actually agree with people when you argue with them...
well, we could all be accused of that one.

However, if the line is lossless, you can achieve maximum power
transfer anyway even in the face of a high SWR.


If Zo=50-j5 and Zload=50+j5, you will have a conjugate match,
and max power delivered to the load.


Slick

Frankly, I haven't paid any attention to your ducking, dodging, and
hand-waving. You haven't been able to produce an analysis showing the
voltages, currents, and powers in the same simple circuit I analyzed. As
far as I'm concerned, nothing you've posted constitutes a proof of anything.

One thing I have gotten from your postings, though, is an appreciation
for what you said about your alma mater being a military school. They
obviously taught you to always present a moving target, and you learned
the lesson well.

I return the readers now to tau, s11, n-port networks, optics, virtual
photons, and whatever else can be produced to avoid directly facing the
stark reality of Ohm's and Kirchoff's laws. Enjoy!

Roy Lewallen, W7EL

Cecil Moore wrote:
Roy Lewallen wrote:

The calculation used for reflection coefficient is based on its
definition, namely reflected voltage divided by forward voltage.


Unfortunately, you did not correctly identify the forward voltage
and reflected voltage. V1*tau is only one of the forward voltage
components. There is another one, V2*rho. Same for current.

Did you see my example where by adding one wavelength of lossless
feedline, it can be proven that reflected power can never be greater
than forward power?

Roy Lewallen wrote:
Frankly, I haven't paid any attention to your ducking, dodging, and
hand-waving. You haven't been able to produce an analysis showing the
voltages, currents, and powers in the same simple circuit I analyzed. As
far as I'm concerned, nothing you've posted constitutes a proof of
anything.

If one leads a horse to water and it refuses to drink, digging another
lake is just a waste of time. Analyze the following and see if you
get the same results. I'm betting you will catch your error.

Z0=68-j39
---lossy feedline---+---1WL 50 ohm lossless line---10+j50 load
Vfwd1-- Vfwd2--
--Vref1 --Vref2

Vfwd1 = Vfwd1*rho1 + Vfwd1*tau1 one forward, one reflected component

Vref2 = Vref2*rho2 + Vref2*tau2 one forward, one reflected component

Vref1 = Vfwd1*rho1 + Vref2*tau2 both reflected components added together

Vfwd2 = Vfwd1*tau1 + Vref2*rho2 both forward components added together

Note that every voltage has two components. You chose only one component
for your Vfwd. You ignored the other component of Vfwd. Hint: you cannot
have voltages left over from calculating the total forward voltage and
the total reflected voltage.
--
73, Cecil http://www.qsl.net/w5dxp



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