Reflection Coefficient Smoke Clears a Bit
 

Hello,


Actually, my first posting:

Reflection Coefficient =(Zload-Zo)/(Zload+Zo)

was right all along, if Zo is always purely real. No argument there.



However, from Les Besser's Applied RF Techniques:

"For passive circuits, 0=[rho]=1,

And strictly speaking:

Reflection Coefficient =(Zload-Zo*)/(Zload+Zo)
Where * indicates conjugate.

But MOST of the literature assumes that Zo is real, therefore
Zo*=Zo."

This is why most of you know the "normal" equation.


And then i looked at the trusty ARRL handbook, 1993, page 16-2,
and lo and behold, the reflection coefficient equation doesn't have a
term for line reactance, so both this book and Pozar have indeed
assumed that the Zo will be purely real.


Here's a website that describes the general conjugate equation:


http://www.zzmatch.com/lcn.html



Additionally, the Kurokawa paper ("Power Waves and the
Scattering Matrix") describes the voltage reflection coefficient
as the same conjugate formula, but he rather foolishly calls it a
"power wave R. C.", which when the magnitude is squared, becomes the
power R. C.

Email me for the paper.



As Reg points out about the "normal" equation:


"Dear Dr Slick, it's very easy.

Take a real, long telephone line with Zo = 300 - j250 ohms at 1000 Hz.

(then use ZL=10+j250)

Magnitude of Reflection Coefficient of the load, ZL, relative to line
impedance

= ( ZL - Zo ) / ( ZL + Zo ) = 1.865 which exceeds unity,

and has an angle of -59.9 degrees.

The resulting standing waves may also be calculated.

Are you happy now ?"
---
Reg, G4FGQ



Well, I was certainly NOT happy at this revelation, and researched
it until i understood why the normal equation could incorrectly give
a R.C.1 for a passive network (impossible).

If you try the calculations again with the conjugate formula, you
will see that you can never have a [rho] (magnitude of R.C.)
greater than 1 for a passive network. You need to use the conjugate
formula if Zo is complex and not purely real.

How could you get more power reflected than what you put into
a passive network(do you believe in conservation of energy, or do
you think you can make energy out of nothing)? If you guys can tell
us, we could fix our power problems in CA!

Thanks to Reg for NOT trusting my post, and this is a subtle detail
that is good to know.


Slick

"Dr. Slick" wrote in message
om...
As Reg points out about the "normal" equation:


"Dear Dr Slick, it's very easy.

Take a real, long telephone line with Zo = 300 - j250 ohms at 1000 Hz.

(then use ZL=10+j250)

Magnitude of Reflection Coefficient of the load, ZL, relative to line
impedance

= ( ZL - Zo ) / ( ZL + Zo ) = 1.865 which exceeds unity,

and has an angle of -59.9 degrees.

The resulting standing waves may also be calculated.

Are you happy now ?"
---
Reg, G4FGQ



Well, I was certainly NOT happy at this revelation, and researched
it until i understood why the normal equation could incorrectly give
a R.C.1 for a passive network (impossible).

According to Adler, Chu, and Fano, "Electromagnetic Energy Transmission and
Radiatin", John Wiley, 1960, (60-10305),
when they talk about lossy lines, and say that Zo is complex in the general
case, they come up with a maximum value for the reflection coefficient of (1
+ SQRT(2)). Eq 5.14b. Remember, it is a lossy line; so, the reflected
voltage gets smaller as you move away from the load. Somebody might want to
check this out, in case I misunderstood something. BTW, the three authors
were all MIT profs.

Tam/WB2TT

The problem is in leaping to the conclusion that a reflection
coefficient greater than one means that more energy is coming back from
the reflection point than is incident on it. It's an easy conclusion to
reach if your math skills are inadequate to do a numerical analysis
showing the actual power or energy involved, or if you have certain
misconceptions about the meaning of "forward power" and "reverse power".
But it's an incorrect conclusion. Then, having come to the wrong
conclusion, the search is on for ways to modify the reflection
coefficient formula so that a reflection coefficient greater than one
can't happen and thereby disturb the incorrect view of energy movement.
It's simply an example of faulty logic combined with an inability to do
the math. Adler, Chu, and Fano do understand the law of conservation of
energy, and they are able to do the math.

Roy Lewallen, W7EL

Tarmo Tammaru wrote:
"Dr. Slick" wrote in message
om...

As Reg points out about the "normal" equation:


"Dear Dr Slick, it's very easy.

Take a real, long telephone line with Zo = 300 - j250 ohms at 1000 Hz.

(then use ZL=10+j250)

Magnitude of Reflection Coefficient of the load, ZL, relative to line
impedance

= ( ZL - Zo ) / ( ZL + Zo ) = 1.865 which exceeds unity,

and has an angle of -59.9 degrees.

The resulting standing waves may also be calculated.

Are you happy now ?"
---
Reg, G4FGQ



Well, I was certainly NOT happy at this revelation, and researched
it until i understood why the normal equation could incorrectly give
a R.C.1 for a passive network (impossible).


According to Adler, Chu, and Fano, "Electromagnetic Energy Transmission and
Radiatin", John Wiley, 1960, (60-10305),
when they talk about lossy lines, and say that Zo is complex in the general
case, they come up with a maximum value for the reflection coefficient of (1
+ SQRT(2)). Eq 5.14b. Remember, it is a lossy line; so, the reflected
voltage gets smaller as you move away from the load. Somebody might want to
check this out, in case I misunderstood something. BTW, the three authors
were all MIT profs.

Tam/WB2TT

"Tarmo Tammaru" wrote

It might be worthwhile explaining how they came up with Gamma max =
2.414,
instead of some huge number. They say that the phase angle of Zo is
constrained to +/- 45 degrees for R, G, L, and C non-negative.
=================================

Tam, who are "They" ?

Are "they" the "One million housewives who can't be wrong" ?

Or might it be Oliver Heaviside around 1872 ?

It would be a mistake to found a restart of these arithmetical arguments on
rumour.
---
Yours, Reg, G4FGQ ;o)

Reg Edwards wrote:
"Tarmo Tammaru" wrote

It might be worthwhile explaining how they came up with Gamma max =
2.414,
instead of some huge number. They say that the phase angle of Zo is
constrained to +/- 45 degrees for R, G, L, and C non-negative.
=================================

Tam, who are "They" ?

Are "they" the "One million housewives who can't be wrong" ?

Or might it be Oliver Heaviside around 1872 ?


It doesn't matter who says so - the only thing that matters is that the
result is correct. The same correct result is always there, to be found
by anybody who can.


--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
Editor, 'The VHF/UHF DX Book'
http://www.ifwtech.co.uk/g3sek

"Reg Edwards" wrote in message
...
=================================

Tam, who are "They" ?

They were MIT EE professors. I think Fano has written a more recent book on
this. MIT is often considered to be the best engineering school in the US.
(Keep forgetting you live "over there")

You are making me work my tail off trying to understand just what they did.
You have a line of impedance Zo with load Zr at point z=0. Normalize,
Zn=Zr/Zo. Since the angle of Zo is within +/- 45 degrees, the angle of Zn is
within +/-135 degrees. He draws some vectors and decides maximum gamma is
when the angle of Zn is +/-135. He solves for gamma^2, takes the square
root, and ends up with gamma =

1 + SQRT(2)

I couldn't massage the numbers just right, but the decimal number I got
suggest that max Gamma occurs when

Zo = k(1 - j1)
Zr = jkSQRT(2) k is the same k

He goes on to say that as you move away from z=0, the reflection coefficient
becomes smaller by e**2alpha|z|

This is probably a never ending discussion, but I wanted to point out that
these guys don't think there is anything wrong with your gamma of 1.8 ;
especially since Slick brought it up again. I do not want to retake Fields &
Waves

Tam/WB2TT

Tam, I did not say your value of 1+Sqrt(2) was incorrect.

But when 3 guys you happen to have heard of say so, it hardly constitutes a
proof. Why bother to mention them.

If you have any doubts about a particular matter the only way to understand
what goes on is to work it out for yourself with pencil and paper.
Otherwise you will remain dependent on mere acceptance of numbers found in
books - if you can find a book. And has been re-discovered in these
threads - books disagree with each other.

Good books teach you how to work things out for yourself from first
principles. Then you can stop referring to authors. But these days so-called
engineers are more inclined to misplace their blind faith in computer
programs. ;o)

Yours, Reg, G4FGQ

"Reg Edwards" wrote in message ...
....
By the way, you've told us only half the story. What's the value of the
load impedance which maximises the reflection coefficient?

Hey, Reg, it's just a simple high-school (well, maybe first-year
college) differential calculus problem. Just let Garvin work through
it for us. Hey, good Dr., could you do that for us? Just write an
expression for |Vr/Vf| = |(Zl-Zo)/(Zl+Zo)| in terms of Rl and Xl and
find the partial derivatives with respect to those two variables, and
set both equal to zero, while letting Ro=Xo. It's mostly just a bunch
of bookkeeping. You should come up with values of Rl and Zl in terms
of Ro, and you can check to be sure that's actually a maximum and not
a minimum or saddle point. You should see a symmetry for Ro=-Xo, the
more usual limiting case.

Cheers,
Tom

If anyone is interested in really getting to the bottom of this endless
jousting, turn to page 136 of "Theory and Problems of Transmission Lines" by
Robert A. Chipman. This is a Schaum's Outline book - mine is dated 1968.
Many professionals acknowledge that this is one of the most succinct and
revealing accounts of t-line theory to be found. Mathematical enough to be
rigorous but readable and highly useful.


Starting in Section 7.6, Chipman derives the full set of equations for lines
with complex characteristic impedance. I will make no effort here to repeat
the development with ASCII non-equation symbols, but the bottom line is that
in the general case, Zo is indeed a complex number which can be highly
frequency-dependent.

Under the condition of certain combinations of physical parameters of the
line, Zo does indeed become actually real - the so-called Heaviside Line
where R/L=G/C where the symbols have the usual meanings - and independent of
frequency. This is the only case wherein a lossy line can have a real Zo.

Finally, he clearly shows how terminating an actual physical line
appropriately can result in a reflection coefficient as large as 2.41.

This revelation DOES NOT imply that the reflected wave would bear more power
than the incident wave. For a line to display this behavior, it must first
of all have a high attenuation per wavelength. Due to this high attenuation,
the power in the reflected wave is high for only a short distance from the
termination.

A couple of surprising consequences of this:

1. in order to terminate a line with complex Zo such that rho is greater
than 1, the reactance of the load must be equal and opposite to the reactive
term of Zo. In other words, the line and the load form a resonant circuit
separated from "the rest of the system" by the very lossy line.

2. calculation of the power at any point on a line with real Zo, lossy or
not, is simply Pf - Pr. But for a complex Zo, this is no longer true and a
much more complex set of equations - given by Chipman - must be used. See
his equations 7.34 and 7.35.

Finally, it should be understood that these effects are found almost
entirely on low-frequency transmission lines. Dealing with complex Zo is
routine with audio/telephone cable circuits and the like.

At HF, the reactive component of Zo for most common lines is so small as to
be safely and conveniently neglected. For example, RG-213 at 14 MHz has a Zo
of 50-j0.315 ohms. The same line at 1000 Hz has a Zo of 50-j35.733 ohms.
(Values taken from the TLDetails program)

When terminated in 50+j0 ohms, the SWR on the line is 2.012.
When terminated in 50-j35.733 ohms, the SWR is 1:1 as would be expected. But
when terminated in 50+j35.733 ohms, the SWR is a whopping 5.985.

RG-213 is nowhere near lossy enough to display the resonant-load effects
Chipman discusses, but these data give some idea of the perhaps unexpected
consequences of using even a common line like RG-213 at a low frequency.

Taken to 100 Hz, we find Zo = 50 - j 113.969 ohms and when terminated in 50
+ j 112.969, rho is determined to be 2.25839. Note that the termination is a
passive circuit in all these examples.

I urge anyone seriously interested in understanding transmission line theory
to include Chipman on their bookshelf. Despite its assumed low station as a
Schaum's Outline book, it provides a source of information and understanding
seldom matched by any text.

73/72, George
Amateur Radio W5YR - the Yellow Rose of Texas
Fairview, TX 30 mi NE of Dallas in Collin county EM13QE
"In the 57th year and it just keeps getting better!"







----- Original Message -----
From: "Dr. Slick"
Newsgroups: rec.radio.amateur.antenna
Sent: Wednesday, August 27, 2003 1:18 AM
Subject: Reflection Coefficient Smoke Clears a Bit


Hello,


Actually, my first posting:

Reflection Coefficient =(Zload-Zo)/(Zload+Zo)

was right all along, if Zo is always purely real. No argument there.



However, from Les Besser's Applied RF Techniques:

"For passive circuits, 0=[rho]=1,

And strictly speaking:

Reflection Coefficient =(Zload-Zo*)/(Zload+Zo)
Where * indicates conjugate.

But MOST of the literature assumes that Zo is real, therefore
Zo*=Zo."

This is why most of you know the "normal" equation.


And then i looked at the trusty ARRL handbook, 1993, page 16-2,
and lo and behold, the reflection coefficient equation doesn't have a
term for line reactance, so both this book and Pozar have indeed
assumed that the Zo will be purely real.


Here's a website that describes the general conjugate equation:


http://www.zzmatch.com/lcn.html



Additionally, the Kurokawa paper ("Power Waves and the
Scattering Matrix") describes the voltage reflection coefficient
as the same conjugate formula, but he rather foolishly calls it a
"power wave R. C.", which when the magnitude is squared, becomes the
power R. C.

Email me for the paper.



As Reg points out about the "normal" equation:


"Dear Dr Slick, it's very easy.

Take a real, long telephone line with Zo = 300 - j250 ohms at 1000 Hz.

(then use ZL=10+j250)

Magnitude of Reflection Coefficient of the load, ZL, relative to line
impedance

= ( ZL - Zo ) / ( ZL + Zo ) = 1.865 which exceeds unity,

and has an angle of -59.9 degrees.

The resulting standing waves may also be calculated.

Are you happy now ?"
---
Reg, G4FGQ



Well, I was certainly NOT happy at this revelation, and researched
it until i understood why the normal equation could incorrectly give
a R.C.1 for a passive network (impossible).

If you try the calculations again with the conjugate formula, you
will see that you can never have a [rho] (magnitude of R.C.)
greater than 1 for a passive network. You need to use the conjugate
formula if Zo is complex and not purely real.

How could you get more power reflected than what you put into
a passive network(do you believe in conservation of energy, or do
you think you can make energy out of nothing)? If you guys can tell
us, we could fix our power problems in CA!

Thanks to Reg for NOT trusting my post, and this is a subtle detail
that is good to know.


Slick

"Reg Edwards" wrote in message ...
....
But these days so-called
engineers are more inclined to misplace their blind faith in computer
programs. ;o)

Computer programs...computer programs...now where have I seen them.
Oh, yes, it's this chap in Great Britain that offers a bunch of them
for free, imperfections and all...

;o) backatcha -- and of course, since this is an amateur group, there
are no engineers here.

Cheers,
Tom
who comes equipped with _pen_, paper and computer programs--and
sometimes maybe even a brain (smarter than the average bear?).
Pencils waste too much time. (Though not so bad as newsgroups in that
regard.)

On Thu, 28 Aug 2003 06:27:40 GMT, "George, W5YR"
wrote:

... "Theory and Problems of Transmission Lines" by
Robert A. Chipman. This is a Schaum's Outline book - mine is dated 1968.
Many professionals acknowledge that this is one of the most succinct and
revealing accounts of t-line theory to be found. Mathematical enough to be
rigorous but readable and highly useful.


Hi George,

I have notice you recommended this author several times, and yet you
have casually dismissed his rather straightforward coverage relating
to the characteristic Z of a Transmitter:
There is no need to know, since its value, whatever it might be, plays no
role in the design and implementation of the external portion of the system
driven by the transmitter.

How do you reconcile this with his coverage entitled
"9.10. Return loss, reflection loss, and transmission loss."

You may wish to observe the clearly marked figure 9-26 and
specifically the paragraph that follows (or the entire section for
that matter) that quite clearly reveals what is everywhere else
implied: that ALL SWR discussion presumes a Zc matched source. You
may observe that Chapman thus refutes your statement above. Further,
Chapman goes to some length to describe the Smith Chart's appended
line evaluation scales at the bottom to this very matter.

To substantiate this from other sources I have offered a very simple
example that shows this importance that to date has defied "first
principle" analysis (not first principles however, merely the claim of
its being practiced analytically in this regard). I will offer it
again, lest you missed it.

The scenario begins:

"A 50-Ohm line is terminated with a load of 200+j0 ohms.
The normal attenuation of the line is 2.00 decibels.
What is the loss of the line?"

Having stated no more, the implication is that the source is matched
to the line (source Z = 50+j0 Ohms). This is a half step towards the
full blown implementation such that those who are comfortable to this
point (and is in fact common experience) will observe their answer and
this answer a

"A = 1.27 + 2.00 = 3.27dB"

"This is the dissipation or heat loss...."

we then proceed:

"...the generator impedance is 100+0j ohms, and the line is 5.35
wavelengths long."

Beware, this stumper has so challenged the elite that I have found it
dismissed through obvious embarrassment of either lacking the means to
compute it, or the ability to simply set it up and measure it. It
takes two resistors and a hank of transmission line, or what has been
described by one correspondent as:
There is no institutionalized ignorance, just a
lot of skepticism regarding the reliability of the
analysis methods and the measurement methods.
Clearly a low regard for many correspondent's abilities here, and
hardly a prejudice original to me. Imagine the incapacity of so many
to measure relative power loss - a CFA salesman's dream population.

Actually it is quite obvious several recognize that follow-through
would dismantle some cherished fantasies. Chapman clearly knocks the
underpinnings from beneath them without any further effort on my part.
But then, as you offer, they would merely dismiss it by confirming
another prejudice:
its assumed low station as a Schaum's Outline book

I would point out to all, that Chapman's material dovetails with what
would have been then current research and teachings of the National
Bureau of Standards. Prejudice has "refuted" those findings too. :-)

73's
Richard Clark, KB7QHC

George, W5YR wrote:
I urge anyone seriously interested in understanding transmission line theory
to include Chipman on their bookshelf.

It's out of print, George. How much will you take for yours? :-)
--
73, Cecil http://www.qsl.net/w5dxp



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Richard Clark wrote:
"...the generator impedance is 100+0j ohms, and the line is 5.35
wavelengths long."

What does the generator impedance have to do with line losses?
--
73, Cecil http://www.qsl.net/w5dxp



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"George, W5YR" wrote in message
...
If anyone is interested in really getting to the bottom of this endless
jousting, turn to page 136 of "Theory and Problems of Transmission Lines"
by
Robert A. Chipman. This is a Schaum's Outline book - mine is dated 1968.

George,

I took a course from Dr Chipman. The text he used was Adler, Chu, and Fano.
I bet he references that book.

Tam/WB2TT

On Thu, 28 Aug 2003 09:02:40 -0400, "Tarmo Tammaru"
wrote:


"George, W5YR" wrote in message
...
If anyone is interested in really getting to the bottom of this endless
jousting, turn to page 136 of "Theory and Problems of Transmission Lines"
by
Robert A. Chipman. This is a Schaum's Outline book - mine is dated 1968.

George,

I took a course from Dr Chipman. The text he used was Adler, Chu, and Fano.
I bet he references that book.

Tam/WB2TT


Hi Tam,

It is the second reference and it is found on page 8. No doubt those
authors also understand that source characteristic Z must be equal to
transmission line Z to characterize SWR on the line. Of course, at
this point I cannot vouchsafe for that specifically, however, it seems
unlikely anyone here will negate the premise.
Except to say "t'ain't so." ;-)

I said "at this point" as this could be resolved (or from the other 11
references) by my visiting my engineering library at the U. This will
not prohibit others from denial however which simply mocks Chapman's
work and those he references.

I won't put the challenge I have offered others to you. You probably
would have answered it by now if you could have.

73's
Richard Clark, KB7QHC

On Thu, 28 Aug 2003 05:58:09 -0500, W5DXP
wrote:

Richard Clark wrote:
"...the generator impedance is 100+0j ohms, and the line is 5.35
wavelengths long."

What does the generator impedance have to do with line losses?

Hi Cecil,

From Chapman (you following this George?) page 28:

"It is reasonable to ask at this point how, for the circuit of
Fig. 3-1(b), page 18, on which the above analysis is based, there
can be voltage and current waves traveling in both directions on
the transmission line when there is only a single signal source.
The answer lies in the phenomenon of reflection, which is very
familiar in the case of light waves, sound waves, and water waves.
Whenever traveling waves of any of these kinds meet an obstacle,
i.e. encounter a discontinuous change from the medium in which
they have been traveling, they are partially or totally
reflected."
...
"The reflected voltage and current waves will travel back along
the line to the point z=0, and in general will be partially
re-reflected there, depending on the boundary conditions
established by the source impedance Zs. The detailed analysis of
the resulting infinite series of multiple reflections is given in
Chapter 8."

The Challenge that I have offered more than several here embody such
topics and evidence the exact relations portrayed by Chapman (and
others already cited, and more not). The Challenge, of course, dashes
many dearly held prejudices of the Transmitter "not" having a
characteristic source Z of 50 Ohms. Chapman also clearly reveals that
this characteristic Z is of importance - only to those interested in
accuracy.

Those hopes having been dashed is much evidenced by the paucity of
comment here; and displayed elsewhere where babble is most abundant in
response to lesser dialog (for the sake of enlightening lurkers no
less). Clearly those correspondents hold to the adage to choose
fights you can win. I would add so do I! The quality of battle is
measured in the stature of the corpses littering the field. :-)

So, Cecil (George, Peter, et alii), do you have an answer? Care to
take a measure at the bench? As Chapman offers, "just like optics."
Shirley a man of your erudition can cope with the physical proof of
your statements. ;-)

The only thing you and others stand to lose is not being able to
replicate decades old work. Two resistors and a hank of line is a
monumental challenge.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
So, Cecil (George, Peter, et alii), do you have an answer?

Years ago, I had a discussion with Jeff, WA6AHL, here on this
newsgroup. I suggested that the impedance looking back into
the source might be Vsource/Isource, i.e. the transformed
dynamic load line. However, I have never taken a strong stand
on source impedance. If reflections are blocked from being
incident upon the source, as they are in most Z0-matched
systems, the source impedance doesn't matter since there
exists nothing to reflect from the source impedance.

My basic approach is to achieve a Z0-match and therefore
forget about source impedance.
--
73, Cecil http://www.qsl.net/w5dxp



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On Thu, 28 Aug 2003 12:18:44 -0500, W5DXP
wrote:

Richard Clark wrote:
So, Cecil (George, Peter, et alii), do you have an answer?

Years ago, I had a discussion with Jeff, WA6AHL, here on this
newsgroup. I suggested that the impedance looking back into
the source might be Vsource/Isource, i.e. the transformed
dynamic load line. However, I have never taken a strong stand
on source impedance. If reflections are blocked from being
incident upon the source, as they are in most Z0-matched
systems, the source impedance doesn't matter since there
exists nothing to reflect from the source impedance.

My basic approach is to achieve a Z0-match and therefore
forget about source impedance.

Hi Cecil,

That's all fine and well. It exhibits a rather standard behavior and
confirms conventional expectations. I take by this response that you
have no interest in the confirmation of interference in both Optical
and RF metaphors being visited at the bench. That is fine too. It is
a rather tough example to replicate - except when stumbled upon, then
we hear cries for exorcism being needed (my cue).

My missives simply offer touchstones of clarity in contrast to the
murky sea of un-fettered statements. We are presented with fantastic
notions that the characteristic source Z of a transmitter is
unknowable, and this statement is usually closely allied to the notion
that this same "unknowable" Z is actually responsible for reflecting
all power arriving at the antenna terminal. Few of those who utter
these witless jokes have any response to the straight line "So what is
this Z that does all that reflecting?" In their chagrin, they fail
even to repeat "it is unknowable...." Absolutely none can venture a
guess that it is either: "much less than 50 Ohms," or it is "much more
than 50 Ohms." This would be two obvious rejoinders and yet neither
is uttered. Such is faith. The universal silence condemns their
specious claims absolutely.

These absurd notions deserve a hearty laugh, because it invalidates
the need for a tuner which is purposely inserted between the source
and load to serve that very purpose (and which you describe as your
typical habit which is a nearly universal application).

But, again, this discussion is generally reserved only for those
interested in accuracy. :-)

73's
Richard Clark, KB7QHC

On Thu, 28 Aug 2003 12:18:44 -0500, W5DXP
wrote:

Richard Clark wrote:
So, Cecil (George, Peter, et alii), do you have an answer?

Years ago, I had a discussion with Jeff, WA6AHL, here on this
newsgroup. I suggested that the impedance looking back into
the source might be Vsource/Isource, i.e. the transformed
dynamic load line. However, I have never taken a strong stand
on source impedance. If reflections are blocked from being
incident upon the source, as they are in most Z0-matched
systems, the source impedance doesn't matter since there
exists nothing to reflect from the source impedance.

My basic approach is to achieve a Z0-match and therefore
forget about source impedance.

Hi Cecil,

That's all fine and well. It exhibits a rather standard behavior and
confirms conventional expectations. I take by this response that you
have no interest in the confirmation of interference in both Optical
and RF metaphors being visited at the bench. That is fine too. It is
a rather tough example to replicate - except when stumbled upon, then
we hear cries for exorcism being needed (my cue).

My missives simply offer touchstones of clarity in contrast to the
murky sea of un-fettered statements. We are presented with fantastic
notions that the characteristic source Z of a transmitter is
unknowable, and this statement is usually closely allied to the notion
that this same "unknowable" Z is actually responsible for reflecting
all power arriving at the antenna terminal. Few of those who utter
these witless jokes have any response to the straight line "So what is
this Z that does all that reflecting?" In their chagrin, they fail
even to repeat "it is unknowable...." Absolutely none can venture a
guess that it is either: "much less than 50 Ohms," or it is "much more
than 50 Ohms." This would be two obvious rejoinders and yet neither
is uttered. Such is faith. The universal silence condemns their
specious claims absolutely.

These absurd notions deserve a hearty laugh, because it invalidates
the need for a tuner which is purposely inserted between the source
and load to serve that very purpose (and which you describe as your
typical habit which is a nearly universal application).

But, again, this discussion is generally reserved only for those
interested in accuracy. :-)

73's
Richard Clark, KB7QHC

On Thu, 28 Aug 2003 12:18:44 -0500, W5DXP
wrote:

My basic approach is to achieve a Z0-match and therefore
forget about source impedance.

Hi Cecil,

This is a cavalier attitude if you can afford it. Otherwise, those
who so desperately hammer out the last 0.1 dB antenna gain are going
to fall to their knees in wrack when they discover that their rig's
characteristic Z of, say, 70 Ohms meeting the discontinuity of their
low pass filter's 50 Ohms turns that effort into heat behind the
antenna jack.

I have long since stopped being surprised by those who spin on like
whirling dervishes over trivial matters in the face of 10 fold losses
in front of them. This, of course, is even more trivial when they
gush on about their premium equipment that behind the knobs
"efficiently" transforms 20 - 25 Amperes of DC current into 100 Watts
RF. Now, that puts perspective to the topic: smoke and reflection
coefficient.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
But, again, this discussion is generally reserved only for those
interested in accuracy. :-)

Like I say, my solution is to block any reflections from being
incident upon the source. But I have a question. Since we are
discussing coherent sine waves, it seems to me that any reflection
from the source impedance will become indistinguishable from the
generated wave. In fact, the present convention of generated power
equals forward power minus reflected power is designed to overcome
that very problem.
--
73, Cecil, W5DXP

Richard Clark wrote:

W5DXP wrote:
My basic approach is to achieve a Z0-match and therefore
forget about source impedance.

This is a cavalier attitude if you can afford it.

It's all part of my "Work Smarter, Not Harder" nature. The elimination
of reflected energy incident upon the source is extremely rewarding
in multiple ways.
--
73, Cecil, W5DXP

Tom, to save everybody a lot of trouble -

The greatest theoretical value of the magnitude of the
reflection coefficient occurs when the angle of Zo is
-45 degrees, and the terminating impedance is a pure
inductive reactance of |Zo| ohms.

Do you think I should have mentioned this when I
began this and other threads by saying a reflection
coefficient greater than unity can occur?

The riot police can now return to barracks.
----
Reg, G4FGQ.

====================================
---
"Tom Bruhns" wrote
"Reg Edwards" wrote
By the way, you've told us only half the story.
What's the value of the
load impedance which maximises the reflection
coefficient?
====================================
Hey, Reg, it's just a simple high-school (well,
maybe first-year
college) differential calculus problem. Just let
Garvin work through
it for us. Hey, good Dr., could you do that for
us? Just write an
expression for |Vr/Vf| = |(Zl-Zo)/(Zl+Zo)| in terms
of Rl and Xl and
find the partial derivatives with respect to those
two variables, and
set both equal to zero, while letting Ro=Xo. It's
mostly just a bunch
of bookkeeping. You should come up with values of
Rl and Zl in terms
of Ro, and you can check to be sure that's actually
a maximum and not
a minimum or saddle point. You should see a
symmetry for Ro=-Xo, the
more usual limiting case.

(Of course, that's not quite right, as I'm sure the
good Dr. and Reg
both know. Since we're talking passive here, you
need to insure that
Rl stays positive, so you just may need to check
along the boundary
where Rl=0. And you should convince yourself that
the most reactive
possible line really does yield the largest possible
|Vr/Vf|. So it
becomes a task of finding the maximum value of a
function f(Rl, Xl,
Xo) with Ro fixed positive non-zero, under the
constraints that Rl=0
and |Xo|=Ro.)

On Thu, 28 Aug 2003 12:33:53 -0700, W5DXP
wrote:

Richard Clark wrote:
But, again, this discussion is generally reserved only for those
interested in accuracy. :-)

Like I say, my solution is to block any reflections from being
incident upon the source. But I have a question. Since we are
discussing coherent sine waves, it seems to me that any reflection
from the source impedance will become indistinguishable from the
generated wave. In fact, the present convention of generated power
equals forward power minus reflected power is designed to overcome
that very problem.

Hi Cecil,

So you DO want to perform this test?

Your presumption of coherency is false unless you engineer the
solution.

I got there first and made sure that wasn't gonna happen. :-)

Any random attempt has only a one in 360 chance of being correct
within one degree of coherent. This is simple interference math after
all. Most individuals would just notice a 10 degree error which would
boost your chances to slightly less than 3% - not very good coherency
wise.

73's
Richard Clark, KB7QHC

On Thu, 28 Aug 2003 12:39:25 -0700, W5DXP
wrote:

Richard Clark wrote:

W5DXP wrote:
My basic approach is to achieve a Z0-match and therefore
forget about source impedance.

This is a cavalier attitude if you can afford it.

It's all part of my "Work Smarter, Not Harder" nature. The elimination
of reflected energy incident upon the source is extremely rewarding
in multiple ways.

Hi Cecil,

If smarter were hotter, then you could toast bread at 10 feet.
Casting back ten watts by burning 20 hardly qualifies for more.

73's
Richard Clark, KB7QHC

"George, W5YR" wrote in message ...


Finally, he clearly shows how terminating an actual physical line
appropriately can result in a reflection coefficient as large as 2.41.

This revelation DOES NOT imply that the reflected wave would bear more power
than the incident wave. For a line to display this behavior, it must first
of all have a high attenuation per wavelength. Due to this high attenuation,
the power in the reflected wave is high for only a short distance from the
termination.


George, with all due respect, even if the SWR measurement was
done right at a short or open, the highest rho you could get would be
1.

If the power reflection coefficient is the square of the
MAGNITUDE of the voltage reflection coefficient, how can you have a
voltage RC greater than one without the power RC being also greater
than one??


Slick

"Tarmo Tammaru" wrote in message ...

They were MIT EE professors. I think Fano has written a more recent book on
this. MIT is often considered to be the best engineering school in the US.
(Keep forgetting you live "over there")


And they never make mistakes or typos? Ok...


You are making me work my tail off trying to understand just what they did.
You have a line of impedance Zo with load Zr at point z=0. Normalize,
Zn=Zr/Zo. Since the angle of Zo is within +/- 45 degrees, the angle of Zn is
within +/-135 degrees. He draws some vectors and decides maximum gamma is
when the angle of Zn is +/-135. He solves for gamma^2, takes the square
root, and ends up with gamma =



What exactly do you mean by Zr at point z=0? i don't fully
understand the page you sent, and neither do you obviously.



1 + SQRT(2)

I couldn't massage the numbers just right, but the decimal number I got
suggest that max Gamma occurs when

Zo = k(1 - j1)
Zr = jkSQRT(2) k is the same k

He goes on to say that as you move away from z=0, the reflection coefficient
becomes smaller by e**2alpha|z|

This is probably a never ending discussion, but I wanted to point out that
these guys don't think there is anything wrong with your gamma of 1.8 ;
especially since Slick brought it up again. I do not want to retake Fields &
Waves

Tam/WB2TT


Maybe you should retake it.

If the power RC is the square of the MAGNITUDE of the voltage
RC, then a voltage RC 1 will lead to a power RC 1.

How do you get more reflected power than incident power into a
passive network, praytell??


Slick

On Thu, 28 Aug 2003 14:22:55 -0700, W5DXP
wrote:
I guess I don't understand any of the above. Coherency just means the
signals are of the identical frequency. Coherency doesn't specify phase.
The phase of a reflected wave can be anything depending on feedline
length and load.

Hi Cecil,

This shows the lack of your "optics." A laser which amplifies by
virtue of coherency, consists of a phase locked aggregation of what
would have been incoherent illuminations. It would be an LED
otherwise.

As I have said for quite a while now, it is a simple matter of
interference math. Such math shows everything of coherency or
differences. A coherent signal, is by definition of the same
frequency of another who matches that coherency.

To put it ironically, the challenge I offer is deliberately incoherent
to give that math a deliberate solution that is other than the result
of simple addition or subtraction.

73's,
Richard Clark, KB7QHC

"Dr. Slick" wrote
What about the ARRL?
================================

Dear Slick, you must be new round this neck of the
woods.

Don't you realise the ARRL bibles are written by the
same sort of people who haggle with you on this
newsgroup?

"Dr. Slick" wrote in message
om...
What exactly do you mean by Zr at point z=0? i don't fully
understand the page you sent, and neither do you obviously.


Lower case z is distance, with the load at z=0

If the power RC is the square of the MAGNITUDE of the voltage
RC, then a voltage RC 1 will lead to a power RC 1.

He squares it to get the magnitude of the vector. There is still a phase
angle

How do you get more reflected power than incident power into a
passive network, praytell??


You don't. at gamma =2.41, the phase angle is about 65 degrees, and the real
part of gamma =1.0


Now try this: using the conjugate formula, calculate gamma for the case
where the line is terminated in a short circuit, and tell us how that meets
the boundary condition.

Tam/WB2TT

Ian White, G3SEK wrote:
The reason no-one will take on your challenge is that it's an empty one:
the source impedance has no effect on the SWR, so there's nothing there
for us to prove.

I'm still trying to understand the challenge. Do you understand where
the alleged incoherence comes from?
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
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Yes, Richard . . .

Did you mean "Chipman" by chance?

That is the author's name . . .

--
73/72, George
Amateur Radio W5YR - the Yellow Rose of Texas
Fairview, TX 30 mi NE of Dallas in Collin county EM13QE
"In the 57th year and it just keeps getting better!"






"Richard Clark" wrote in message
...
On Thu, 28 Aug 2003 05:58:09 -0500, W5DXP
wrote:

Richard Clark wrote:
"...the generator impedance is 100+0j ohms, and the line is 5.35
wavelengths long."

What does the generator impedance have to do with line losses?

Hi Cecil,

From Chapman (you following this George?) page 28:

"It is reasonable to ask at this point how, for the circuit of
Fig. 3-1(b), page 18, on which the above analysis is based, there
can be voltage and current waves traveling in both directions on
the transmission line when there is only a single signal source.
The answer lies in the phenomenon of reflection, which is very
familiar in the case of light waves, sound waves, and water waves.
Whenever traveling waves of any of these kinds meet an obstacle,
i.e. encounter a discontinuous change from the medium in which
they have been traveling, they are partially or totally
reflected."
...
"The reflected voltage and current waves will travel back along
the line to the point z=0, and in general will be partially
re-reflected there, depending on the boundary conditions
established by the source impedance Zs. The detailed analysis of
the resulting infinite series of multiple reflections is given in
Chapter 8."

The Challenge that I have offered more than several here embody such
topics and evidence the exact relations portrayed by Chapman (and
others already cited, and more not). The Challenge, of course, dashes
many dearly held prejudices of the Transmitter "not" having a
characteristic source Z of 50 Ohms. Chapman also clearly reveals that
this characteristic Z is of importance - only to those interested in
accuracy.

Those hopes having been dashed is much evidenced by the paucity of
comment here; and displayed elsewhere where babble is most abundant in
response to lesser dialog (for the sake of enlightening lurkers no
less). Clearly those correspondents hold to the adage to choose
fights you can win. I would add so do I! The quality of battle is
measured in the stature of the corpses littering the field. :-)

So, Cecil (George, Peter, et alii), do you have an answer? Care to
take a measure at the bench? As Chapman offers, "just like optics."
Shirley a man of your erudition can cope with the physical proof of
your statements. ;-)

The only thing you and others stand to lose is not being able to
replicate decades old work. Two resistors and a hank of line is a
monumental challenge.

73's
Richard Clark, KB7QHC

On Thu, 28 Aug 2003 21:01:54 -0500, W5DXP
wrote:

Richard Clark wrote:
To put it ironically, the challenge I offer is deliberately incoherent
to give that math a deliberate solution that is other than the result
of simple addition or subtraction.

So how do you get the reflections in a single source system to be
incoherent?

Hi Cecil,

Two reflective interfaces with an aperiodic distance between.

The cable (or any transmission line) falls in between. So does most
instrumentation to measure power. All fall prey to this indeterminacy
(unless, of course, it is made determinant through the specification
of distance, which it is for the challenge). As I offered, this
challenge is not my own hodge-podge of boundary conditions, it was
literally drawn from a standard text many here have - hence the quote
marks that attend its publication by me. I am not surprised no one
has caught on, I also pointed out this discussion is covered in the
parts of Chapman that no one reads. Whatchagonnado?

The example of the challenge serves to illuminate (pun intended) the
logical shortfall of those here who insist that a Transmitter exhibits
no Z, or that it is unknowable (to them, in other words), or that it
reflects all power that returns to it (to bolster their equally absurd
notion that the Transmitter does not absorb that power). Chapman is
quite clear to this last piece of fluff science - specifically and to
the very wording. Engineers and scientists simply converse with the
tacit agreement that the source matches the line when going into the
discussion of SWR (and why Chapman plainly says this up front on the
page quoted earlier). This is so commonplace that literalists who
lack the background (and skim read) fall into a trap of asserting some
pretty absurd things. It follows that for these same literalists, any
evidence to the contrary is anathema, heresy, or insanity - people
start wanting to "help" you :-P

Ian grasped at the straw that the discussion simply peters out by the
steady state and wholly disregards the compelling evidence (and
further elaboration of Chapman to this, but he lacks another voice,
the same Chapman, to accept it) with a forced mismatch at both ends of
the line. It is impossible to accurately describe the power delivered
to the load without knowing all parameters, the most overlooked is
distances traversed by the power (total phase in the solution for
interference). I put the challenge up to illustrate where the heat
goes (the line); and it is well into the steady state, as I am sure no
one could argue, but could easily gust
"t'ain't so!"
At least I saved them from the prospect of strangling on their own
spit sputtering "shades of conjugation." [Another topic that barely
goes a sentence without being corrupted with a Z-match
characteristic.]

Using this example for the challenge forces out the canards that the
source is adjusting to the load (in fact, the challenge presents no
such change in the first place) and dB cares not a whit what power is
applied unless we have suddenly entered a non-linear physics. None
have gone that far as they have already fallen off the edge earlier.

Now, be advised that when I say "accurately" that this is of concern
only to those who care for accuracy. Between mild mismatches the
error is hardly catastrophic, and yet with the argument that the
Transmitter is wholly reflective, it becomes catastrophic. The lack
of catastrophe does not reject the math, it rejects the notion of the
Transmitter being wholly reflective. This discussion in their terms
merely drives a stake through their zombie theories.

I would add there has been another voice to hear in this matter. The
same literalist skim readers suffer the same shortfall of perception.
We both enjoy the zen-cartwheels so excellently exhibited by the drill
team of naysayers. ;-)

73's
Richard Clark, KB7QHC

On Fri, 29 Aug 2003 03:01:50 GMT, "George, W5YR"
wrote:

Yes, Richard . . .

Did you mean "Chipman" by chance?

That is the author's name . . .

Hi George,

Ha! You got me there! ;-)

And here I've been ignoring my spell checker. :-(

This will no doubt vindicate many from the minutes of drudgery of
working over a hot bench to reduce my challenge to ashes.
"The best-laid schemes o' Mice an' Men
gang aft a-gley...."

73's
Richard Clark, KB7QHC

Well, I really was hoping I'd shame someone (especially Garvin) into
_actually_ going through the math exercise. It's not all that
difficult, and as you've said before, and as I agree, they'd benefit
from actually doing it, and also from thinking about what's going on.
Some of the more subtle physics (such as phase shifts associated with
skin effect) isn't so easily accessible, but surely these things are
to those who are willing. It seems like everyone agrees fairly
readily that Zo=Vf/If=-Vr/Ir (to a good approximation, anyway), and
also to the couple other things you need to let you find Vr/Vf, but
things rather rapidly seem to fall apart along the way to Vr/Vf. I've
given up trying to understand why, Reg, so I might as well get a bit
of dry humor out of it all.

Actually, I think you _did_ state the value once or twice recently in
these annals.

Cheers,
Tom


"Reg Edwards" wrote in message ...
Tom, to save everybody a lot of trouble -

The greatest theoretical value of the magnitude of the
reflection coefficient occurs when the angle of Zo is
-45 degrees, and the terminating impedance is a pure
inductive reactance of |Zo| ohms.

Do you think I should have mentioned this when I
began this and other threads by saying a reflection
coefficient greater than unity can occur?

The riot police can now return to barracks.
----
Reg, G4FGQ.
....