(Dr. Slick) wrote in message . com...
Actually, my first posting was right all along, if Zo is always real.

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."


Fascinating... Please have a look at the following reply I got from
Besser... I still wish people would go through the simple math
themselves, and make up their own minds what's correct and what isn't.
I gather that Slick has made up his own mind, though see no evidence
that it's on the basis of the simple calcs from what I believe he
already agrees with. Oh, well, not MY problem. (This is twice now,
recently, that I've followed up on other people's references and found
them to be at best questionable in some way.)

Cheers,
Tom

=-=-=-=-=-=-=-=-= Beginning of quoted material =-=-=-=-=-=-=-=-=-=-=-

Hello Tom-

Thank you for your message. I do not know which specific course was
referenced by the person you mentioned in your message, but I did
check
the notes for our more popular course which covers linear RF circuits.
In the manuals for that course, the formula is given as you described,
except that the Zo term in the numerator is _not_ the complex
conjugate.
Thus the formula in the manual reads:

Gamma = Vr/Vf = (Zl-Zo)/(Zl+Zo)

This is in agreement with Guillermo Gonzalez's text, "Microwave
Transistor Amplifiers," which is one of the references used in writing
the course.

Please let me know if this information addresses your concern.

Have a good day.

Regards,

Rex


From: ]
Sent: Thursday, August 21, 2003 11:11 AM
To:
Subject: Other concern/question


Below is the result of your feedback form. It was submitted by
) on Thursday, August 21, 2003 at 14:10:53
------------------------------------------------------------------------
---

name: Tom Bruhns

body: I have recently seen someone attribute to Besser Associates
training a formula for reflection coefficient at a load Zl as Vr/Vf =
(Zl-Zo*)/(Zl+Zo), where Zo* is the complex conjugate of the line
characteristic impedance Zo. I'm curious if this is actually what you
teach, as it is counter to what is commonly in texts, and is also
counter to the commonly accepted boundary conditions on a TEM line at
such a load.

Yours in the interest of accurate models,
Tom Bruhns
--------
....
Rex Frobenius
Engineering Director
Besser Associates
650-949-3300
650-949-4400 FAX

www.besserassociates.com

=-=-=-=-=-=-=-=-= End of quoted material =-=-=-=-=-=-=-=-=-=-=-

Roy:

[snip]
"Roy Lewallen" wrote in message
...
One more thing. I've never seen that conjugate formula for voltage
reflection coefficient and can't imagine how it might have been derived.
I've got a pretty good collection of texts, and none of them show such a
thing.
[snip]

You are absolutely correct Roy, that formula given by "Slick" is just plain
WRONG!

rho = (Z - R)/(Z + R)

Always has been, always will be.

Where does that "Slick" guy get his information? And where does "Slick" get
off with all of his "potifications"??? I dunno... *He* thinks "Besser",
"Pozar" and
ARRL are authoritative sources for transmission line technology!!!

Me?

I have made a living as a professional Engineer designing transmission
equipment over
the past four decades, currently more than $4BB gross shipped to world wide
markets,
where the Zo I used is neither real, nor a constant!

And what is more... I have never consulted any of those three authorities
referenced by
"Slick". I certainly don't think of them as being authoritative, "cream
skimmers"
perhaps, but not certainly not authoritative.

I believe that "Slick" has gotta stop "pontificating" and start reading in
better circles...
much better!

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

William E. Sabin wrote:

Roy Lewallen wrote:

A big deal is being made of the general assumption that Z0 is real.

As anyone who has studied transmission lines in any depth knows, Z0
is, in general, complex. It's given simply as

Z0 = Sqrt((R + jwL)/(G + jwC))

where R, L, G, and C are series resistance, inductance, shunt
conductance, and capacitance per unit length respectively, and w is
the radian frequency, omega = 2*pi*f. This formula can be found in
virtually any text on transmission lines, and a glance at the formula
shows that Z0 is, in general, complex.


A good approximation to Z0 is:

Z0 = R0 sqrt(1-ja/b)

where Ro = sqrt(L/C)
a is matched loss in nepers per meter.
b is propagation constant in radians per meter.

The complex value of Z0 gives improved accuracy in calculations of
input impedance and losses of coax lines. With Mathcad the complex value
is easily calculated and applied to the various complex hyperbolic
formulas.

Reference: QEX, August 1996

Bill W0IYH


The usage of complex conjugate Z0* becomes
significant when calculating very large values of
VSWR, according to some authors. But for these
very large values of standing waves, the concept
of VSWR is a useless numbers game anyway. For
values of VSWR less that 10:1 the complex Z0 is
plenty good enough for good quality coax.

W.C. Johnson points out on page 150 that the concept:

Pload = Pforward - Preflected

is strictly correct only when Z0 is pure
resistance. But the calculations of real power
into the coax and real power into the load are
valid and the difference between the two is the
real power loss in the coax. For these
calculations the complex value Z0 for moderately
lossy coax is useful and adequate.

The preoccupation with VSWR values is unfortunate
and excruciatingly exact answers involve more
nitpicking than is sensible.

Bill W0IYH

Roy Lewallen wrote in message ...

Quite a number of the things we "know" about transmission lines are
actually true only if the assumption is made that Z0 is purely real;
that is, they're only approximately true, and only at HF and above with
decent cable. Among them are the three I've already mentioned, the
simplified formula for Z0, the relationship between power components,
and the optimum load impedance. Yet another is that the magnitude of the
reflection coefficient is always = 1.


That would be only into a passive network.



As people mainly concerned with
RF issues, we have the luxury of being able to use the simplifying
approximation without usually introducing significant errors. But
whenever we deal with formulas or situations that have to apply outside
this range, we have to remember that it's just an approximation and
apply the full analysis instead.

Tom, Ian, Bill, and most of the others posting on this thread of course
know all this very well. We have to know it in order to do our jobs
effectively, and all of us have studied and understood the derivation
and basis for Z0 calculation. But I hope it'll be of value to some of
the readers who might be misled by statements that "authorities" claim
that Z0 is purely real.

Roy Lewallen, W7EL


No one ever said that Zo is always purely real. But many texts do
approximate it this way. Even the ARRL "bible".


Slick

So another way for the lurkers to check all this: assume a line Zo =
50-j5, and a load Zload = 1+j100. Assume some convenient Vf at the
load. Calculate rho = Vr/Vf from the equation quoted below. Now find
Vr, and from the line impedance and Vf and Vr, find If and Ir. Add
the V terms and I terms to get the net line voltage and current at the
load. Does that correspond to the expected load current for the given
Zload? If so, fine; if not, where does the difference in current come
from? If you assume the line current is correct from your If and Ir
calcs, and the load current is correct as the net line voltage = net
load voltage, and use Zload to get Iload, does the line power
dissipation plus the load power dissipation equal the power fed in
from a generator? Try all those calcs after revising the Vr/Vf
formula to match what Besser is now teaching, and see if things line
up a bit better.

The truth is all there to be seen with just a bit of work.

Cheers,
Tom

(yeah, I've done it, as you might guess. And so have a lot of
others.)

(Dr. Slick) wrote in message . com...
Actually, my first posting was right all along, if Zo is always real.

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."


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.

That doesn't mean Zload cannot have reactance (be complex).

Try your calculation again, and you will see that you can never
have a [rho] (magnitude of R.C.)greater than 1 for a passive network.

How could you get more power reflected than what you put in (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!

But thanks for checking my work, and this is a subtle detail that
is good to know.


Slick

(Dr. Slick) wrote in message . com...
(Tom Bruhns) wrote in message om...

Fascinating... Please have a look at the following reply I got from
Besser... I still wish people would go through the simple math
themselves, and make up their own minds what's correct and what isn't.
I gather that Slick has made up his own mind, though see no evidence
that it's on the basis of the simple calcs from what I believe he
already agrees with. Oh, well, not MY problem. (This is twice now,
recently, that I've followed up on other people's references and found
them to be at best questionable in some way.)



I have no problem admitting i am wrong, when i am wrong. But you
haven't given me any reason to think so.

Well, you may not think I have, but...

What is your definition of a conjugate match? When do you think
max. power transfer occurs?

I'd be happy to answer this more directly after you show us the steps,
as I suggested, to get from the basic TEM transmission line relations
and the load boundary conditions to Vr/Vf. But for now, I'll let you
consider, if you wish, the case where you have a long transmission
line with reactive Zo, terminated so you have no reflected wave. Rho =
0. SWR = 1:1. I trust you'll agree you "see" an impedance equal to
Zo looking into the source-end of the line. Now imagine that you have
cut this line at some point; you also see Zo looking into that cut,
right? (The side with the load attached, that is.) So, can you
simply connect those two pieces back up and still see no reflection on
the piece on the source side? I _do_ believe that the line can't tell
whether the impedance it's connected to is a load right there, or the
impedance presented by another length of line, so it should be obvious
from that what I believe the line must be connected to, to get rho=0.

Cheers,
Tom

"Peter O. Brackett" wrote in message nk.net...
Roy:

[snip]
"Roy Lewallen" wrote in message
...
One more thing. I've never seen that conjugate formula for voltage
reflection coefficient and can't imagine how it might have been derived.
I've got a pretty good collection of texts, and none of them show such a
thing.
[snip]

You are absolutely correct Roy, that formula given by "Slick" is just plain
WRONG!

rho = (Z - R)/(Z + R)

Always has been, always will be.



As long as they are all purely real. Roy disagrees even when he
is wrong, because too many people read this NG, and it might make him
look bad (i.e., Not the All-Knowing Guru he pretends to be).




Where does that "Slick" guy get his information? And where does "Slick" get
off with all of his "potifications"??? I dunno... *He* thinks "Besser",
"Pozar" and
ARRL are authoritative sources for transmission line technology!!!



Bwa! HAah! Much, much, MUCH more than you will ever be!


Me?

I have made a living as a professional Engineer designing transmission
equipment over
the past four decades, currently more than $4BB gross shipped to world wide
markets,
where the Zo I used is neither real, nor a constant!


I feel sorry for your customers...



And what is more... I have never consulted any of those three authorities
referenced by
"Slick". I certainly don't think of them as being authoritative, "cream
skimmers"
perhaps, but not certainly not authoritative.


Dr. Besser kicks your ass backwards when it comes to RF knowledge.

And the ARRL is extremely well known. Pozar not so much, but the
guy is out there on the PhD level. I don't give a Sh** who you think
is an authority.

Look them up, they have way more credentials than either you or I.


I believe that "Slick" has gotta stop "pontificating" and start reading in
better circles...
much better!


Much better than the likes of you, then yes, you would certainly
be correct!

The conjugate formula is correct. If you believe in cancellation
of reactance. Why else would the magnitude rho (numerator of
Reflection Coefficient) be zero when Zload=Zo*???


Slick

Oh, my! I really should be changing the name on the thread, as you
suggest, to something about viewing r.r.a.a. as a wonderful source of
humor! Thank you very much for your contribution.

(Dr. Slick) wrote in message . com...

Contrary to popular belief, you will still have reflections going
from Zo=50-j5 to Zload=50-j5.

So, you can't even connect a line to another piece of the same
impedance line without getting reflections? :-) Wonderful!

This is what impedance matching is all about: getting rid of the
reactance in the line and load, and making sure the resistive
impedances left are equivalent.

Only when Zload=Zo*, will this happen. I.E.: Zo=50-j5 and
Zload=50+j5.

If you plug these into Reflection Coefficient =

(Zload-Zo*)/(Zload-Zo)

Where * indicates conjugate, you will see that the reactances cancel
to zero, and the numerator is zero.

Um, you should try that in your equation above for Zo=50-j5 and
Zload=50-j4. What magnitude rho do you get for that, hmmm?? Oh, this
is great fun!

This doesn't happen with the regular (Zload-Zo)/(Zload-Zo).

No, of course that one never gets larger than unity. Nor does it get
smaller. It doesn't evaluate well at Zload=Zo, but we might surmise
it stays unity there too.

It almost time for me to leave this to others to prove to you, as
the communication here is almost non-existant.

Seems to be, indeed, though you never know. The lurkers may well have
learned a thing or two. The one reference you did post now disavows
the form you posted. You've been invited to do some simple math that
would show you the truth and you apparently refuse. You are posting
any number of ideas contrary to what's easy to show from fundamentals
and what's in a large number of published papers and texts and what
has been posted here by many contributors recently and over the years.
It's been done with both symbolic math and specific examples.
Several inconsistencies demonstrate clearly that Vr/Vf does NOT equal
(Zload-Zo*)/(Zload+Zo), and of course most certainly a (Zload-Zo)
denominator is going to get you quickly into trouble. The
inconsistencies have been pointed out here by me and by others, but
apparently you've missed them. I'm sure it's apparent to most lurking
where the communications is breaking down. But the formulas you
posted above have given me a good laugh tonight, at least! Thanks!

Cheers,
Tom

Seems to be, indeed, though you never know. The lurkers may well have
learned a thing or two. The one reference you did post now disavows
the form you posted. You've been invited to do some simple math that
would show you the truth and you apparently refuse. You are posting
any number of ideas contrary to what's easy to show from fundamentals
and what's in a large number of published papers and texts and what
has been posted here by many contributors recently and over the years.
It's been done with both symbolic math and specific examples.
Several inconsistencies demonstrate clearly that Vr/Vf does NOT equal
(Zload-Zo*)/(Zload+Zo), and of course most certainly a (Zload-Zo)
denominator is going to get you quickly into trouble. The
inconsistencies have been pointed out here by me and by others, but
apparently you've missed them. I'm sure it's apparent to most lurking
where the communications is breaking down. But the formulas you
posted above have given me a good laugh tonight, at least! Thanks!

Cheers,
Tom

When a fine engineer, with a good education and a distinguished
career, stoops to argue with an anonymous fellow who doesn't
have a firm grasp of even the most basic ideas of wave mechanics,
the result is bound to be a certain amount of frustration. You might
want to ask yourself, Tom, whether Slick is arguing in good faith,
or whether he has other motives.
73,
Tom Donaly, KA6RUH

Slick:

[snip]
[snip]

You are absolutely correct Roy, that formula given by "Slick" is just
plain
WRONG!

rho = (Z - R)/(Z + R)

Always has been, always will be.
[snip]

After consideration, I must agree with Slick.

Slick is RIGHT and I was WRONG!

Slick please accept my apologies!!! I was wrong, and I admit it!

Indeed, the correct formula for the voltage reflection coefficient "rho"
when computed using a "reference impedance" R, which is say the, perhaps
complex, internal impedance R = r + jx of a generator/source which is loaded
by a perhaps complex load impedance Z = ro + j xo must indeed be:

rho = (Z - conj(R))/(Z + conj(R)) = (Z - r + jx)/(Z + r - jx)

For indeed as Slick pointed out elsewhere in this thread, how else will the
reflected voltage equal zero when the load is a conjugate match to the
generator.

Slick thanks for directing the attention of this "subtlety" to the
newsgroup, and again...

Slick, please accept my apologies, I was too quick to criticize!

Good work, and lots of patience... :-)

Regards,

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