Dan wrote:

So Chipman states quite clearly that zero reflected voltage wave
magnitude does _not_ mean maximum power transfer. On the contrary,
maximum power is transferred only when there is a non-zero voltage wave
reflection (assuming a complex Zo line). Counter arguments along the
lines of "Well that doesn't seem right to me so therefore Chipman must
be wrong" don't carry much weight given Chipman's credentials.

Thanks for that posting, Dan, and for what looks like a very clear
summary.

Just one point, about that very last word: what are Chipman's
"credentials", really? They are not that he is a well-known[*] textbook
author, college professor, PhD, or anything like that. This discussion
is already way overloaded with personal "credentials" of that kind!

Chipman's true credentials are that he has thought about this subject,
noticed the apparent problem, worked it out, and presented clear,
correct conclusions in a way that other people can follow. Those are the
only credentials that really count.


[*] Well-known to some college students in the USA, perhaps? I'd never
heard of him, but Dan's summary suggests this book might be worth
looking for.


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

Roy Lewallen wrote:
Although it's not really relevant to the discussion at hand, I believe a
valid argument could be made that if a2 isn't equal to zero, then S11
isn't a reflection coefficient at all. It surely isn't the reflection
coefficient at port 1, anyway.

Actually, it is, Roy. s11 is the *physical* reflection coefficient.
For instance, in the following two-port network:

source---50 ohm feedline---+---1/2WL 150 ohm feedline---50 ohm load

s11 is *defined* as the input reflection coefficient with the output
port terminated by a matched load (ZL=150 ohms sets a2=0). s11
continues to be *defined* as 0.5 even when a2 is not zero.

s11 = (150-50)/(150+50) = 0.5

Since a Z0-match exists at '+', the reflection coefficient on the
50 ohm feedline is zero. rho = Sqrt(Pref/Pfwd)

For a two-port network with a2 not equal to zero, the reflection
coefficient 's11' is NOT equal to the reflection coefficient 'rho'.

The energy analysis on my web page deals only with physical reflection
coefficients. If 'rho' is not a physical reflection coefficient, then
it is the END RESULT of a mathematical calculation and is not the
CAUSE of anything. If a source doesn't "see" a physical impedance
discontinuity, it doesn't "see" anything except forward and reflected
waves. Coherent waves traveling in opposite directions are "unaware" of
each other. Coherent waves traveling in the same direction merge, lose
their separate identies, and become indistinguishable from one another.
--
73, Cecil http://www.qsl.net/w5dxp



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Dan wrote:
Now that the various typo mistakes have been corrected, and putting
aside for the moment the name calling and ad hominem arguments, could
it be that _both_ sides in this discussion are correct? Camp 'A' says
that the reflection coefficient is computed the classical way, without
using Zo conjugate, and offers various mathematical proofs and
discussions of infinitely long lines. Camp 'B' says the reflection
coefficient is computed with Zo* (Zo conjugate) in the numerator, and
offers explanations dealing with the conservation of energy and
maximum transfer of power.

Both sides may be correct since they are talking about _two different_
meanings for the term "reflection coefficient." One has to do with
voltage (or current) traveling waves and the other has to do with
power.

If a lossy line is terminated with the complex Z0,
there is no reflection from the load, but the
maximum possible power is not delivered. If the
*load* is made equal to the complex conjugate of
Z0 the maximum *forward power* is delivered but
there is a reflected power (VSWR is not 1:1).

It is difficult to say that the maximum *power* is
delivered without knowing the generator impedance,
since it is involved in any so-called "conjugate
match". For a lossy line, the idea of conjugate
match is, at best, very approximate anyway. And
generator impedance is a mystery in most, but not
all, transmitter PA situations. One possible
exception: a large amount of negative feedback
helps to determine, to some extent, output
impedance, for a signal with time-varying
amplitude (e.g. SSB).

It seems to me to be clear that the use of Z0* in
the reflection coefficient equation has not been
corroborated (see Roy's post), but the use of
ZL=ZO* has been. The two ideas are not equivalent.

After looking at some examples, using the exact
complex hyperbolic equations with Mathcad, it is
obvious that a line must be very lossy to make a
significant difference whether ZL or ZL* is used
to terminate the line. Still, it is important to
understand the basic principles involved, so this
exercise is not foolishness at all.

A word about "credentials". We all respect
established and competent authors. But I have
noticed on several occasions that blind faith has
some exceptions. As an experienced author, I am
personally familiar with this problem.

G. Gonzalez (highly respected) "Microwave
Transistor Amplifiers" second edition, has a good
discussion of Power Waves, based on Kurokawa (I
also have his article). There are no transmission
lines, and the term ZS* (ZS=generator impedance)
is used. In particular, a power wave reflection
coefficient is defined:

Gp = (ZL-ZS*)/(ZL+ZS)

which looks quite familiar, with ZS replacing Z0.
Also, a voltage reflection coefficient:

Gv = [Zs/Zs*] x [(ZL-ZS*)/(ZL+ZS)]

and a current reflection coefficient

Gv = Gp.

The author also defines two-port scattering
parameters in terms of power waves, in which ZS*
and ZL* appear.

For the purposes of the present topic, involving
transmission lines, it seems best to stay away
from power waves, without a lot more studying.

Bill W0IYH

Cecil:

[snip]
s11 is a reflection coefficient that has the special condition that
a2 must be equal zero. When a2 is not equal zero, the s11 reflection
coefficient and the apparent reflection coefficient are not the same.
--
73, Cecil http://www.qsl.net/w5dxp
[snip]

No! The scattering paramters, e.g for a two-port the s11, s12, s21 and s22
are all parameters fixed by the network and are not dependent upon either
the independent or dependent variables! i.e. b1 = s11*a1 + s12*a2, and b2
= s21*a1 + s22* a2.

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

Roy:

[snip]
"Roy Lewallen" wrote in message
...
This is interesting. But how did it lead you to the equation you
determined must be correct? That is, what definition of reflection
coefficient did you start with, where did you get it, and how did you
get from there to the reflection coefficient equation you presented?

I assume that, consistent with the admonition in the last paragraph of
your posting, you were "careful to follow through and be consistent with
your definitions, measurements, algebra, and arithmetic". It would be
very instructive for us to be able to follow the process you did in
coming to what you feel is the "right answer".

Roy Lewallen, W7EL
[snip]

I followed up with a complete, and I hope simple and easy to follow,
algebraic development in another nearby posting. Have a look and let us
know what you think.

BTW... I don't necessarily agree with Slick's defintition of the reflection
coefficient and for sure, his is not the one I use. But I will defend to
the death his right to use the one he defines, as long as all of his
subsequent calculations and measurements are consistent with that
definition.

Slice and I will always end up with the same voltages v and currents i, it's
just that our wave variables a and b won't agree!

Viewing "waves" is just a viewpoint! One has to view them "through" an
instrument called a reflectometer. When viewed through ammeters and
voltmeters we will all measure the same things.

Only the "electricals" the v and I are "real"! The "waves" the a and b are
just different manifestations of v and i as viewed through and instrument
[reflectometer] using a, perhaps arbitrary, reference impedance, or matrix
transformation.

Sorry Cecil. :-)

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

Reg:

[snip]
"Reg Edwards" wrote in message
...
Peter, what an excellent, straight-forward, plain
-English, explanation. And you didn't enlist the
aid of a single guru. Not even Terman or the
ARRL handbook. ;o)
-----
Reg
[snip]

Heh, heh...

I beleive in working it all out from first principles, can't trust anybody
else, except of course you and your wonderful programs. :-)

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

William E. Sabin wrote:
Dan wrote:

Now that the various typo mistakes have been corrected, and putting
aside for the moment the name calling and ad hominem arguments, could
it be that _both_ sides in this discussion are correct? Camp 'A' says
that the reflection coefficient is computed the classical way, without
using Zo conjugate, and offers various mathematical proofs and
discussions of infinitely long lines. Camp 'B' says the reflection
coefficient is computed with Zo* (Zo conjugate) in the numerator, and
offers explanations dealing with the conservation of energy and
maximum transfer of power.

Both sides may be correct since they are talking about _two different_
meanings for the term "reflection coefficient." One has to do with
voltage (or current) traveling waves and the other has to do with
power.


If a lossy line is terminated with the complex Z0, there is no
reflection from the load, but the maximum possible power is not
delivered. If the *load* is made equal to the complex conjugate of Z0
the maximum *forward power* is delivered but there is a reflected power
(VSWR is not 1:1).

It is difficult to say that the maximum *power* is delivered without
knowing the generator impedance, since it is involved in any so-called
"conjugate match". For a lossy line, the idea of conjugate match is, at
best, very approximate anyway. And generator impedance is a mystery in
most, but not all, transmitter PA situations. One possible exception: a
large amount of negative feedback helps to determine, to some extent,
output impedance, for a signal with time-varying amplitude (e.g. SSB).

It seems to me to be clear that the use of Z0* in the reflection
coefficient equation has not been corroborated (see Roy's post), but the
use of ZL=ZO* has been. The two ideas are not equivalent.

After looking at some examples, using the exact complex hyperbolic
equations with Mathcad, it is obvious that a line must be very lossy to
make a significant difference whether ZL or ZL*

Correction: Z0 or Z0*

is used to terminate the
line. Still, it is important to understand the basic principles
involved, so this exercise is not foolishness at all.

A word about "credentials". We all respect established and competent
authors. But I have noticed on several occasions that blind faith has
some exceptions. As an experienced author, I am personally familiar with
this problem.

G. Gonzalez (highly respected) "Microwave Transistor Amplifiers" second
edition, has a good discussion of Power Waves, based on Kurokawa (I also
have his article). There are no transmission lines, and the term ZS*
(ZS=generator impedance) is used. In particular, a power wave reflection
coefficient is defined:

Gp = (ZL-ZS*)/(ZL+ZS)

which looks quite familiar, with ZS replacing Z0. Also, a voltage
reflection coefficient:

Gv = [Zs/Zs*] x [(ZL-ZS*)/(ZL+ZS)]

and a current reflection coefficient

Gv = Gp.

Correction: Gi = Gp


The author also defines two-port scattering parameters in terms of power
waves, in which ZS* and ZL* appear.

For the purposes of the present topic, involving transmission lines, it
seems best to stay away from power waves, without a lot more studying.

Bill W0IYH

Slick:

[snip]
Correction: rho = (Z - conj(R))/(Z + (R)), the conjugate being
only in the denominator.

Slick
[snip]

Well here we have to part company.

Not using the same "thing" in both numerator and denominator *is* being
inconsistent!

See my algebraic development in another posting on this thread.

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

On Sun, 24 Aug 2003 15:27:02 GMT, "Peter O. Brackett"
wrote:

See anything wrong with this analysis?


Hi Peter,

One thing: you are expecting everyone to agree that the source has a
characteristic Z.

The chasm that separates factions is found in this alone where many
who say, no "it is NOT 50 Ohms" (or "it doesn't matter") are loath to
come up with an actual value to conjugate (in other words, a sterile
position). Such a forced choice leads obviously to the deflation of
pet theories. To date their best argument is you cannot possibly know
that value (for any of a variety of reasons, unrelated to simply
sitting down at the bench and measuring an actual value). In short,
institutionalized ignorance, embraced with a mystic missionary zeal,
is their crowing logic.

But I do enjoy their examples and logic puzzles reminiscent of the
necromancer's formulæ for transmutation of gold into lead. The
unrequited dreams would be fulfilled if only the discovery of the
Philosopher's Stone could be realized. Hence debate proceeds with the
leaps and twirls of zen-cartwheeling.

73's
Richard Clark, KB7QHC

Richard Clark wrote:


To date their best argument is you cannot possibly know
that value (for any of a variety of reasons, unrelated to simply
sitting down at the bench and measuring an actual value). In short,
institutionalized ignorance, embraced with a mystic missionary zeal,
is their crowing logic.

The problem lies in the difficulty of measuring or
calculating Zs, especially for signals that have
large variations in amplitude, such as SSB.

There is no institutionalized ignorance, just a
lot of skepticism regarding the reliability of the
analysis methods and the measurement methods.

Bill W0IYH