It can be convenient to define a reference impedance for S-paramters
which is not the characteristic impedance of all the pieces of
transmission line in the system, and keep the same reference impedance
for all your work. For example, 50 ohms is commonly used, even though
the system contains sections of microstrip of various impedances.
But that's just a convenience for system analysis and design. If you
want to try to assign even a little physical significance to
reflection coefficient as used on a piece of line, you really should
be using the line's characteristic impedance as the reference
impedance. In addition, you should realize that it's going to make
sense only in a linear, time-invariant system with steady-state
excitation, with only one source of excitation (at a time). In
addition, it is of course a function of frequency, just as the line's
characteristic impedance is.

As others have noted, the magnitude of the reflection coefficient can
be greater than unity with a passive line and load. Don't try to read
too much physical significance into that, however.

Although the classic definition of (V)SWR involves knowing a voltage
maximum and a voltage minimum on a line, I much prefer a definition in
terms of forward and reverse voltages. That allows me to think about
SWR at a point on a uniform line, and realize that it will be
different at different points (because of line attenuation). In fact,
the _definition_ I use for reflection coefficient is Er/Ef, or
equivalently the ratio of electric fields (or magnetic fields)
associated with forward and reverse waves (which then applies also to
non-TEM waveguides). From that definition, it's straightforward to
determine that rho = (Zl-Zo)/(Zl+Zo). And in keeping with the idea
that you cannot have a voltage magnitude minimum less than zero, and
because I believe it's more practical than the classic definition to
have an SWR definition I can apply to any point on a line, my working
SWR defintion is SWR = (|Ef|+|Er|)/(|(|Ef|-|Er|)|). This will align
well with the usual formula that SWR = (1+|rho|)/(1-|rho|) when
|rho|=1, but it never gives you a negative SWR. If you can accept my
definition of SWR, we can talk about SWR. If you can't, then I just
won't talk with you about SWR, and limit the discussion to reflection
coefficient which we presumably would be able to agree on.

Cheers,
Tom

(Dr. Slick) wrote in message . com...
From Pozar's Microwave Engineering (Pg. 606):

Reflection Coefficient looking into load = (Zl-Zo)/(Zl+Zo)

Where Zl is a purely real load impedance, and Zo is the
purely real characteristic impedance reference.

When you change Zo, you change the normalized center of the
Smith Chart, and therefore the Reflection Coefficient and SWR, looking
into the same load.



Check it out...


Slick

wrote:
Do not be afraid to admit that you have changed the definition of P = V
x I and therefore do not accept the standard definition.

Well, I was taking 'x' as a multiplication sign. Did you mean it as
a cross product sign? In any case, your Vinst is *NET* voltage and
your Iinst is *NET* current. We know that the feedline Z0 forces
Vfwd*Ifwd to be a constant value for a lossless line. We know that
the feedline Z0 forces Vref*Iref to be a constant value for a lossless
line. Vfwd+Vref is the *NET* voltage. Ifwd+Iref is the *NET* current.
Of course, their product, in any form, is going to be *NET* power.

When I learned Pinst = Vinst x Iinst there were no caveats about how
Pinst meant Pnet. Instantaneous energy is flowing or it is not. When
Pinst is 0 for all time, then there is no energy flowing.

But RF energy cannot stand still so if it exists, it must necessarily
flow. If there is no energy flowing, then there is no RF. If there is
no RF, then your statements are irrelevant to this newsgroup. :-)

To satisfy your theory (and minimize double think), you have had to
change this to Pnet is zero to allow these cancelling powers to flow.
So be it.

Your Vinst is *NET* voltage equal to Vfwd+Vref. Your Iinst is *NET*
current equal to Ifwd+Iref. Of course, their product will be *NET*
power. It cannot be anything else.

True, sort of.

Ramo, Whinnery, and Van Duzer will be impressed that you "sort of"
agree with them. :-)

It is not flowing all the way to the end of the
line and then back. There is not enough time for this to happen (on a
multi-wavelength line) since it changes direction every quarter cycle.

Just as I suspected, you are confusing the carriers of the energy with
the energy itself in the waves which moves at the speed of light. A
quarter cycle of time is very, very large compared to the speed of light.

Since water molecules cannot travel at the speed of sound in the ocean,
I assume you would argue that the energy in a tsunami wave cannot travel
at 500 mph, right?

Not quite. Standing voltage and current waves (which are not waves in
the normal sense) can be observed on the line. They can be measured with
real voltage and current instruments; as can real energy flows with
a real (V x I) power meter (but not a 'Bird watt' meter which
is doing something quite different). It happens that if you assume the
existence of forward and reverse voltage and current waves, mathematical
functions can be derived that will produce the same distribution of
voltage and current as observed on the line. This is extraordinarily
convenient some analysis but does not mean that these assumed waves are
real.

So please amaze me with a model that produces standing waves without actual
forward and reflected waves (in a single source, single feedline, single load
system).

A mechanical analogue would be to look at a guy wire on a pole. You can
analyze the forces as two vectors at 90 degrees (or any other angle of
convenience!), but never make the mistake of assuming that there are
actually two guy wires present. Just because it is mathematically
convenient to assume the existence of two vectors does not mean they
exist.

Nobody is rejecting it. If the lossless stub is one second long, it takes
two seconds of *POWER* to bring it to steady-state. If the stub contains
no moving energy, where did all those joules go?

This energy is indeed stored in the stub. None of it moves across zero
voltage or current boundaries.

What exactly, keeps energy from crossing the boundary? Here is an example.

source-------------50 ohm coax--------------+----1/4WL stub-----open

What mechanism of physics keeps energy from crossing the '+' point? Note
that there is no physical impedance discontinuity at point '+'.

This is what I (and Ayn Rand) call "primacy of consciousness" type thinking.
If you believe it strongly enough, your math model will dictate reality.
Something about being able to move mountains with the faith of a grain of
mustard seed. Something about being able to change the SWR by changing the
normalization of a Smith Chart on a sheet of paper. OTOH, I believe in
"primacy of existence", where reality dictates my math models. They may
be wrong but are as close to reality as I can get.

All you have to do to convince me that you are right is explain exactly
how standing waves can be sustained without a forward wave and a reflected
wave (in a system with a single source, single feedline, and single load).
--
73, Cecil http://www.qsl.net/w5dxp
"One thing I have learned in a long life: that all our science, measured
against reality, is primitive and childlike ..." Albert Einstein



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Reg Edwards wrote:
Magid has the most rigorous derivation of power and energy flow on
transmission lines,

==========================
The following short question is adressed to all contributors to this
newsgroup who feel impelled to bolster their lack of self-confidence by
dragging in the chapter and verse of their favourite worshipped authors and
Gurus, most of whom nobody has ever heard of and highly unlikely ever to get
their hands on.

How do you know that?

I multiplied v(t) and i(t) in the forward and reverse waves and added
them as a function of position to get the instantaneous power at each
point along the line. Then I integrated to find the energy. As I
mentioned in the part of the posting you excluded from your quote, I
discovered that I hadn't evaluated the constant of integration.
Somewhere along the line, I got sidetracked, and didn't want to get
sucked into the interminable argument going on (which I see I've started
up again -- my sincere apology to all), so didn't go back and clean it
up. I had, however, reached the same conclusion as Magid, so apparently
the constant was zero, or didn't impact the results. Magid follows the
same process, although I haven't yet followed it through completely.

You've now heard of Magid, and you can very likely find a used copy on
the Internet for the price of a couple of bottles of mediocre Pinot Noir
in much less time than it would take to drink it (unless perhaps you're
a speed drinker). You could get your hands on one with even less effort
than I've taken -- I had to walk a few blocks, while you can do it all
from your easy chair, only having to rise and face the Sun when the
postman comes with your book.

Shoot, you can even get it from the same store where I got mine, if they
have another copy just now. http://www.powellsbooks.com.

Roy Lewallen, W7EL
Certified Reg's Old Wife, Nitpicker, Busy-Body, Lacker of
Self-Confidence, Worshipper of Authors and Gurus, and Other Notable
Distinctions and Honours which are Bestowed Almost Daily

Dr. Slick wrote:
Therefore, the reflected voltage can never be greater than the
input voltage for a passive network, and the reflection coefficient
can never be greater than 1 for such a case.

What must be realized is that the s-parameter reflection coefficients
are *PHYSICAL* reflection coefficients while 'rho' is not a physical
reflection coefficient. s11 and 'rho' do not usually have the same
value. There are physical constraints on s11. The s11 physical
constraints do not apply to 'rho'. s11 is the square root of the
ratio of Pref to Pfwd under special conditions. 'rho' is the square
root of the ratio of Pref to Pfwd under all conditions. There's a
big difference. s11 does not usually equal 'rho' anywhere except
at a one-port load.
--
73, Cecil http://www.qsl.net/w5dxp



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Roy Lewallen wrote in message ...
....
I omit Tom from this second list only because I haven't yet
met him in person and otherwise haven't gotten any hints of his age --
but I'll take a gamble and spot him 10 years at least.

Well, you can find archived postings from me from 10 years ago that I
think demonstrate that I understood how SWR meters actually work back
then. And you could probably find my name on a patent that would give
you a clue that I was at least starting to learn a little something
about transmission lines in 1969 or so, though I readily admit to not
worrying about "reflection coefficient" back then. Just hacked
through the raw, unabridged transmission line equations. I suppose
Reg would think that a better way to learn the stuff anyway. I had
bought the King, Mimno and Wing book back then, but didn't get around
to actually reading it till much, much later.

Cheers,
Tom

Roy Lewallen wrote:
You've now heard of Magid, ...

Unfortunately, every author and guru that I have ever encountered,
at some point, confuses cause and effect. I'm sorry I can't get over
to the Texas A&M library right now but Magid seems to believe that
standing waves can be sustained without a forward wave and a reflected
wave. Does he explain how that is possible? In all honesty, it is an easy
mistake to make. Even Ramo, Whinnery, and Van Duzer make the same
mistake. Not exactly a quote but: The reflection coefficient is caused
by the ratio of the reflected power to the forward power. Therefore,
the ratio of the reflected power to the forward power is caused by
the reflection coefficient. "Logic" like this seems to abound in
the field of transmission lines.
--
73, Cecil http://www.qsl.net/w5dxp



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Tom Bruhns wrote:
W5DXP wrote:
We know that the feedline Z0 forces
Vfwd*Ifwd to be a constant value for a lossless line. We know that
the feedline Z0 forces Vref*Iref to be a constant value for a lossless
line.

I trust I haven't taken that too far out of context. And...I hope you
meant that Zo = Vf/If = -Vr/Ir, or something equivalent. Surely the
product of Vf and If is independent of Zo.

Yep, sorry, brain fart. Should have been a '/' instead of a '*'.
The point was (is) that (Vfwd + Vref) can be zero but in a feedline
with reflections Vfwd and Vref cannot be zero. Same for the component
currents.
--
73, Cecil http://www.qsl.net/w5dxp



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"George, W5YR" wrote in message ...
Roy, Chipman on page 138 of "Theory and Problems of Transmission Lines"
makes the statement

" The conclusion is somewhat surprising, though inescapable, that a
transmission line can be terminated with a reflection coefficient whose
magnitude is as great as 2.41 without there being any implication that the
power level of the reflected wave is greater than that of the incident wave.


How did he set this up? How did he measure this excactly? How
can you get a reflection coefficient greater than one into a passive
network? I'd really like to know.


Slick

Dr. Slick wrote:
W5DXP wrote in message ...

What must be realized is that the s-parameter reflection coefficients
are *PHYSICAL* reflection coefficients while 'rho' is not a physical
reflection coefficient. s11 and 'rho' do not usually have the same
value. There are physical constraints on s11. The s11 physical
constraints do not apply to 'rho'. s11 is the square root of the
ratio of Pref to Pfwd under special conditions. 'rho' is the square
root of the ratio of Pref to Pfwd under all conditions. There's a
big difference. s11 does not usually equal 'rho' anywhere except
at a one-port load.

[s11]=rho, rho being just the magnitude of the s11.

I just told you that is not always true.

s11 is the reflection coefficient when a2=0

|rho| is the reflection coefficient when a2=a2

In a Z0-matched system with reflections, they are NOT equal.
--
73, Cecil http://www.qsl.net/w5dxp



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