Dr. Slick wrote:
Cecil, email me privately and i will send you the paper. He calls
the voltage reflection coefficient the "power wave reflection
coefficient". And then squares this to get the "power reflection
coefficient".

It's really a bad nomenclature, and no wonder there is confusion.

I agree, it is bad nomenclature. He should have called it the amplitude
or voltage reflection coefficient, the square of which is the power
reflection coefficient.
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

"Dr. Slick" wrote in message
om...
"David Robbins" wrote in message
...
"Dr. Slick" wrote in message
om...

[s]**2 = [(ZL - Zo*) / (ZL + Zo)]**2 the "power reflection
coefficent".

Note the squares.

yes, please do note the squares.... and remember, just because

[s]**2 = [(ZL - Zo*) / (ZL + Zo)]**2
does NOT mean that
s = (ZL - Zo*) / (ZL + Zo)

this is the one big trap that all you guys that like to use power in
your
calculations fall into. just because you know the power doesn't mean
that
you know squat about the voltage and current on the line. you can not
work
backwards. that is why it is always better to work with voltage or
current
waves and then in the end after you have solved all those waves you can
always calculate power if you really need to know it.


yes, but he does say that s = (ZL - Zo*) / (ZL + Zo) , first.

But he foolishly calls it a "power wave R. C."

Then he squares the magnitudes [s]**2 = [(ZL - Zo*) / (ZL +
Zo)]**2

And calls this the "power R. C."


The bottom label is fine, we've all see this before, as the ratio
of the RMS incident and reflected voltages, when squared, should give
you the ratio of the average incident and reflected powers, or the
power R. C.


But to call the voltage reflection coefficient a "power wave R.
C."
is really foolish, IMO.


Slick

i don't know what he is refering to as the 'power wave rc' but its not the
voltage or current reflection coefficient, they do not have a conjugate in
the numerator.

Richard,

Thanks. *Really* sharp guy. Must be 90 years old by now.

Tam/WB2TT
"Richard Clark" wrote in message
...
On Sun, 24 Aug 2003 12:57:36 -0400, "Tarmo Tammaru"
wrote:


"Richard Clark" wrote in message
.. .
Chipman also discusses the relevancy of the characteristic Z of a
source to SWR, which is tucked away in the unread part. ;-)

73's
Richard Clark, KB7QHC

Richard,

There used to be a Dr. Chipman who taught a fields/waves course at the
University of Toledo (OH) in the 60s. Do you know if it is the same guy?

Tam/WB2TT


Hi Tam,

According to the front cover, one in the same.

73's
Richard Clark, KB7QHC

David Robbins wrote:
i don't know what he is refering to as the 'power wave rc' but its not the
voltage or current reflection coefficient, they do not have a conjugate in
the numerator.

And since the power reflection coefficient (Reflectance) is simply the
square of the voltage (amplitude) reflection coefficient, presumably
neither would it. There is no conjugate in these equations in the field
of optics.
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

"David Robbins" wrote in message ...

i don't know what he is refering to as the 'power wave rc' but its not the
voltage or current reflection coefficient, they do not have a conjugate in
the numerator.


Incorrect. You need the conjugate in the numerator if the Zo is
complex. If it is purely real, WHICH MOST TEXTS ASSUME, then you can
use the normal equation.

Look he

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

And look up Les Besser's notes on the Fundamentals of RF.


Slick

W5DXP wrote in message ...
Dr. Slick wrote:
Cecil, email me privately and i will send you the paper. He calls
the voltage reflection coefficient the "power wave reflection
coefficient". And then squares this to get the "power reflection
coefficient".

It's really a bad nomenclature, and no wonder there is confusion.

I agree, it is bad nomenclature. He should have called it the amplitude
or voltage reflection coefficient, the square of which is the power
reflection coefficient.

Agreed. I will send you the paper.


Slick

"Dr. Slick" wrote in message
om...
"David Robbins" wrote in message
...

i don't know what he is refering to as the 'power wave rc' but its not
the
voltage or current reflection coefficient, they do not have a conjugate
in
the numerator.


Incorrect. You need the conjugate in the numerator if the Zo is
complex. If it is purely real, WHICH MOST TEXTS ASSUME, then you can
use the normal equation.


sorry, the derivation for the table in the book i sent before is for the
general case of a complex Zo. they then go on to simplify for an ideal line
and for a nearly ideal line... nowhere does a conjugate show up.

and that reference you give is not for a load on a transmission line, it is
talking about a generator supplying power to a load... a completely
different animal.

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.

No one from "Camp B" has given any justification for the assumption that
the condition for minimum reflection is the condition for maximum power
transfer. We're lacking either a proof, a derivation from known
principles, or even a numerical example. I maintain that this assumption
is false.

Likewise, there's no evidence that the conventional and universally
accepted (within the professional community) formula for reflection
coefficient violates the conservation of energy. If it did, it would
have been shown to be in error long ago.

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. . .

Perhaps. Yet both groups have used it as though it's a voltage
reflection coefficient, and as justification for statements made about
the reflection of voltage waves.

If people want to argue about the reflection of power waves, I'll gladly
bow out and let Cecil and his colleagues resume their interminable
arguments without me. If anyone wants to discuss voltage or current
waves, I'll try to continue to contribute, as long I don't have to deal
with Slick and the insults he uses in place of supporting evidence.

. . .

So, it seems to me, everybody can agree as long as it is understood
that there are different meanings for the term "reflection
coefficient." One meaning, and its mathematical definition, applies
to voltage or current waves. The other, with a slightly different
mathematical definition, applies to the power transfer from a line to
a load. They are one and the same only when the reactive portion of
Zo (Xo) is ignored. It may or may not be acceptable to do so,
depending on the attenuation of the line and the frequency. Lossy
lines and lower frequencies yield more negative values for the Xo
component of Zo.

I suggest that those who are using "reflection coefficient" as meaning
the ratio of reflected to forward power so state, and restrict their
conclusions dervived from it to power waves.

. . .

Roy Lewallen, W7EL

Hey, I've got it. It's sort of a "virtual reflection coefficient". Now I
understand fully. Thanks!

Roy Lewallen, W7EL

W5DXP wrote:
. . .
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.

Roy Lewallen wrote:
If people want to argue about the reflection of power waves, I'll gladly
bow out and let Cecil and his colleagues resume their interminable
arguments without me.

I don't think there's anything to argue about. From _Optics_, by Hecht:
"We define the reflectance R to be the ratio of the reflected power to
the incident power." "When we talk about the 'amount' of light illuminating
a surface, we are referring to something called the irradiance, denoted by
I - the average energy per unit area per unit time." Light and RF are both
EM waves. These scientific facts concerning light have only been known to
physics for about 300 years.
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

Peter O. Brackett wrote:
But I maintain that is "unatural" and "Mother Nature" naturally likes the
classical

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

Thoughts, comments?

I agree with you, Peter. That's what I have been calling the physical
reflection coefficient. At the junction of two transmission lines of
different characteristic impedances, it becomes s11=(Z02-Z01)/(Z02+Z01)
and is usually not equal to rho=Sqrt(Pref/Pfwd).
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

I'm trying to follow this, but have gone astray on the first couple of
steps.

Peter O. Brackett wrote:

The definition of the reflection coefficient is dependent upon what you
define the "reflected voltage" to be.

Consider the classical bridge circuit for measuring reflection coefficients.

If Z is an unknown load presented to a generator of internal impedance R and
that internal impedance R is used as the "reference" impedance to
observe/measure the reflected voltage b and that reflected voltage b is
calculated/measured by observation of the voltage v across the load Z and
the current i through the load Z then the classical definition of a
reflected voltage would be calculated as:

b = v - Ri = Zi - Ri = (Z - R)i Volts.

First of all, you're speaking of a circuit with a source impedance R and
load impedance Z, rather than a terminated transmission line. Forward
and reflected wave terminology is widely used in S parameter analysis,
which also uses this model, so I'll be glad to follow along to see if
and how S parameter terminology differs from the transmission line
terminology we've been discussing so far. Please correct me where my
assumptions diverge from yours.

Your "classical definition" of b isn't one familiar to me. v + Ri would
of course be the source voltage (which I'll call Vs). So v - Ri is Vs -
2*Ri. Where does this come from and what does it mean?

From your equation, and given source voltage Vs, i = Vs/(R+Z).
Therefore, your "classical definition" of reflected voltage b is, in
terms of Vs, Vs*((Z-R)/(Z+R)).

and the incident voltage a would be the Thevinins equivalent voltage across
the sum of Z and R, i.e.

a = (Z + R)i

Since i = Vs(Z+R), you're saying that a = the source voltage Vs (from
your two equations). So what you're calling the "incident voltage" is
simply the source voltage Vs.

Let's do a consistency check. The voltage at the load should be a + b =
Vs + Vs*((Z-R)/(Z+R)) = Vs*2Z/(Z+R). Inspection of the circuit as I
understand it shows that the voltage at the load should be half this
value. So, we already diverge. Which is true:

1. I've goofed up my algebra (a definite possibility)
2. I've misinterpreted your circuit, or
3. The voltage at the load is not equal to the sum of the forward and
reflected voltages a and b, as you use the terms "forward voltage" and
"reflected voltage". If v isn't equal to a + b, then what is the
relationship between v, a, and b, and what are the physical meanings of
the forward and reflected voltages?

I'd like to continue with the remainder of the analysis, but can't
proceed until this problem is cleared up.

. . .

Roy Lewallen, W7EL

Roy Lewallen wrote:
As soon as anyone starts arguing about average power waves, I'm outta
here. I'd just as soon argue about the temperature of ghosts.

You probably don't discuss light waves all that often, eh? :-)
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

Thanks for the suggestion, Reg, and it's absolutely true. But even more
information is thrown away when you take the average of the power.
Remember the statistician who drowned when crossing the creek whose
average depth is only three feet.

As soon as anyone starts arguing about average power waves, I'm outta
here. I'd just as soon argue about the temperature of ghosts.

Roy Lewallen, W7EL

Reg Edwards wrote:
Dear Roy,

To reduce the amount of bafflegab to an absolute minimum why don't you just
say that immediately the value of the reflection coefficient is squared (to
allow 'power' to be introduced) half of the information it contains is
tossed into the nearest garbage heap.

Any conclusions drawn from following calculations are inevitably ambiguous
and highly suspicious to say the least.

To mention one well-known example, that's why it is impossible to deduce the
value of the line-terminating impedance from the calculated SWR.

Ignorance is the root cause of these silly, time-wasting arguments.

Get back to basics, erase Smith Charts, mis-quoted worshipped idols, and
ill-conceived inventions from your minds and start afresh from R, L, C, G, F
and little t.

Fortunately, the success of proposed missions to Mars does not depend on the
deliberations of this newsgroup.

Cec, by the way, are there any vinyards in Texas? It *is* as big as France.
----
Yours, Reg, G4FGQ

"David Robbins" wrote in message ...

Incorrect. You need the conjugate in the numerator if the Zo is
complex. If it is purely real, WHICH MOST TEXTS ASSUME, then you can
use the normal equation.


sorry, the derivation for the table in the book i sent before is for the
general case of a complex Zo. they then go on to simplify for an ideal line
and for a nearly ideal line... nowhere does a conjugate show up.


Please post this derivation again.

When they say "ideal line" do they mean purely real?


and that reference you give is not for a load on a transmission line, it is
talking about a generator supplying power to a load... a completely
different animal.

Not at all really. The impedance seen by the load can be from
either a source or a source hooked up with a transmission line. It
doesn't matter with this equation.


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.

Load it with a real resistor of 10 ohms in series with a real
inductance of
40 millihenrys.

The inductance has a reactance of 250 ohms at 1000 Hz.

If you agree with the following formula,

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 wasn't happy, because how can you have a R.C. greater than
one into a passive network??? Quite impossible.

But, if you use the conjugate formula, the R.C. will indeed be
less than one.

Convince yourself.


Slick

(Tdonaly) wrote in message
...

Very impressive. You've designed 5/8s vertical ground planes,
1/4 wavelength [something or others, I guess] and dipoles.
Where are you working now? Did you go to Lowell?
73,
Tom Donaly, KA6RUH


Did you skip the part about U. C. Davis?

I'm working part-time in the RF field, after being laid off among
what seems like everyone else. Gives me time to paint my next masterpiece!

Tit for Tat, maybe you can tell us something about you, Tom.

last school attended? Job responsibilities?


Slick



My pitifully inadequate education could be of no interest to you, Garvin; I'm
just a humble ham. (This is an _amateur_ newsgroup after all.) It is
interesting to me, though, that a person of your age and attainments
would pose as a potty-mouth little black-faced god whenever someone
disagreed with you about something as abstruse as the reflection
coefficient on a transmission line. I can only suppose that your social
education was deficient, or that you really do want your name to be the
most popular in the group's collective killfile. Anyway, you're wasting your
time with the infantile behavior. Most of the fellows on this group are old
men
who gave up that form of discourse when they learned to talk.
By the way, some of your art isn't half bad and shows the influence of some
training. Did you have an art minor in college?
73,
Tom Donaly, KA6RUH

W5DXP wrote:

Nope, they're not Reg. For Z0-matched systems (which most ham systems are),
rho^2 is all you need to know along with the forward and reflected powers
to completely solve the voltage, current, and phase conditions at the
impedance discontinuity.

There in one sentence is the whole problem with the "power" approach.
For a complete solution including phase conditions, you have to assume a
Z0-match, and even Cecil acknowledges that is only true for "most ham
systems".

As Reg says, this is because the power approach throws away the phase
information at the start, and if you want it back again, you have to
make assumptions.

So the problem is not that the "power" approach cannot give a complete
solution, but that it cannot do it for all cases. In other words, it
isn't completely general - and that flaw is fatal.

The conventional approach based on voltage (or current) waves doesn't
discard the phase information, but uses it to give a complete solution
for every case. It is completely general, and that's precisely why
engineers use it.


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

Roy:

[snip]
b = v - Ri = Zi - Ri = (Z - R)i Volts.

First of all, you're speaking of a circuit with a source impedance R and
load impedance Z, rather than a terminated transmission line. Forward
and reflected wave terminology is widely used in S parameter analysis,
which also uses this model, so I'll be glad to follow along to see if
and how S parameter terminology differs from the transmission line
terminology we've been discussing so far. Please correct me where my
assumptions diverge from yours.

Your "classical definition" of b isn't one familiar to me. v + Ri would
of course be the source voltage (which I'll call Vs). So v - Ri is Vs -
2*Ri. Where does this come from and what does it mean?
[snip]

Yes it should be familiar to you because it is the most common definition
and one you seem to agree with. I presume that you are not used to seeing
the use
of the symbols "a" and "b" for those quantities. The use of "a" and "b" is
widely
used in Scattering Formalism and is less confusing to many than using
subscripts.
In your terminology above the "Vs" symbol is nothing more than the incident
voltage
usually given the symbol "a" in the Scattering Formalism, or the symbol V
with a "+"
sign subscript in many developments. Often you will find authors use a V
with a plus
sign "+" as a subscript to indicate the "a" voltage and a V with a minus
sign "-" subscript
to idicate the "b" voltage. Personally I find the use of math symbols "-"
and "+" or other
subscripts to variables to be confusing, I much prefer the use of "a" and
"b" for forward
or incident and reflected voltages.

Simply put, if a generator with "open circuit" voltage "a" and "internal
impedance" R
is driving a load Z [Z could be a transmission line driving point impedance,
for instance
Z would be the characteristic or surge impedance Zo of a transmission line
if
the generator was driving a semi-infinite line.] then v is the voltage drop
across Z
and I is the current through Z, and so...

a = v + Ri = Zi - Ri = (Z - R)i

is simply the [usual] forward voltage or incident voltage applied by the
generator to the
to the load Z, which may be a lumped element load or if you prefer to talk
about transmission
lines, Z can be just the driving point impedance of a transmsision line,
whatever you wish.

Then its'just a simple application of Ohms Law tosee that b = v - Ri = Zi -
Ri = (Z - R)i is
the [usual] reflected voltage. b is just the difference between the voltage
across Z which is
calculated as Zi and the voltage that would be across Z if Z was actually
equal to R. i.e. the
reflected voltage b is just the voltage that would exist across Z if there
was an "image match"
between Z and R. [If Z is the Zo of a semi-infinite transmsision line you
could call this a Zo match].

Taking the ratio of "b" to "a" just yeilds the [usual] reflection
coefficient as
b/a = (Z - R)i/(Z + R)i = (Z - R)/(Z + R). A well known result. Simple?

[snip]
From your equation, and given source voltage Vs, i = Vs/(R+Z).
Therefore, your "classical definition" of reflected voltage b is, in
terms of Vs, Vs*((Z-R)/(Z+R)).

and the incident voltage a would be the Thevinins equivalent voltage
across
the sum of Z and R, i.e.

a = (Z + R)i
[snip]

Yep you got it all right!

[snip]
Since i = Vs(Z+R), you're saying that a = the source voltage Vs (from
your two equations). So what you're calling the "incident voltage" is
simply the source voltage Vs.
[snip]

Yes, mathematically "a" = "Vs", what else would it be? Nothing mysterious
about
that. The incident voltage is always simply the open circuit voltage of the
source. In
words a is not the source voltage because the source is a Thevinin
equivalent made up
of the ideal voltage generator Vs = a behind the "internal" source impedance
R. A better
way to describe Vs = a in words would be the incident voltage a is the "open
circuit source
voltage".

[snip]
Let's do a consistency check. The voltage at the load should be a + b =
Vs + Vs*((Z-R)/(Z+R)) = Vs*2Z/(Z+R). Inspection of the circuit as I
understand it shows that the voltage at the load should be half this
value. So, we already diverge. Which is true:
[snip]

No, the voltage at the load is not (a + b) rather it is [the quite obvious
by Ohms Law] v = Zi.

and the sum of the incident and reflected voltage is simply

a + b = (v + Ri) + (v - Ri) = 2v = 2Zi

Now if there is an "image match" and the "unknown" Z is actually equal to R,
i.e. let Z = R
in all of the above, then...

a = Vs

b = 0

a + b = 2Ri

and i = Vs/2R = a/2R.

[snip]
1. I've goofed up my algebra (a definite possibility)
[snip]

Only a little :-)

[snip]
2. I've misinterpreted your circuit, or
[snip]

No you have it correct!

[snip]
3. The voltage at the load is not equal to the sum of the forward and
reflected voltages a and b, as you use the terms "forward voltage" and
"reflected voltage". If v isn't equal to a + b, then what is the
relationship between v, a, and b, and what are the physical meanings of
the forward and reflected voltages?
[snip]

I showed those relationships above. There is nothing new here... these are
the [most] widely accepted definitions of incident and reflected voltages.

[snip]
I'd like to continue with the remainder of the analysis, but can't
proceed until this problem is cleared up.

Roy Lewallen, W7EL
[snip]

OK, let's carry on.

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

Thanks, it's becoming clear why we're getting different results.

When analyzing a transmission line, the forward and reflected voltages
have a meaning that comes from the solutions to the wave equations. One
of the fundamental properties of these waves is that their sum is the
total voltage in the transmission line. (Likewise for current.) We
assume that these are the only voltage waves on the line, so their sum
is necessarily the total voltage. We sum these waves, for example, and
look at the resulting maxima and minima to get the standing wave ratio.
So it was a basic tenet of my analysis that the sum of the forward and
reverse voltage waves at any point on the line (including the end)
equals the voltage at that point. (Again, likewise for current, with
attention paid to the defined direction of positive flow.) This was
explicitly given as equation 5 (for voltage) and 6 (for current) of my
analysis.

Another property of the waves is that the ratio of V to I of either of
the waves equals the Z0 of the cable (equations 1 and 2).

Again making sure I see your model circuit correctly, it's a voltage
source of voltage a or V+, connected to R in series with Z. If that's
correct, then i = a / (Z + R), so your calculated value of b in your
analysis below, (Z - R)i, then equals a * (Z - R) / (Z + R). The sum of
a and b is a * (1 + (Z - R) / (Z + R)) = 2 * Z * a / (Z + R).

While in or at the ends of a transmission line the voltage always equals
the sum of the forward and reflected voltages, the sum of a and b, which
you call forward and reflected voltages, don't sum to the voltage at the
load. The voltage at the load is, from inspection of the circuit, a * Z
/ (Z + R); the sum of a and b is twice that value.

Of course, if we define "forward voltage" and "reflected voltage" to be
something other than the waves we're familiar with on a transmission
line, while maintaining a definition of voltage reflection coefficient
as being the ratio of forward to reverse voltage, we can come up with
any number of formulas for reflection coefficient.

And this seems to be done. I have only two texts which deal with S
parameters in any depth. One, _Microwave Transistor Amplifiers: Analysis
and Design_ By Guillermo Gonzalez, consistently uses forward and reverse
voltage to mean exactly what they do in transmission line analysis.
Consequently, he consistently ends up with the same equation for voltage
reflection coefficient I've been using, and states several places that
the reflection is zero when the line or port is terminated in its
characteristic or source impedance (not conjugate). And this all without
an assumption that Z0 or source Z is purely real. The other book,
however, _Microwave Circuit Design Using Linear and Nonlinear
Techniques_ by Vendelin, Pavio, and Rohde, uses a different definition
of V+, V- than either of us does, and different a and b than you do. To
them, a = V+ * sqrt(Re(Zg)) / Zg* where Zg is the source impedance, and
b = V- * sqrt(Re(Zg))/Zg. They end up with three different reflection
coefficients, Gammav, Gammai, and one they just give as Gamma. Gammav is
V-/V+, Gammai is I-/I+, and plain old Gamma, which they say is equal to
b/a, turns out to be equal to Gammai. Incidentally, their equation for
Gammav, the voltage reflection coefficient, is:

Gammav = [Zg(Z - Zg*)]/[Zg*(Z + Zg)]

Which is different from yours, Slick's, and mine.

The whole trick seems to be in defining what forward and reflected or
reverse voltage mean. In transmission line analysis, the meaning is, I
hope, pretty universal and agreed upon. If not, a whole bunch of
equations, statements, assumptions, and definitions have to go out the
window, along with the idea that those are the only voltages on the
line. If you use those widely accepted meanings, you unavoidably end up
with the common equation I've been giving for voltage reflection
coefficient. (At least nobody reputable so far seems to want to define
voltage reflection coefficient as anything but the ratio of reflected to
forward voltage, thankfully.) On the other hand, you and the authors of
at least one book put a different meaning of forward and reflected
voltage (and you two use different meanings), and therefore come up with
correspondingly different formulas for reflection coefficient.

At this point I have to concede that in some S parameter analysis at
least, various different meanings are given to "forward" or "incident",
and "reverse" or "reflected" voltage than are used in transmission line
analysis. And the two books I have disagree with each other, and both
disagree with you, as to what they do mean. With that kind of
non-standardization, it's useless to argue which is "more right" than
another. It just points out the importance of carefully defining what
you mean by forward and reverse voltages before you begin your analysis
-- and being very careful about what conclusions you draw from the
"reflections" or lack of them. When the definitions are different from
those used with transmission lines, the meaning and consequences of
reflections and impedance match are correspondingly different.

Your analysis is self consistent, given your definitions of forward and
reverse voltage. So are the analyses in the two books I have dealing
with S parameters. So all three of you reach different but valid
conclusions. Unless someone comes up with a convincing argument that one
definition of forward and reverse voltages is better or more meaningful
than another in that context, I have to agree that any of these three,
or any of an infinite number of other possibilities, is equally valid
for S parameter analysis.

But not for transmission lines. There, forward and reverse voltages do
have real meaning and a rigorous derivation. So anyone redefining them
in that context is certainly deviating from very well understood usage.

Consequently, I don't see how it would be productive, or add insight to
the problem of voltages, currents, and reflections in a transmission
line, to bring in S parameter terminology which obviously differs and in
an inconsistent way from author to author. I'll be glad to continue
discussing transmission lines, which is what this discussion originally
involved, with the first step being for someone disagreeing with the
formula for voltage reflection coefficient to point out which of the
equations or assumptions preceding it are incorrect. Your analysis
disagrees with equations 5 and 6 and, I believe, 1 and 2, by virtue of
your different definition of forward and reverse voltage. I don't
believe this can be justified within and at the end of a transmission
line -- if the forward and reverse voltages on the line don't add up to
the total, then you have to come up with at least one more voltage wave
you assume is traveling along the line (which summed with the others
does equal the total), and justify its existence.

Roy Lewallen, W7EL

Peter O. Brackett wrote:
Roy:

[snip]

b = v - Ri = Zi - Ri = (Z - R)i Volts.

First of all, you're speaking of a circuit with a source impedance R and
load impedance Z, rather than a terminated transmission line. Forward
and reflected wave terminology is widely used in S parameter analysis,
which also uses this model, so I'll be glad to follow along to see if
and how S parameter terminology differs from the transmission line
terminology we've been discussing so far. Please correct me where my
assumptions diverge from yours.

Your "classical definition" of b isn't one familiar to me. v + Ri would
of course be the source voltage (which I'll call Vs). So v - Ri is Vs -
2*Ri. Where does this come from and what does it mean?

[snip]

Yes it should be familiar to you because it is the most common definition
and one you seem to agree with. I presume that you are not used to seeing
the use
of the symbols "a" and "b" for those quantities. The use of "a" and "b" is
widely
used in Scattering Formalism and is less confusing to many than using
subscripts.
In your terminology above the "Vs" symbol is nothing more than the incident
voltage
usually given the symbol "a" in the Scattering Formalism, or the symbol V
with a "+"
sign subscript in many developments. Often you will find authors use a V
with a plus
sign "+" as a subscript to indicate the "a" voltage and a V with a minus
sign "-" subscript
to idicate the "b" voltage. Personally I find the use of math symbols "-"
and "+" or other
subscripts to variables to be confusing, I much prefer the use of "a" and
"b" for forward
or incident and reflected voltages.

Simply put, if a generator with "open circuit" voltage "a" and "internal
impedance" R
is driving a load Z [Z could be a transmission line driving point impedance,
for instance
Z would be the characteristic or surge impedance Zo of a transmission line
if
the generator was driving a semi-infinite line.] then v is the voltage drop
across Z
and I is the current through Z, and so...

a = v + Ri = Zi - Ri = (Z - R)i

is simply the [usual] forward voltage or incident voltage applied by the
generator to the
to the load Z, which may be a lumped element load or if you prefer to talk
about transmission
lines, Z can be just the driving point impedance of a transmsision line,
whatever you wish.

Then its'just a simple application of Ohms Law tosee that b = v - Ri = Zi -
Ri = (Z - R)i is
the [usual] reflected voltage. b is just the difference between the voltage
across Z which is
calculated as Zi and the voltage that would be across Z if Z was actually
equal to R. i.e. the
reflected voltage b is just the voltage that would exist across Z if there
was an "image match"
between Z and R. [If Z is the Zo of a semi-infinite transmsision line you
could call this a Zo match].

Taking the ratio of "b" to "a" just yeilds the [usual] reflection
coefficient as
b/a = (Z - R)i/(Z + R)i = (Z - R)/(Z + R). A well known result. Simple?

[snip]

From your equation, and given source voltage Vs, i = Vs/(R+Z).
Therefore, your "classical definition" of reflected voltage b is, in
terms of Vs, Vs*((Z-R)/(Z+R)).

and the incident voltage a would be the Thevinins equivalent voltage

across

the sum of Z and R, i.e.

a = (Z + R)i

[snip]

Yep you got it all right!

[snip]

Since i = Vs(Z+R), you're saying that a = the source voltage Vs (from
your two equations). So what you're calling the "incident voltage" is
simply the source voltage Vs.

[snip]

Yes, mathematically "a" = "Vs", what else would it be? Nothing mysterious
about
that. The incident voltage is always simply the open circuit voltage of the
source. In
words a is not the source voltage because the source is a Thevinin
equivalent made up
of the ideal voltage generator Vs = a behind the "internal" source impedance
R. A better
way to describe Vs = a in words would be the incident voltage a is the "open
circuit source
voltage".

[snip]

Let's do a consistency check. The voltage at the load should be a + b =
Vs + Vs*((Z-R)/(Z+R)) = Vs*2Z/(Z+R). Inspection of the circuit as I
understand it shows that the voltage at the load should be half this
value. So, we already diverge. Which is true:

[snip]

No, the voltage at the load is not (a + b) rather it is [the quite obvious
by Ohms Law] v = Zi.

and the sum of the incident and reflected voltage is simply

a + b = (v + Ri) + (v - Ri) = 2v = 2Zi

Now if there is an "image match" and the "unknown" Z is actually equal to R,
i.e. let Z = R
in all of the above, then...

a = Vs

b = 0

a + b = 2Ri

and i = Vs/2R = a/2R.

[snip]

1. I've goofed up my algebra (a definite possibility)

[snip]

Only a little :-)

[snip]

2. I've misinterpreted your circuit, or

[snip]

No you have it correct!

[snip]

3. The voltage at the load is not equal to the sum of the forward and
reflected voltages a and b, as you use the terms "forward voltage" and
"reflected voltage". If v isn't equal to a + b, then what is the
relationship between v, a, and b, and what are the physical meanings of
the forward and reflected voltages?

[snip]

I showed those relationships above. There is nothing new here... these are
the [most] widely accepted definitions of incident and reflected voltages.

[snip]

I'd like to continue with the remainder of the analysis, but can't
proceed until this problem is cleared up.

Roy Lewallen, W7EL

[snip]

OK, let's carry on.

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

Roy:

[snip]
Consequently, I don't see how it would be productive, or add insight to
the problem of voltages, currents, and reflections in a transmission
line, to bring in S parameter terminology which obviously differs and in
an inconsistent way from author to author. I'll be glad to continue
discussing transmission lines, which is what this discussion originally
involved, with the first step being for someone disagreeing with the
formula for voltage reflection coefficient to point out which of the
equations or assumptions preceding it are incorrect. Your analysis
disagrees with equations 5 and 6 and, I believe, 1 and 2, by virtue of
your different definition of forward and reverse voltage. I don't
believe this can be justified within and at the end of a transmission
line -- if the forward and reverse voltages on the line don't add up to
the total, then you have to come up with at least one more voltage wave
you assume is traveling along the line (which summed with the others
does equal the total), and justify its existence.

Roy Lewallen, W7EL
[snip]

Thanks for following along with my development. I like to develop stuff
from first principles, instead of quoting often questionable sources.

Roy apart from a few typos and a small factor of 1/2 it seems that we agree
on everything!

Sorry if I messed up a little with typos, and... there is that potentially
confusing but unimportant factor of 1/2 that appears in my definitions of
the incident "waves" a and b.

Your claim as to my definitions being quite different from the "mainstream"
of transmission line theory was a bit hasty, because in fact with a closer
look I believe that you will see that my definitions and yours [Which are
hhe mainstream transmission line definitions and equations] only differ by a
simple numerical factor of 2. I don't use that factor of 1/2 because it
drops out whenever you take a ratio of waves anyway.

Perhaps I should have defined my a to be a = 1/2(v + Ri) and b = 1/2(v - Ri)
instead of a = v + Ri and b = v - Ri as I have done. Including that factor
of 1/2 in my a and b makes them identical to your incident and reflected
voltages.

This factor of 1/2 is a very minor "scaling" difference in the "waves" and
there is absolutely no difference in reflection coefficient, or indeed in
Scattering Matrix definitions since the factor of 1/2 in each of "my" wave
definitions simply cancels out in rho = b/a, when you divide b by a to get
rho or indeed in calculating with wave vectors and Scattering Matrixs of any
order. My definition of the scaling factor [1/2] for the wave variables
works as well as any other as long as consistency is maintained. Like you I
have found that different Scattering Theory books often use a variety of
different scaling factors in defining the waves, for instance some use a
factor of 1/2*sqrt(R) = 1/2*sqrt(Zo) in the definition of the waves, etc...
It simply doesn't matter as long as you are consistent.

In any case, the scaling value in the definition of the "waves" was not my
point.

The point I was trying to make was to address the subtle point initiated by
Slick, i.e. the one about the definition of rho which is the ratio of
reflected to incident waves, where the scaling factors drop out, and whether
the CONJUGATE of the reference impedance should be used in the definition
for rho or not.

My point was that the conventional definition of rho = (Z - R)/(Z + R)
without the CONJUGATE is in fact the "natural" definition for wave motion
whether on transmission lines or in impedance matching to a generator.
And...

That with the conventional definition of rho in the case of a general Zo the
reflected voltage will *NOT* be zero at a conjugate match. At a conjugate
match, the classical rho and b will only be null in the special case of the
reference impedance Zo being a pure real resistance.

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

Roy Lewallen wrote:


I have only two texts which deal with S
parameters in any depth. One, _Microwave Transistor Amplifiers: Analysis
and Design_ By Guillermo Gonzalez, consistently uses forward and reverse
voltage to mean exactly what they do in transmission line analysis.
Consequently, he consistently ends up with the same equation for voltage
reflection coefficient I've been using, and states several places that
the reflection is zero when the line or port is terminated in its
characteristic or source impedance (not conjugate). And this all without
an assumption that Z0 or source Z is purely real. The other book,
however, _Microwave Circuit Design Using Linear and Nonlinear
Techniques_ by Vendelin, Pavio, and Rohde, uses a different definition
of V+, V- than either of us does, and different a and b than you do. To
them, a = V+ * sqrt(Re(Zg)) / Zg* where Zg is the source impedance, and
b = V- * sqrt(Re(Zg))/Zg. They end up with three different reflection
coefficients, Gammav, Gammai, and one they just give as Gamma. Gammav is
V-/V+, Gammai is I-/I+, and plain old Gamma, which they say is equal to
b/a, turns out to be equal to Gammai. Incidentally, their equation for
Gammav, the voltage reflection coefficient, is:

Gammav = [Zg(Z - Zg*)]/[Zg*(Z + Zg)]

This formula is Gonzalez's definition of voltage
reflection coefficient, based on *power wave*
theory (not *transmission line* theory) on page 48
of his *second edition*. We need to keep in mind
that a power wave is a different kind of wave than
the ones that we are used to thinking about in
transmission lines (Gonzalez's words).

If you don't have his second edition, I suggest
get on-line and buy it. It has a lot of stuff not
found in the first edition. The discussion of
power waves is excellent and readable, with some
mental suffering.

The power wave concept is quite valid. We need to
come to grips with this and learn to accept it. It
is the actual basis for microwave simulation
programs. In these programs transmission lines are
treated as "circuit elements" with certain
properties and calculated scattering parameters.
But we must wear a different "hat" when dealing
with it. The idea of "power wave" requires some
meditation.

I discussed some of this in a previous post.

Bill W0IYH

William E. Sabin wrote:

Roy Lewallen wrote:



I have only two texts which deal with S parameters in any depth. One,
_Microwave Transistor Amplifiers: Analysis and Design_ By Guillermo
Gonzalez, consistently uses forward and reverse voltage to mean
exactly what they do in transmission line analysis. Consequently, he
consistently ends up with the same equation for voltage reflection
coefficient I've been using, and states several places that the
reflection is zero when the line or port is terminated in its
characteristic or source impedance (not conjugate). And this all
without an assumption that Z0 or source Z is purely real. The other
book, however, _Microwave Circuit Design Using Linear and Nonlinear
Techniques_ by Vendelin, Pavio, and Rohde, uses a different definition
of V+, V- than either of us does, and different a and b than you do.
To them, a = V+ * sqrt(Re(Zg)) / Zg* where Zg is the source impedance,
and b = V- * sqrt(Re(Zg))/Zg. They end up with three different
reflection coefficients, Gammav, Gammai, and one they just give as
Gamma. Gammav is V-/V+, Gammai is I-/I+, and plain old Gamma, which
they say is equal to b/a, turns out to be equal to Gammai.
Incidentally, their equation for Gammav, the voltage reflection
coefficient, is:

Gammav = [Zg(Z - Zg*)]/[Zg*(Z + Zg)]


This formula is Gonzalez's definition of voltage reflection coefficient,
based on *power wave* theory (not *transmission line* theory) on page 48
of his *second edition*. We need to keep in mind that a power wave is a
different kind of wave than the ones that we are used to thinking about
in transmission lines (Gonzalez's words).

If you don't have his second edition, I suggest get on-line and buy it.
It has a lot of stuff not found in the first edition. The discussion of
power waves is excellent and readable, with some mental suffering.

The power wave concept is quite valid. We need to come to grips with
this and learn to accept it. It is the actual basis for microwave
simulation programs. In these programs transmission lines are treated as
"circuit elements" with certain properties and calculated scattering
parameters.

Mason's Rule is then applied to the collection of
circuit elements to get the system response.

But we must wear a different "hat" when dealing
with it. The
idea of "power wave" requires some meditation.

I discussed some of this in a previous post.

Bill W0IYH


Bill W0IYH

Ian White, G3SEK wrote:
There in one sentence is the whole problem with the "power" approach.
For a complete solution including phase conditions, you have to assume a
Z0-match, and even Cecil acknowledges that is only true for "most ham
systems".

But Ian, what we have been arguing about for two years is what happens
to the energy around a *Z0-match point*. Now you admit that, for a Z0-
matched system (which most ham systems are) the power approach yields
a "complete solution including phase conditions". We are making progress.

As Reg says, this is because the power approach throws away the phase
information at the start, and if you want it back again, you have to
make assumptions.

For an energy analysis, you don't need the phase information. Energy,
like SWR, is the same for 50+j50 and 50-j50.

So the problem is not that the "power" approach cannot give a complete
solution, but that it cannot do it for all cases. In other words, it
isn't completely general - and that flaw is fatal.

You don't understand the purpose of a "power" approach. It is not to
solve for the phases. It is to analyze the energy flow. For that purpose,
like SWR, it is not necessary to know the sign of the reactance. I have
specifically said that the power approach does not attempt to replace
conventional approaches. It augments conventional approaches to determine
the details of the energy flow, something the conventional approach sadly
lacks.
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

Roy Lewallen wrote:
Consequently, I don't see how it would be productive, or add insight to
the problem of voltages, currents, and reflections in a transmission
line, to bring in S parameter terminology which obviously differs and in
an inconsistent way from author to author.

A good reference is HP's application note, AN 95-1, available for download
from Agilent: http://contact.tm.agilent.com/Agilen...5-1/index.html

Another good reference is: _Fields_and_Waves_... by Ramo, Whinnery, and
Van Duzer, section 11.09. The basic equations are pretty simple:

b1 = s11*a1 + s12*a2 b2 = s21*a1 + s22*a2
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

William E. Sabin wrote:
The power wave concept is quite valid.

In fact, power waves are used almost exclusively in the field of optics,
the "other" EM waves. Since the phase of light is extremely hard to
measure, it is deduced from the irradiance (power) patterns. The same
deductive logic can be used with RF transmission lines (if anyone actually
cares about logical thought).
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

In transmission line analysis, we're not free to rescale the forward and
reverse voltage waves, unless we also scale all the voltages, currents
and powers accordingly. The forward and reverse waves have to add to the
total voltage in the line and at its ends, and the ratio of each
component to the corresponding current component has to equal the Z0 of
the line. It's quite apparent that in S parameter analysis you're quite
free to scale them as you wish, as you have. Vendelin et al didn't just
scale them, but chose a set of V+ and V- which aren't even related to a
and b by the same constant.

By defining V+ and V- as we wish, we can make the reflection coefficient
V-/V+ to be zero when there's a Z0 match, when there's a conjugate
match, or when any other impedance of our choice is used as a
termination. And when we relieve the requirement that the sum of V+ and
V- add to the total voltage, we can have any value of V+ we choose, when
V- is zero. The various analyses I've seen have made different choices,
and arrived at different V+, V-, and voltage reflection coefficient values.

Again, though, when dealing with a transmission line we don't have the
luxury of choosing any definitions of V+ and V- we want. Consequently,
in a transmission line, the ratio of V-/V+, universally defined at the
voltage reflection coefficient, can be calculated with the familiar
non-conjugate formula. The formula can be derived as I did it, from
basic principles. And from it or other methods, we can conclude that
when a transmission line is terminated in its characteristic impedance,
there is no reflection of the voltage (or current) wave. When it's
terminated in the complex conjugate of its characteristic impedance, or
any other impedance except its characteristic impedance, there is a
reflection.

Roy Lewallen, W7EL

Peter O. Brackett wrote:
Roy:

[snip]

Consequently, I don't see how it would be productive, or add insight to
the problem of voltages, currents, and reflections in a transmission
line, to bring in S parameter terminology which obviously differs and in
an inconsistent way from author to author. I'll be glad to continue
discussing transmission lines, which is what this discussion originally
involved, with the first step being for someone disagreeing with the
formula for voltage reflection coefficient to point out which of the
equations or assumptions preceding it are incorrect. Your analysis
disagrees with equations 5 and 6 and, I believe, 1 and 2, by virtue of
your different definition of forward and reverse voltage. I don't
believe this can be justified within and at the end of a transmission
line -- if the forward and reverse voltages on the line don't add up to
the total, then you have to come up with at least one more voltage wave
you assume is traveling along the line (which summed with the others
does equal the total), and justify its existence.

Roy Lewallen, W7EL

[snip]

Thanks for following along with my development. I like to develop stuff
from first principles, instead of quoting often questionable sources.

Roy apart from a few typos and a small factor of 1/2 it seems that we agree
on everything!

Sorry if I messed up a little with typos, and... there is that potentially
confusing but unimportant factor of 1/2 that appears in my definitions of
the incident "waves" a and b.

Your claim as to my definitions being quite different from the "mainstream"
of transmission line theory was a bit hasty, because in fact with a closer
look I believe that you will see that my definitions and yours [Which are
hhe mainstream transmission line definitions and equations] only differ by a
simple numerical factor of 2. I don't use that factor of 1/2 because it
drops out whenever you take a ratio of waves anyway.

Perhaps I should have defined my a to be a = 1/2(v + Ri) and b = 1/2(v - Ri)
instead of a = v + Ri and b = v - Ri as I have done. Including that factor
of 1/2 in my a and b makes them identical to your incident and reflected
voltages.

This factor of 1/2 is a very minor "scaling" difference in the "waves" and
there is absolutely no difference in reflection coefficient, or indeed in
Scattering Matrix definitions since the factor of 1/2 in each of "my" wave
definitions simply cancels out in rho = b/a, when you divide b by a to get
rho or indeed in calculating with wave vectors and Scattering Matrixs of any
order. My definition of the scaling factor [1/2] for the wave variables
works as well as any other as long as consistency is maintained. Like you I
have found that different Scattering Theory books often use a variety of
different scaling factors in defining the waves, for instance some use a
factor of 1/2*sqrt(R) = 1/2*sqrt(Zo) in the definition of the waves, etc...
It simply doesn't matter as long as you are consistent.

In any case, the scaling value in the definition of the "waves" was not my
point.

The point I was trying to make was to address the subtle point initiated by
Slick, i.e. the one about the definition of rho which is the ratio of
reflected to incident waves, where the scaling factors drop out, and whether
the CONJUGATE of the reference impedance should be used in the definition
for rho or not.

My point was that the conventional definition of rho = (Z - R)/(Z + R)
without the CONJUGATE is in fact the "natural" definition for wave motion
whether on transmission lines or in impedance matching to a generator.
And...

That with the conventional definition of rho in the case of a general Zo the
reflected voltage will *NOT* be zero at a conjugate match. At a conjugate
match, the classical rho and b will only be null in the special case of the
reference impedance Zo being a pure real resistance.

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

W5DXP wrote:
I don't think there's anything to argue about. From _Optics_, by Hecht:
"We define the reflectance R to be the ratio of the reflected power to
the incident power."

He certainly wasn't including Max Born and Emil Wolf when he said "We".
They define reflectance in terms of indices of refraction i.e.
(n1-n2)/(n1+n2).

73, ac6xg

Roy Lewallen wrote:
It's quite apparent that in S parameter analysis you're quite
free to scale them as you wish, as you have.

The scaling is defined by the s-parameter specification. Nobody is
free "to scale them as you wish". For instance, a1 is defined as:

(V1+I1*Z0)/2*Sqrt(Z0)
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

W5DXP wrote:

Jim Kelley wrote:

W5DXP wrote:
I don't think there's anything to argue about. From _Optics_, by Hecht:
"We define the reflectance R to be the ratio of the reflected power to
the incident power."

He certainly wasn't including Max Born and Emil Wolf when he said "We".
They define reflectance in terms of indices of refraction i.e.
(n1-n2)/(n1+n2).

The Reflectance is equal to the square of the amplitude reflection
coefficient.
R = Ir/Ii = [(n1-n2)/(n1+n2)]^2

Again, Born and Wolf disagree with Hecht. They define Reflectivity as
being the square of the reflection coefficient.

Hecht says the definition "leads to" the last term above.

Certainly he didn't feel that some relative amounts of power are what
determine the indices of refraction of the system. That would be
ridiculous.

73, ac6xg

"Dr. Slick" wrote in message
om...
"David Robbins" wrote in message
...

Incorrect. You need the conjugate in the numerator if the Zo is
complex. If it is purely real, WHICH MOST TEXTS ASSUME, then you can
use the normal equation.


sorry, the derivation for the table in the book i sent before is for the
general case of a complex Zo. they then go on to simplify for an ideal
line
and for a nearly ideal line... nowhere does a conjugate show up.


Please post this derivation again.

sorry, i don't have time for this. its really quite simple, just apply
kirchoff's and ohm's laws at the connection point and it falls right out.


When they say "ideal line" do they mean purely real?

yes, purely real with no loss terms.



and that reference you give is not for a load on a transmission line, it
is
talking about a generator supplying power to a load... a completely
different animal.

Not at all really. The impedance seen by the load can be from
either a source or a source hooked up with a transmission line. It
doesn't matter with this equation.


the reference you gave is looking at a generator connected to a load. true,
it doesn't matter if there is a transmission line in between the generator
and the 'load' but the impedance being used is the one transformed back to
the generator end of the line, not the one at the far end of the line... so
basically that equation is not a transmission line equation, it is a
generator to load reflection calculation done to maximize power not to
satisfy kirchoff.

On Tue, 26 Aug 2003 22:35:29 -0000, "David Robbins"
wrote:
the reference you gave is looking at a generator connected to a load. true,
it doesn't matter if there is a transmission line in between the generator
and the 'load' but the impedance being used is the one transformed back to
the generator end of the line, not the one at the far end of the line... so
basically that equation is not a transmission line equation, it is a
generator to load reflection calculation done to maximize power not to
satisfy kirchoff.

Hi David,

If it is time invariant (linear), it doesn't matter.

73's
Richard Clark, KB7QHC

Richard Clark wrote in message . ..

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"

Interesting. I'd first have asked if the line was really 50 ohms,
completely nonreactive. If so, L/C=R/G and I'd have said A=3.266dB.
If the line was just 50 ohms nominal, then I can think of at least one
scenario in which A=0.60dB. And I can think of another in which A=
5.2dB. The definition I have used for loss in those cases is
A=-10*log10(P1/P2), where P2 is the power delivered to the (line+load)
and P1 is the power delivered to the load, with steady-state
excitation. The answer, given that definition, never depends on
source impedance of the driving source. Of course it could with a
different definition, for example involving the maximum available
power from the source, but that just confuses the issue by lumping
"(source) mismatch loss" with acutal line loss, as has been pointed
out before.

Cheers,
Tom

Roy:

[snip]
"Roy Lewallen" wrote in message
...
In transmission line analysis, we're not free to rescale the forward and
reverse voltage waves, unless we also scale all the voltages, currents
and powers accordingly. The forward and reverse waves have to add to the
total voltage in the line and at its ends, and the ratio of each
component to the corresponding current component has to equal the Z0 of
the line.
[snip]

I agree, that's why I say the definition of rho with Zo and not the
conjugate is
actually Mother Natures definition. Simply because that's the way the
solution
to the wave equation [The Telegraphists Equation] turns out.

[snip]
It's quite apparent that in S parameter analysis you're quite
free to scale them as you wish, as you have. Vendelin et al didn't just
scale them, but chose a set of V+ and V- which aren't even related to a
and b by the same constant.
[snip]

Actually you are free!

Just define the waves a and b as any linear combination of i and v and as
long as the linear combination is non-singular you will be just fine! You
can Engineer systems to your hearts content and get all the right answers.
[It's sort of like the assumption of current flow in conductors from + to -,
even though we "know" electrons flow the other way, it always
gives us the correct Engineering answers, so who cares!]

[snip]
basic principles. And from it or other methods, we can conclude that
when a transmission line is terminated in its characteristic impedance,
there is no reflection of the voltage (or current) wave. When it's
terminated in the complex conjugate of its characteristic impedance, or
any other impedance except its characteristic impedance, there is a
reflection.

Roy Lewallen, W7EL
[snip]

Roy my friend we are in violent agreement!

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

Cecil:

[snip]
The scaling is defined by the s-parameter specification. Nobody is
free "to scale them as you wish". For instance, a1 is defined as:

(V1+I1*Z0)/2*Sqrt(Z0)
--
73, Cecil http://www.qsl.net/w5dxp
[snip]

I like that definition best of all in a theoretical setting... but be
prepared...
there are many others to be found in the literature.

Even though I like the definition you have shown above, I find the
definitions...

a = v + Zo*i and b = v - Zo*i

To be very convenient in practice since they correspond to a very easy to
understand, visualize and manipulate single Operational Amplifier
reflectometer
circuit.

As long as the relationship between v and i and a and b are simple linear
combinations
without singularities, i.e. the transformation matrix M which allows you to
transform between
the [a, b] vectors and the [i, v] vectors is non-singular then you are just
fine, as long as
you remain consistent with your initial definition. You can perform
reliable and accurate
Engineering with any definition of the "waves" [a, b] that are a suitable
linear combination of the
"electricals" [i, v].

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

Richard:

[snip]
I know you eschew academic references in favor of "first principles,"
but others may want more material than the simple puzzle aspect.
They can consult "Transmission Lines & Networks," Walter C. Johnson,
Chapter 13, "Insertion Loss and Reflection Factors." But lest those
who go there for the answer, I will state it is from another
reference, Johnson simply is offered as yet another reference to
balance the commonly unstated inference of SWR mechanics being
conducted with a Z matched source. "Transmission Lines," Robert
Chipman is another (and not the source of the puzzle either).

73's
Richard Clark, KB7QHC
[snip]

I hear you...

I don't eschew academic references, but when it comes to systems
Engineering, I do try to follow what our great President Regan once said,
"Trust, but Verify!"

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

Roy:

[snip]
You didn't show differently in your analysis, and no one has stepped
forward with a contrary proof, derivation from known principles, or
numerical example that shows otherwise.

Roy Lewallen, W7EL
[snip]

Yes I did. I guess that you missed that post.

I'll paste a little bit of that posting here below so that you can see it
again.

[begin paste]
We are discussing *very* fine points here, but...

[snip]
ratio of the reflected to incident voltage as rho = b/a would yeild the
usual formula:

rho = b/a = (Z - R)i/(Z + R)i = (Z - R)/(Z+ R).

In which no conjugates appear!

Now if we take the internal/reference impedance R to be complex as R = r +
jx then for a "conjugate match" the unknown Z would be the conjugate of the
internal/reference impedance and so that would be:

Z = r - jx

Thus the total driving point impedance faced by the incident voltage a would
be 2r:

R + Z = r + jx + r - jx = 2r

and the current i through Z would be i = a/2r with the voltage v across Z
being v = a/2.

Now the reflected voltage under this conjugate match would not be zero,
rather it would be:

b = (Z - R)i = ((r - jx) - (r + jx))i = (r - r -jx -jx)i = -2jxi = -2jxa/2r
= -jax/r

and the reflection coefficient value under this conjugate match would be
simply:

b/a = rho = - jx/r

Thus I conclude that, under the classical definitions, when one has a
"conjugate match" [i.e. maximum power transfer] the reflected voltage and
the reflection coefficient are not zero.
:
:
In summary:

Under the classical definition of rho = (Z - R)/(Z + R) rho will be not be
zero for a "conjugate match" and in fact there will be a "residual"
reflected voltage of -jx/r times the incident voltage at a conjugate match.
The only time the classical definition of rho and the reflected voltage is
null is for an "image match" when the load equals the reference impedance.
:
:
Unless one changes ones definition of the reflected voltage/reflection
coefficient to utilize the conjugate of the internal impedance as the
"reference" impedance then the reflected voltage is not zero at a conjugate
match. End of story.
[snip]

Regards,

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

Jim Kelley wrote:
Again, Born and Wolf disagree with Hecht. They define Reflectivity as
being the square of the reflection coefficient.

From the IEEE dictionary: "reflectivity - The reflectance of the surface
of a material so thick that the reflectance does not change with increasing
thickness" Looks like Born and Wolf are wrong.
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----