On Fri, 17 Jun 2005 22:44:13 -0400, "Walter Maxwell"
wrote:

[snip]


Hi Owen,

From the general use I'm familiar with, rho alone refers to the abs value, while
the two vertical bars on each side of rho indicates the magnitude alone.
However, following Hewlett-Packard's usage in their AP notes, in Reflections I
use a bar over rho for the absolute, and rho alone for the magnitude. However, I
explain the term in the book to avoid confusion.

Confusion reigns.

Four years ago in another thread I posted thus:

Quote

On Mon, 12 Feb 2001 15:25:28 -0800, Roy Lewallen
wrote:

Just a point of clarification. Rho in these equations is the magnitude
of the reflection coefficient, not the reflection coefficient itself.
The reflection coefficient is actually a complex number. Rho is
unfortunately used to sometimes represent the (complex) reflection
coefficient and sometimes (like here) its magnitude, although some
people (me included) prefer to use uppercase gamma for the complex
reflection coefficient and lowercase rho for its magnitude.

Roy raises a good point. Tom Bruhns already took me to task for a
somewhat careless use of rho. Although I did define it below, as Roy
and Tom said, it is often used as a complex number.

I too prefer upper case Gamma for the complex number and rho for the
magnitude but unfortunately the literature is full of confusing usage.
Some of the literature was even published by Tom's employer, the
former H-P, now Agilent (how do you pronounce that again?)

My autographed copy of Steve Adam's, book "Microwave Theory and
Applications", published by H-P, shows on page 23:

" |Gamma| = rho "

Similarly, my handy dandy H-P "Reflectometer calculator" sliderule
says that SWR = (1 + rho) / (1- rho) which bears a striking
resemblence to what I wrote below.

But then in H-P's App Note 77-3, "Measurement of Complex Impedance
1-1000 MHZ", it says that rho is a vector quantity and it shows:

SWR = (1 +|rho| ) / (1 - |rho| )

Finally, the best reference I have is General Radio's "Handbook of
Microwave Measurements" (out of print but reissued by Gilbert
Engineering) and it says that Gamma is complex and rho isn't.

End quote.

"Owen" wrote in message
...
.............................
I do note that my ARRL Antenna Handbook (18th edition) and ARRL Handbook
(2000) both use rho, however they reckon that rho=(Za-Zo*)/(Za+Zo) (where
Zo* means the conjugate of Zo). They do this without derivation, and seem
to be in conflict with the derivation in most texts. I suppose the
derivation is buried in some article in QST and in the members only
section of the ARRL website.


Owen,

There was a big discussion about this last year, and somebody posted that
the ARRL was going to eliminate the conjugate reference.

Tam/WB2TT

Back to notation, accepting that the preferred pronumeral for the voltage
reflection coefficient is rho, is there a pronumeral used for abs(rho)?

Owen

Tam/WB2TT wrote:

There was a big discussion about this last year, and somebody posted that
the ARRL was going to eliminate the conjugate reference.

Ok, I take that to mean the ARRL handbooks are in error in stating
rho=(Za-Zo*)/(Za+Zo) (where Zo* means the conjugate of Zo), and that
they will now use rho=(Za-Zo)/(Za+Zo). Kirchoff lives! I guess we wait
and see if it comes to print.

Thanks Tam.

Owen

Tam/WB2TT wrote:
There was a big discussion about this last year, and somebody posted that
the ARRL was going to eliminate the conjugate reference.

Another problem that needs to be fixed is the difference between
the "virtual" rho and the physical rho. What is rho looking
into point '+' from the XMTR side?

XMTR---50 ohm coax---+---1/4WL 75 ohm coax---112.5 ohm load

The physical rho is (75-50)/(75+50) = 0.2 which is the same
as 's11' in an S-parameter analysis.

The "virtual" rho is SQRT(Pref/Pfor) which, in a Z0-matched
system is zero. (The 50 ohm coax "sees" a V/I ratio of 50 ohms)

Rho, looking into the load, is (112.5-75)/(112.5+75) = 0.2.

The virtual rho, looking back at point '+' from the load side
is |1.0| but that same reflection coefficient, s22 for an
S-parameter analysis, is (50-75)/(50+75) = -0.2.
--
73, Cecil http://www.qsl.net/w5dxp


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Tam/WB2TT wrote:
"Owen" wrote in message
...
.............................
I do note that my ARRL Antenna Handbook (18th edition) and ARRL Handbook
(2000) both use rho, however they reckon that rho=(Za-Zo*)/(Za+Zo) (where
Zo* means the conjugate of Zo). They do this without derivation, and seem
to be in conflict with the derivation in most texts. I suppose the
derivation is buried in some article in QST and in the members only
section of the ARRL website.


Owen,

There was a big discussion about this last year, and somebody posted that
the ARRL was going to eliminate the conjugate reference.


Les Besser agrees with the ARRL Handbook except he
uses gamma for the complex reflection coefficient:

gamma=(Za-Zo*)/(Za+Zo) (where Zo* means the conjugate of Zo)


But for most practical calculations, the Zo is assumed to
be purely real, so many texts give gamma=(Za-Zo)/(Za-Zo).

rho=[gamma]=absolute value of gamma=magnitude of gamma


Rho can never be greater than one going into a passive
network. Only when you have an active device, or gain, can
you move outside of the unity circle on the Smith Chart.


Slick




Tam/WB2TT

Back to notation, accepting that the preferred pronumeral for the voltage
reflection coefficient is rho, is there a pronumeral used for abs(rho)?

Owen

Tam/WB2TT wrote:
"Owen" wrote in message
...
.............................
I do note that my ARRL Antenna Handbook (18th edition) and ARRL Handbook
(2000) both use rho, however they reckon that rho=(Za-Zo*)/(Za+Zo) (where
Zo* means the conjugate of Zo). They do this without derivation, and seem
to be in conflict with the derivation in most texts. I suppose the
derivation is buried in some article in QST and in the members only
section of the ARRL website.



Thank you, Owen. Les Besser agrees with the
ARRL.

However, in almost all practical calculations,
Zo is purely real, so that gamma=(Za-Zo)/(Za+Zo) is
used in most texts, and the results are the same.




Owen,

There was a big discussion about this last year, and somebody posted that
the ARRL was going to eliminate the conjugate reference.

Tam/WB2TT



Going to? It says 2000 on that ARRL Handbook!

They are NOT going to eliminate the conjugate
reference, because it's correct.



Slick

You've noted what I've noted before in this forum, if you say that
"(V)SWR" is the SWR that would result if the forward and reverse waves
at a particular point on the line (the point at which you've measured
rho) were allowed to develop a voltage maximum and a voltage minimum
(or a current maximum and minimum). I happen to believe that is more
in keeping with the original meaning of (V)SWR than the formula which
says VSWR=(1+rho)/(1-rho).

Of course, this all gets quickly into people trying to assign physical
significance to rho which is not really there; they get confused when
rho1.

If you are clear and consistent with your definitions, I don't see that
any problems result either way. I happen to believe that the formula
you came up with is a better one than the one you commonly see in
texts, but I also agree with Roy that you'd better be clear about it if
you use it, because it goes against the commonly accepted grain. On
the other hand, I've seen texts that derive it in the same way you
have, which come up with the "wrong" answer (without the abs) based on
their initial premises.

Cheers,
Tom