"Roy Lewallen" wrote in message
...
Owen wrote:

I note that any textbook I pick up shows that VSWR=(1+rho)/(1-rho) where rho
is the magnitude of Gamma (Gamma=(Z-Zo)/(Z+Zo)); rho=abs(Gamma)).

Now, reading TL theory texts can be confusing because of the sometimes subtle
swithes to and from an assumption of lossless line (under which rho cannot
exceed 1).

To complicate matters, roughly half the textbooks use rho instead of Gamma for
the complex reflection coefficient. You've got to be careful.

Since VSWR is the ratio of the magnitude of the voltage at a maximum in the
standing wave pattern to the magnitude of the voltage at a minimum in the
standing wave pattern, if we are to infer SWR at a point on a line (if that
makes sense anyway) from rho (which is a property of a point on a lossy
line), isn't the formula VSWR=abs(1+rho)/abs(1-rho) correct in the general
case (lossy or lossless line)?

The whole concept of VSWR gets flakey on a lossy line, and really loses its
meaning. It's often analytically convenient to define a quantity at a point
and call it "VSWR", although in the presence of loss it no longer means the
ratio of maximum to minimum voltage on the line. Since it's lost its original
meaning, it comes to mean just about anything you'd like. And the generally
accepted definition then is the equation you gave in your first paragraph.
That is, in the presence of loss, VSWR is something which is *defined* by that
equation, rather than the equation being a means of calculating some otherwise
defined property.

Under the right conditions and if loss is large enough, rho can be greater
than 1, in which case the VSWR as defined by the equation in the first
paragraph becomes negative. Again, this is no longer a ratio of voltages along
a line, but a quantity defined by an equation. If you alter the equation,
you're defining a different quantity. Now, there's no reason that your "VSWR"
definition isn't just as good as the conventional one (first paragraph
equation). But the conventional one is pretty universally used, and yours is
different, so if you're interested in communicating, it would be wise to give
it a different name or at least carefully show what you mean when you use it.

Given that rho cannot be negative (since it is the magnitude of a complex
number), the general formula can be simplified to VSWR=(1+rho)/abs(1-rho).

But it can be greater than one. See above.

Seems to me that texts almost universally omit the absolute operation on the
denominator without necessarily qualifying it with the assumption of lossless
line.

If VSWR=(1+rho)/abs(1-rho), then doesn't it follow that rho is not a function
of VSWR (except in the lossless line case where VSWR=(1+rho)/(1-rho) and
therefore rho=(VSWR-1)/(VSWR+1))?

Rho is never a function of VSWR. VSWR is a function of rho. Unlike actual VSWR
(that is, the ratio of maximum to minimum voltage along a line), the
reflection coefficient can be and is rigorously and meaningfully defined at
any point along a line, lossy or not.

Roy Lewallen, W7EL

Good response, Roy, but concerning rho and gamma to represent reflection
coefficient, I refer you to Reflections, Sec 3.1,

"Prior to the 1950s rho and sigma, and sometimes 'S' were used to represent
standing wave ratio. The symbol of choice to represent reflection coefficient
during that era was upper case gamma. However, in 1953 the American Standards
Association (now the NIST) announced in its publication ASA Y10.9-1953, that rho
is to replace gamma for reflection coefficient, with SWR to represent standing
wave ratio (for either voltage or current), and VSWR specifically for voltage
standing wave ratio. Most of academia responded to the change, but some
individuals did not. Consequently, gamma is occasionally seen representing
reflection coefficent, but only rarely."

Hope this clarifies any misunderstanding concerning the use of gamma for
reflection coefficient.

Incidentally, Roy, I recently mailed you a CD containing Laport's book, "Radio
Antenna Engineering." I'm wondering if you received it, or did it go astray?

Walt, W2DU

Walter Maxwell wrote:
Good response, Roy, but concerning rho and gamma to represent reflection
coefficient, I refer you to Reflections, Sec 3.1,

"Prior to the 1950s rho and sigma, and sometimes 'S' were used to represent
standing wave ratio. The symbol of choice to represent reflection coefficient
during that era was upper case gamma. However, in 1953 the American Standards
Association (now the NIST) announced in its publication ASA Y10.9-1953, that rho
is to replace gamma for reflection coefficient, with SWR to represent standing
wave ratio (for either voltage or current), and VSWR specifically for voltage
standing wave ratio. Most of academia responded to the change, but some
individuals did not. Consequently, gamma is occasionally seen representing
reflection coefficent, but only rarely."

Most interesting. I have on my library shelf 14 texts which deal
primarily or in a major way with electromagnetic waves and/or
transmission lines, and two with microwave circuit design. Of those,

8 (including both microwave design texts) use Gamma
4 use rho
2 use K
2 use k

If NIST's pronouncement had any effect at all, it was the opposite of
what was intended -- the four texts using rho were copyrighted in 1951,
53, 63, and 65; the 8 using Gamma were copyrighted in 1960 - 2000, 6 of
them after 1965. So it appears from my sampling that Gamma is becoming
more, not less, prevalant.

Hope this clarifies any misunderstanding concerning the use of gamma for
reflection coefficient.

I'm afraid it doesn't, unless my collection is very atypical. I don't
think it is, because it includes many of the classics.

Incidentally, Roy, I recently mailed you a CD containing Laport's book, "Radio
Antenna Engineering." I'm wondering if you received it, or did it go astray?

I did indeed, Walt, and please forgive me for not acknowledging your
very kind and thoughtful gift more promptly.

Roy Lewallen, W7EL

Walter Maxwell wrote:

Good response, Roy, but concerning rho and gamma to represent reflection
coefficient, I refer you to Reflections, Sec 3.1,

"Prior to the 1950s rho and sigma, and sometimes 'S' were used to represent
standing wave ratio. The symbol of choice to represent reflection coefficient
during that era was upper case gamma. However, in 1953 the American Standards
Association (now the NIST) announced in its publication ASA Y10.9-1953, that rho
is to replace gamma for reflection coefficient, with SWR to represent standing
wave ratio (for either voltage or current), and VSWR specifically for voltage
standing wave ratio. Most of academia responded to the change, but some
individuals did not. Consequently, gamma is occasionally seen representing
reflection coefficent, but only rarely."


Thanks for the information Walter. I must have a few "rare" texts that
use Gamma (Gamma to mean uppercase gamma) for the voltage reflection
coefficient.

I wonder if the recommendation / standard to which you refer is taken up
in any international standard?

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.

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

Owen

"Owen" wrote in message
...
Walter Maxwell wrote:

Good response, Roy, but concerning rho and gamma to represent reflection
coefficient, I refer you to Reflections, Sec 3.1,

"Prior to the 1950s rho and sigma, and sometimes 'S' were used to represent
standing wave ratio. The symbol of choice to represent reflection coefficient
during that era was upper case gamma. However, in 1953 the American Standards
Association (now the NIST) announced in its publication ASA Y10.9-1953, that
rho is to replace gamma for reflection coefficient, with SWR to represent
standing wave ratio (for either voltage or current), and VSWR specifically
for voltage standing wave ratio. Most of academia responded to the change,
but some individuals did not. Consequently, gamma is occasionally seen
representing reflection coefficent, but only rarely."


Thanks for the information Walter. I must have a few "rare" texts that use
Gamma (Gamma to mean uppercase gamma) for the voltage reflection coefficient.

I wonder if the recommendation / standard to which you refer is taken up in
any international standard?

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.

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

Owen

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.

Walt, W2DU

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

On 18 Jun 2005 14:20:34 -0700, wrote:

[snip]

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.


You better raise your deflection shield.

Go ahead Tom, you have the honor.