Walter Maxwell wrote in
:

....
that rho is to replace upper case lambda as the standard symbol for
reflection coefficient, and SWR to represent standing wave ratio. Most

Chipman's formulae that you quoted work correctly if rho means the
magnitude of the complex reflection coefficient (rather than the
(complex) reflection coefficient as you say above).

The formulae were probably written when we used slide rules and worked
out the real and imaginary parts separately, whereas today with access to
tools that treat complex numbers as such, we can carry a complex value
through calculations as a single value then separate out the real an
imaginary parts at the end. There is also no real burden in treating Zo
as complex instead of the lossless / distortionless line approximation.

The different notation is painful, isn't it. I write Gamma to mean
uppercase-gamma, and use Gamma for the complex reflection coefficient,
rho for the magnitude of Gamma, lambda for wavelength, don't use Lambda
(I don't think), and gamma for the complex line propagation constant. It
think it is a fairly common convention, but if what you say above is
literally correct, it is not compliant with ASA Y10.9-1953.

Owen

On Apr 4, 8:38 pm, Walter Maxwell wrote:
On Thu, 05 Apr 2007 03:01:11 GMT, Owen Duffy wrote:
Walter Maxwell wrote in
:

...
R/Zo = (1 - rho squared)/(1 + rho squared - 2 rho cos phi)

X/Zo = (2 rho sin phi)/(1 + rho squared - 2 rho cos phi)
...

These appear to depend on Zo=Ro to be correct, perhaps they would be more
correctly expressed using Ro instead of Zo.

Owen

Owen, for historical accuracy, at least in the US, prior to 1950, rho, sigma, and S were used to represent
standing wave ratio. The symbol of choice used to represent reflection coefficient during that early era was
upper case lambda. However, in 1953 the American Standards Association (now NIST) announced in its publication
ASA Y10.9-1953, that rho is to replace upper case lambda as the standard symbol for reflection coefficient,
and SWR to represent standing wave ratio. Most of academia responded to the change, but a few have not. I
don't know about Australia, but in the US lambda is rarely seen as the symbol for reflection coefficient.

WRT Ro vs Zo, I was simply copying directly from Chipman, where Zo is routinely considered the characteristic
impedance of a transmission line, and where it's usually considered sufficiently low loss to the thought of as
Ro.

Walt

About Zo being reasonably approximated by Ro, or not:

I made a note to myself some time ago, and I believe it's reasonably
accurate, that neglecting dielectric loss, for a TEM line, given Zo =
Ro+jXo, then to a good approximation

Xo = -0.180*Ro*A*Vf/f

where A = line attenuation in dB/100ft
Vf = line velocity factor
f = frequency in MHz.

So for small diameter 50 ohm polyethylene dielectric line at 1.8MHz,
the worst case for most ham applications, Xo/Ro is about .18. For
that, I used 2.7dB/100ft for RG174 type line. That's getting to be
pretty significant, a ten degree phase angle away from purely
resistive. As Owen posted, it's so easy these days to deal with
complex numbers that you may as well just carry them all along. Given
the above formula, it's easy to figure the complex Zo for a line where
you know the nominal attenuation, the velocity factor, and the
frequency, and of course the nominal high frequency Zo value.

Cheers,
Tom

On Thu, 05 Apr 2007 01:50:52 GMT, "Wayne" wrote:

OK, I used to be able to do this years ago, but I can't seem to find the
right references now.

If an antenna reflection coefficient is measured at, for example. 0.333
at -100 degrees, how is Z calculated? I think I can do this with a smith
chart, but the result does not match my attempted calculations.

TIA
Wayne


Wayne, I just put the pertinent equations into an email addressed to , which I sent.
Is this your correct address? If not, please give me your correct address in an email to me at .

Walt, W2DU

Yes, that strange email address is correct. I received your word document.
Thanks very much.
Wayne
"Walter Maxwell" wrote in message
...
On Thu, 05 Apr 2007 01:50:52 GMT, "Wayne"
wrote:

OK, I used to be able to do this years ago, but I can't seem to find the
right references now.

If an antenna reflection coefficient is measured at, for example. 0.333
at -100 degrees, how is Z calculated? I think I can do this with a smith
chart, but the result does not match my attempted calculations.

TIA
Wayne


Wayne, I just put the pertinent equations into an email addressed to
, which I sent.
Is this your correct address? If not, please give me your correct address
in an email to me at .

Walt, W2DU