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

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


Hello Wayne,

The first reference I can give you is in "Theory and Problems of Transmission Lines," by Robert Chipman, in
Schaum's Outline Series, Page 128, Eqs. 7.9a and 7.9b.

If you don't have access to Schaum, I'll reconstitute the equations for you in Word, and send them via email.

In addition, I ran across these equations a day or so ago on this NG--I'll try to find them and direct you to
them on this NG.

Walt,W2DU

Walter, W2DU wrote:
"The first reference I can give you is in "Theory and Problems of
Transmission Lines" by Robert Chipman, in Schaum`s Outline Series, page
128 Eqs 7.9a and 7.9b."

Alas, I don`t have Chipman`s book. Another source is Terman`s 1955
"Electronic and Radio Engineering". He solves the differential equations
for a transmission line, starting on page 84 for solution of traveling
wave problems.

Best regards, Richard Harrison, KB5WZI

"Wayne" wrote in
news:0CYQh.11100$P84.5052@trnddc07:

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



The expression for Gamma that springs to mind is (Zl-Zo)/(Zl+Zo).

Rearranging the terms gives Zl=-Zo(Gamma+1)/(Gamma-1) doesn't it?

Owen

Owen Duffy wrote in news:Xns99097DA18D708nonenowhere@
61.9.191.5:

Rearranging the terms gives Zl=-Zo(Gamma+1)/(Gamma-1) doesn't it?

That probably looks better written as Zl=Zo(1+Gamma)/(1-Gamma)

Owen

On Thu, 05 Apr 2007 02:21:06 GMT, Owen Duffy wrote:

"Wayne" wrote in
news:0CYQh.11100$P84.5052@trnddc07:

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



The expression for Gamma that springs to mind is (Zl-Zo)/(Zl+Zo).

Rearranging the terms gives Zl=-Zo(Gamma+1)/(Gamma-1) doesn't it?

Owen

Owen, l just now sent Wayne the equations from Chipman, using the eq editor in Word.

In case others would like the equations I'll try to format them here without the Word editor.

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)

Walt, W2DU

Walter Maxwell wrote in
:

On Thu, 05 Apr 2007 02:21:06 GMT, Owen Duffy wrote:

"Wayne" wrote in
news:0CYQh.11100$P84.5052@trnddc07:

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



The expression for Gamma that springs to mind is (Zl-Zo)/(Zl+Zo).

Rearranging the terms gives Zl=-Zo(Gamma+1)/(Gamma-1) doesn't it?

Owen

Owen, l just now sent Wayne the equations from Chipman, using the eq
editor in Word.

In case others would like the equations I'll try to format them here
without the Word editor.

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)

Walt, W2DU

Walt, I take that to use rho to mean to magnitude of the reflection
coefficient Gamma.

My formula appears correct for Gamma, and the answer to Wayne's example
is 36-j27.

There is an uglier formula with tanh terms in it that gives the impedance
at a distance along a line with a given propagation constant... but it is
much more complicated to calculate than my expression when the distance
is zero.

Owen

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 and Walt--
Thanks for the info. Now things are working out right.
--Wayne

"Owen Duffy" wrote in message
...
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

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