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