Reactive musings
Cecil got me thinking about writing exact expressions for the maximum
reactance for a given SWR, or equivalently for a given magnitude of
reflection coefficient. Barring clerical errors (and I've checked a
couple sample cases that seem OK), the following should be true.
Given r = magnitude of reflection coefficient in a system with a
real-valued reference impedance Z0, the maximum reactance will occur
when the reflection coefficient is
Rho = [2*r^2 + j*r*(1-r^2)]/(1+r^2)
Minimum reactance is obviously the complex conjugate of that.
The corresponding impedance is
Z = Z0 * (1+r^2 + j*2*r)/(1-r^2)
This may be commonly available in texts, or otherwise well known, but
I don't recall seeing it before, so thought I'd post it.
(Maximum and minimum resistance should be obvious)
Cheers,
Tom
|