On the determination of the terminal impedances of a nonuniform transmission line

The problem of determining the terminal impedance values of a lossless nonuniform transmission line is addressed. The transmission line is assumed to have discontinuities at input and output with local reflection coefficients
\Gamma_{1}
and
\Gamma_{2}
, respectively. A set of formulas is given which allows
\Gamma_{1}
and
\Gamma_{2}
to be recovered once high-frequency data for
S_{11}
(
\omega
) is specified; the formulas extend the generality of earlier theory to the case where
\Gamma_{1}
or
\Gamma_{2}
may be either positive or negative. It is also shown that
S_{11} (\omega)
) magnitude and phase information is necessary to uniquely determine
\Gamma_{1}
and
\Gamma_{2}
.