Single-Ended Transmission Path Measurements

New time-domain formulas for the attenuation dispersion
d\alpha/ d\omega
and group delay dispersion
d^{2}\phi/d\omega^{2}
of a transmission path are derived. It is shown how they can be used to measure
d\alpha/d\omega
and
d^{2}\phi/d\omega^{2}
accurately. The formulas involve only output quantities and thus can be used for measurements on very long transmission paths, where the input and output are not simaltaneously accessible.