On the time-domain realizability conditions for cascaded transmission-line networks

This paper considers the time-domain realizability conditions for networks consisting of cascaded sections of uniform lossless transmission lines. It is first demonstrated that the necessary and sufficient conditions for a sequence of real numbers to represent the amplitude coefficients of the reflected impulse response of such a network are equivalent to those for the existence of a solution to a given set of equations. Subsequently, it is proved that a sufficient condition is that a certain symmetric matrix be positive semidefinite.