Cascade synthesis of a class of multivariable positive real functions

Abstract

Necessary and sufficient conditions are developed for the realization of a multivariable positive real function (MPRF) as the driving-point function of an extracted single-variable lossless two-port with a termination whose driving-point function is an MPRF in the rest of the variables as the load. Conditions are also obtained for the case when an extraction of a lossless two-port is possible in either of the two variables <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_{i}</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p_{j}</tex> .