A multivariable array and its applications to ladder networks

A multivariable array is developed by means of which the realizability conditions for the
n
-variable low-pass ladder network are obtained. By means of suitable transformations, other types of
n
- variable ladder networks are derived. The following applications are discussed. 1) The
n
-variable ladder networks so obtained can be replaced by lumped reactive elements and noncommensurate short-circuited and open-circuited stubs. 2) An equivalence relation between the cascade of unit elements (UE's) separated by series lumped inductors on one side and shunt lumped capacitors on the other side and the two-variable low-pass ladder network (TLPL) is established.