On the application of multivariable synthesis to a class of distributed RC networks

The distributed
RC
networks considered in this paper involve connections of short-circuited and open-circuited
RC
transmission lines. Synthesis of driving-point immittances of these networks are considered. By using Wyndrum's classical transformations, driving-point functions are transformed into multivariable reactance functions, which correspond to impedances of transformerless networks that are positive multiples of
s_{i}
and
1/s_{i}
, where each impedance introduces a new variable. Some necessary conditions for realizability of such multivariable functions are given and sufficient conditions are derived in terms of a synthesis procedure.