Characterization and synthesis of homogeneous two-variable reactance functions

It is shown in this paper that Homogeneous Two-variable Reactance Polyno- mials (HTRP's) can be expressed as a product of linear factors in the two-variables. Further, a Homogeneous Two-variable Reactance Function (HTRF) can be characterized in terms of the alteration property involving the coefficients of the linear factors of the HTRP in the numerator and denominator. Synthesis procedures for HTRF's are discus- sed; these realizations follow from the single variable RL- or RC-functions associated with a HTRF. Additional properties of HTRF, which will enable us to generate Two- variable Positive Real Functions and Two-variable Reactance Functions are also discussed.