A semi-analytical procedure to describe lossless two-ports with mixed lumped and distributed elements

In this study, the construction problem of two-variable scattering functions which characterize lossless two-ports consisting of commensurate transmission lines and low-pass type lumped reactance two-ports is considered. Based on the canonic representation of scattering parameters a semi-analytical procedure to generate the descriptive polynomials of mixed element cascaded networks is proposed. The basic idea in the description of the mixed element cascades is that of utilizing the topologic restrictions together with the unitary property of the scattering parameters. Based on the proposed approach, for a special class of lumped low-pass ladders with commensurate lines, explicit expressions for the coefficients of the two-variable descriptive polynomials are obtained.<>