Phase Correction of Asymmetrical Chebyshev Polynomials for Extracted-Pole Fully Canonical Filters

When the characteristic rational functions of a filtering response have been synthesized under a symmetry condition, one asymmetrical distribution of transmissions zero along an in-line fully-canonical topology will cause the occurrence of one uneven admittance inverter in the main-line. This introduces some limitations to transform into a ladder network. Despite circuital transformation can be used to accommodate technology and topology, it is usual that extra reactive elements are necessary to implement phase shifts required for reaching a full synthesis. This work introduces a method capable to identifying a phase correction to equalize all the admittance inverters in the main path to the same value. It has been demonstrated that a suitable pair of phase values can be accurately estimated using the developed hyperbolic model and whose main parameters can be obtained from the transmission and reflection scattering parameters.