Synthesis of Bandpass Filters with Assignable Complex Reflection Zeros Under Non-Normalized Frequency Domain

This paper presents a direct synthesis method for wideband bandpass filters with assignable complex reflection zeros (CRZs). The method constructs reflection polynomials with specified CRZ pairs directly in the non-normalized bandpass domain. Through an iterative procedure, the resulting polynomials retain real coefficients and can be mapped to bandpass prototypes without narrowband limitations. The synthesized prototypes, although containing several CRZs, can be simplified via matrix transformations and realized using conventional in-line topologies as standard Chebyshev filters. Several synthesis examples with wide bandwidths and different CRZs demonstrate the flexibility in adjusting both amplitude and group-delay responses through CRZ distribution.