Optimized Trade-Offs and Flexibility in Microwave Filters: Leveraging Fractional Order Design

This letter presents a synthesis method for fractional-order filters, which transforms the conventional discrete filter order into a continuous number. The method introduces an additional degree of freedom, allowing for an optimized trade-off between insertion loss (IL) and out-of-band suppression (OBS). Furthermore, this flexibility supports the realization of specific topological requirements, such as double-dangling structures. As the order changes, the function obtains response forms similar to reduced Chebyshev and bounded Chebyshev. The proposed approach is validated through a straightforward synthesis process, demonstrated by the design of a 7.5th-order filter and a 6.2156th-order inline filter with two transmission zeros (TZs).