A frequency transformation for co-designed multi-passband/multi-embedded-notch RF filters

A class of multi-resonant RF filtering stage that exhibits a multi-band bandpass filtering transfer function with embedded in-band notches is presented. It is derived from the application of a composed lowpass-to-multi-passband/multi-stopband frequency transformation that converts the normalized lowpass prototype into the proposed multi-passband/multi-embedded-notch filtering cell. Thus, when employed in higher-order filtering networks, high-selectivity multi-band bandpass-filter (BPF) counterparts with embedded in-band stopbands are synthesized. Furthermore, two different approaches for out-of-band transmission-zero (TZ) generation in these type of filters to achieve sharp-rejection characteristics into them are detailed. The operational foundations of the engineered multi-passband/multi-embedded-notch filtering stage are described, along with several illustrative first-to-multi-order theoretical design examples with/without stopband TZs. Moreover, for experimental-demonstration purposes, a proof-of-concept microstrip prototype of a third-order dual-band BPF with two and one embedded notches in its lower and upper transmission bands, respectively, is manufactured and characterized.