Hybrid Acoustic-Wave-Lumped-Element Resonators (AWLRs) for High-<formula formulatype="inline"><tex Notation="TeX">$Q$</tex> </formula> Bandpass Filters With Quasi-Elliptic Frequency Response

A new class of bandpass filters with quasi-elliptic frequency response, small physical size, and effective quality factors (Qs _eff ) of the order of 1000 are presented. They are based on novel hybrid acoustic-wave-lumped-element resonator (AWLR) modules that enable the realization of bandpass filters with fractional bandwidths (FBWs) that are much larger (0.91-5.1 k _t ² ) than the electromechanical coupling coefficient (k _t ² ) of conventional acoustic wave (AW) resonator filters that exhibit FBWs between 0.4-0.8 k _t ² . In addition, they exhibit Qs _eff that are 25-50 times larger than in traditional lumped-element filter architectures. Quasi-elliptic single-pole bandpass filters (one pole and two zeros) made up of commercially available one-port surface AW resonators and surface-mount-device components are manufactured and measured at 418 MHz. Various passbands with FBW between 0.07% and 0.4% and insertion loss below 1.25 dB (i.e., Qs _eff in the range of 1525-5150) are demonstrated. Second-order bandpass filters (two poles and four zeros) with 0.24% FBW and less than 1.15 dB of insertion loss (i.e., Qs _eff of 4000) are also shown to improve the passband selectivity and out-of-band rejection. These filters feature dynamic stopband characteristics by tuning the position of their transmission zeros. The operating principle, theoretical analysis, and design guidelines of the AWLR module, as well as a comparison with traditional all-AW ladder-type filters, are also reported. An original and rather simple RLC-circuit equivalent of AW resonators that facilitates the incorporation of spurious modes into a simple Butterworth-Van-Dyke model for a more accurate synthesis of AWLR-based filters is extracted from measured two-port S-parameters.