Exact Synthesis of Hybrid Acoustic–Electromagnetic Filters With Wideband Chebyshev Responses

Conventional synthesis methods used in the design of acoustic-wave (AW) microwave filters suffer from limited achievable fractional bandwidth (FBW) and weak out-of-band (OOB) rejection. This work presents the complete polynomial-based synthesis of a new class of hybrid acoustic–electromagnetic (hybrid-ACEM) filters to overcome both of the limitations by employing one or two electromagnetic (EM) resonators that are placed at purposefully selected locations within the design. In addition, cross-coupling mechanisms can help significantly with reducing the required electromechanical coupling coefficient in certain filter orders. Altogether, the proposed method can achieve much larger FBW values and stronger OOB rejection compared to the conventionally synthesized ladder AW filters. The effect of the finite quality factor of the EM resonators is analyzed. It is shown with the simulations that a filter for the 5g n77 band can be designed with AW resonators having
$k_{t}^{2}$
values of as low as 7.3%, while the quality factor values of the EM resonators are 50. As a proof of concept, a sixth-order hybrid-ACEM prototype with a center frequency of 2.66 GHz and an FBW of 11.2% designed and fabricated using AW resonators with
$k_{t}^{2}$
values of 3.5%. A comparison table shows larger achievable FBW-to-
$k_{t}^{2}$
ratios compared to similar studies in the literature.