Nonstandard Transmission Responses Enabling Feasible Microwave-Acoustic Ladder Filters

Microwave-acoustic ladder filter devices are enabled by piezoelectricity, but achievable filter responses are harshly constrained by material properties and complex resonator geometries. While a response depicting an equiripple return loss (RL) is known to provide the highest out-of-band (OoB) rejection, such response might not be feasible after considering material-related constraints, due to footprint limitations or to an excess of helper reactive elements to be implemented in the laminate. This article explores how the ladder filter structure composed of acoustic wave (AW) resonators can trade the location of reflection zeros (RZs) of the transfer function in exchange for greater flexibility to accommodate technological constraints, such as the electromechanical coupling coefficient. This work proposes to move away from the classical generalized Chebyshev (GC) response toward a solution space defined by nonstandard transmission responses. For this purpose, two methods based on a rigorous and accurate filter synthesis methodology are proposed to deal with the arrangement of RZs. The first proposes detuning the RZs along imaginary axis producing a non-equiripple (NE) response, while the second proposes arranging the RZs in the complex plane. This arrangement on the complex plane is carried out in such a way the device shows an equiripple RL but depicting shallow RZs in comparison with the deep ones of the Chebyshev response. Two synthesis examples validate the proposal reaching filters where all resonators require a common electromechanical coupling coefficient, while the ideal equiripple response would require resonators made of different materials, and so, the use of external reactive elements. The solution that in which RZs are arranged into the complex plane depicts an OoB rejection close to that achievable with an ideal equiripple response.