US Patent 9166552 Filter and duplexer

A filter includes one or a plurality of parallel resonators coupled in parallel and one or a plurality of a film bulk acoustic resonators coupled in series, the film bulk acoustic resonator having a substrate, a lower electrode, a piezoelectric membrane, and an upper electrode, wherein: at least one of the lower electrode and the upper electrode has a thick membrane region having a thickness larger than that of a center portion of a resonance region at an edge of the resonance region, the resonance region being a region where the lower electrode and the upper electrode face with each other through the piezoelectric membrane; and a width of the thick membrane region is smaller than a wavelength of an acoustic wave propagating in a direction crossing a thickness direction of the piezoelectric membrane.