Limits of performance of mechanical band-pass filters used in energy scavenging

In this note, the performance of mechanical band-pass filters to be used in energy scavengers is studied. Such a filter consists of an ensemble of cantilever beams where at the tip of each beam a mass, known as the proof mass, is mounted. Two questions are raised regarding the performance of the filter: (i) What is the best possible performance of the filter? (ii) How can a filter with such a performance be designed? In answering these questions, the limits of performance of the filter are determined. Knowledge of such limits leads to a systematic procedure for determining dimensions of the beams and masses of the proof masses of high-performance band-pass filters.