Encapsulated mechanically coupled fully-differential breathe-mode ring filters with ultra-narrow bandwidth

We present hermetically encapsulated, mechanically coupled, 20 MHz breathe-mode ring filters with ultra narrow bandwidths of 5.9 kHz and 8.9 kHz, which correspond to 0.029% and 0.044% bandwidth with less than 2.7 dB insertion loss. This is the narrowest percent bandwidth achieved by a mechanically coupled MEMS filter. The ability to attain an insertion loss this small for such a small percent bandwidth is made possible by employing encapsulated MEMS resonators with Q´s ~ 280,000. We also explore the effect of the coupling beam width on the filter bandwidth and experimentally demonstrate that the bandwidth is directly proportional to the width of the coupling beam. This work provides guidance for coupling beam design in future MEMS filters.