Finite element analysis of monolithic filters

A method is presented in selecting the resonator configuration based on the results obtained from three-dimensional FEM analysis of monolithic filters. The primary concern in the design of monolithic filters for high frequency is the complexity involved in tuning control circuits in order to achieve small fractional bandwidths. The bandwidth of the resonating system depends on parameters such as the electrode thickness and external termination resistance. The performance of the monolithic filters as a function of the resonator geometry, acoustic gap and electrode thickness is studied. In addition to the electrical parameters for filters, vibration energies within the electrodes and the acoustic gap are used as relative measures for the filter performance. In particular, a 1 GHz AT-cut quartz, two-port monolithic filter was designed. Both free and forced vibration analyses were employed to select the physical parameters of the filter, such as the filter dimensions, electrode dimensions and acoustic gap. The frequency response from a forced vibration analysis was used to find the equivalent circuit parameters and S-parameters of the filter.