Accurate Formula for Quality Factor Q of Thin Film Bulk Acoustic Resonators with Close Series and Parallel Resonance Frequencies

This paper presents improved formula accuracy for quality factor Q of thin film bulk acoustic resonators (FBARs) with close series and parallel resonance frequencies. Traditionally, the series and parallel resonance behaviors are treated independently. The FBAR piezoelectric coupling coefficient is only a few percentages with the series and parallel frequencies close enough to influence each other. The FBARs with two-port configuration are fabricated using silicon bulk micro-machining technology. Including the FBAR transmission lines are analyzed to probe their characteristics using a network analyzer. The signal power loss of the transmission lines is modeled to characterize the FBARs using two-port S parameter measurement data.