Calculation of radiated electromagnetic power from bulk acoustic wave resonators

A general technique for calculating the radiated electromagnetic fields from an electrically small bulk acoustic wave (BAW) resonator in the vicinity of acoustic resonance is presented. The BAW resonator is analyzed as an electrically small microstrip antenna on a piezoelectric substrate. By the application of the surface equivalence principle, the device is replaced by equivalent sources. The radiated far fields found from the equivalent sources are integrated over the upper half plane to determine the total amount of radiated electromagnetic (EM) power as a function of frequency. The result is general enough to characterize the EM radiation from arbitrarily shaped metallizations, and the antenna pattern and polarization of the radiation may also be determined. The theoretical results are experimentally confirmed by measuring the radiated EM power spectrum from lithium niobate and quartz resonators