2D mode-matching theory is used to explore differences between the two types of thin-film bulk-acoustic wave (BAW) resonator, based on membrane (FBAR) and Bragg reflector (SBAR). Issues of mode-conversion and energy-trapping are explored. Lateral acoustic coupling is addressed in the presentation. The most significant finding is that the SBAR reflector plays a significant part in the reduction of spurious responses close to the fundamental frequency of BAW resonators and filters.Index Terms -Bulk acoustic wave devices, thin-film devices, piezoelectric resonator filters, mode matching methods.