Energy Trapping and Related Studies of Multiple Electrode Filter Crystals

Abstract

Summary Energy trapping is proposed as an explanation for the behavior of high frequency quartz filter crystals. Published elastic wave theory for lossless wafers includes a cut-off phenomenon: If the portion of the wafer surrounding the resonator has a cut-off frequency higher than the exciting frequency:, the resulting vibratory energy is essentially confined to the resonator with an energy distribution decreasing exponentially with distance away from the resonator. This exponential decay is not associated with energy loss but acts to trap the oscillating energy within a confined region. This energy trapping gives a basis for the high Qm observed for crystals mounted on low Q supports and for the low inter-resonator coupling observed for multi-resonator wafers. Measurements which support the energy trapping mechanism theory for exponential energy decay with distance have been obtained by varying inter-resonator spacing or distance from resonator to wafer edge These findings are applicable to improved design for high frequency filter crystals with both single and multiple electrode pairs.