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Vibration modes of a micromechanical square-plate resonator were studied using a scanning laser interferometer. The resonator consists of a square plate released from a silicon substrate and has its main resonance at 13.1 MHz. The resonator is designed to utilize a square-extensional vibration mode in which the vibrations mainly take place in the direction parallel to the surface of the plate. A special detection scheme was used to allow measurement of the in-plane vibrations in addition to the out-of-plane component detected by the interferometer. The measured vibration modes were compared to numerical finite-element simulations with good agreement. In particular, it was found out that the out-of-plane vibration field measured at the resonance frequency of the main mode is a superposition of a parasitic vertical vibration mode and the out-of-plane component of the main mode. Furthermore, the measurements revealed undesirable vibrations in the anchor regions indicating energy leakage from the resonator causing additional losses. The quality factors of the vibration modes were also determined from the laser-probe measurements and they agree quite well with those determined from electrical measurements.
A novel surface acoustic wave filter on a leakywave substrate is studied. It features a hiccup-type resonance occurring around a distributed gap between two long interdigital transducers. Compared to a classical coupled resonator filter, it enables a relatively narrow passband (1% to 2% of center frequency) with low insertion loss, steep skirts, and improved suppression levels. The structure consists of long transducers having the number of fingers greater than 1=K 2 and 1= , where K 2 is the coupling coefficient of the substrate material and is the reflectivity per wavelength, separated with short transducer sections constituting a distributed gap. A strong, localized resonance is formed in the gap region, in addition to the resonance arising in the long structures-hence, the name doubleresonance filter. The substrate studied here is 42 -rotated lithium tantalite. We show experimental results for both single-ended and unbalanced-to-balanced filters at 1.6 GHz, having a minimum insertion loss of 1.07 dB, suppressions of 30 dB, and absolute ;3-dB bandwidth of 29 MHz (1.9% of the center frequency). For the balanced device, the amplitude imbalance over the passband ranges from ;0.6 dB to 2 dB and the phase imbalance from 1 to 4.5 . Furthermore, we have measured the acoustical power distributions using a scanning laser interferometer, and we compare these results with the profiles simulated using a coupling-of-modes model.
Vibrations in a micromechanical 13.1 MHz bulk acoustic mode silicon resonator have been imaged with a scanning Michelson laser interferometer. A novel detection scheme utilising the Michelson interferometer is developed, which enables imaging the in-plane vibrations in addition to the out-of-plane component. The novel imaging technique is demonstrated by measuring the vibrations of the extensional and Lamé modes in a square plate resonator.
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