Dependence of SAW resonator 1/f noise on device size

Experiments were conducted with eight 450-MHz two-port SAW (surface acoustic wave) resonators of four different designs which demonstrate that a resonator's 1/f noise depends approximately inversely on the active acoustic area of the device. The ion-etched groove resonators were all fabricated from a single piece of quartz. The active acoustic areas of these devices ranged from approximately 1.7 /spl times/ 10/sup 4/ square wavelengths (3.4 /spl times/ 10/sup -2/ cm/sup 2/). The measured flicker noise levels varied from S/sub y/ (f = 1 Hz) = 3.4 /spl times/ 10/sup -23/ to 6.4 /spl times/ 10/sup -24//Hz, with the smallest-area devices exhibiting the highest noise levels. This observation is consistent with the theory that 1/f noise in acoustic resonators can be caused by localized, independent, velocity (or dimensional) fluctuations in the quartz. The fractional velocity fluctuations would have to have a magnitude close to S/sup v/ (f = 1 Hz) /spl ap/ 2 /spl times/ 10/sup -19//Hz in order to cause the observed level of frequency fluctuations. Additional experimental data in the literature suggest that the average distance between these localized fluctuations is on the order of 10 /spl mu/m.<>