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 × 10 ⁴ square wavelengths (3.4 × 10^-2 cm² ). The measured flicker noise levels varied from S_y (f = 1 Hz) = 3.4 × 10^-23 to 6.4 × 10^-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^v (f = 1 Hz) ≈ 2 × 10^-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 μm