In this paper, we report a multi-ring disk resonator with elliptic spokes for compensating the aniso-elasticity of (100) single crystal silicon. The structural coupling between each ring segments can be controlled by replacing the straight beam spokes with the elliptic spokes. The degeneration of two n = 2 wineglass modes could be realized by optimizing the design parameters of the elliptic spokes. The mode-matched resonator could be obtained when the design parameter, aspect ratio of the elliptic spokes was 25/27. The proposed principle was demonstrated by both numerical simulation and experiment. A frequency mismatch as small as 1330 ± 900 ppm could be experimentally demonstrated, which was much smaller than that of the conventional disk resonator, which achieved as high as 30,000 ppm.
Keywords: (100) single crystal silicon; disk resonator; elliptic spoke; frequency mismatch; mode matched resonator; multi-ring structure.