A High-Performance Mechanically Coupled Quadruple Breathing Mode Ring Resonator

This letter reports a mechanically coupled quadruple breathing mode ring (QBR) resonator, in which four identical rings are located at the four corners of a square plate with proper design for achieving favorable mechanical coupling. The coupled QBR resonator is purposely designed and forced into vibrating in a square extensional (SE)-coupled-breathing ring (BR) mode by applying electrostatic forces to the electrodes distributed both within and surrounding the rings. Measurement results illustrate that the fabricated coupled QBR resonator has a high quality factor (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {Q}$</tex-math> </inline-formula>) of 322,110 and a low motional impedance of 18.12 k<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $</tex-math> </inline-formula> at its resonant frequency of 10.12 MHz. The measured frequency shift is less than ±67 ppm over the entire industrial temperature range of −40 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+ 85~^{\circ } $</tex-math> </inline-formula>C, with a turnover point near room temperature. Compared with a standalone SE mode or BR resonator, the reported coupled QBR resonator demonstrates a notable reduction in motional impedance and superior frequency-temperature stability, thanks to the large transduction area of the coupled QBR resonator and the excellent frequency-temperature stability of the SE mode resonator as the core coupling element. In light of its decent performance, the coupled QBR resonator has promising application prospects in the field of temperature-compensated MEMS oscillators (TCMOs). [2025-0054]