本論文利用In-house製程平台完成耦合式高階模態壓電支撐換能器結構共振器及振盪器的設計。該設計以壓電效應為基礎，設計出高品質因子、低運動阻抗及雜散模態之耦合式高階模態支撐傳感器拓樸之共振器，並且運用全域且平衡式的差動驅動與感測，有效的抑制雜散模態，提高訊號雜訊比。
於50 Ω開迴路量測中，最佳長寬比之二階寬度伸縮模態共振器品質因子約為6100、運動阻抗約為81 Ω，而耦合式高階模態共振器品質因子約為5400、運動阻抗達到31 Ω。而在50 Ω閉迴路測量中，最佳長寬比之寬度伸縮模態振盪器相位雜訊在1 kHz 偏移頻率及1 MHz偏移頻率取紀錄點分別為 -118.95 /-134.14 dBc/Hz，而艾倫偏差最低點為79 ppb，耦合式高階模態振盪器相位雜訊在1 kHz 偏移頻率及1 MHz偏移頻率取紀錄點分別為 -117.75 / -133.54 dBc/Hz，而艾倫偏差最低點為52 ppb，在商用被動電路實現振盪器進行相位雜訊量測之結果為，最佳長寬比之寬度伸縮模態振盪器相位雜訊在1 kHz 偏移頻率及1 MHz偏移頻率取紀錄點分別為 -101 / -144 dBc/Hz，而耦合式高階模態振盪器相位雜訊在1 kHz 偏移頻率及1 MHz偏移頻率取紀錄點分別為 -124 / -160 dBc/Hz。
本論文成功地驗證利用支撐傳感器耦合高階單晶矽共振器可以有效地提升系統之品質因子、降低運動阻抗，進而讓其振盪器的相位雜訊可以有效地降低，而在量測中可以使用差動手法，有效地抑制散模態，提升訊雜比。未來將以對於耦合式高階模態共振器進行更完整的優化，選擇更高的動態等效質量之共振器，以利提升整體共振器之品質因子，降低振盪器之相位雜訊。

This work presents a design of a coupled higher-order mode piezoelectric Support- Transducer Topology resonator and oscillator by using an in-house processing platform. The design is based on the piezoelectric effect. Additionally, this work completes the design of the coupled higher-order mode resonator with increase of the quality factor, decrease of the motional, and suppress the spurious mode. The design allows to operate in a balanced differential driving and sensing mode. This approach effectively suppresses spurious modes and enhances the Signal-to-Noise Ratio.
In the 50 Ω opened-loop measurement, the quality factor of second-order Width Extensional mode resonators with optimal aspect ratios is 6100, with a motional resistance of 81 Ω. For the coupled higher-order mode resonator, the quality factor is about 5400, and the motional resistance reaches 31 Ω. In the 50 Ω closed-loop measurement, the phase noise of the optimal aspect ratio Width Extensional mode oscillator at 1 kHz and 1MHz frequency offset are recorded at -118.95 / -134.14 dBc/Hz, with the Allan deviation of 79 ppb. The phase noise of the coupled higher-order mode oscillator at the same frequency offsets is -117.75 / -133.54 dBc/Hz, with the Allan deviation of 52 ppb. The phase noise measurement results for oscillators implemented using commercial passive circuits are as follows. For the width-extensional mode oscillator with the optimal aspect ratio, the phase noise values at 1 kHz and 1MHz frequency offset are recorded at -101 / -144 dBc/Hz. In contrast, for the coupled higher-order mode oscillator, the phase noise values at 1 kHz and 1 MHz frequency offsets are recorded at -124 / -160 dBc/Hz.
This work successfully demonstrates that utilizing Support Transducer Topology coupled a Single Crystal Silicon higher-order mode resonator is able to effectively enhance the quality factor and reduce the motional resistance, which can decrease the phase noise of the oscillator. Measuring in differential driving and sensing mode can suppress spurious modes and improve the Signal-to-Noise Ratio. In the future, further comprehensive optimization will be conducted for the coupled high-order mode resonator. Higher dynamic and equivalent mass resonators will be selected to enhance the overall quality factor of the resonator, thereby reducing the phase noise of the oscillator.

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