非線性對微機械共振式開關穩定性影響之研究

A Study on the Influence of Nonlinearity on Stability of Micromechanical Resoswitches

蔡淳樸(Chun-Pu Tsai)

指導教授 ： 李尉彰

國立臺灣大學/工學院/應用力學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201900685

摘要

非線性操作由於其上轉換(up-conversion)的頻率或相位噪音將使得元件輸出訊號精確度下降，因此大部分微機電共振元件皆避免操作於非線性響應。然而，近期研究發現在非線性頻譜響應中出現的分叉點(或稱跳點)(bifurcation point or jump point)，由於具有(1)較好的訊號雜訊比與(2)較低的振幅-頻率轉換與相位-頻率轉換(phase frequency conversion)，反而具有較好的短時區頻率穩定度，目前已有文獻探討電性與機械性非線性對穩定度之影響。有別於此，本論文首次透過實驗量測探討一靜電力驅動共振式開關操作於「非線性輕敲模式(nonlinear tapping mode)」下與頻率穩定性之關係。本論文測試元件基於互補式金屬氧化物半導體-微機電系統(CMOS-MEMS)製程平台及自行製作的共振式開關，其結構可統一表示為電容式靜電力驅動、共振器結構與抑動檔塊結構組成，操作於一機械性與電性非線性共存之響應狀態。在高度非線性下，共振器頻譜響應可觀測得四個分叉點—分別為機械性上、下分叉點與電性上、下分叉點。最終，系統於不同相位點之穩定度已透過艾倫偏差進行評估，實驗結果顯示(1)由於較低的振幅-頻率轉換與相位-頻率轉換，機械性上分叉點與電性上分叉點具有較好的穩定度；(2)比較起驅動電壓0.5 V下，在1.6 V時頻率穩定度可提升至2倍；(3)相較於結構組成或材料產生之機械非線性，非線性輕敲模式造成之機械性非線性與接觸材料性質、碰撞間距相關，並與驅動力有較強的相依性。此二結論提供更多設計參數，如高頻寬與低頻寬元件之操作最佳化設計，並將有助於相關元件之開發，例如：降低微機電振盪電路之相位雜訊、增加感測器之解析度，並可透過此非線性調整元件頻率。本論文最後將討論環境雜訊影響及相關解決方案並提出未來研究發展方向。

關鍵字

互補式金屬氧化物半導體-微機電系統 ； 非線性 ； 艾倫偏差 ； 共振式開關 ； 頻率穩定性 ； 鎖相迴路

並列摘要

This thesis presents characterizations of the frequency stability of micromechan-ical clamped-clamped beam resonators operated under nonlinear tapping mode. Unlike traditional operation of MEMS resonators, which prefers linear operation for better frequency stability, nonlinear operation, as recently being demonstrated in several ap-plications, could in fact improve the frequency stability in some circumstances. This work extends the topic further by investigating MEMS resonators under highly non-linear tapping mode—that essentially perform as resonant switches, i.e., resoswitch-es.The resoswitches used in this work are manufactured by both CMOS-MEMS fabri-cation process and in-house developed SOI process. In general, a resoswitch consists of the capacitively driven input scheme, the core vibrating structure, and the output stop-per configuration. The resonant system operates in a combined electrical and mechan-ical nonlinear state, resulting in four bifurcation point in the frequency transmission response. From the classical point of view, although higher driving force yields higher Signal-to-Noise Ratio (SNR), which is helpful to enhance the precision of signal, the higher driving force also induces nonlinearity and increases the up-conversion phase/frequency noise. However, nonlinearities change the frequency-response curves and therefore some specific operation points—bifurcation point (so-called jump point)—would exhibit lower phase noise. Recently, the short-term stability has been shown to improve due to reduced amplitude-frequency conversion (A-f effect) and phase-frequency conversion at these points . Several frequency stability characteriza-tions of both electrical and mechanical nonlinearities in MEMS devices have also been studied previously. Differing from previously reported stability characterization of nonlinear MEMS devices, this work provides the first time experimental study of fre-quency stability on micromechanical resoswitches. The measurement results show that (1) two out of the four bifurcation points (i.e. top mechanical and electrical bifurcation point) performs lower short-term Allan deviation values—2× improvement has been achieved for a driving voltage of 0.5 V compared to 1.6 V; (2) the nonlinearity due to tapping operation depends on the driving voltage, gap distance, and contact material properties, providing other design parameters that might be helpful for the phase noise reduction/resolution enhancement in the relevant applications. Finally, this thesis dis-cusses some imperfections, especially in the measurement set-up such as high level input referred noise, DC polarization voltage noise and low frequency noise generated by commercially TIA, that need to be fixed as a future work. In addition, the work can be further extended for more driving conditions on the influence of nonlinearity on stability and for the stability at other bifurcation points.

並列關鍵字

Allan deviation ； CMOS-MEMS ； Frequency stability ； Nonlinearities ； Phase locked loop ； Resonant switches

參考文獻

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