對於現代工業而言，位置檢測是一項非常重要的技術，編碼器因應而生，根據量測原理可以分為機械、光學與磁性三類，近年來磁性編碼器的性能已經相當接近光學編碼器，而在工業的應用上，磁性編碼器具有諸多優勢，相同的成本可以獲得比光學編碼器更優良的性能，對於振動、粉塵的耐受度也比較高。在磁感測技術中，磁阻效應感測器具有高靈敏度與高穩定性，較小的能耗與體積，以及較短的響應時間，磁阻感測技術中又以穿隧磁阻效應感測器具有最好的性能。
本研究以背磁式穿隧效應磁阻感測元件為基礎，進行線性增量式編碼器之設計與分析，以高靈敏度及解析度之商用穿隧效應磁阻元件設計讀取頭，並進行編碼尺之磁路設計與解碼訊號之研究，再使用敏感度分析對編碼器的設計進行優化，最後根據結果製作出工程原型，經量測實驗驗證本研究所設計之編碼器絕對準確度為±12μm，且重複度為±3μm。

Compared with other magnetic sensing technologies, magnetoresistive sensors have higher sensitivity and stability, smaller energy consumption and volume, and shorter response time. Among magnetoresistive sensing technologies, tunneling magnetoresistance effect sensors have the best performance.
In this study, the linear incremental encoder design analysis is based on the tunneling effect magnetoresistive sensing element. Use high-sensitivity and high-resolution commercial TMR components to design the read head, and conduct research on magnetic circuit design and decoding signals. Finally, the encoder design is optimized by sensitivity analysis, and a verification prototype is actually produced according to the results. The measurement experiment can verify that the absolute accuracy of the encoder designed in this research is ±12μm, and the repeatability is ±3μm.

摘 要 i
Abstract ii
致謝 iii
目錄 iv
表目錄 viii
圖目錄 ix
第一章 簡介 1
1-1 研究背景 1
1-2 研究動機 2
1-3 研究目的 2
1-4 文獻回顧 3
1-4-1 編碼器 3
1-4-2 電磁感測技術 4
1-4-3 磁阻感測技術 5
第二章 基礎理論介紹 8
2-1 基礎電磁學原理 8
2-1-1 馬克士威方程式 8
2-1-3 磁阻效應 11
2-2 磁感測技術 11
2-2-1 霍爾效應感測器 12
2-2-2 異向磁阻感測器 13
2-2-3 巨磁阻感測器 14
2-2-4 穿隧磁阻效應感測器 15
2-3 編碼原理 16
2-3-1 增量式與絕對式編碼 16
2-3-2 面磁式與背磁式感測器 17
2-4 切割加工技術 18
2-4-1 金屬切割 18
2-4-2 雷射加工原理 20
2-4-3 固體雷射 22
2-4-4 氣體雷射 23
2-4-5 半導體雷射 24
2-4-6 光纖雷射 25
第三章 編碼器設計與模擬驗證 29
3-1 有限元素法分析 29
3-1-1 電腦輔助軟體 30
3-1-2 穩態分析 31
3-1-3 時變暫態分析 32
3-1-4 敏感度分析 32
3-2 模擬與分析結果 33
3-2-1 節距分析 34
3-2-2 氣隙分析 34
3-2-3 齒深與軛部厚度分析 34
第四章 編碼器工程原型製作與量測實驗 37
4-1 讀取頭 37
4-1-1 磁阻感測器 37
4-1-2 磁源 38
4-1-3 讀取頭組立 39
4-2 編碼尺 39
4-2-1 編碼尺材料 39
4-2-2 編碼尺加工 40
4-2-3 編碼尺組立 43
4-3 機構、動力系統與解碼器 44
4-3-1 機構 44
4-3-2 運動控制系統 45
4-3-3 解碼器 46
4-3-4 編碼器組立 47
4-4 量測實驗與結果 48
4-4-1 實驗環境建置 48
4-4-2 準確度 49
4-4-3 重複度 49
第五章 結論與未來展望 66
5-1 結論 66
5-2 未來工作 68
5-3 未來展望 70
參考文獻 71

[1] D. Kacprzak, T. Taniguchi, K. Nakamura, S. Yamada, and M. Iwahara, "Superposition of signal components during inspection of printed circuit boards by an eddy current testing probe with a solenoid pick-up coil," IEEE Transactions on Magnetics, vol. 37, no. 4, pp. 2794-2796, 2001, doi: 10.1109/20.951309.
[2] E. Eleftheriou, "Nanopositioning for Storage Applications," IFAC Proceedings Volumes, vol. 44, no. 1, pp. 2003-2011, 2011/01/01/ 2011, doi: https://doi.org/10.3182/20110828-6-IT-1002.03537.
[3] P. Ripka, M. Mirzaei, and J. Blažek, "Magnetic position sensors," Measurement Science and Technology, vol. 33, no. 2, p. 022002, 2021/12/09 2022, doi: 10.1088/1361-6501/ac32eb.
[4] G. Rieger, K. Ludwig, J. Hauch, and W. Clemens, "GMR sensors for contactless position detection," Sensors and Actuators A: Physical, vol. 91, no. 1, pp. 7-11, 2001/06/05/ 2001, doi: https://doi.org/10.1016/S0924-4247(01)00480-0.
[5] J. Rigelsford, "Sensors and Signal Conditioning 2/e," Sensor Review, vol. 22, no. 2, pp. 179-179, 2002, doi: 10.1108/sr.2002.08722bae.001.
[6] Y. Kim Ho and H. Kazuhiro, Electromagnetic Fields and Waves. IntechOpen, 2019.
[7] A. Fert, "The origin, development and future of spintronics," Uspehi fiziceskih nauk, vol. 178, no. 12, p. 1336, 2008, doi: 10.3367/UFNr.0178.200812f.1336.
[8] M. A. Khan, J. Sun, B. Li, A. Przybysz, and J. Kosel, "Magnetic sensors-A review and recent technologies," Eng. Res. Express, vol. 3, no. 2, 2021, doi: 10.1088/2631-8695/ac0838.
[9] J. E. Davies, J. D. Watts, J. Novotny, D. Huang, and P. G. Eames, "Magnetoresistive sensor detectivity: A comparative analysis," Applied physics letters, vol. 118, no. 6, p. 62401, 2021, doi: 10.1063/5.0038187.
[10] H. Lei, K. Wang, X. Ji, and D. Cui, "Contactless Measurement of Magnetic Nanoparticles on Lateral Flow Strips Using Tunneling Magnetoresistance (TMR) Sensors in Differential Configuration," Sensors (Basel), vol. 16, no. 12, pp. 2130-2130, 2016, doi: 10.3390/s16122130.
[11] M. Julliere, "Tunneling between ferromagnetic films," Physics Letters A, vol. 54, no. 3, pp. 225-226, 1975/09/08/ 1975, doi: https://doi.org/10.1016/0375-9601(75)90174-7.
[12] P. Noel, "Dynamical spin injection and spin to charge current conversion in oxide-based Rashba interfaces and topological insulators," 2019.
[13] W. Thomson, "On the Electro-Dynamic Qualities of Metals:--Effects of Magnetization on the Electric Conductivity of Nickel and of Iron," Proceedings of the Royal Society of London, vol. 8, pp. 546-550, 1856, doi: http://doi.org/10.1098/rspl.1856.0144.
[14] E. H. Hall, "On a New Action of the Magnet on Electric Currents," American journal of mathematics, vol. 2, no. 3, pp. 287-292, 1879, doi: 10.2307/2369245.
[15] E. Borgonovo and E. Plischke, "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, vol. 248, no. 3, pp. 869-887, 2016/02/01/ 2016, doi: https://doi.org/10.1016/j.ejor.2015.06.032.
[16] G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, "Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange," Phys Rev B Condens Matter, vol. 39, no. 7, pp. 4828-4830, 1989, doi: 10.1103/PhysRevB.39.4828.
[17] M. N. Baibich et al., "Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices," Phys Rev Lett, vol. 61, no. 21, pp. 2472-2475, 1988, doi: 10.1103/PhysRevLett.61.2472.
[18] C. F. Horig, S. H. Mao, and P. J. Wang, "Design and Analysis of Inductive Reluctance Position Sensor," in 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 1-4 Aug. 2018 2018, pp. 621-626, doi: 10.23919/PIERS.2018.8598214.
[19] W. Han, L. Minhao, C. Xin, C. Xindu, C. Nian, and X. Pan, "Novel linear optical encoder with absolute imaging position," in 2014 IEEE International Conference on Consumer Electronics - China, 9-13 April 2014 2014, pp. 1-2, doi: 10.1109/ICCE-China.2014.7029874.
[20] V. S. Kantamneni, N. Goyal, T. Werthy, and M. Ortner, "Stability characteristics of the double pole wheel for accurate magnetic speed sensing," in SENSORS, 2014 IEEE, 2-5 Nov. 2014 2014, pp. 1180-1183, doi: 10.1109/ICSENS.2014.6985219.
[21] I. Anastasiadis, T. Werth, and K. Preis, "Evaluation and Optimization of Back-Bias Magnets for Automotive Applications Using Finite-Element Methods," IEEE Transactions on Magnetics, vol. 45, no. 3, pp. 1332-1335, 2009, doi: 10.1109/TMAG.2009.2012618.