本研究提出一種應用正弦脈寬調變概念於薄型軸向磁阻式解角器之平面轉子設計方法。相較於傳統軸向磁阻式解角器利用曲面轉子改變氣隙長度，本研究將轉子改為平面挖孔結構，並以正弦脈寬調變概念將理想正弦磁導分布轉換為離散化之導磁區域與挖孔區域，使轉子旋轉時之有效磁通面積隨角度變化，進而產生與轉子位置相關之兩相感應訊號。
為提升挖孔轉子之高速機械穩定性，本研究亦於挖孔區域導入蜂巢狀支撐結構。研究中首先建立簡化等效磁路模型，用以初步分析轉子幾何對磁通、磁交鏈與感應電壓波形之影響，並透過三維有限元素模擬驗證其電磁特性與結構可行性。模擬流程包含取得兩相感應電壓、同步解調、低通濾波、反正切角度解算，接著進行快速傅立葉分析、總諧波失真與位置誤差分析，以評估不同平面轉子設計對訊號品質與解角器性能之影響。
模擬與實作驗證結果顯示，實測總諧波失真與模擬結果相近，但因實作定子軛部磁路不對稱造成較明顯的直流偏移，使位置誤差均方根增加。後續將正弦脈寬調變參考波由半週期改為完整週期後，總諧波失真與位置誤差均方根可明顯降低。結果顯示，正弦脈寬調變平面轉子具備應用於薄型磁阻式解角器之可行性，透過定子軛部修正、轉子幾何參數與蜂巢結構最佳化，可能有辦法進一步提升性能。

This thesis proposes a thin axial-flux variable reluctance resolver using a planar rotor designed with the concept of sinusoidal pulse width modulation (SPWM). Unlike conventional axial-flux variable reluctance resolvers that rely on a three-dimensional curved rotor to modulate the axial air-gap length, the proposed design uses a planar perforated rotor to modulate the effective magnetic flux area. The SPWM concept is applied to convert an ideal sinusoidal permeance distribution into discrete magnetic and non-magnetic regions. A honeycomb support structure is also introduced into the perforated region to improve the mechanical stability of the rotor under high-speed operation. An equivalent magnetic circuit model, three-dimensional finite element analysis (FEA), structural analysis, and prototype experiments are conducted to verify the feasibility of the proposed design. The initial SPWM planar rotor achieved a simulated total harmonic distortion (THD)of 12.21% and a root mean square position error of 0.8482°. The prototype test showed a similar THD of 11.95%, but the root mean square position error increased to 1.88° due to a significant direct-current offset caused by magnetic asymmetry in the stator yoke. By changing the SPWM reference from a half-period waveform to a full-period waveform, the simulated THD was reduced to 2.636%, and the root mean square position error was reduced to 0.338°.

[1] Corporation, A. K. M. "Hall Sensors." Retrieved July 3, 2026, from https://www.akm.com/global/en/products/hall-sensor/.
[2] Company, E. P. (2017). "Encoders 101: An Introduction to Encoders." Retrieved July 3, 2026, from https://www.youtube.com/watch?v=N5EMTY70PX8.
[3] Company, E. P. "Model 925 Absolute Accu-Coder®." Retrieved July 3, 2026, from https://www.encoder.com/model-925.
[4] Corporation, A. K. M. "#05 Principle and advantages of magnetic encoder." Retrieved July 4, 2026, from https://www.akm.com/global/en/products/rotation-angle-sensor/tutorial/magnetic-encoder/.
[5] RLS. "Orbis™." Retrieved July 4, 2026.
[6] Gsuns. "磁阻式旋變74XU7105B-旋轉變壓器." Retrieved July 4, 2026.
[7] Kadam, A. (2026). "Global Resolvers Market 2024–2033." Retrieved July 1, 2026, from https://www.custommarketinsights.com/report/resolvers-market/#.
[8] Sharma, R. (2025). "Resolver Market." Retrieved July 1, 2026, from https://dataintelo.com/report/resolver-market.
[9] Kronacher, G. (1957). "Design, performance and application of the Vernier resolver." The Bell System Technical Journal 36(6): 1487-1500.
[10] Carlstein, J. (1964). Variable reluctance hall effect resolver. U. S. P. a. T. Office. United States: 5.
[11] Ringland, W. L., et al. (1972). ROTARY INDUCTOR. U. S. P. a. T. Office. United States: 22.
[12] Nagarkatti, A., et al. (1986). Harmonically graded airgap reluctance-type rotating electric resolver. U. S. P. a. T. Office. United States: 13.
[13] Ishizaki, A., et al. (1995). "Theory and Characteristics on Novel Variable Reluctance 1X Resolver." IEEJ Transactions on Industry Applications 115(5): 598-604.
[14] Ge, X., et al. (2015). "A Novel Variable Reluctance Resolver with Nonoverlapping Tooth–Coil Windings." IEEE Transactions on Energy Conversion 30(2): 784-794.
[15] Ge, X., et al. (2016). "A Novel Variable Reluctance Resolver for HEV/EV Applications." IEEE Transactions on Industry Applications 52(4): 2872-2880.
[16] Ge, X. and Zhu, Z. Q. (2016). "A Novel Design of Rotor Contour for Variable Reluctance Resolver by Injecting Auxiliary Air-Gap Permeance Harmonics." IEEE Transactions on Energy Conversion 31(1): 345-353.
[17] Xiao, L., et al. (2018). Optimization of a Reluctance Resolver. 2018 Asia-Pacific Magnetic Recording Conference (APMRC).
[18] Xiao, L., et al. (2020). "An Optimization Approach to Variable Reluctance Resolver." IEEE Transactions on Magnetics 56(2): 1-5.
[19] Xiao, L. and Bi, C. (2021). "An optimization approach of rotor contour for variable reluctance resolver." CES Transactions on Electrical Machines and Systems 5(3): 257-261.
[20] Xiao, L. and Bi, C. (2019). Optimization of Absolute Variable Reluctance Resolver with Taguchi and FEM. 2019 22nd International Conference on Electrical Machines and Systems (ICEMS).
[21] 黃偉宸，「積層製造應用於軸向型磁阻解角器之設計」，碩士論文，國立成功大學電機工程學系電機設計與驅動產業碩士班，2022年9月。
[22] Tootoonchian, F. and Nasiri-Gheidari, Z. (2016). An optimized axial flux variable reluctance resolver with concentric windings. 2016 24th Iranian Conference on Electrical Engineering (ICEE).
[23] Chang, T. W., et al. (2023). "Additive Manufacturing High Fault-Tolerant Axial Flux Variable Reluctance Resolver." IEEE Transactions on Magnetics 59(11): 1-5.
[24] Sun, L., et al. (2022). "A Slotless PM Variable Reluctance Resolver With Axial Magnetic Field." IEEE Transactions on Industrial Electronics 69(6): 6329-6340.
[25] Sun, L., et al. (2024). "The Leaf-Style Axial Field Variable Reluctance Resolver With an Efficient Decoding System." IEEE Transactions on Industrial Electronics 71(9): 11581-11591.
[26] TAMAGAWA SEIKI CO., L. (2026). Smartsyn-Rotation angle sensor with excellent environmental resistance performance Brushless resolver, TAMAGAWA SEIKI CO., LTD.
[27] TAMAGAWA SEIKI CO., L. (2026). Singlsyn-VR Type Resolver, TAMAGAWA SEIKI CO., LTD.
[28] Gross, G., et al. (2005). All-digital resolver-to-digital conversion. 2005 European Conference on Power Electronics and Applications.
[29] Sarma, S., et al. (2008). "Software-Based Resolver-to-Digital Conversion Using a DSP." IEEE Transactions on Industrial Electronics 55(1): 371-379.
[30] Analog Devices, I. (2021). AD2S1210: Variable Resolution, 10-Bit to 16-Bit R/D Converter with Reference Oscillator Data Sheet, Analog Devices, Inc.
[31] Kuntz, S., et al. (2022). "Harmonic analysis of the arctangent function regarding the angular error introduced by superimposed Fourier series for application in sine/cosine angle encoders." Sensors and Actuators A: Physical 344: 113585.
[32] Szymczak, J., et al. (2014). "Precision Resolver-to-Digital Converter Measures Angular Position and Velocity." Analog Dialogue 48(3): 1-6.
[33] Clarke, D. J., et al. (2023). "A systematic numerical and experimental study into the mechanical properties of five honeycombs." Composites Part B: Engineering 264: 110895.
[34] Jez, R. and Polit, A. (2014). Influence of air-gap length and cross-section on magnetic circuit parameters. Proc. COMSOL Conf.
[35] 南京艾浮坦電子科技有限公司 (2014). 旋變角度採集模塊DF2031使用說明: 5.
[36] Prakht, V., et al. (2025) Traction Synchronous Motors with Rotor Field Winding: A Literature Review. World Electric Vehicle Journal 16, 633 DOI: 10.3390/wevj16110633