本論文旨在解決傳統微波感測器動態範圍受限（<180°）與多變數解耦高度依賴複雜演算法之瓶頸，提出創新之「雙路徑多功能微波感測系統」。
本研究有效結合層疊式三環互補式開口諧振環形共振腔（Stacked TCSRR）與互補式閉合圓環共振腔（CCRR）。針對角度感測， 透過TCSRR第三環正交配置引入非對稱性，有效延後了頻率折返現象，將無模糊量測之單調區間拓展至 200°， 單一架構平均角度靈敏度達 19.88 𝑀𝐻𝑧/°，快速變動區更上升至 31.68 𝑀𝐻𝑧/°。
在雙路徑系統中，平均角度靈敏度因空間分集之工程權衡調整為 5.63 𝑀𝐻𝑧/°，但主導模態 𝑓𝑧1,𝑇𝐶𝑆𝑅𝑅 仍穩定維持涵蓋 200° 之連續單調頻偏。更關鍵的是，本系統達成了免演算法之「硬體級互斥解耦」：純旋轉時，CCRR 處於物理休眠以確保角度量測純淨；當發生水平位移時，𝑓𝑧1,𝑇𝐶𝑆𝑅𝑅 因金屬屏蔽導致其共振邊界被破壞而使特徵大幅衰退，整體頻率響應改由 𝑓𝑧,𝐶𝐶𝑅𝑅 主導，精準追蹤 2 𝑚𝑚 至 6 𝑚𝑚 之水平位移，平均位移靈敏度高達 270𝑀𝐻𝑧/𝑚𝑚。
總結而言，本研究將角度感測動態範圍擴展至 200°，並透過硬體級互斥機制實現角度與水平位移之獨立量測，無須額外解調演算法。此架構可為工業 4.0 機台狀態監控提供一種低成本之射頻感測方案。

This thesis proposes an innovative "dual-path multi-function microwave sensor system" to address the bottlenecks of limited dynamic range (typically < 180°) and the high reliance on complex algorithms for multi-variable decoupling in traditional microwave sensors.
This research effectively integrates a stacked triple complementary split-ring resonator (Stacked TCSRR) and a complementary circular ring resonator (CCRR). For angular sensing, structural asymmetry is introduced by orthogonally orienting the gaps of the TCSRR's third rings. This design effectively delays the frequency fold-back phenomenon, extending the monotonic range of unambiguous measurement to 200°. The single-architecture average angular sensitivity reaches 19.88 MHz/°, peaking at 31.68 MHz/° in the fast-varying region.
In the dual-path system, the average angular sensitivity is adjusted to 5.63 MHz/° due to spatial-diversity engineering trade-offs, but the dominant mode 𝑓𝑧1,𝑇𝐶𝑆𝑅𝑅 still stably maintains a continuous monotonic frequency shift covering the 200° range. More crucially, the system achieves an algorithm-free "hardware-level mutually exclusive decoupling": during pure rotation, the CCRR remains physically inactive to ensure pure angular measurement; when horizontal translation occurs, the resonance boundary of 𝑓𝑧1,𝑇𝐶𝑆𝑅𝑅 is disrupted by metal shielding, causing its features to severely degrade. The overall frequency response is instead dominated by 𝑓𝑧,𝐶𝐶𝑅𝑅, accurately tracking horizontal displacements from 2 𝑚𝑚 to 6 𝑚𝑚 with an average displacement sensitivity up to 270 MHz/mm.
In conclusion, this research extends the angular dynamic range to 200° and achieves independent, algorithm-free measurement of both rotational and horizontal displacements, providing a low-cost RF solution for Industry 4.0 condition monitoring.

[1] S. Hosseinzadeh, A. R. Mehrabad, M. R. Saviz, and M. Yousefi, "Microwave-based linear displacement sensors with via-less zero-order resonators," Sensors and Actuators A: Physical, p. 117273, 2025.
[2] Z. Mehrjoo, A. Ebrahimi, and K. Ghorbani, "Microwave resonance-based reflective mode displacement sensor with wide dynamic range," IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1–9, 2021.
[3] M. Hernandez-Aguila, J.-L. Olvera-Cervantes, A.-E. Perez-Ramos, and A. Corona-Chavez, "WiFi sensor node with high sensitivity and linearity based on a quarter-wavelength resonator for measuring crack width," IEEE Sensors Journal, vol. 23, no. 23, pp. 28883–28890, 2023.
[4] J.-M. Meza-Arenas, J.-L. Olvera-Cervantes, and A. Corona-Chavez, "High Linearity Microwave Displacement Sensor," IEEE Sensors Journal, vol. 24, no. 24, pp. 40819–40826, 2024.
[5] A. K. Jha, A. Lamecki, M. Mrozowski, and M. Bozzi, "A microwave sensor with operating band selection to detect rotation and proximity in the rapid prototyping industry," IEEE Transactions on Industrial Electronics, vol. 68, no. 1, pp. 683–693, 2020.
[6] M. Abdolrazzaghi and M. Daneshmand, "Multifunctional ultrahigh sensitive microwave planar sensor to monitor mechanical motion: Rotation, displacement, and stretch," Sensors, vol. 20, no. 04, p. 1184, 2020.
[7] A. K. Horestani, Z. Shaterian, and F. Martin, "Rotation sensor based on the cross-polarized excitation of split ring resonators (SRRs)," IEEE Sensors Journal, vol. 20, no. 17, pp. 9706–9714, 2020.
[8] A. K. Jha, N. Delmonte, A. Lamecki, M. Mrozowski, and M. Bozzi, "Design of microwave-based angular displacement sensor," IEEE Microwave and Wireless Components Letters, vol. 29, no. 4, pp. 306–308, 2019.
[9] P. Cheong and K. Wu, "Full-range CSRR-based angular displacement sensing with multiport interferometric platform," IEEE Transactions on Microwave Theory and Techniques, vol. 69, no. 11, pp. 4813–4821, 2021.
[10] A. K. Jha, A. Lamecki, M. Mrozowski, and M. Bozzi, "A highly sensitive planar microwave sensor for detecting direction and angle of rotation," IEEE Transactions on Microwave Theory and Techniques, vol. 68, no. 4, pp. 1598–1609, 2020.
[11] J. Naqui and F. Martín, "Angular displacement and velocity sensors based on electric-LC (ELC) loaded microstrip lines," IEEE Sensors Journal, vol. 14, no. 4, pp. 939–940, 2013.
[12] C. Teng, C. H. Chio, K. W. Tam, and P. Y. Lau, "An angular displacement microwave sensor with 360° dynamic range using multi-mode resonator," IEEE Sensors Journal, vol. 21, no. 3, pp. 2899–2907, 2020.
[13] C. Teng, C.-H. Chio, K.-W. Tam, and P.-Y. Lau, "Analysis of multimode circular cross-shaped resonator with asymmetric via and its application to microwave angular displacement sensor," IEEE Microwave and Wireless Technology Letters, vol. 33, no. 5, pp. 607–610, 2023.
[14] J.-J. Chen, W.-J. Wu, D.-W. Wang, W. Sun, and W.-S. Zhao, "A High-Linearity Planar Angular Displacement Sensor Based on Dual-Mode Tapered RingResonator," IEEE Microwave and Wireless Technology Letters, 2025.
[15] C. H. Chio, R. Gómez‐García, L. Yang, K. W. Tam, W. W. Choi, and S. K. Ho, "Directional‐coupler‐based microwave sensors for differential angular‐displacement measurement," International Journal of RF and Microwave Computer‐Aided Engineering, vol. 30, no. 10, p. e22338, 2020.
[16] C.-H. Chio, R. Gómez-García, L. Yang, K.-W. Tam, W.-W. Choi, and S.-K. Ho, "An angular-displacement microwave sensor using an unequal-length-bi-path transversal filtering section," IEEE Sensors Journal, vol. 20, no. 2, pp. 715–722, 2019.
[17] C. H. Chio, R. Gómez-García, L. Yang, K. W. Tam, W.-W. Choi, and S. K. Ho, "An angular displacement sensor based on microwave transversal signal interference principle," IEEE Sensors Journal, vol. 20, no. 19, pp. 11237–11246, 2020.
[18] P. Regalla and A. P. Kumar, "A microwave dielectric resonator based sensor for detecting both linear and angular displacements," in 2022 Asia-Pacific Microwave Conference (APMC), 2022: IEEE, pp. 533–535.
[19] S. Alam et al., "Dual functional liquid displacement and angular detection based on band stop response microwave sensor," IEEE Access, vol. 12, pp. 94861–94869, 2024.
[20] Z. Zhang et al., "Integrated Microwave Sensor for Simultaneous Angular and Linear Displacement Sensing Based on Hybrid Series–Parallel Wing Structure," IEEE Transactions on Microwave Theory and Techniques, 2025.
[21] D. M. Pozar, Microwave engineering. John wiley & sons, 2011.
[22] A. A. Saleh and A. S. Abdullah, "A novel design of patch antenna loaded with complementary split-ring resonator and L-shape slot for (WiMAX/WLAN) applications," Int. J. Wireless and Microwave Technologies, vol. 3, pp. 16–25, 2014.
[23] J. D. Baena et al., "Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines," IEEE transactions on microwave theory and techniques, vol. 53, no. 4, pp. 1451–1461, 2005.
[24] 王得舫, "線性地震儀使用八角形微波感測器結合倒單擺及折疊式機械架構應用於地震感測," 2023.
[25] J. Naqui, M. Durán-Sindreu, and F. Martín, "Modeling split-ring resonator (SRR) and complementary split-ring resonator (CSRR) loaded transmission lines exhibiting cross-polarization effects," IEEE Antennas and Wireless Propagation Letters, vol. 12, pp. 178–181, 2013.
[26] A. J. A. Al-Gburi, N. A. Rahman, Z. Zakaria, and M. Palandoken, "Detection of semi-solid materials utilizing triple-rings CSRR microwave sensor," Sensors, vol. 23, no. 6, p. 3058, 2023.
[27] J. Yang, G. Liu, and E. Hong, "A Differential Microwave Angular Displacement Sensor System Based on Magnetic LC Structure and Single-Frequency Phase Variation," IEEE Microwave and Wireless Technology Letters, 2026.
[28] N. Nikkhah, R. Keshavarz, M. Abolhasan, J. Lipman, and N. Shariati, "Highly sensitive differential microwave sensor using enhanced spiral resonators for precision permittivity measurement," IEEE Sensors Journal, vol. 24, no. 9, pp. 14177–14188, 2024.
[29] J.-K. Wu et al., "Microwave-sensor array for decoupling detection of distance, shape, dielectric, and morphology," IEEE Transactions on Instrumentation and Measurement, vol. 72, pp. 1–10, 2023.
[30] A. M. Albishi, M. K. El Badawe, V. Nayyeri, and O. M. Ramahi, "Enhancing the sensitivity of dielectric sensors with multiple coupled complementary split-ring resonators," IEEE Transactions on Microwave Theory and Techniques, vol. 68, no. 10, pp. 4340–4347, 2020.
[31] C.-H. Chio, K.-W. Tam, and R. Gómez-García, "Filtering angular displacement sensor based on transversal section with parallel-coupled-line path and U-shaped coupled slotline," IEEE Sensors Journal, vol. 22, no. 2, pp. 1218–1226, 2021.
[32] A. Banerjee, F. Fatima, N. K. Tiwari, and M. Akhtar, "Flexible printed electrically small microwave resonator for automated displacement tracking," Journal of Electromagnetic Waves and Applications, vol. 37, no. 17, pp. 1409–1424, 2023.
[33] Z. Zhang et al., "Microwave linear displacement sensors integrated with filtering antenna for simultaneous sensing and wireless communication," IEEE Transactions on Microwave Theory and Techniques, 2025.
[34] K. Ren et al., "A complementary split-ring resonator (CSRR)-based 2D displacement sensor," Symmetry, vol. 14, no. 6, p. 1116, 2022.
[35] S. Li, O. Alsalman, J. Huang, and C. Zhu, "In-plane and out-of-plane 2-D microdisplacement sensor based on a single microwave resonator with machine learning," IEEE Transactions on Microwave Theory and Techniques, vol. 73, no. 7, pp. 3939–3952, 2024.
[36] V.-M. Cante-Saloma, J.-L. Olvera-Cervantes, M. Tecpoyotl-Torres, and A. Corona-Chavez, "One-port and high-sensitivity angular displacement sensor based on a microwave quarter-wavelength resonator," IEEE Sensors Journal, 2025.
[37] V.-M. Cante-Saloma, J.-L. Olvera-Cervantes, and M. Tecpoyotl-Torres, "Single-Port and High-Linearity Angular Displacement Sensor based on a Microwave Angular Resonator and a Radial Stub," IEEE Sensors Journal, 2026.
[38] R.-C. Wang and C.-L. Yang, "Highly Sensitive CSRR-Based Angular Displacement Sensor with Extended Wide Dynamic Range," in 2026 IEEE MTT-S Radio Frequency Systems and Applications Symposium (IMS RFSA), 2026: IEEE, pp. 345–348.