{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T05:18:10Z","timestamp":1787980690565,"version":"build-2784847793"},"reference-count":146,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T00:00:00Z","timestamp":1787788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006141","name":"Military University of Technology","doi-asserted-by":"publisher","award":["531-000154-W600-22"],"award-info":[{"award-number":["531-000154-W600-22"]}],"id":[{"id":"10.13039\/501100006141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The operating frequency of a resonant oscillator is determined by the coupled behavior of the resonator, sustaining electronics, package, power supply, mounting conditions, and operating environment. Frequency stability is critical in sensor systems, where oscillators provide references for sampling, synchronization, phase-sensitive measurements, sensor fusion, and distributed sensing. This review examines how these factors affect the short- and long-term stability of quartz oscillators (XOs, TCXOs, and OCXOs) and microelectromechanical systems (MEMS) oscillators. Organized by physical cause rather than device type, the review covers temperature, including gradients and hysteresis, aging, acceleration, vibration, shock, pressure, humidity, power-supply and load variations, electric and magnetic fields, electromagnetic interference, and ionizing radiation. For each factor, the dominant degradation mechanisms and compensation methods are compared across both technologies. The comparison indicates that OCXOs retain an advantage in low-noise timekeeping over long averaging times, whereas advanced MEMS oscillators can approach quartz performance in selected operating regimes while offering smaller size, monolithic integration, and, in ruggedized products, 0.01 ppb\/g acceleration sensitivity and 20,000 g shock ratings. In the literature reviewed, appropriate measurement methods exist but are applied inconsistently across technologies. Oscillator selection should therefore be based on a comprehensive error budget covering all relevant environmental and system-level factors.<\/jats:p>","DOI":"10.3390\/s26175425","type":"journal-article","created":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T13:26:03Z","timestamp":1787837163000},"page":"5425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Frequency Stability Degradation in Quartz and MEMS Oscillators"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0079-1960","authenticated-orcid":false,"given":"Mariusz","family":"M\u015bcichowski","sequence":"first","affiliation":[{"name":"Institute of Optoelectronics, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5744-5981","authenticated-orcid":false,"given":"Pawe\u0142","family":"Kwiatkowski","sequence":"additional","affiliation":[{"name":"Faculty of Electronics, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-9303-0303","authenticated-orcid":false,"given":"Klaudia","family":"Majchrowicz","sequence":"additional","affiliation":[{"name":"Institute of Optoelectronics, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3085-013X","authenticated-orcid":false,"given":"Ryszard","family":"Szplet","sequence":"additional","affiliation":[{"name":"Faculty of Electronics, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yi\u011fitler, H., Badihi, B., and J\u00e4ntti, R. (2020). Overview of Time Synchronization for IoT Deployments: Clock Discipline Algorithms and Protocols. Sensors, 20.","DOI":"10.3390\/s20205928"},{"key":"ref_2","unstructured":"(2022). Network Limits for Time Synchronization in Packet Networks with Full Timing Support from the Network (Standard No. G.8271.1\/Y.1366.1)."},{"key":"ref_3","unstructured":"Kaplan, E.D., and Hegarty, C. (2017). Understanding GPS\/GNSS: Principles and Applications, Artech House. [3rd ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10291-020-01036-4","article-title":"Performance of miniaturized atomic clocks in static laboratory and dynamic flight environments","volume":"25","author":"Jain","year":"2021","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/MIM.2022.9847197","article-title":"Time Synchronization for Smart Grids Applications: Requirements and Uncertainty Issues","volume":"25","author":"Macii","year":"2022","journal-title":"IEEE Instrum. Meas. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"110208","DOI":"10.1016\/j.ijepes.2024.110208","article-title":"Internal clock errors in synchrophasor ambient data: Effects, detection, and a posteriori estimation-based correction","volume":"161","author":"Mishra","year":"2024","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Namyar, P., Li, Y., Wang, W., Dukkipati, N., Yap, K., Gong, J., Chen, C., Gao, P., Ray, D., and Kumar, G. (2025). Firefly: Scalable, Ultra-Accurate Clock Synchronization for Datacenters. SIGCOMM \u201925: Proceedings of the ACM SIGCOMM 2025 Conference, Association for Computing Machinery.","DOI":"10.1145\/3718958.3750502"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bednarz, K., Wojtu\u0144, J., Kelner, J.M., and R\u00f3\u017cyc, K. (2024). Frequency Instability Impact of Low-Cost SDRs on Doppler-Based Localization Accuracy. Sensors, 24.","DOI":"10.3390\/s24041053"},{"key":"ref_9","first-page":"1","article-title":"Frequency stability of software-defined radios\u2014part I. Measurements","volume":"32","author":"Bednarz","year":"2025","journal-title":"Metrol. Meas. Syst."},{"key":"ref_10","first-page":"1","article-title":"Frequency stability of software-defined radios\u2014part II. Modeling for simulation studies","volume":"32","author":"Bednarz","year":"2025","journal-title":"Metrol. Meas. Syst."},{"key":"ref_11","unstructured":"(2022). IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology\u2013Random Instabilities (Standard No. IEEE Std 1139-2022 (Revision of IEEE Std 1139-2008))."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rubiola, E. (2008). Phase Noise and Frequency Stability in Oscillators, Cambridge University Press.","DOI":"10.1017\/CBO9780511812798"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1109\/58.139120","article-title":"Environmental sensitivities of quartz oscillators","volume":"39","author":"Walls","year":"1992","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1109\/58.393101","article-title":"Fundamental limits on the frequency stabilities of crystal oscillators","volume":"42","author":"Walls","year":"1995","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_15","unstructured":"Vig, J.R. (1992). Introduction to Quartz Frequency Standards, Army Research Laboratory. Technical report."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1080\/23080477.2016.1181948","article-title":"Heating and thermostatic analysis of an oven-controlled quartz crystal oscillator","volume":"4","author":"Huang","year":"2016","journal-title":"Smart Sci."},{"key":"ref_17","first-page":"013001","article-title":"A review of MEMS oscillators for frequency reference and timing applications","volume":"22","author":"Puers","year":"2011","journal-title":"J. Micromech. Microeng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"021330","DOI":"10.1063\/5.0201566","article-title":"A review on temperature coefficient of frequency (TCf) in resonant microelectromechanical systems (MEMS)","volume":"12","author":"Sui","year":"2025","journal-title":"Appl. Phys. Rev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1492","DOI":"10.1109\/TUFFC.2018.2843781","article-title":"A \u00b10.3 ppm Oven-Controlled MEMS Oscillator Using Structural Resistance-Based Temperature Sensing","volume":"65","author":"Liu","year":"2018","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/JMEMS.2020.2970609","article-title":"Low-Power Dual Mode MEMS Resonators with PPB Stability over Temperature","volume":"29","author":"Kwon","year":"2020","journal-title":"J. Microelectromech. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1109\/JMEMS.2020.3020787","article-title":"MEMS Resonators for Frequency Reference and Timing Applications","volume":"29","author":"Wu","year":"2020","journal-title":"J. Microelectromech. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"17854","DOI":"10.1109\/JSEN.2023.3286897","article-title":"The Oven-Controlled MEMS Oscillators in Timing and Sensing Applications: A Review","volume":"23","author":"Feng","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1109\/58.79613","article-title":"Hysteresis in quartz resonators-a review","volume":"38","author":"Kusters","year":"1991","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Matko, V., and Milanovi\u010d, M. (2020). Detection Principles of Temperature Compensated Oscillators with Reactance Influence on Piezoelectric Resonator. Sensors, 20.","DOI":"10.3390\/s20030802"},{"key":"ref_25","unstructured":"Riley, W.J. (2008). Handbook of Frequency Stability Analysis, National Institute of Standards and Technology. NIST Special Publication 1065."},{"key":"ref_26","first-page":"297","article-title":"Timing jitter calculation using simplified phase noise integration method","volume":"10","author":"Szplet","year":"2003","journal-title":"Metrol. Meas. Syst."},{"key":"ref_27","unstructured":"(2023). IEEE Guide for Measurement of Environmental Sensitivities of Standard Frequency Generators (Standard No. IEEE Std 1193-2022 (Revision of IEEE Std 1193-2003))."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Vig, J., and Meeker, T. (1991). The aging of bulk acoustic wave resonators, filters and oscillators. Proceedings of the 45th Annual Symposium on Frequency Control 1991, IEEE.","DOI":"10.1109\/FREQ.1991.145888"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1109\/PROC.1966.4634","article-title":"Statistics of atomic frequency standards","volume":"54","author":"Allan","year":"1966","journal-title":"Proc. IEEE"},{"key":"ref_30","unstructured":"Kartaschoff, P. (1978). Frequency and Time (Monographs in Physical Measurement), Academic Press."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2996","DOI":"10.1109\/TMTT.2023.3238267","article-title":"The Companion of Enrico\u2019s Chart for Phase Noise and Two-Sample Variances","volume":"71","author":"Rubiola","year":"2023","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Wang, Z., and Wu, J. (2020). A Method to Increase the Frequency Stability of a TCXO by Compensating Thermal Hysteresis. Sensors, 20.","DOI":"10.3390\/s20236812"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Fang, C.H., Lin, C.Y., Yang, S., Tsou, S.C., Wen, S.H., Chen, K.D., and Lin, T.H. (2024). A 185-\u00b5W, \u00b12.5-ppm \u221240 \u00b0C\u201380 \u00b0C Analog TCXO with a Differential-Pair-Based Polynomial Temperature Compensation Technique. 2024 IEEE Asian Solid-State Circuits Conference (A-SSCC), IEEE.","DOI":"10.1109\/A-SSCC60305.2024.10849211"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1109\/JRPROC.1956.274879","article-title":"Frequency-Temperature-Angle Characteristics of AT-Type Resonators Made of Natural and Synthetic Quartz","volume":"44","author":"Bechmann","year":"1956","journal-title":"Proc. IRE"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2745","DOI":"10.1109\/TUFFC.2020.3013664","article-title":"New Method for 100-MHz High-Frequency Temperature-Compensated Crystal Oscillator","volume":"67","author":"Tan","year":"2020","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1109\/TCSI.2022.3221374","article-title":"A High Precision Analog Temperature Compensated Crystal Oscillator Using a New Temperature Compensated Multiplier","volume":"70","author":"Zeng","year":"2023","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Yin, J., Deng, W., Jia, H., Wang, M., and Chi, B. (2024, January 18\u201321). A 48 MHz Temperature Compensated Crystal Oscillator Utilizing Time-Domain Accuracy Boosting Techniques Achieving \u00b11.4 ppm Frequency Stability from \u221255 \u00b0C to 115 \u00b0C. Proceedings of the 2024 IEEE Asian Solid-State Circuits Conference (A-SSCC), Hiroshima, Japan.","DOI":"10.1109\/A-SSCC60305.2024.10849114"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Hsieh, W.L., Hsu, C.L., Chen, C.W., Weng, C.Y., and Kao, S.H. (2018, January 21\u201324). Highly Stable Miniaturized OCXO with Heater-Embedded Ceramic Package. Proceedings of the 2018 IEEE International Frequency Control Symposium (IFCS), Olympic Valley, CA, USA.","DOI":"10.1109\/FCS.2018.8597561"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Hsieh, W.L., Wang, W.C., Hsu, E.S., Kao, S.H., and Wang, M.H. (2021, January 7\u201317). The World\u2019s Smallest Quartz-Based OCXO for 5G Synchronization Applications. Proceedings of the 2021 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF\/IFCS), Gainesville, FL, USA.","DOI":"10.1109\/EFTF\/IFCS52194.2021.9604264"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Thorax, D., Candelier, V., Ferreira, A., Henchiri, H., Billebault, J.C., and Vittrant, F. (2021, January 7\u201317). Very New Small OCXO with Low Short and Medium Term Noise and Low Thermal Sensitivity. Proceedings of the 2021 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF\/IFCS), Gainesville, FL, USA.","DOI":"10.1109\/EFTF\/IFCS52194.2021.9604271"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Esterline, J., and Stange, D. (2020, January 19\u201323). Secondary Frequency Versus Temperature Compensation of an OCXO Using a Segmented Polynomial Array. Proceedings of the 2020 Joint Conference of the IEEE International Frequency Control Symposium and International Symposium on Applications of Ferroelectrics (IFCS-ISAF), Keystone, CO, USA.","DOI":"10.1109\/IFCS-ISAF41089.2020.9234937"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Chang, S.J., Wang, W.C., Kao, S.H., and Hsieh, W.L. (2023, January 15\u201319). A Miniature Oven-Controlled Crystal Oscillator (OCXO) with ppt Stability over Temperature Using High-Order Polynomial Temperature Control. Proceedings of the 2023 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF\/IFCS), Toyama, Japan.","DOI":"10.1109\/EFTF\/IFCS57587.2023.10272037"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Magni, M., Scaccabarozzi, D., Palomba, E., Zampetti, E., and Saggin, B. (2022). Characterization of Thermal Gradient Effects on a Quartz Crystal Microbalance. Sensors, 22.","DOI":"10.3390\/s22197256"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Xu, J., Li, Z., Yang, R., Gao, L., and Chen, M. (2017, January 21\u201323). Simulation and demonstration for the thermoelectric cooler to improve warm-up time of OCXO. Proceedings of the 2017 7th IEEE International Conference on Electronics Information and Emergency Communication (ICEIEC), Macau, China.","DOI":"10.1109\/ICEIEC.2017.8076616"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"e27481","DOI":"10.1016\/j.heliyon.2024.e27481","article-title":"Reliability of MEMS inertial devices in mechanical and thermal environments: A review","volume":"10","author":"Xu","year":"2024","journal-title":"Heliyon"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"244107","DOI":"10.1063\/1.2748092","article-title":"Temperature-compensated high-stability silicon resonators","volume":"90","author":"Melamud","year":"2007","journal-title":"Appl. Phys. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1409","DOI":"10.1109\/JMEMS.2009.2030074","article-title":"Temperature-Insensitive Composite Micromechanical Resonators","volume":"18","author":"Melamud","year":"2009","journal-title":"J. Microelectromech. Syst."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2656","DOI":"10.1109\/TED.2013.2270434","article-title":"Temperature-Stable Silicon Oxide (SilOx) Micromechanical Resonators","volume":"60","author":"Tabrizian","year":"2013","journal-title":"IEEE Trans. Electron Devices"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"015319","DOI":"10.1063\/5.0074694","article-title":"Temperature frequency stability study of extensional mode N-doped silicon MEMS resonator","volume":"12","author":"Ahmed","year":"2022","journal-title":"AIP Adv."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1109\/TUFFC.2014.3007","article-title":"Determination of doping and temperature-dependent elastic constants of degenerately doped silicon from MEMS resonators","volume":"61","author":"Jaakkola","year":"2014","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1109\/JMEMS.2015.2443379","article-title":"Design Rules for Temperature Compensated Degenerately n-Type-Doped Silicon MEMS Resonators","volume":"24","author":"Jaakkola","year":"2015","journal-title":"J. Microelectromech. Syst."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1109\/TED.2013.2243451","article-title":"Turnover Temperature Point in Extensional-Mode Highly Doped Silicon Microresonators","volume":"60","author":"Shahmohammadi","year":"2013","journal-title":"IEEE Trans. Electron Devices"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1109\/JMEMS.2022.3189202","article-title":"Temperature Compensated Bulk-Mode Capacitive MEMS Resonators with \u00b116 ppm Temperature Stability over Industrial Temperature Ranges","volume":"31","author":"Han","year":"2022","journal-title":"J. Microelectromech. Syst."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1109\/LED.2021.3094319","article-title":"A Temperature-Stable and Low Impedance Piezoelectric MEMS Resonator for Drop-in Replacement of Quartz Crystals","volume":"42","author":"Chen","year":"2021","journal-title":"IEEE Electron Device Lett."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"2005","DOI":"10.1109\/LED.2022.3206819","article-title":"Corrections to \u201cA Temperature-Stable and Low Impedance Piezoelectric MEMS Resonator for Drop-in Replacement of Quartz Crystals\u201d [Sep 21 1382-1385]","volume":"43","author":"Chen","year":"2022","journal-title":"IEEE Electron Device Lett."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"115435","DOI":"10.1016\/j.sna.2024.115435","article-title":"Geometrically engineered mass sensing CMOS-MEMS resonators for temperature compensation via folded anchors","volume":"373","author":"Verd","year":"2024","journal-title":"Sens. Actuators A Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/OJUFFC.2026.3681525","article-title":"Passive Thermal Compensation of Silicon Resonators Through Modal Engineering","volume":"6","author":"Zare","year":"2026","journal-title":"IEEE Open J. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1109\/JMEMS.2023.3260079","article-title":"Mechanically Coupled Single-Crystal Silicon MEMS Resonators for TCF Manipulation","volume":"32","author":"Han","year":"2023","journal-title":"J. Microelectromech. Syst."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1109\/JMEMS.2024.3524384","article-title":"Turnover Temperature Point Adjustment in Mechanically Coupled Single-Crystal Silicon MEMS Resonators","volume":"34","author":"Xiao","year":"2025","journal-title":"J. Microelectromech. Syst."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1109\/JMEMS.2025.3605143","article-title":"Q Enhancement and TCF Reduction for Piezoelectric MEMS Resonators via Mechanical Coupling","volume":"34","author":"Li","year":"2025","journal-title":"J. Microelectromech. Syst."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"44547","DOI":"10.1109\/JSEN.2025.3621771","article-title":"Unbiased DFT-Based MEMS Oscillator Temperature Compensation System","volume":"25","author":"Huang","year":"2025","journal-title":"IEEE Sens. J."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"116019","DOI":"10.1016\/j.sna.2024.116019","article-title":"An oven controlled piezoelectric MEMS dual-resonator platform with frequency stability of \u00b1100 ppb over industrial temperature range","volume":"380","author":"Xiao","year":"2024","journal-title":"Sens. Actuators A Phys."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1109\/LED.2023.3285622","article-title":"A Micro-Oven Controlled Dual-Mode Piezoelectric MEMS Resonator with \u00b1 190 ppb Stability over \u221240 to 105 \u00b0C Temperature Range","volume":"44","author":"Xiao","year":"2023","journal-title":"IEEE Electron Device Lett."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Sahasrabudhe, S., Wen, H., Junek, G.V., and Ayazi, F. (July, January 29). Heavily-Doped Dual-Mode Distributed Lam\u00e9 Resonator (DLR) for Temperature-Compensated Mems Oscillators. Proceedings of the 2025 23rd International Conference on Solid-State Sensors, Actuators and Microsystems (Transducers), Orlando, FL, USA.","DOI":"10.1109\/Transducers61432.2025.11111561"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"He, K., Feng, R., Zheng, Y., Guo, L., Liao, Q., Xiang, Y., Zhang, H., Wang, J., and Li, X. (July, January 29). A Micro-Oven-Controlled Wafer-Level Vacuum Packaging Process Platform for MEMS Resonant Devices. Proceedings of the 2025 23rd International Conference on Solid-State Sensors, Actuators and Microsystems (Transducers), Orlando, FL, USA.","DOI":"10.1109\/Transducers61432.2025.11111560"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Wang, C., Xu, Y., Shao, G., Lv, J., and Wei, X. (2025, January 11\u201314). An Ultra-Stable MEMS Oscillator Based on High-Q Micromechanical Resonator and a Two-Stage Temperature Compensation System. Proceedings of the 2025 IEEE 20th International Conference on Nano\/Micro Engineered and Molecular Systems (NEMS), Zhuhai, China.","DOI":"10.1109\/NEMS67320.2025.11170103"},{"key":"ref_67","unstructured":"Yan, J., Kim, J., Islam, R., Yang, J., Elmeligy, K., Bozkurt, A., Kenny, T.W., Hanumolu, P.K., and Bahl, G. (2026). A Micromechanical Frequency Reference with Parts-per-Trillion Holdover Stability. arXiv."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Kim, J., Islam, R., Jing, J., Yan, J., Vukasin, G., Kwon, R., Saxena, S., Kenny, T.W., Hanumolu, P.K., and Bahl, G. (2024, January 2\u20136). Ultra-stable MEMS oscillator with 42 ppt fractional frequency stability at 85 seconds. Proceedings of the 2024 Solid-State Sensors, Actuators, and Microsystems Workshop, Hilton Head Island, SC, USA.","DOI":"10.31438\/trf.hh2024.11"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1038\/s41378-025-01025-y","article-title":"An ultra-stable MEMS resonator with \u00b114 ppb frequency stability realized by nonlinearity-mediated drift suppression","volume":"11","author":"Xu","year":"2025","journal-title":"Microsyst. Nanoeng."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"133503","DOI":"10.1063\/5.0239027","article-title":"A temperature-insensitive nonlinear silicon bulk acoustic oscillator","volume":"126","author":"Dabas","year":"2025","journal-title":"Appl. Phys. Lett."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1038\/ncomms1813","article-title":"Frequency stabilization in nonlinear micromechanical oscillators","volume":"3","author":"Antonio","year":"2012","journal-title":"Nat. Commun."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"114619","DOI":"10.1016\/j.sna.2023.114619","article-title":"Exploiting and tailoring 1:2 internal resonance in a stepped beam micromechanical resonator for frequency stabilization","volume":"362","author":"Yu","year":"2023","journal-title":"Sens. Actuators A Phys."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"054055","DOI":"10.1103\/PhysRevApplied.22.054055","article-title":"Extraordinary frequency stabilization by resonant nonlinear mode coupling","volume":"22","author":"Shoshani","year":"2024","journal-title":"Phys. Rev. Appl."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1038\/s41378-025-01070-7","article-title":"A multi-functional MEMS resonator for simultaneously dual-mode physical sensing and ppb-level timing","volume":"11","author":"Xu","year":"2025","journal-title":"Microsyst. Nanoeng."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1038\/s41378-026-01210-7","article-title":"Exploring the synergic effect of thermal tuning and mode-coupling for frequency stabilization in micromechanical resonators","volume":"12","author":"Xiao","year":"2026","journal-title":"Microsyst. Nanoeng."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1109\/PROC.1966.4682","article-title":"A simple model of feedback oscillator noise spectrum","volume":"54","author":"Leeson","year":"1966","journal-title":"Proc. IEEE"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1049\/el.2016.1021","article-title":"Reviews of leeson model of oscillator phase noise","volume":"52","author":"Huang","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/4.826814","article-title":"Oscillator phase noise: A tutorial","volume":"35","author":"Lee","year":"2000","journal-title":"IEEE J. Solid-State Circuits"},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Parajuli, M., Sobreviela, G., Zhang, H., and Seshia, A.A. (2021, January 20\u201324). A Silicon MEMS Disk Resonator Oscillator Demonstrating 36 ppt Frequency Stability. Proceedings of the 2021 21st International Conference on Solid-State Sensors, Actuators and Microsystems (Transducers), Orlando, FL, USA.","DOI":"10.1109\/Transducers50396.2021.9495722"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"100108","DOI":"10.1016\/j.chip.2024.100108","article-title":"Q-enhancement of piezoelectric micro-oven-controlled MEMS resonators using honeycomb lattice phononic crystals","volume":"3","author":"Xiao","year":"2024","journal-title":"Chip"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1109\/TUFFC.2023.3312159","article-title":"Five Low-Noise Stable Oscillators Referenced to the Same Multimode AlN\/Si MEMS Resonator","volume":"70","author":"Kaisar","year":"2023","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1109\/JMEMS.2015.2391832","article-title":"The Impact of Damping on the Frequency Stability of Nonlinear MEMS Oscillators","volume":"24","author":"Zou","year":"2015","journal-title":"J. Microelectromech. Syst."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"1446","DOI":"10.1109\/JMEMS.2006.883586","article-title":"Long-Term and Accelerated Life Testing of a Novel Single-Wafer Vacuum Encapsulation for MEMS Resonators","volume":"15","author":"Candler","year":"2006","journal-title":"J. Microelectromech. Syst."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.sna.2006.10.040","article-title":"Frequency stability of wafer-scale film encapsulated silicon based MEMS resonators","volume":"136","author":"Kim","year":"2007","journal-title":"Sens. Actuators A Phys."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/JMEMS.2016.2537829","article-title":"A Unified Epi-Seal Process for Fabrication of High-Stability Microelectromechanical Devices","volume":"25","author":"Yang","year":"2016","journal-title":"J. Microelectromech. Syst."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.sna.2005.10.034","article-title":"Stability of wafer level vacuum encapsulated single-crystal silicon resonators","volume":"130\u2013131","author":"Kaajakari","year":"2006","journal-title":"Sens. Actuators A Phys."},{"key":"ref_87","unstructured":"SiTime Corporation (2026, June 06). SiT5811: 10 to 60 MHz, 12-Hour Holdover OCXO. Data Sheet. Available online: https:\/\/www.sitime.com\/products\/programmable-ocxos\/holdover-ocxos\/sit5811."},{"key":"ref_88","unstructured":"SiTime Corporation (2026, June 06). SiT7101: Ruggedized MEMS OCXO. Data Sheet. Available online: https:\/\/www.sitime.com\/products\/ruggedized-timing\/ocxos\/sit7101."},{"key":"ref_89","unstructured":"SiTime Corporation (2026, June 06). SiT5543: 1 to 60 MHz Endura Ruggedized Precision Super-TCXO. Data Sheet. Available online: https:\/\/www.sitime.com\/products\/ruggedized-timing\/super-tcxos\/sit5543."},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"Lian, Y., Li, Y., Chen, F., Yang, J., Zhou, J., Wang, C., Kraft, M., Wei, X., Chen, J., and Lei, K.m. (2026, January 25\u201329). Achieving 2.0-ppb Frequency Stability with a Curved-Beam Piezoelectric MEMS Resonator via Multiple TCf Regulation Method. Proceedings of the 2026 IEEE 39th International Conference on Micro Electro Mechanical Systems (MEMS), Salzburg, Austria.","DOI":"10.1109\/MEMS64181.2026.11419564"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"065002","DOI":"10.1088\/1361-6439\/ad42a7","article-title":"Adaptive frequency-stabilization of MEMS oscillators using mode coupling","volume":"34","author":"Huan","year":"2024","journal-title":"J. Micromech. Microeng."},{"key":"ref_92","unstructured":"SiTime Corporation (2026, June 06). SiT5812: 60 to 220 MHz, 12-Hour Holdover OCXO. Data Sheet. Available online: https:\/\/www.sitime.com\/products\/programmable-ocxos\/holdover-ocxos\/sit5812."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1109\/T-SU.1985.31674","article-title":"Dynamic Models for Quartz-Resonator Thermal Transient Response","volume":"32","author":"Chow","year":"1985","journal-title":"IEEE Trans. Sonics Ultrason."},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Magni, M., Scaccabarozzi, D., and Saggin, B. (2023). Compensation of Thermal Gradients Effects on a Quartz Crystal Microbalance. Sensors, 23.","DOI":"10.3390\/s23010024"},{"key":"ref_95","doi-asserted-by":"crossref","unstructured":"Beauto, G., Billebault, J.C., Khouri, R., and Candelier, V. (2024, January 25\u201327). Smallest OCXO with 1.5US over 24H Holdover for Demanding Synchronization Application. Proceedings of the 2024 European Frequency and Time Forum (EFTF), Neuch\u00e2tel, Switzerland.","DOI":"10.1109\/EFTF61992.2024.10722754"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1109\/TUFFC.2023.3285252","article-title":"How Does Ambient Temperature Fluctuation Influence the Short-Term Frequency Stability of OCXO?","volume":"70","author":"Xu","year":"2023","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"115016","DOI":"10.1016\/j.sna.2024.115016","article-title":"Actuators linearization of a large volume environmental simulation chamber via pulse code modulation","volume":"366","author":"Savchenkov","year":"2024","journal-title":"Sens. Actuators A Phys."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1109\/JMEMS.2013.2252422","article-title":"Thermal Nonlinearities in Contour Mode AlN Resonators","volume":"22","author":"Piazza","year":"2013","journal-title":"J. Microelectromech. Syst."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1109\/58.105240","article-title":"Sensitivity of quartz oscillators to the environment: Characterization methods and pitfalls","volume":"37","author":"Gagnepain","year":"1990","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1109\/TUFFC.2021.3118929","article-title":"Dynamic Frequency\u2013Temperature Characteristic Modeling for Quartz Crystal Resonator Based on Improved Echo State Network","volume":"69","author":"Deng","year":"2022","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_101","unstructured":"Watanabe, Y., Ozaki, K., Goka, S., Sato, T., and Sekimoto, H. (2001, January 8). Frequency stability and phase noise characteristics of digital OCXOs using dual-mode excitation. Proceedings of the 2001 IEEE International Frequncy Control Symposium and PDA Exhibition (Cat. No.01CH37218), Seattle, WA, USA."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1007\/s00542-024-05691-2","article-title":"Predicting frequency deviation of a crystal oscillator based on long short-term memory network and transfer learning technique","volume":"31","author":"Su","year":"2025","journal-title":"Microsyst. Technol."},{"key":"ref_103","unstructured":"Kim, B., Candler, R., Hopcroft, M., Agarwal, M., Park, W.T., and Kenny, T. (2005, January 5\u20139). Frequency stability of wafer-scale encapsulated MEMS resonators. Proceedings of the 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS \u201905, Seoul, Republic of Korea."},{"key":"ref_104","doi-asserted-by":"crossref","unstructured":"Miller, J.M., Zhang, Z., Bousse, N.E., Coso, D., Sadat, S., Kwon, H.K., Vukasin, G.D., Majumdar, A., and Kenny, T.W. (2020, January 18\u201322). Temperature Hysteresis in Piezoresistive Microcantilevers. Proceedings of the 2020 IEEE 33rd International Conference on Micro Electro Mechanical Systems (MEMS), Vancouver, BC, Canada.","DOI":"10.1109\/MEMS46641.2020.9056428"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1109\/JSEN.2012.2227708","article-title":"Stability of Silicon Microelectromechanical Systems Resonant Thermometers","volume":"13","author":"Ng","year":"2013","journal-title":"IEEE Sens. J."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"055106","DOI":"10.1063\/5.0041304","article-title":"Intelligent aging compensation scheme for oven-controlled crystal oscillators of batch production based on statistical distribution","volume":"92","author":"Miao","year":"2021","journal-title":"Rev. Sci. Instrum."},{"key":"ref_107","doi-asserted-by":"crossref","unstructured":"Li, Z., Peng, J., Miao, M., and Wang, Z. (2025). Compensation Method Based on Phase Shift Between Pins of Crystal Resonator. Sensors, 25.","DOI":"10.3390\/s25030932"},{"key":"ref_108","doi-asserted-by":"crossref","unstructured":"Tu, S., Wang, H., and Jin, Z. (2023, January 15\u201317). Temperature and Aging Compensated Kalman Filter Algorithm for High-Precision Timing System of Microsatellites. Proceedings of the 2023 IEEE 7th Information Technology and Mechatronics Engineering Conference (ITOEC), Chongqing, China.","DOI":"10.1109\/ITOEC57671.2023.10291230"},{"key":"ref_109","doi-asserted-by":"crossref","unstructured":"Henry, R., and Kenny, D. (2008, January 19\u201321). Comparative analysis of MEMS, programmable, and synthesized frequency control devices versus traditional quartz based devices. Proceedings of the 2008 IEEE International Frequency Control Symposium, Honolulu, HI, USA.","DOI":"10.1109\/FREQ.2008.4623027"},{"key":"ref_110","doi-asserted-by":"crossref","unstructured":"Xu, Y., Liu, S., He, C., Wu, H., Cheng, L., Huang, Q., and Yan, G. (2023). Research on Packaging Reliability and Quality Factor Degradation Model for Wafer-Level Vacuum Sealing MEMS Gyroscopes. Micromachines, 14.","DOI":"10.3390\/mi14101956"},{"key":"ref_111","doi-asserted-by":"crossref","unstructured":"Fry, S.J., and Burnett, G.A. (2010, January 1\u20134). Reducing the acceleration sensitivity of AT-strip quartz crystal oscillators. Proceedings of the 2010 IEEE International Frequency Control Symposium, Newport Beach, CA, USA.","DOI":"10.1109\/FREQ.2010.5556379"},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"1562","DOI":"10.1109\/TUFFC.2006.1678183","article-title":"An estimate on the second-order normal acceleration sensitivity of a quartz resonator","volume":"53","author":"Yang","year":"2006","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_113","doi-asserted-by":"crossref","unstructured":"Yang, G., Huang, X., Tan, K., Chen, Q., and Pan, W. (2023). Study of Force-Frequency Characteristics in AT-Cut Strip Quartz Crystal Resonators with Different Rotation Angles. Sensors, 23.","DOI":"10.3390\/s23062996"},{"key":"ref_114","doi-asserted-by":"crossref","unstructured":"Yang, C.C., Chen, Y.C., Chang, C.Y., and Li, S.S. (2024, January 22\u201326). Low-G Sensitivity Design and Implementation for Commercial Quartz Crystal Oscillators. Proceedings of the 2024 IEEE Ultrasonics, Ferroelectrics, and Frequency Control Joint Symposium (UFFC-JS), Taipei, Taiwan.","DOI":"10.1109\/UFFC-JS60046.2024.10794175"},{"key":"ref_115","doi-asserted-by":"crossref","unstructured":"Chang, C.Y., Hsieh, P.C., Yao, C.W., Yang, C.C., and Li, S.S. (2023, January 9\u201313). A Selective Overtone MEMS-based Quartz Oscillator with Low Acceleration Sensitivity. Proceedings of the 2023 International Electron Devices Meeting (IEDM), San Francisco, CA, USA.","DOI":"10.1109\/IEDM45741.2023.10413831"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"012010","DOI":"10.1088\/1742-6596\/2889\/1\/012010","article-title":"Techniques on Crystal Oscillator Vibration Compensation","volume":"2889","author":"Mossammaparast","year":"2024","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_117","doi-asserted-by":"crossref","unstructured":"Kim, B., Olsson, R.H., Smart, K., and Wojciechowski, K.E. (2011, January 28\u201331). MEMS resonators with extremely low vibration and shock sensitivity. Proceedings of the SENSORS, 2011, IEEE, Limerick, Ireland.","DOI":"10.1109\/ICSENS.2011.6127186"},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1109\/58.20450","article-title":"The acceleration sensitivity of quartz crystal oscillators: A review","volume":"35","author":"Filler","year":"1988","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1109\/TIM.2017.2784082","article-title":"A High-Stability Quartz Crystal Resonator Humidity Sensor Based on Tuning Capacitor","volume":"67","author":"Yu","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"9504009","DOI":"10.1109\/TIM.2023.3347786","article-title":"A Highly Linear and Sensitive QCM Humidity Sensor Based on High-Frequency Quartz Crystal Transducer","volume":"73","author":"Ding","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"015016","DOI":"10.1088\/0960-1317\/23\/1\/015016","article-title":"The hermeticity of sealed microstructures under low temperature helium and hydrogen exposure","volume":"23","author":"Sparks","year":"2012","journal-title":"J. Micromech. Microeng."},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"101","DOI":"10.4236\/jst.2013.34016","article-title":"Output drifting of vacuum packaged MEMS sensors due to room temperature helium exposure","volume":"3","author":"Sparks","year":"2013","journal-title":"J. Sens. Technol."},{"key":"ref_123","doi-asserted-by":"crossref","unstructured":"Rautmann, L.L., and Kosleck, S. (2024, January 23\u201326). Introduction of a Standardised Testing Methodology for Electronic Components in Pressure Tolerant Systems. Proceedings of the OCEANS 2024-Halifax, Halifax, NS, Canada.","DOI":"10.1109\/OCEANS55160.2024.10753840"},{"key":"ref_124","doi-asserted-by":"crossref","unstructured":"Rautmann, L.L., and Kosleck, S. (2025, January 16\u201319). High-Pressure Performance Evaluation of Crystal Quartz and MEMS Oscillators for Pressure-Tolerant Systems in Deep-Sea Applications. Proceedings of the OCEANS 2025 Brest, Brest, France.","DOI":"10.1109\/OCEANS58557.2025.11104756"},{"key":"ref_125","unstructured":"Walls, F. (1988, January 1\u20133). The influence of pressure and humidity on the medium and long-term frequency stability of quartz oscillators. Proceedings of the 42nd Annual Frequency Control Symposium, Baltimore, MD, USA."},{"key":"ref_126","doi-asserted-by":"crossref","unstructured":"Hsieh, W.L., Hsu, E.S., Yen, Y.S., Kao, S.H., Huang, Y.C., and Wang, M.H. (2020, January 19\u201323). A Novel Miniature OCXO Using Hermetically Sealed Ceramic Package. Proceedings of the 2020 Joint Conference of the IEEE International Frequency Control Symposium and International Symposium on Applications of Ferroelectrics (IFCS-ISAF), Keystone, CO, USA.","DOI":"10.1109\/IFCS-ISAF41089.2020.9234843"},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1109\/JMEMS.2021.3077633","article-title":"Experimental Observation of Temperature and Pressure Induced Frequency Fluctuations in Silicon MEMS Resonators","volume":"30","author":"Pandit","year":"2021","journal-title":"J. Microelectromech. Syst."},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"e192","DOI":"10.1002\/adc2.192","article-title":"Study of oscillation characteristics for quartz crystal oscillators based on equivalent multi-physics model","volume":"6","author":"Chen","year":"2024","journal-title":"Adv. Control Appl."},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1109\/JSSC.2021.3139649","article-title":"A 43 nW, 32 kHz, \u00b14.2 ppm Piecewise Linear Temperature-Compensated Crystal Oscillator with \u0394\u03a3-Modulated Load Capacitance","volume":"57","author":"Park","year":"2022","journal-title":"IEEE J. Solid-State Circuits"},{"key":"ref_130","first-page":"2016","article-title":"A Temperature-Compensated Crystal Oscillator with Piecewise Polynomial Varactor Compensation Achieving \u00b13.75-ppm Inaccuracy from \u221230 \u00b0C to 90 \u00b0C","volume":"69","author":"Lin","year":"2022","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1109\/TUFFC.2020.2969530","article-title":"Low-Power MEMS-Based Pierce Oscillator Using a 61-MHz Capacitive-Gap Disk Resonator","volume":"67","author":"Naing","year":"2020","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"084707","DOI":"10.1063\/5.0215044","article-title":"Investigating the impact of supply voltage fluctuations on phase noise in quartz crystal oscillators","volume":"95","author":"Xu","year":"2024","journal-title":"Rev. Sci. Instrum."},{"key":"ref_133","doi-asserted-by":"crossref","unstructured":"Rohde, U.L., and Poddar, A.K. (2010, January 12\u201314). Electromagnetic interference and start-up dynamics in high frequency crystal oscillator circuits. Proceedings of the 2010 IEEE Sarnoff Symposium, Princeton, NJ, USA.","DOI":"10.1109\/SARNOF.2010.5469744"},{"key":"ref_134","doi-asserted-by":"crossref","first-page":"023502","DOI":"10.1063\/1.5083172","article-title":"Temperature-frequency drift suppression via electrostatic stiffness softening in MEMS resonator with weakened duffing nonlinearity","volume":"114","author":"Chen","year":"2019","journal-title":"Appl. Phys. Lett."},{"key":"ref_135","doi-asserted-by":"crossref","unstructured":"Salzenstein, P., Bassir, D., and Lefebvre, F. (2025, January 15\u201317). Advanced Control Engineering for Frequency Stability in Quartz Oscillators. Proceedings of the 2025 3rd International Conference on Artificial Intelligence and Automation Control (AIAC), Paris, France.","DOI":"10.1109\/AIAC68175.2025.11332406"},{"key":"ref_136","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1109\/58.535482","article-title":"Influence of a magnetic field on quartz crystal resonators","volume":"43","author":"Brendel","year":"1996","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_137","unstructured":"Brendel, R., El Hassani, C., Brunet, M., and Robert, E. (June, January 31). Influence of magnetic field on quartz crystal oscillators. Proceedings of the 43rd Annual Symposium on Frequency Control, Denver, CO, USA."},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"114803","DOI":"10.1016\/j.sna.2023.114803","article-title":"Magnetic field tunable piezoelectric resonator for MEMS applications","volume":"364","author":"Kumar","year":"2023","journal-title":"Sens. Actuators A Phys."},{"key":"ref_139","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/TNS.1973.4327381","article-title":"Transient Change in Q and Frequency of At-Cut Quartz Resonators Following Exposure to Pulse X-Rays","volume":"20","author":"King","year":"1973","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_140","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1109\/TNS.1996.4324355","article-title":"Effects of Pulsed Ionizing Radiation on Some Selected Quartz Oscillator Crystals","volume":"13","author":"Poll","year":"1966","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_141","unstructured":"Martin, J. (June, January 31). Radiation induced frequency offsets and acoustic loss in AT-cut quartz crystals. Proceedings of the 43rd Annual Symposium on Frequency Control, Denver, CO, USA."},{"key":"ref_142","doi-asserted-by":"crossref","unstructured":"H\u00f6tting, M., Kr\u00f6ninger, K., Mentzel, F., Weingarten, J., Markgraf, M., Pitann, J., and Sp\u00f6rl, A. (2020, January 12\u201314). Study of radiation-induced frequency shifts in quarz crystal oscillators. Proceedings of the 2020 IEEE International Conference on Wireless for Space and Extreme Environments (WiSEE), Vicenza, Italy.","DOI":"10.1109\/WiSEE44079.2020.9262639"},{"key":"ref_143","doi-asserted-by":"crossref","first-page":"79280E","DOI":"10.1117\/12.873466","article-title":"Effects of radiation on MEMS","volume":"Volume 7928","author":"Ramesham","year":"2011","journal-title":"Reliability, Packaging, Testing, and Characterization of MEMS\/MOEMS and Nanodevices X"},{"key":"ref_144","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1109\/TNS.2016.2631458","article-title":"Total-Ionizing-Dose Effects in Piezoresistive Micromachined Cantilevers","volume":"64","author":"Gong","year":"2017","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_145","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/TNS.2017.2749180","article-title":"Proton-Induced Displacement Damage and Total-Ionizing-Dose Effects on Silicon-Based MEMS Resonators","volume":"65","author":"Gong","year":"2018","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_146","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.mee.2014.08.015","article-title":"CMOS\u2013MEMS resonators: From devices to applications","volume":"132","author":"Uranga","year":"2015","journal-title":"Microelectron. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5425\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T04:24:29Z","timestamp":1787977469000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5425"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,27]]},"references-count":146,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26175425"],"URL":"https:\/\/doi.org\/10.3390\/s26175425","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,27]]}}}