{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T02:46:16Z","timestamp":1775097976547,"version":"3.50.1"},"reference-count":63,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,16]],"date-time":"2021-11-16T00:00:00Z","timestamp":1637020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["CRC1261"],"award-info":[{"award-number":["CRC1261"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Recently, Delta-E effect magnetic field sensors based on exchange-biased magnetic multilayers have shown the potential of detecting low-frequency and small-amplitude magnetic fields. Their design is compatible with microelectromechanical system technology, potentially small, and therefore, suitable for arrays with a large number N of sensor elements. In this study, we explore the prospects and limitations for improving the detection limit by averaging the output of N sensor elements operated in parallel with a single oscillator and a single amplifier to avoid additional electronics and keep the setup compact. Measurements are performed on a two-element array of exchange-biased sensor elements to validate a signal and noise model. With the model, we estimate requirements and tolerances for sensor elements using larger N. It is found that the intrinsic noise of the sensor elements can be considered uncorrelated, and the signal amplitude is improved if the resonance frequencies differ by less than approximately half the bandwidth of the resonators. Under these conditions, the averaging results in a maximum improvement in the detection limit by a factor of N. A maximum N\u2248200 exists, which depends on the read-out electronics and the sensor intrinsic noise. Overall, the results indicate that significant improvement in the limit of detection is possible, and a model is presented for optimizing the design of delta-E effect sensor arrays in the future.<\/jats:p>","DOI":"10.3390\/s21227594","type":"journal-article","created":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T09:16:11Z","timestamp":1637140571000},"page":"7594","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Modeling and Parallel Operation of Exchange-Biased Delta-E Effect Magnetometers for Sensor Arrays"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4255-5947","authenticated-orcid":false,"given":"Benjamin","family":"Spetzler","sequence":"first","affiliation":[{"name":"Institute of Materials Science, Faculty of Engineering, Kiel University, 24143 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick","family":"Wiegand","sequence":"additional","affiliation":[{"name":"Institute of Materials Science, Faculty of Engineering, Kiel University, 24143 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9839-3890","authenticated-orcid":false,"given":"Phillip","family":"Durdaut","sequence":"additional","affiliation":[{"name":"Institute of Materials Science, Faculty of Engineering, Kiel University, 24143 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9352-2868","authenticated-orcid":false,"given":"Michael","family":"H\u00f6ft","sequence":"additional","affiliation":[{"name":"Institute of Materials Science, Faculty of Engineering, Kiel University, 24143 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8012-6794","authenticated-orcid":false,"given":"Andreas","family":"Bahr","sequence":"additional","affiliation":[{"name":"Institute of Materials Science, Faculty of Engineering, Kiel University, 24143 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4436-0804","authenticated-orcid":false,"given":"Robert","family":"Rieger","sequence":"additional","affiliation":[{"name":"Institute of Materials Science, Faculty of Engineering, Kiel University, 24143 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3367-1655","authenticated-orcid":false,"given":"Franz","family":"Faupel","sequence":"additional","affiliation":[{"name":"Institute of Materials Science, Faculty of Engineering, Kiel University, 24143 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1109\/JSEN.2006.874493","article-title":"Magnetic Sensors and Their Applications","volume":"6","author":"Lenz","year":"2006","journal-title":"IEEE Sens. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1038\/nature03808","article-title":"Tomographic Imaging Using the Nonlinear Response of Magnetic Particles","volume":"435","author":"Gleich","year":"2005","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2086","DOI":"10.1038\/s41598-018-38451-0","article-title":"Magnetic Particle Mapping Using Magnetoelectric Sensors as an Imaging Modality","volume":"9","author":"Friedrich","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1063\/1.1654294","article-title":"Magnetomyography: Magnetic Fields around the Human Body Produced by Skeletal Muscles","volume":"21","author":"Cohen","year":"1972","journal-title":"Appl. Phys. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1109\/TBCAS.2020.2998290","article-title":"Ultrasensitive Magnetoelectric Sensing System for Pico-Tesla MagnetoMyoGraphy","volume":"14","author":"Zuo","year":"2020","journal-title":"IEEE Trans. Biomed. Circuits Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.jelectrocard.2004.08.035","article-title":"Recent Advances in Magnetocardiography","volume":"37","author":"Koch","year":"2004","journal-title":"J. Electrocardiol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1586\/14737159.5.3.291","article-title":"Clinical Application of Magnetocardiography","volume":"5","author":"Fenici","year":"2005","journal-title":"Expert Rev. Mol. Diagn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1016\/j.ijcard.2012.12.056","article-title":"Diagnostic Value of Magnetocardiography in Coronary Artery Disease and Cardiac Arrhythmias: A Review of Clinical Data","volume":"167","author":"Kwong","year":"2013","journal-title":"Int. J. Cardiol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3301","DOI":"10.1016\/j.clinph.2016.08.006","article-title":"Added Diagnostic Value of Magnetoencephalography (MEG) in Patients Suspected for Epilepsy, Where Previous, Extensive EEG Workup Was Unrevealing","volume":"127","author":"Duez","year":"2016","journal-title":"Clin. Neurophysiol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1046\/j.1460-9592.2003.00063.x","article-title":"Phantom Validation of Multichannel Magnetocardiography Source Localization","volume":"26","author":"Fenici","year":"2003","journal-title":"Pacing and Clin. Electrophysiol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Quarteroni, A., Formaggia, L., and Veneziani, A. (2006). Inverse problems in biomedical imaging: Modeling and methods of solution. Complex Systems in Biomedicine, Springer.","DOI":"10.1007\/88-470-0396-2"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yang, J., and Poh, N. (2011). Recent Application in Biometrics, IntechOpen.","DOI":"10.5772\/970"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Murzin, D., Mapps, D.J., Levada, K., Belyaev, V., Omelyanchik, A., Panina, L., and Rodionova, V. (2020). Ultrasensitive Magnetic Field Sensors for Biomedical Applications. Sensors, 20.","DOI":"10.3390\/s20061569"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1534","DOI":"10.1109\/JPROC.2004.833655","article-title":"Superconducting Quantum Interference Devices: State of the Art and Applications","volume":"92","author":"Kleiner","year":"2004","journal-title":"Proc. IEEE"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.sna.2005.11.023","article-title":"Highly Sensitive Magnetometers\u2014A Review","volume":"129","author":"Robbes","year":"2006","journal-title":"Sens. Actuators A Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"27167","DOI":"10.1364\/OE.18.027167","article-title":"Femtotesla Atomic Magnetometry in a Microfabricated Vapor Cell","volume":"18","author":"Griffith","year":"2010","journal-title":"Opt. Express"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6065","DOI":"10.1088\/0031-9155\/58\/17\/6065","article-title":"Multi-Sensor Magnetoencephalography with Atomic Magnetometers","volume":"58","author":"Johnson","year":"2013","journal-title":"Phys. Med. Biol."},{"key":"ref_18","unstructured":"Osborne, J., Orton, J., Alem, O., and Shah, V. (February, January 29). Fully Integrated Standalone Zero Field Optically Pumped Magnetometer for Biomagnetism. Proceedings of the Steep Dispersion Engineering and Opto-Atomic Precision Metrology XI, San Francisco, CA, USA."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Mhaskar, R.R., Knappe, S., and Kitching, J. (2010, January 1\u20134). Low-Frequency Characterization of MEMS-Based Portable Atomic Magnetometer. Proceedings of the 2010 IEEE International Frequency Control Symposium, Newport Beach, CA, USA.","DOI":"10.1109\/FREQ.2010.5556307"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Oelsner, G., IJsselsteijn, R., Scholtes, T., Kr\u00fcger, A., Schultze, V., Seyffert, G., Werner, G., J\u00e4ger, M., Chwala, A., and Stolz, R. (2021). Integrated Optically Pumped Magnetometer for Measurements within Earth\u2019s Magnetic Field. arXiv.","DOI":"10.1103\/PhysRevApplied.17.024034"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.measurement.2017.09.047","article-title":"Evaluation of Magnetoelectric Sensor Systems for Cardiological Applications","volume":"116","author":"Reermann","year":"2018","journal-title":"Measurement"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"022901","DOI":"10.1063\/1.4958728","article-title":"Inverse Bilayer Magnetoelectric Thin Film Sensor","volume":"109","author":"Yarar","year":"2016","journal-title":"Appl. Phys. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Tu, C., Chu, Z.-Q., Spetzler, B., Hayes, P., Dong, C.-Z., Liang, X.-F., Chen, H.-H., He, Y.-F., Wei, Y.-Y., and Lisenkov, I. (2019). Mechanical-Resonance-Enhanced Thin-Film Magnetoelectric Heterostructures for Magnetometers, Mechanical Antennas, Tunable RF Inductors, and Filters. Materials, 12.","DOI":"10.3390\/ma12142259"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1088\/0034-4885\/18\/1\/305","article-title":"Magnetostriction and Magnetomechanical Effects","volume":"18","author":"Lee","year":"1955","journal-title":"Rep. Prog. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Spetzler, B., Golubeva, E.V., M\u00fcller, C., McCord, J., and Faupel, F. (2019). Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors. Sensors, 19.","DOI":"10.3390\/s19214769"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Spetzler, B., Golubeva, E.V., Friedrich, R.-M., Zabel, S., Kirchhof, C., Meyners, D., McCord, J., and Faupel, F. (2021). Magnetoelastic Coupling and Delta-E Effect in Magnetoelectric Torsion Mode Resonators. Sensors, 21.","DOI":"10.3390\/s21062022"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4891","DOI":"10.1109\/JSEN.2016.2553962","article-title":"Adaptive Readout Schemes for Thin-Film Magnetoelectric Sensors Based on the Delta-E Effect","volume":"16","author":"Reermann","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2930","DOI":"10.1063\/1.117327","article-title":"A Microelectromechanical-based Magnetostrictive Magnetometer","volume":"69","author":"Osiander","year":"1996","journal-title":"Appl. Phys. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"223502","DOI":"10.1063\/1.3664135","article-title":"Fully Integrable Magnetic Field Sensor Based on Delta-E Effect","volume":"99","author":"Gojdka","year":"2011","journal-title":"Appl. Phys. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"052414","DOI":"10.1063\/1.4891540","article-title":"Microelectromechanical Magnetic Field Sensor Based on \u0394E Effect","volume":"105","author":"Jahns","year":"2014","journal-title":"Appl. Phys. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"152402","DOI":"10.1063\/1.4932575","article-title":"Phase Modulated Magnetoelectric Delta-E Effect Sensor for Sub-Nano Tesla Magnetic Fields","volume":"107","author":"Zabel","year":"2015","journal-title":"Appl. Phys. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"222401","DOI":"10.1063\/1.4952735","article-title":"Multimode Delta-E Effect Magnetic Field Sensors with Adapted Electrodes","volume":"108","author":"Zabel","year":"2016","journal-title":"Appl. Phys. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"031108","DOI":"10.1063\/5.0042448","article-title":"Influence of the Piezoelectric Material on the Signal and Noise of Magnetoelectric Magnetic Field Sensors Based on the Delta-E Effect","volume":"9","author":"Spetzler","year":"2021","journal-title":"APL Mater."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5269","DOI":"10.1038\/s41598-021-84415-2","article-title":"Exchange Biased Delta-E Effect Enables the Detection of Low Frequency PT Magnetic Fields with Simultaneous Localization","volume":"11","author":"Spetzler","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1038\/srep01985","article-title":"Self-Biased 215 MHz Magnetoelectric NEMS Resonator for Ultra-Sensitive DC Magnetic Field Detection","volume":"3","author":"Nan","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"143510","DOI":"10.1063\/1.4979694","article-title":"Ultra-Sensitive NEMS Magnetoelectric Sensor for Picotesla DC Magnetic Field Detection","volume":"110","author":"Li","year":"2017","journal-title":"Appl. Phys. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"232407","DOI":"10.1063\/5.0010975","article-title":"Large Non-Saturating Shift of the Torsional Resonance in a Doubly Clamped Magnetoelastic Resonator","volume":"116","author":"Staruch","year":"2020","journal-title":"Appl. Phys. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2014.2356852","article-title":"Sensitivity and Noise Evaluation of a Bonded Magneto(Elasto) Electric Laminated Sensor Based on In-Plane Magnetocapacitance Effect for Quasi-Static Magnetic Field Sensing","volume":"51","author":"Zhuang","year":"2015","journal-title":"IEEE Trans. Magn."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"032905","DOI":"10.1063\/1.4994663","article-title":"Frequency Reconfigurable Phase Modulated Magnetoelectric Sensors Using \u0394E Effect","volume":"111","author":"Staruch","year":"2017","journal-title":"Appl. Phys. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"10Q107","DOI":"10.1063\/1.1861375","article-title":"Low-Frequency Noise Measurements on Commercial Magnetoresistive Magnetic Field Sensors","volume":"97","author":"Stutzke","year":"2005","journal-title":"J. Appl. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"056676","DOI":"10.1063\/1.4978465","article-title":"Tunneling Magnetoresistance Sensor with PT Level 1\/f Magnetic Noise","volume":"7","author":"Deak","year":"2017","journal-title":"AIP Adv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"112023","DOI":"10.1016\/j.sna.2020.112023","article-title":"Mapping of Magnetic Nanoparticles and Cells Using Thin Film Magnetoelectric Sensors Based on the Delta-E Effect","volume":"309","author":"Lukat","year":"2020","journal-title":"Sens. Actuators A Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1800484","DOI":"10.1002\/admt.201800484","article-title":"A 1D Magnetoelectric Sensor Array for Magnetic Sketching","volume":"4","author":"Chu","year":"2019","journal-title":"Adv. Mater. Technol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/j.jsamd.2020.06.005","article-title":"Giant Magnetoelectric Effects in Serial-Parallel Connected Metglas\/PZT Arrays with Magnetostrictively Homogeneous Laminates","volume":"5","author":"Cuong","year":"2020","journal-title":"J. Sci. Adv. Mater. Devices"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"112064","DOI":"10.1016\/j.sna.2020.112064","article-title":"Room Temperature Magnetoelectric Sensor Arrays For Application of Detecting Iron Profiles in Organs","volume":"311","author":"Xi","year":"2020","journal-title":"Sens. Actuators A Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"064102","DOI":"10.1063\/5.0011931","article-title":"High Sensitivity Face Shear Magneto-Electric Composite Array for Weak Magnetic Field Sensing","volume":"128","author":"Lu","year":"2020","journal-title":"J. Appl. Phys."},{"key":"ref_47","first-page":"1","article-title":"Microbridge-Structured Magnetoelectric Sensor Array Based on PZT\/FeCoSiB Thin Films","volume":"56","author":"Li","year":"2020","journal-title":"IEEE Trans. Magn."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Kim, H.J., Wang, S., Xu, C., Laughlin, D., Zhu, J., and Piazza, G. (2017, January 22\u201326). Piezoelectric\/Magnetostrictive MEMS Resonant Sensor Array for in-Plane Multi-Axis Magnetic Field Detection. Proceedings of the 2017 IEEE 30th International Conference on Micro Electro Mechanical Systems (MEMS), Las Vegas, NV, USA.","DOI":"10.1109\/MEMSYS.2017.7863352"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1038\/nmat3306","article-title":"Exchange Biasing of Magnetoelectric Composites","volume":"11","author":"Lage","year":"2012","journal-title":"Nat. Mater."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"075115","DOI":"10.1063\/1.4959895","article-title":"Low Temperature Aluminum Nitride Thin Films for Sensory Applications","volume":"6","author":"Yarar","year":"2016","journal-title":"AIP Adv."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"7364","DOI":"10.1109\/JSEN.2017.2759000","article-title":"Noise of a JFET Charge Amplifier for Piezoelectric Sensors","volume":"17","author":"Durdaut","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Jahns, R., Kn\u00f6chel, R., Greve, H., Woltermann, E., Lage, E., and Quandt, E. (2011, January 30\u201331). Magnetoelectric Sensors for Biomagnetic Measurements. Proceedings of the 2011 IEEE International Symposium on Medical Measurements and Applications, Bari, Italy.","DOI":"10.1109\/MeMeA.2011.5966676"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2771","DOI":"10.1109\/TIM.2017.2709478","article-title":"Modeling and Analysis of Noise Sources for Thin-Film Magnetoelectric Sensors Based on the Delta-E Effect","volume":"66","author":"Durdaut","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1109\/JMEMS.2020.3014402","article-title":"Fundamental Noise Limits and Sensitivity of Piezoelectrically Driven Magnetoelastic Cantilevers","volume":"29","author":"Durdaut","year":"2020","journal-title":"J. Microelectromech. Syst."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"183504","DOI":"10.1063\/1.5096001","article-title":"Influence of the Quality Factor on the Signal to Noise Ratio of Magnetoelectric Sensors Based on the Delta-E Effect","volume":"114","author":"Spetzler","year":"2019","journal-title":"Appl. Phys. Lett."},{"key":"ref_56","unstructured":"Durdaut, P. (2019). Ausleseverfahren Und Rauschmodellierung F\u00fcr Magnetoelektrische Und Magnetoelastische Sensorsysteme. [Ph.D. Thesis, Kiel University]."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"064036","DOI":"10.1103\/PhysRevApplied.12.064036","article-title":"Magnetic Sensitivity of Bending-Mode Delta-E-Effect Sensors","volume":"12","author":"Spetzler","year":"2019","journal-title":"Phys. Rev. Appl."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"20120455","DOI":"10.1098\/rsta.2012.0455","article-title":"A Review on Equivalent Magnetic Noise of Magnetoelectric Laminate Sensors","volume":"372","author":"Wang","year":"2014","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1109\/JSEN.2008.2011067","article-title":"Equivalent Magnetic Noise Limit of Low-Cost GMI Magnetometer","volume":"9","author":"Ding","year":"2009","journal-title":"IEEE Sens. J."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"2100294","DOI":"10.1002\/admt.202100294","article-title":"Curvature and Stress Effects on the Performance of Contour-Mode Resonant \u0394E Effect Magnetometers","volume":"6","author":"Matyushov","year":"2021","journal-title":"Adv. Mater. Technol."},{"key":"ref_61","unstructured":"Oppenheim, A.V., Schafer, R.W., and Buck, J.R. (1998). Discrete-Time Signal Processing, Prentice Hall. [2nd ed.]."},{"key":"ref_62","unstructured":"Orfanidis, S.J. (1996). Introduction to Signal Processing, Prentice Hall."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/TAU.1967.1161901","article-title":"The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over a Short, Modified Periodograms","volume":"15","author":"Welch","year":"1967","journal-title":"IEEE Trans. Audio Electroacoust."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7594\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:31:02Z","timestamp":1760167862000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,16]]},"references-count":63,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21227594"],"URL":"https:\/\/doi.org\/10.3390\/s21227594","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,16]]}}}