Editing Wireless power transfer (section)

=== Electrodynamic wireless power transfer ===

An electrodynamic wireless power transfer (EWPT) system utilizes a receiver with a mechanically resonating or rotating permanent magnet.<ref name="Garraud1">A. Garraud and D. P. Arnold, "Advancements in electrodynamic wireless power transmission", IEEE Sensors Conference, Oct. 2016, 82–84</ref><ref name=Mur-Miranda>J. O. Mur-Miranda, S. Cheng and D. P. Arnold, "Improving the efficiency of electrodynamic wireless power transmission," 2013 7th European Conference on Antennas and Propagation (EuCAP), 2013, pp. 2848–2852.</ref> When subjected to a time-varying magnetic field, the mechanical motion of the resonating magnet is converted into electricity by one or more electromechanical transduction schemes (e.g. [[inductive coupling|electromagnetic/induction]], [[piezoelectricity|piezoelectric]], or [[capacitive coupling|capacitive]]).<ref name="Halim">{{cite book | doi=10.1109/MEMS46641.2020.9056444 | chapter=A High-Performance Electrodynamic Micro-Receiver for Low-Frequency Wireless Power Transfer | title=2020 IEEE 33rd International Conference on Micro Electro Mechanical Systems (MEMS) | date=2020 | last1=Halim | first1=Miah A. | last2=Smith | first2=Spencer E. | last3=Samman | first3=Joseph M. | last4=Arnold | first4=David P. | pages=590–593 | isbn=978-1-7281-3581-6 }}</ref><ref name="Spencer">{{cite book | doi=10.1109/MEMS51782.2021.9375416 | chapter=Dual-Transduction Electromechanical Receiver for Near-Field Wireless Power Transmission | title=2021 IEEE 34th International Conference on Micro Electro Mechanical Systems (MEMS) | date=2021 | last1=Smith | first1=Spencer E. | last2=Halim | first2=Miah A. | last3=Rendon-Hernandez | first3=Adrian A. | last4=Arnold | first4=David P. | pages=38–41 | isbn=978-1-6654-1912-3 }}</ref> In contrast to inductive coupling systems which usually use high frequency magnetic fields, EWPT uses low-frequency magnetic fields (<1&nbsp;kHz),<ref name="Truong">Truong, B.D.; Roundy, S. Wireless Power Transfer System with Center-Clamped Magneto-Mechano-Electric (MME) Receiver: Model Validation and Efficiency Investigation. Smart Mater. Struct. 2019, 28, 015004.</ref><ref name="Liu">Liu, G.; Ci, P.; Dong, S. Energy Harvesting from Ambient Low-Frequency Magnetic Field using Magneto-Mechano-Electric Composite Cantilever. Appl. Phys. Lett. 2014, 104, 032908.</ref><ref name="Garraud2">Garraud, N.; Alabi, D.; Varela, J.D.; Arnold, D.P.; Garraud, A. Microfabricated Electrodynamic Wireless Power Receiver for Bio-implants and Wearables. In Proceedings of the 2018 Solid-State Sensor and Actuator Workshop, Hilton Head Island, SC, USA, 3–7 June 2018; pp. 34–37.</ref> which safely pass through conductive media and have higher human field exposure limits (~2 mTrms at 1&nbsp;kHz),<ref name=IEEE1>IEEE. Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz; IEEE Standard C95.1–2010; IEEE: Piscataway, NJ, USA, 2010; pp. 1–238.</ref><ref name=IEEE2>IEEE. Standard for Safety Levels with Respect to Human Exposure to Electromagnetic Fields, 0–3 kHz; IEEE Standard C95.6-2002; IEEE: Piscataway, NJ, USA, 2002; pp. 1–43.</ref> showing promise for potential use in wirelessly recharging [[implant (medicine)|biomedical implants]]. 
For EWPT devices having identical resonant frequencies, the magnitude of power transfer is entirely dependent on critical coupling coefficient, denoted by <math>k</math>, between the transmitter and receiver devices.  For coupled resonators with same resonant frequencies, wireless power transfer between the transmitter and the receiver is spread over three regimes – under-coupled, critically coupled and over-coupled. As the critical coupling coefficient increases from an under-coupled regime (<math>k<k_{crit}</math>) to the critical coupled regime, the optimum voltage gain curve grows in magnitude (measured at the receiver) and peaks when <math>k=k_{crit}</math> and then enters into the over-coupled regime where <math>k>k_{crit}</math> and the peak splits into two.<ref>Stark, Joseph C., Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004, http://hdl.handle.net/1721.1/18036</ref> This critical coupling coefficient is demonstrated to be a function of distance between the source and the receiver devices.<ref>A.P. Sample, D.T. Meyer and J.R.Smith, "Analysis, Experimental Results, and Range Adaptation of Magnetically Coupled Resonators for Wireless Power Transfer", in ''IEEE Transactions on Industrial Electronics'', Vol 58, No. 2, pp 544–554, Feb 2011.</ref><ref>A. A. Rendon-Hernandez, M. A. Halim, S. E. Smith and D. P. Arnold, "Magnetically Coupled Microelectromechanical Resonators for Low-Frequency Wireless Power Transfer," 2022 IEEE 35th International Conference on Micro Electro Mechanical Systems Conference (MEMS), 2022, pp. 648–651.</ref>