A novel analytical model of inductively coupled wireless power transfer is presented. For the first time, the effects of coil misalignment and geometry are addressed in a single mathematical expression. In the applications envisaged, such as radio frequency identification (RFID) and biomedical implants, the receiving coil is normally significantly smaller than the transmitting coil. Formulas are derived for the magnetic field at the receiving coil when it is laterally and angularly misaligned from the transmitting coil. Incorporating this magnetic field solution with an equivalent circuit for the inductive link allows us to introduce a power transfer formula that combines coil characteristics and misalignment factors. The coil geometries considered are spiral and short solenoid structures which are currently popular in the RFID and biomedical domains. The novel analytical power transfer efficiency expressions introduced in this study allow the optimization of coil geometry for maximum power transfer and misalignment tolerance. The experimental results show close correlation with the theoretical predictions. This analytic technique can be widely applied to inductive wireless power transfer links without the limitations imposed by numerical methods.

Wireless Power Transfer in Loosely Coupled Links: Coil Misalignment Model

Preface. Microelectromechanical Systems (MEMS) and Radio Frequency MEMS. MEMS Materials and Fabrication Techniques. RF MEMS Switches and Micro Relays. MEMS Inductors and Capacitors. Micromachined RF Filters. Micromachined Phase Shifters. Micromachined Transmission Lines and Components. Micromachined Antennae. Integration and Packaging for RF MEMS Devices. Index.

RF MEMS and their applications

The high frequency operation of magnetic components, in applications such as filters, makes them ideal candidates for thick film technology along with resistors and capacitors. This in turn leads to distinct advantages over labor intensive wire wound components: improved reliability, repeatability, accuracy and consequential cost reductions. This paper establishes a new set of formulas for the self and mutual impedances of planar coils on ferromagnetic substrates. A planar coil in air is a special case of the generalized formulas. The formulas are derived directly from Maxwell's equations and therefore serve as a useful yardstick for simpler approximations. The formulas take full account of the current density distribution in the coil cross-section and the eddy current losses in the substrate. Experimental and calculated impedances up to 100 MHz are presented for a four layer device with three turns per layer which is 150 /spl mu/m thick and 40 mm/sup 2/ in area. >

Calculation of self and mutual impedances in planar magnetic structures

This paper describes three micromachined planar inductors (a spiral type, a solenoid type, and a toroidal meander type) with electroplated nickel-iron permalloy cores which have been realized on a silicon wafer using micromachining techniques. The electrical properties among the fabricated inductors are compared and the related fabrication issues are discussed, with emphasis on the low-temperature CMOS-compatible process, the high current-carrying capacity, the high magnetic flux density, the closed magnetic circuits, and the low product cost. The micromachined on-chip inductors can be applied for magnetic microelectromechanical systems devices, such as micromotors, microactuators, microsensors, and integrated power converters, which envisages new micropower magnetics on a chip with integrated circuits.

Micromachined planar inductors on silicon wafers for MEMS applications

The scaling laws associated with the miniaturization of planar inductively coupled plasmas (ICPs) are investigated. The applications for miniature ICPs include microelectromechanical systems (MEMS) for chemical analysis and micro ion propulsion systems. Langmuir probe and microwave interferometry measurements of three ICPs with spiral-shaped coil diameters of 5, 10, and 15 mm show that electron density typically falls in the range of 10/sup 16/-10/sup 17/ m/sup -3/. The electron density is about an order of magnitude lower than large-scale ICPs as a result of the large surface-to-volume ratio of small discharges. The measured electron temperature is higher than predicted by a simple "global model" unless the plasma dimensions are determined more precisely by subtracting the sheath width from the chamber dimensions. Since the sheath width does not scale with the plasma size, the sheath width may ultimately limit the minimum size of ICPs. Plasma initiation power is determined to have a minimum at a gas pressure for which the electron collision frequency equals the frequency of the RF power supply. Small scale ICPs operating at 460 MHz can therefore be started most easily at /spl sim/1 torr. The design of the coil is critical to miniature ICP performance. Unlike large-scale ICPs that operate efficiently using a broad range of coil shapes, the miniature coil must be carefully designed and constructed to minimize parasitic resistance.

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Miniaturization of inductively coupled plasma sources

The trend toward size reduction of power-conditioning circuitry is increasing the use of higher switching frequencies (in the megahertz range) for dc-to-dc conversion. For power magnetic components this is requiring novel designs of energy-storage inductors. An investigation is reported of two-dimensional spiral wound air-core inductors. These inductors have the potential advantages of being printable as a thick- or thin-film circuit element and, therefore, inexpensive to manufacture. Via a simplifying approximation, one can reduce a formidable mathematical problem to one in which closedform expressions can be written for the total inductance and the resistance. Our approximate expression for the resistance is meant to account for the skin effect exactly and for the proximity effect in an average way. A comparison is presented between the predicted and measured value of impedance as a function of frequency. Implications of these results and of modeling the effects of parasitic capacitance are discussed in the context of determining an optimized geometry and operating frequency.

E. Whelan

Papers

Modeling of Two-Dimensional Spiral Inductors