Modeling of Two-Dimensional Spiral Inductors

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.