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Efficient modeling of substrate eddy currents for integrated spiral inductor design automation

The automated design of integrated spiral inductors requires efficient substrate eddy current modeling techniques for initial design space exploration. In this paper, we introduce a new multi-layer substrate modeling technique for spiral inductors based on complex image theory. Our substrate modeling approach combines explicit closed-form expressions with techniques that exploit the spiral inductor's geometry. The new approach provides up to 5 orders of magnitude performance improvement over traditional methods using field solvers while providing an average error of 0.1% for inductance and 3.9% for resistance over a wide range of inductor geometries and substrate configurations. Due to its speed, our technique provides a practical substrate modeling solution for rapid inductor automated synthesis.