A Versatile and Accurate Vector-Based Method for Modeling and Analyzing Planar Air-Core Inductors

Abstract

Planar air-core inductors come in a variety of geometrical shapes, including in the form of the conventional spiral geometry and novel complex geometries. In the design phase of a system, the inductance of the employed inductor would need to be ascertained. This is usually ascertained by tedious mathematical derivations on a segment-by-segment (inductor) basis or time-consuming computer modeling, and the complexity can become intractable for complex geometries. In this paper, we propose a versatile, yet accurate, vector-based method to ascertain the inductance of planar air-core inductors with virtually any geometry, including novel complex geometry inductors—rather easily. Our proposed method decomposes the inductor segments into vectors, and thereafter utilizes geometric models to compute the inductance in a systematic fashion. We benchmark our proposed method against the conventional electromagnetic field solver simulations to estimate the inductances of six planar inductors ranging from a conventional spiral air-core inductor to that embodying different and complex geometries. On the basis of these six inductor examples, we show that our method is highly accurate with a worst-case error of $\sim 5$% compared to that obtained using conventional electromagnetic field solver. Of particular interest, our modeling for novel complex geometry planar inductors is relatively simple.