Analythical characterization of variable width integrated spiral inductors

In this paper a general method for characterizing tapered inductors with square, hexagonal or octagonal shape is presented. The method proposed allows the evaluation of the series inductance to integrate in any integrated inductor lumped element model, thus granting the overall characterization of the device and the evaluation of design parameters such as the quality factor or the resonance frequency. In this work, the inductor is divided into several segments and the corresponding self and mutual inductances are calculated. In the end, results obtained for several working examples are compared against a field solver. Relative errors below 3% are obtained for square, hexagonal or octagonal inductors, thus proving the validity of the method proposed. Furthermore, the methodology adopted may be easily applied to any polygonal shape.