Generation of surrogate models of Pareto-optimal performance trade-offs of planar inductors M. Kotti • R. Gonza´lez-Echevarrı ´a • F. V. Ferna´ndez • E. Roca • J. Sieiro • R. Castro-Lo´pez • M. Fakhfakh • J. M. Lo´pez-Villegas Received: 25 February 2013 / Revised: 5 September 2013 / Accepted: 4 November 2013 / Published online: 28 November 2013 Ó Springer Science+Business Media New York 2013 Abstract Systematic design methodologies for wireless transceivers require an efficient design of integrated induc- tors. Early availability of feasible trade-offs between inductance, quality factor, self-resonance frequency and area, is a key enabler towards the improvement of such design methodologies. This paper introduces such an approach in two steps. First, a Pareto-optimal performance front of integrated inductors is generated by embedding a performance evaluator into a multi-objective optimization tool. Then, starting from the optimal front samples, a sur- rogate model of the performance front is obtained. Experi- mental results in a 0.35-lm CMOS technology are provided. Keywords RF circuit design  Integrated planar inductors  Performance modeling  Multi-objective optimization  Surrogate modeling 1 Introduction Increasing integration of wireless transceivers has motivated a growing need for accurate modeling and efficient design of integrated inductors in radiofrequency (RF) circuits. Induc- tor performances are limited by numerous parasitic effects and their accurate evaluation is a difficult and computa- tionally expensive process. Therefore, designers often resort to the libraries of inductors provided by silicon foundries. However, such inductor libraries have usually a very limited offer and the design of RF blocks is conditioned by the number and quality of the available inductors. High-performance RF circuit design benefits from inductors specifically designed for the application at hand. When addressing the design of RF circuits including inductors, the designer is faced with questions like: Is this inductance realizable with this technology at this frequency of operation? Which is the quality factor that can be obtained with this topology for a given inductance in this frequency range? Which is the required inductor area to get a certain inductance and quality factor? A first common approach to inductor design is to use analytical equations or models relating design parameters with inductor performances [1, 2]. Due to the large inac- curacies of these models, high performance design requires lengthy iterations between layout implementation and accurate electromagnetic simulation. Even if the approach is successful, just a single, most likely suboptimal design is obtained as the design space exploration implied by the questions posed above can hardly be accomplished. Different design automation approaches have been reported to optimize inductor-based RF circuit perfor- mances. Most of them are based on iterative loops between optimization algorithms and performance evaluators. Dif- ferences arise in the performance evaluation technique used for the inductors, ranging from those based on fast but inaccurate analytical models to those based on slow but accurate electromagnetic simulation. For instance, the approaches in [3, 4], use equivalent circuit models with M. Kotti  M. Fakhfakh University of Sfax, Sfax, Tunisia R. Gonza´lez-Echevarrı ´a  F. V. Ferna´ndez (&)  E. Roca  R. Castro-Lo´pez Institute of Microelectronics of Seville (IMSE-CNM), CSIC and University of Seville, Avda. Americo Vespucio s/n, Isla de la Cartuja., 41092 Seville, Spain e-mail: pacov@imse-cnm.csic.es; Francisco.Fernandez@imse-cnm.csic.es J. Sieiro  J. M. Lo´pez-Villegas Grup de Radiofrequ¨e`ncia, Facultat de Fı ´sica, Universitat de Barcelona, Martı ´ Franque`s. 1, 08028 Barcelona, Spain 123 Analog Integr Circ Sig Process (2014) 78:87–97 DOI 10.1007/s10470-013-0230-8