Rapid multi-objective design of integrated on-chip inductors by means of Pareto front exploration and design extrapolation

ABSTRACT

Identification of the best trade-offs between conflicting design objectives allows for making educated design decisions as well as assessing suitability of a given component or circuit for a specific application. In case of inductors, the typical objectives include maximization of the quality factor and minimization of the layout area, as well as maintaining a required inductance at a given operating frequency. This work demonstrates low-cost multi-objective design optimization of integrated inductors. The primary technique utilized here is a point-by-point Pareto front exploration where subsequent Pareto-optimal designs are obtained by moving along the front using local search methods. Considerable reduction of the design cost is achieved by extrapolating inductor dimensions at the subsequent optimal point, based on already available data as well as size constraints. The proposed methodology is verified using two examples of spiral inductors implemented in 65-nm CMOS technology. Comparisons with point-by-point optimization without extrapolation are also provided.

KEYWORDS:

• EM analysis
• integrated inductors
• multi-objective design
• simulation-driven optimization
• size reduction

Acknowledgement

The authors would like to thank Computer Simulation Technology AG, Darmstadt, Germany, for making CST Microwave Studio available.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the Icelandic Centre for Research (RANNIS) [grant number 163299051] and by National Science Centre of Poland [grant number 2015/17/B/ST6/01857].

Notes on contributors

Slawomir Koziel

Slawomir Koziel received the M.Sc. and Ph.D. degrees in electronic engineering from Gdańsk University of Technology, Poland, in 1995 and 2000, respectively. He also received the M.Sc. degrees in theoretical physics and in mathematics, in 2000 and 2002, respectively, as well as the PhD in mathematics in 2003, from the University of Gdańsk, Poland. He is currently a Professor with the School of Science and Engineering, Reykjavik University, Iceland. His research interests include CAD and modeling of microwave and antenna structures, simulation-driven design, surrogate-based optimization, space mapping, circuit theory, analog signal processing, evolutionary computation and numerical analysis.

Piotr Kurgan

Piotr Kurgan received the M.Sc. and Ph.D. degrees in electronic engineering from Gdańsk University of Technology, Poland, in 2008 and 2017, respectively. He is currently an Assistant Professor with the Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Poland. His research interests include CAD of complex microwave circuits and integrated inductors involving surrogate-based modeling and optimization techniques.