Radio-Frequency Inductor Synthesis Using Evolutionary Computation and Gaussian-Process Surrogate Modeling

In recent years, the application of evolutionary computation techniques to electronic circuit design problems, ranging from digital to analog and radiofrequency circuits, has received increasing attention. The level of maturity runs inversely to the complexity of the design task, less complex in digital circuits, higher in analog ones and still higher in radiofrequency circuits. Radiofrequency inductors are key culprits of such complexity. Their key performance parameters are inductance and quality factors, both a function of the frequency. The inductor optimization requires knowledge of such parameters at a few representative frequencies. Most common approaches for optimization-based radiofrequency circuit design use analytical models for the inductors. Although a lot of effort has been devoted to improve the accuracy of such analytical models, errors in inductance and quality factor in the range of 5% to 25% are usual and it may go as high as 200% for some device sizes. When the analytical models are used in optimization-based circuit design approaches, these errors lead to suboptimal results, or, worse, to a disastrous non-fulfilment of specifications. Expert inductor designers rely on iterative evaluations with electromagnetic simulators, which, properly configured, are able to yield a highly accurate performance evaluation. Unfortunately, electromagnetic simulations typically take from some tens of seconds to a few hours, hampering their coupling to evolutionary computation algorithms. Therefore, analytical models and electromagnetic simulation represent extreme cases of the accuracy-efficiency trade-off in performance evaluation of radiofrequency inductors. Surrogate modeling strategies arise as promising candidates to improve such trade-off. However, obtaining the necessary accuracy is not that easy as inductance and quality factor at some representative frequencies must be obtained and both performances change abruptly around the self-resonance frequency, which is particular to each device and may be located above or below the frequencies of interest. Both, offline and online training methods will be considered in this work and a new two-step strategy for inductor modeling is proposed that significantly improves the accuracy of offline methods. The new strategy is demonstrated and compared for both, singleobjective and multi-objective optimization scenarios. Numerous experimental results show that the proposed two-step approach outperforms simpler application strategies of surrogate modelling techniques, getting comparable performances to approaches based on electromagnetic simulation but with orders of magnitude less computational effortPeer reviewe