On the Dynamic Rounding-off in Analogue and RF Optimal Circuit Sizing

Frequently used approaches to solve discrete multivariable optimisation problems consist of computing solutions using a continuous optimisation technique. Then, using heuristics, the variables are rounded-off to their nearest available discrete values to obtain a discrete solution. Indeed, in many engineering problems, and particularly in analogue circuit design, component values, such as the geometric dimensions of the transistors, the number of fingers in an integrated capacitor or the number of turns in an integrated inductor, cannot be chosen arbitrarily since they have to obey to some technology sizing constraints. However, rounding-off the variables values a posteriori and can lead to infeasible solutions (solutions that are located too close to the feasible solution frontier) or degradation of the obtained results (expulsion from the neighbourhood of a ‘sharp’ optimum) depending on how the added perturbation affects the solution. Discrete optimisation techniques, such as the dynamic rounding-off technique (DRO) are, therefore, needed to overcome the previously mentioned situation. In this paper, we deal with an improvement of the DRO technique. We propose a particle swarm optimisation (PSO)-based DRO technique, and we show, via some analog and RF-examples, the necessity to implement such a routine into continuous optimisation algorithms.