Multi-objective metaheuristics are over and over again used by analog designers. They allow generating a set of non-dominated solutions (i.e. the Pareto front). In this chapter, the authors highlight the fact, via the application of six multi-objective algorithms to the optimization of conflicting performances of four analog and RF circuits, that the generated fronts highly depend on the used algorithm. They propose a solution consisting of combining metaheuristics to generate a “better” front by merging results obtained thanks to different algorithms and the application of a dominance routine. Viability of the proposed idea is shown through examples.
TopIntroduction
Over the last two decades substantial attention of analogue, mixed and RF (AMS/RF) designers has been focusing (and continues to be) on applications of optimization algorithms to the analogue circuit design, sizing and synthesis (Tlelo-Cuautle et al., 2010); (Fakhfakh et al., 2010); (Lourenço et al., 2013).
Actually, analogue circuit design has long been considered as a field that mainly relies on the designer experience and expertise.
C. Toumazou et al. stated in (Toumazou et al., 2002) that ‘‘… analogue design is a knowledge intensive, multiphase and iterative task, which usually sketches over a significant period of time and is performed by designers with a large portfolio of skills…’’. In fact, many reasons are behind such affirmations, mainly the lack of analogue circuit design formalism. Indeed, unlike the digital counterpart, where formal mapping of function to circuit realization is possible, the analogue design realm presents an extra large spectrum of circuit performances and tradeoffs (for instance, SNR, CMRR, offsets, distortion, slew-rate, parasitic elements, phase margin, frequency operating range, etc.). In addition, AMS/RF design is subject to a large number of constraints and companion formula that have to be satisfied. Figure 1 illustrates a pictorial representation of such a complex AMS/RF design problem (Pereira et al., 2012).
Figure 1.
Pictorial view of a design optimization approach
Endeavours are being made to alleviate such problems. In this context, two approaches are being developed (in parallel) and it is important to mention that it is not foreseen that one will prevail over the other in the near future.
TopDevelopment Of Symbolic Analyzers
Symbolic analysis considers the generation of the circuit transfer function(s), H(s), and to present it in its symbolic form, i.e. components are kept as symbols and are not replaced by their numerical values, as it is shown by (1), where s is the Laplace variable, and xi represents the corresponding symbolic parameter.
(1)In this context many approaches were/are considered, mainly matrix generation methods and graph based approaches (Fernández, Rodríguez-Vázquez, Huertas, & Gielen, 1998); (Fakhfakh et al., 2010); (Pierzchala, & Fakhfakh, 2011); (Fakhfakh, & Pierzchala, 2013).
Due to the increasing complexity of the considered circuits and systems, these techniques were implemented in order to automate that task, see for instance (Seda et al.,1988); (Gielen et al., 1989); (Fernández et al.,1991); (Hassoun, & Lin,1995); (Biolek,2000); (Sommer et al., 2000); (Luchetta et al., 2001); (Tlelo-Cuautle et al., 2004); (Fakhfakh, & Loulou, 2010); (Sánchez-López et al., 2011); (Pierzchala, & Fakhfakh, 2013).