Simulation-Based Multi-Objective Optimization of Current Conveyors: Performance Evaluations A. Sallem 1 , B. Benhala 2 , M. Kotti 1 , M. Fakhfakh 1 , A. Ahaitouf 2 , M. Loulou 1 1 : LETI-ENIS, University of Sfax, Tunisia 2 : LSSC-FST, University of Sidi Mohamed Ben Abdellah, Morocco sallem.amin@yahoo.com, mourad.fakhfakh@ieee.org, ali_ahitouf@yahoo.fr Abstract—Multi-objective metaheuristics are over and over again used by analog designers. Pareto fronts linking conflicting parameters are usually generated using different optimisation techniques. Conclusions on these fronts are generally made in a subjective manner; no performance measures are used! In this paper we deal with the use of two metrics, namely the C-metric and the hypervolume indicator. The simulation-based technique is used to generate the non-dominated set of points of the Pareto fronts. Two current mode circuits are considered: a conventional and a differential CMOS current conveyor. The used metrics are detailed, their utility is highlighted, and the results are discussed I. INTRODUCTION Analog circuit design is becoming more and more complex; there is a pressing need for analog circuit design automation to meet the time to market constraints. Analog design automation can provide solutions to some of, or reduce, the problems in analog design. The main goals of analog design automation can be summarized as follows: try to decrease the design time, increase the circuit’s performance [1-3]. Recent advances in design automation have led to a gradual transition from the hand-calculation based design namely knowledge-based design, to the optimization-based design. The first, i.e. the knowledge-based design is one of the earlier approaches. Its basic idea is to have a predefined design plan [4] for sizing circuits to meet the performance specifications. The second one, i.e. the simulation based approach, is based on the use of an optimization algorithm rather than the designer experience. Two different subcategories can be distinguished. The first is the equation-based optimization, which uses symbolic expressions of both performances and constraints to evaluate the circuit’s performance(s) and generate the optimal values of the circuit’s parameters. These equations can be derived by using symbolic analyzers [5-7]. The second approach is the known as the simulation-based optimization. It is based on the use of a circuit simulator such as SPICE, which evaluates the circuit’s performance(s) and the constraints, as well [8-10]. The simulation-based approach is adopted in this work. Its basic idea consists of ‘by-passing’ the modeling stage in the sizing problem and to use directly a simulator to evaluate the objective functions, and to check the circuit’s constraints, as well. In other words, in each iteration of the optimization, the circuit simulator is called to measure the circuit’s performance(s) for a set of design parameters. In analog circuit optimization, two kinds of optimizations are used: the mono-objective optimization and the multi- objective optimization. A general optimization problem can be defined in the following format: [ ] p , 1 i , x x x where R ) x ( h ; 0 ) x ( h and R ) x ( g ; 0 ) x ( g : to subject R ) x ( f ); x ( f Minimize Ui i Li n m ∈ ≤ ≤ ∈ = ∈ ≤ ∈ (1) where, m inequality constraints to satisfy, n equality constraints to assure, p parameters to manage. L x  and U x  are lower and upper boundaries vectors of the parameters. Actually, circuit optimization problems involve more than one objective. For instance, for the MOSFET amplifier, more than one objective function (OF) may be optimized, such as gain, noise figure, slew-rate, bandwidth, etc. Consequently expression (2) should be modified as: [ ] p , 1 i , x x x where R ) x ( h ; 0 ) x ( h and R ) x ( g ; 0 ) x ( g : to subject R ) x ( f ); x ( f Minimize Ui i Li n m k ∈ ≤ ≤ ∈ = ∈ ≤ ∈   (2) where, k number of objectives ( ≥ 2 ), m inequality constraints to satisfy, n equality constraints to assure, p parameters to manage. Commonly designers transform the multi-objective problem into a mono-objective one using the weighting technique [11]. The latter requires the designer to select values of weights for each objective. The so obtained mono-objective function can be written as:  = = k 1 i i i ) x ( f  ) x ( F   (3) ], k , 1 [ i ,  i ∈ are weighting coefficients. However, it has been proven that this technique is not suitable and may lead to non optimal solutions (see for instance [12]). 2012 International Conference on Design & Technology of Integrated Systems in Nanoscale Era - 1 - 978-1-4673-1928-7/12/$31.00 ©2012 IEEE