Multi-objective Genetic Approach for Analog Circuit Sizing using SVM Macro-model D. Boolchandani Dept. of ECE NIT Jaipur, India - 302017 Email: dbool@ieee.org Anupam Kumar Centre for Development of Telematics Mehrauli Road, New Delhi, India - 110 016 Email: anupam.mnit@yahoo.co.in Vineet Sahula Dept. of ECE NIT Jaipur, India - 302017 Email: sahula@ieee.org Abstract—Analog Circuit sizing is the task to determine the sizes of all components in the circuit during automated synthesis. Randomized combinatorial optimization algorithms are desired for quicker determination of a set of optimal sizes of the com- ponents. These algorithms require set of multiple performance parameters, for a very large number of sized circuits. Therefore the reduction in time required to estimate these performance parameters is also highly desired. For the purpose of estimation of performance parameters, we employ Support Vector Machine (SVM) based macro-models of analog circuits, instead of using SPICE simulation. These SVM macro-models are not only faster to evaluate, but use of efficient kernel functions has also made them almost as accurate as SPICE. In this paper, we report multi-objective genetic algorithm for simultaneous optimization of multiple performance parameters. We compute the Pareto optimal points for various performance parameters of a two- stage op-amp circuit in 180 nm technology. We perform SVM classification and regression using Least Square SVM toolbox [1] with MATLAB. HSPICE was used to generate data-set from simulation of two-stage op-amp, which was used to train the SVM macro-model. The results pertaining to total time consumed in sizing task are very encouraging. We observed ’time taken’ in one evaluation by SVM macromodel as compared to HSPICE is upto two order smaller, resulting in speed-up of approximately 20. I. I NTRODUCTION Circuit synthesis of analog circuit is the task to determine the size of all components in the circuit so that it is able to meet the set of performance specifications. Optimum sizes of the components are determined using stochastic combinatorial optimization method such as simulated annealing and genetic algorithms. Since, performance parameters for great number of circuit sizing values are needed by these algorithms, the reduc- tion in time is highly desired to estimate these performances. Many macromodeling techniques have been proposed to match the non-linear performance functions to design param- eters [2]–[4]. In this paper, we have used Support Vector Machine (SVM) [5]–[7] based macro-models to provide robust and accurate estimate of performance parameters for two stage op amps. The utility of these models is demonstrated in circuit sizing methodology using multi-objective genetic algorithm optimization. The SVM models used in this work were trained using data generated directly from SPICE and therefore are able to provide SPICE level accuracy. Since, the evaluation This research work was supported by grant from Ministry of Communica- tion & IT, Government of India under the sponsored project SMDP-VLSI-2. time taken by the SVM models is much less than the time needed for a full SPICE simulation, the models can be used inside an optimization loop as cost function during circuit synthesis. Performance Macromodeling usually consist of two steps: feasibility design space identification and performance macro- models generation. A feasibility design space is defined as a multidimensional space in which every design satisfies all the design constraints. The minimum set of constraints is the one that ensures the correct functionality of the given circuit topology. Performance macromodels are only constructed and thereby valid in the functionally correct design space. Support vector machines (SVMs) are used as classifier to identify the feasible design space of analog circuits and then as regressor to model performance function of the circuits. Once SVM models are developed for different performance parameters of op-amp, one model for each of the parameter, the op amp can then be synthesized for different performance specifications using general genetic algorithm. However, often a number of parameters in the performance functions compete against each other. Hence, selecting the design variable such that one of the performance parameter is optimal will generally not result in optimal values for other parameters. Thus, the circuit optimization problem turns out to be a multi objective optimization problem. Using multi-objective genetic algorithm, hyper surface of Pareto-optimal design points is calculated that is helpful to designer to make trade-offs between different performance parameters. This multi-objective optimization ap- proach is evaluated while sizing the two stage op amp circuit. Our contribution lies in using efficient kernel functions for SVM classification as well as regression during circuit sizing. We illustrate the efficacy and applicability of the macro- models to multi-objective circuit sizing of select analog cir- cuits. Support vector machine based classification & regression are discussed next, in Section II, along with Pareto surface generation method. In Section III, we illustrate experimental setup for single objective as well as multi-objective sizing of two stage op amp. We also report results in Section III. We conclude in Section IV. 978–1–4244–4547–9/09/$26.00 c  2009 IEEE TENCON 2009 Authorized licensed use limited to: MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY. Downloaded on February 1, 2010 at 02:02 from IEEE Xplore. Restrictions apply.