Alexander Zemliak, Fernando Reyes Cortés



The process of analog circuit optimization is defined mathematically as a controllable dynamical system. In this context, we can formulate the problem of minimizing the CPU time as the minimization problem of a transitional process of a dynamical system. To analyse the properties of such a system, we propose to use the concept of the Lyapunov function of a dynamical system. This function allows us to analyse the stability of the optimization trajectories and to predict the CPU time for circuit optimization by analysing the characteristics of the initial part of the process.

Keywords: Circuit optimization, control theory, Lyapunov function, minimal-time system design, time-optimal strategy.



El proceso de la optimización del circuito analógico es definido matemáticamente como un sistema dinámico controlable. En este contexto, podemos formular el problema de minimizar el tiempo de la CPU como el problema de minimización de un proceso de transición de un sistema dinámico.  Para analizar las propiedades de tal sistema, proponemos de usar el concepto de la función de Lyapunov de un sistema dinámico. Esta función permite analizar la estabilidad de las trayectorias de optimización y predecir el tiempo de la CPU para la optimización del circuito analizando las características de la parte inicial del proceso.

Palabras Claves: Diseño del sistema en el tiempo mínimo, estrategia óptima en el tiempo, función de Lyapunov, optimización del circuito, teoría de control.

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Brayton, R.K., Hachtel, G.D. & Sangiovanni-Vincentelli, A.L. A survey of optimization techniques for integrated-circuit design. Proc. IEEE, V. 69, No. 10, 1334-1362, 1981.

Bunch, J.R. & Rose, D.J. (Eds), Sparse Matrix Computations, New York, Acad. Press, 1976.

Hershenson, M., Boyd, S. & Lee, T. Optimal design of a CMOS op-amp via geometric programming. IEEE Trans. CAD Integr. Circ. Sys. V. 20, No. 1, 1–21, 2001.

Kashirskiy, I.S. & Trokhimenko, Y.K. General optimization of electronic circuits. Kiev, Tekhnika, 1979.

Koziel, S., Bandler, J.W. & Madsen, K. Space-mapping-based interpolation for engineering optimization. IEEE Trans. MTT, V. 54, No. 6, 2410-2421, 2006.

Ochotta, E.S., Rutenbar, R.A. & Carley, L.R. Synthesis of high-performance analog circuits in ASTRX/OBLX. IEEE Trans. CAD Integr. Circ. Sys., V. 15, 273–294, 1996.

Rabat, N., Ruehli, A.E., Mahoney, G.W. & Coleman, J.J. A survey of macromodelling. Proc. of IEEE Int. Sym. CAS, 139-143, June 1985.

Rizzoli, V., Costanzo, A. & Cecchetti, C. Numerical optimization of broadband nonlinear microwave circuits. Proc. IEEE MTT-S Int. Symp., 335–338, Dallas, USA, May 1990.

Stehr, G., Pronath, M., Schenkel, F., Graeb, H. & Antreich, K. Initial sizing of analog integrated circuits by centering within topology-given implicit specifications. Proc. IEEE/ACM Int. Conf. CAD, 241–246, 2003.

Tadeusiewicz, M. & Kuczynski, A. A very fast method for the DC analysis of diode-transistor circuits. Circ. Sys. Sign. Proces., V. 32, No. 3, 433-451, 2013.

Zemliak, A.M. Analysis of Dynamic Characteristics of a Minimal-Time Circuit Optimization Process, Int. J. of Mathematic Models and Methods in Applied Sciences, V. 1, 1-10, 2007.

Osterby, O. & Zlatev, Z. Direct Methods for Sparse Matrices. New York, Springer-Verlag, 1983.

Zemliak, A.M. Analog System Design Problem Formulation by Optimum Control Theory. IEICE Trans. Fundam., V. E84-A, 2029-2041, 2001.

Zemliak, A.M. Comparative Analysis of the Lyapunov Function for Different Strategies of Analogue Circuits Design. Radioelect. and Communic. Sys., V. 51, 233-238, 2008.

Zemliak, A. Analog circuit optimization on basis of control theory approach. COMPEL: The Int. J. Comp. and Math. in Electrical Electronic Engineering, V. 33, 2180-2204, 2014.

Zemliak, A. & Markina, T. Behavior of Lyapunov´s function for different strategies of circuit optimization. Int. J. Electronics, Vol. 102, No. 4, 619-634, 2015.

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