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In this paper, a procedure for the analysis and design of nonlinear circuits based on the Carleman linearization is presented. Since this procedure starts with the general network equations which are derived by Kirchhoff’s law, it can be used for a variety of circuits. The proposed procedure is applied for oscillator and RF mixer circuits which are a crucial part of every wireless communication system. Based on the general network equations, a transformation into equivalent polynomial differential equations is performed using the not widely known method of Kerner. This polynomial differential equation is further transformed into an equivalent infinite-dimensional system of linear differential equations. Since the infinite-dimensional linear system cannot be solved in general, an approximation by a finite one is performed using a self-consistent technique. The obtained finite linear system is used for the approximation of the infinite-dimensional linear system on a predefined interval. The approximation is utilized for the design and analysis process of the circuit, which is a challenging problem until now. [ABSTRACT FROM AUTHOR]

This paper presents a design environment for continuous-time sigma-delta analog-to-digital converters for automatic coefficient scaling using a genetic algorithm. In order to provide an interactive design tool which enables the designer to transform and refine basic performance specifications into the desired, detailed high-level filter description, a short response time is mandatory. Previously published heuristic-search-based design tools have response times in the range of several ten minutes up to hours and are mostly not freely available. In contrast, the design environment presented in this paper provides results in less than a minute due the utilization of a fast simulation method implemented on a graphics card processor. Our hardware supported approach allows performing between 10 k and 67 k simulations and evaluations per second for internal model orders of one to eight, allowing to investigate millions of settings in less than a minute. The presented tool is freely accessible under www.sigma-delta.de. [ABSTRACT FROM AUTHOR]