Abstract
Traditionally, model order reduction methods have been used to reduce the computational complexity of mathematical models of dynamic systems, while preserving their functional characteristics. This technique can also be used to fasten analog circuit simulations without sacrificing their highly nonlinear behavior. In this paper, we present an iterative approach for reducing the computational complexity of nonlinear analog circuits using piecewise linear approximations, $k$ -means clustering, and Krylov space projection techniques. We model primary circuit inputs, design initial conditions, and circuit parameters as fuzzy variables with different distributions in qualitative simulations. We then iteratively fine-tune the reduced models until a model is achieved that meets a predefined performance and accuracy conformance criteria. We demonstrate the effectiveness of our method using several key nonlinear circuits: 1) a transmission line; 2) a ring oscillator; 3) a voltage controlled oscillator; 4) a phase-locked loop; and 5) an analog comparator circuit. Our experiments show that the reduced model simulations are fast and accurate compared with the existing techniques.
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