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. Index Terms-Analog circuits, clustering, Krylov space, model order reduction (MOR), qualitative simulation (QS). 1063-8210

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The generation of fast models for device level circuit descriptions is a very active area of research. Model order reduction is an attractive technique for dynamical models size reduction. In this paper, we propose an approach based on clustering, curve-fitting, linearization and Krylov space projection to build reduced models for nonlinear analog circuits. We demonstrate our model order reduction method for three nonlinear circuits: a voltage controlled oscillator, an operational amplifier and a digital frequency divider. Our experimental results show that the reduced models lead to an improvement in simulation speed while guaranteeing the representation of the behavior of the original circuit design.

This paper presents a method for characterizing the DC operating points of analog circuits. We construct fuzzy DC equations that model circuit parameter variations and apply a global optimization algorithm to estimate the location of DC points. We applied our method to analyze the stability of a ring oscillator and the influence of the input voltage offset on the DC characteristic of a differential pair. Our results prove the effectiveness of our method in describing circuits DC performance parameters and predicting possibilities of undesired circuit operations.

Simulation cannot give a full coverage of Phase Locked Loop (PLL) behavior in presence of process variation, jitter and varying initial conditions. Qualitative Simulation is an attracting method that computes behavior envelopes for dynamical systems over continuous ranges of their parameters. Therefore, this method can be employed to verify PLLs locking property given a model that encompasses their imperfections. Extended System of Recurrence Equations (ESREs) offer a unified modeling language to model analog and digital PLLs components. In this paper, an ESRE model is created for both PLLs and their imperfections. Then, a modified qualitative simulation algorithm is used to guarantee that the PLL locking time is sound for every possible initial condition and parameter value. We used our approach to analyze a Charge Pump-PLL for a 0.18μm fabrication process and in the presence of jitter and initial conditions uncertainties. The obtained results show an improvement of simulation coverage by computing the minimum locking time and predicting a non locking case that statistical simulation technique fails to detect.