Abstract-The impact of parameter variations in integrated analog circuits is usually analyzed by MonteCarlo methods with a high number of simulation runs. Few approaches based on interval arithmetic were not successful due to tremendous overapproximations. In this paper, we describe an innovative approach computing transient and DC simulations of nonlinear analog circuits with symbolic range representations that keeps correlation information, and hence has a very limited overapproximation. The methods are based on affine and quadratic arithmetic. Ranges are represented by unique symbols so that linear correlation information is preserved. We demonstrate feasibility of the methods by simulation results using complex analog circuits.

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In recent times, range based modeling and simulation techniques have emerged for systems with parameter tolerances and deviations. They are used to perform a semisymbolic simulation and to analyze the examined systems for their time domain behavior. The system quantities in such simulations are represented as range based signals using the concept of Affine Arithmetic. Transforming the range based signals from a time domain to a frequency domain representation significantly increases the analysis capabilities and provides a broader insight into the system's behavior. Such a transformation enriches the expressiveness of semi-symbolic system quantities and simultaneously allows frequency based analysis techniques to be applicable. We use the Discrete Fourier Transform to compute a range based frequency representation and finally discuss the method and interpretation of the frequency spectrum on two examples.

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