Many approaches to analog performance parameter macro modeling have been investigated by the research community. These models are typically derived from discrete data obtained from circuit simulation using numerous input combinations of component sizes for a given circuit topology. The simulations are computationally intensive, therefore it is advantageous to reduce the number of simulations necessary to build an accurate macro model. We present a new algorithm for adaptively sampling multi-dimensional black box functions based on Duchon pseudo-cubic splines. The splines readily and accurately model high dimensional functions based on discrete unstructured data and require no tuning of parameters as seen in many other interpolation methods. The adaptive sampler, in conjunction with pseudo-cubic splines, is used to accurately model various analog performance parameters for an operational amplifier topology using fewer sample points than traditional gridded and quasi-random sampling methodologies.

Abstract — Efficient algorithms are presented to generate approximate expressions for transfer functions and characteristics of large linear analog circuits. The algorithms are based on a compact determinant decision diagram (DDD) representation of exact transfer functions and characteristics. Several theoretical properties of DDDs are characterized, and three algorithms, namely, based on dynamic programming, based on consecutive k-shortest path based, and based on incremental k-shortest path, are presented in this paper. We show theoretically that all three algorithms have time complexity linearly proportional to |DDD|, the number of vertices of a DDD, and that the incremental kshortest path based algorithm is fastest and the most flexible one. Experimental results confirm that the proposed algorithms are the most efficient ones reported so far, and are capable of generating thousands of dominant terms for typical analog blocks in CPU seconds on a modern computer workstation. Index Terms — analog symbolic analysis, circuit simulation, determinant decision diagrams, matrix determinant, behavioral modeling I.