Evaluation of error-control strategies for the linear symbolic analysis of analog integrated circuits

Abstract

The generation of approximate linear symbolic expressions for analog integrated circuits requires the use of an appropriate error-control strategy. The error-control strategy determines both correctness and compactness of the approximate expression. This paper presents an evaluation of different errorcontrol strategies that fit within the flat symbolic analysis, using simplification during generation techniques for large analog integrated circuits. The theoretical exposition is illustrated with experimental results that allow a comparison of the proposed methods.

Behavioral Modeling of Mixed-Mode Integrated Circuits

“…The generation algorithm is most efficient known but many generated bases may not be common to the three matroids. In this case, error mechanisms that control the error in each coefficient of the transfer function can be used, for instance, by means of a sensitivity driven mechanism (Daems et al, 1999). …”

Efficient Approximation of Symbolic Expressions for Analog Behavioral Modeling and Analysis

“…We use D.counter to keep track of the number of dominant terms generated for the vertex D (D is included in the terms). We use an ordered array, denoted as D.termlist, to keep track of those generated dominant terms in the minor represented by D, where D.term-list [1], D.termlist [2],... represents the largest term (first dominant term), the second largest term (second dominant term). D.counter is initially set to 1 for all 1-edge pointed vertices, and can be increased up to k.…”

“…) − s 1 (gm6CC)+ s 2 (c db2 + c db4 + cgs6 + CL)CC (1) Notice that the symbolic approximation are typically carried out around some nominal numerical values (points) of the devices involved, the generated model will approximate actual devices well when the sized device parameters are close to the nominal values used for model generation. However, when using a staged optimization approach, the nominal points will move and model will be updated adaptively.…”

“…As a result, the optimized devices will be very close to the nominal points of the model generated in the final stage (as the model is recentered after every stage). Such nominal point approximation strategy used in this work is also adopted by most of symbolic approximation methods [1]- [7]. During the approximation, we monitor both magnitudes and phases of the transfer functions until errors are within the user-specified error bounds for the frequency range.…”

Implementation of topological circuit reduction

“…For example, the number of terms of the voltage transfer function of type 741 operational amplifier is estimated to be 10 19 [2]. If we restrict the range of frequency and circuit parameters appropriately, the majority of symbolic terms can be removed from large expressions without any significant numerical error [3]. The basic prerequisite is the knowledge of at least approximate values of network parameters, which servers for the identification of negligible terms.…”