Efficient simplification strategies for symbolic circuit expressions of linear analog integrated circuits

Abstract

Analog circuit design is a very knowledge-intensive process, which heavily relies on the designer's understanding of circuit's behaviour. Symbolic Circuit Analysis gives the designer an additional insight and helps to gain a better understanding of circuit functionality. Moreover Symbolic Analysis plays a major role in analog circuit design automation process and is complementary to the numerical (SPICE) circuit simulation. Therefore automatic generation of symbolic circuit expressions or models has currently become a topic of heightened interest. The main difficulty of symbolic circuit analysis is that: the number of product terms in a symbolic expression increases exponentially with the size of the circuit. In order to handle circuits of large sizes several simplification and approximation strategies have been suggested in the literature, but the interpretability of the derived expressions has received insufficient attention from the symbolic analysis community. Symbolic expressions of relatively small circuits are not in readable format even for experienced designers, besides being complex for classroom teaching. This paper presents efficient strategies that can be adopted while simplifying large symbolic circuit expressions, aimed at preserving the accuracy and interpretability of circuit expressions better. The goal is to show that exploiting certain information from the device model and taking Miller effect of feedback elements into consideration will result in more meaningful simple expressions in nested formats that can be easily expanded as well. The strategies suggested in this paper are illustrated with different practical MOS and bipolar circuit examples, with emphasis on the compactness and interpretability of the circuit expressions.