Topological Approach to Symbolic Pole–Zero Extraction Incorporating Design Knowledge

Abstract

This paper addresses the problem of automatic analytical pole-zero (PZ) extraction for multistage operational amplifiers (opamps) with frequency compensation. Traditional methods mainly rely on numerical reference to derive approximate PZ expressions without incorporating any design knowledge. Such methods suffer from bad interpretability of the auto-generated results. This paper takes a topological approach and attempts to advocate that certain form of design knowledge can be incorporated in the symbolic term selection process for PZ generation. The generation engine selects the dominant terms by a formal inspection on the token patterns that are correlated to gain factors and compensation elements. Since the gain factors and compensation elements of an opamp are pertinent to the topological details of a circuit, the proposed PZ extraction method is closer to design conception than other numerical reference-based methods. Consequently, the generated pole/zero results are better interpretable. Application to a class of multistage opamps with a variety of compensation structures demonstrates that the proposed method is effective and can match human-derived results.