A regularity-based hierarchical symbolic analysis method for large-scale analog networks

This paper presents a novel hierarchical symbolic analysis method for automatically producing relationships between the parameters of an analog network and the building blocks of the network. The originality of the symbolic technique stems from exploiting regularity aspects for addressing the exponential complexity of the symbolic expressions. The regularity aspects that were identified are: 1) structural regularity: majority of the network blocks are connected in identical templates and 2) symbolic parameter regularity: parameters for a connection template require similar sets of operations. The paper discusses the three components of the proposed symbolic analysis method: 1) an efficient representation of symbolic expressions, 2) an algorithm for construction of symbolic expressions; and 3) a decomposition technique for extracting the structural regularity of a network. For large networks, the size of the symbolic models produced by our symbolic analysis method is much less than the size of the models produced by other methods such as the two-graph method. We mathematically show that the generated models are of polynomial size if the two kinds of regularity are exploited. The described symbolic technique was implemented and used successfully for synthesis and optimization of different analog systems such as filters and communication systems.