Efficient derivation of exact s-expanded symbolic expressions for behavioral modeling of analog circuits

This paper presents an efficient method for deriving exact s-expanded symbolic expressions for behavioral modeling of analog circuits. The key idea is to introduce a graph-based representation called multi-root Determinant Decision Diagram (DDD), where each root represents the symbolic coefficient of a particular power of s. By exploiting sharing and sparsity, a huge number of symbolic product terms can be compactly represented and efficiently manipulated. Experimental results have demonstrated that this method can produce the exact s-expanded-symbolic transfer function for μA741 op amps in several CPU seconds on an UltraSparc-I workstation, and the use of generated symbolic expression for frequency-domain simulation achieved a speedup of about 50 over SPICE3F5