| Symbolic circuit analysis derives analytic transfer functions in terms of circuit parameters. It can be important for analog integrated circuit design. However, its practical use is limited due to the vast complexity of symbolic expressions, which increase exponentially with the size of the circuit. To cope with large analog circuits a graph representation of symbolic determinants and cofactors, called determinant decision diagram (DDD), has been presented. DDD-based symbolic analysis algorithms have time and space complexities proportional to the number of DDD vertices. In general, the number of DDD vertices is orders of magnitude smaller than the number of product terms.;In this research, we first present exact and heuristic algorithms to minimize DDD size. Our new contributions to DDD optimization are two-folds. First, we show how vertex signs, which are specific to DDDs, can be handled during neighboring vertex reordering. Second, we develop lower bounds tailored to the DDD structures. On a set of DDD examples, experimental results have demonstrated that the presented lower-bound based reordering algorithms can effectively reduce DDD sizes. It has also been demonstrated that sifting with lower bounds uses about 55% less computation compared to sifting without using lower bounds, and sifting with the new lower bounds reduces the computation further by up to 10% compared to sifting with known lower bounds for BDDs.;We further study symbolic techniques for analyzing circuit nonlinearity. For high performance analog/radio-frequency system-on-chip design, it is well known the effect of device nonlinearity is critical on the system performance. Unfortunately, there are no efficient tools for analyzing circuit nonlinearity. Therefore, we first formulate piecewise linear circuit equations using the framework of Modified Nodal Analysis. Secondly, a novel graph representation of the explicit LCP solving process of Bokhoven and Leenaerts is presented. The new graph exploits the computational sharing inherently in the algorithm, and uses less than 1% of computations for relatively large circuits, in comparison to the straightforward implementation of the algorithm. In addition, we exploit the compact data structure, DDD, to represent all the manipulations from MLCP to LCP symbolically. |
