Symbolic analysis of electric networks with higher order summative cofactors and parameter decision diagrams

Summary The paper introduces the concept of higher order summative cofactors (HOSCs) to the circuit analysis. Although the concept is not new, it is not well known. In the paper, some mathematical background of HOSCs is presented. The further development of the concept of HOSC will yield computer implementation arithmetic of HOSC. A cancellation‐free symbolic analysis technique, which is based on HOSC arithmetic, is presented. This technique allows results to be created directly from a netlist in the form of a binary decision diagram, which is called a parameter decision diagram. Additionally, HOSC arithmetic allows the calculation to be started in many places (sometimes distant) simultaneously. The techniques of rolling up the already analyzed parts of a circuit, which is built into HOSC arithmetic, result in a novel multilevel hierarchical analysis method that is called hierarchical parameter decision diagram (HPDD). Unlike in most hierarchical methods, the results that are obtained based on the subcircuit representation in HPDD always maintain a cancellation‐free form. The HPDD always represents the sum of the product form, which is heavily compressed due to the self‐similarities of the actual circuit. The time that is required for any recalculation of the transfer functions is greatly reduced. Analysis of models that are based on pathological components is also a natural consequence of using HOSC arithmetic. The paper introduces the concept of higher order summative cofactors arithmetic in circuit analysis. This arithmetic is the basis for creating a new hierarchical approach to circuit analysis that to the best of our knowledge has never been published by others. Furthermore, the method permits parallel and distributing computation in a natural way. In addition, the method presented here is applicable in solving many of the problems in modern circuit analysis, which are briefly presented in the paper.