The implementation of the method of reduced matrix D-trees in the Udf MAOPCs environment

Abstract

The article explores the content of the MatrixDtrees function, which extends the functionality of the UDF MAOPCs and is designed to generate symbolic transfer functions of linear parametric circuits. This function represents a software implementation of the Transformed Matrix D-trees method. This method is an extension of the symbolic d-trees method, developed for constant parameters circuits, to parametric circuits. The extension involves the transition from algebraic operations with numbers and symbols in the d-trees method to matrix algebraic operations, taking into account the non-commutativity of matrix multiplication. The Transformed Matrix D-trees method significantly reduces computational time for modeling parametric circuits by factoring out similarities in complex symbolic expressions generated during the analysis process. The MatrixDtrees function allows for the steady-state analysis in highly complex parametric circuits. By such circuits, we mean circuits that contain dozens or hundreds of nodes and elements (including parametric ones). The article includes the results of analyzing a parametric long line model, which is represented by a combination of lumped parameters and consists of many cascaded elementary sections. Each of these sections is a combination of parametric inductance and constant capacitance. The paper presents the results of an experiment to determine the output voltage of a long line model containing 1025 nodes, 1024 constant capacitances, and 1024 parametric inductances. The results are comparable to calculations of the same long line model using the MicroCap program. The relative deviation between the calculation results for both programs was less than 1%. The calculation time for the Transformed Matrix D-trees method using the MatrixDtrees function was 18 minutes, whereas for the MicroCap program, it was 36 hours.