Signal Flow Graphs as Mathematical Apparatus for Describing 3D Printing Filament Defects
DOI:
https://doi.org/10.20535/RADAP.2024.96.42-49Keywords:
signal flow graph, transmission coefficient, reflection coefficient, dielectric, defectAbstract
The relevance of the work lies in the study of filament defects using graphical models such as signal flow graphs.
The object of research is a graphic model of a filament defect for 3D printing. A review of modern publications showed that the Nicholson-Ross-Weir method for measuring dielectric parameters is used in serial vector network analyzers, which indicates its advantages over other measurement methods, but it has reserves for improvement. This method is based on a model in the form of signal flow graphs. The improvement of the Nicholson-Ross-Weir method consists, first, in the development of a graphic model due to the addition of a defect in the form of a part of an signal flow graph. Secondly, the analysis of the analytical model built on the basis of oriented graphs revealed that the transmission coefficient of S21 is included in the reflection coefficient of S11, which became useful when solving the system of nonlinear equations for S11 and S21.
The purpose of the work is to create a graphic model, which is distinguished by the fact that it takes into account the defects of dielectrics, that is, the filament. The transition from a graphic model to an analytical model is carried out using such methods of simplification or reduction of oriented graphs as the topological method of Kuhn's rules and the algebraic method, namely Mason's rule of non-touching contours.
As a result, analytical expressions for the transmission coefficient of an signal flow graph, which is a model of a dielectric with a defect inside, at the output of S21 and the reflection coefficient at the input of S11 were obtained in two ways, and the results were compared with each other. The use of two independent topological and algebraic methods according to the classification of Somlo and Hunter allows to verify the obtained expressions for the elements of the scattering matrix S11 and S21, which in turn are used in the Nicholson-Ross-Weir method.
Using the method of analogies of the classic Nicholson-Ross-Weir method and the same method with consideration of the defect for the defective material of the filament, an analytical dependence is derived that connects S21 and S11 by a functional relationship.
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