Graphical Models for Defectoscopy of Dielectrics

The graphical models of reflection and transmission electromagnetic wave in thin slab of dielectric is presented in this report. The mathematical apparatus is theory of microwave circuits, signal flow graphs, bounce diagram. This graphical models lead to formulas and analytical models, that are applied to determining the complex permittivity of dielectric materials. The first part of the report deals with the connection between bounce diagrams and signal flow graphs. The bounce diagram is a time sweep of wave reflections from the beginning and end of the line. Upon reflection, the wave attenuates, the losses are taken into account by exponential terms, but the attenuations are insignificant and in some cases they are neglected. The main difference between a signal flow graph graph and a bounce diagram is that the former represents a mathematical structure with vertices and edges, while the latter is a graphical representation of a physical phenomenon that reflects the direction and level of electromagnetic wave reflection from surfaces with different propertiesThe signal flow graphs represent a visual representation of the model. It is convenient to transit from graphical to analytical models. The second part of report considers what will happen if there is a defect in the dielectric sample under study. Two cases are proposed for a defect included in a cascade in the signal flow graph and a defect as a recursion within the pattern of signal flow graph. There are known the bonce diagram for a cable defect, that could be used by us after little upgrading. The cascade connection in signal flow graph was early explored by Ross G.F. and might be helpful. The recursive model remained unexplored. So such problems have to be solved: a bounce diagram with a defect, a transition to a signal flow graph with accounting on a defect from a bounce diagram, than signal flow graph reduction if it necessary and possible, the creation of a analytic model on the base of a signal flow graph, than compare it to a model without a defect, checking the adequacy of the model, verifying the model, search of solution methods and extraction of information about dielectric permittivity, reflection coefficients from model.