Models to analyse the coupling between resonators and transmission lines of stochastic geometry

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The analysis of transmission lines with random geometry in a resonator requires time-consuming numerical solutions to calculate the statistical properties of voltages and currents along the line and at the terminal. Moreover, the calculations of the response of deterministic transmission lines inside a resonator as well as the response of stochastic transmission lines in free space are also very tedious. During the usual numerical simulation it is often difficult to explain the differences between results of different configurations. These can be either caused by peculiarities of the used model or are of a deeper physical nature. A consequent and accurate analysis of the situation can only be done by using analytical methods.In a previous project a model-independent theory of transmission lines with stochastic geometry was developed. Furthermore, effective analytical and semi-analytical methods for the fast analysis of the response of deterministic transmission lines in resonators were developed.In this project further developments of the methods are intended with the aim to carry out the investigation of stochastic lines in a resonator. It is planed to study the statistical properties of the scattering matrix (reflection and transmission coefficients) of transmission lines, the current distribution in the central region of the line and the response of the line to the external electromagnetic interferences by use of analytical methods.