Models to analyse the coupling between resonators and transmission lines of stochastic geometry
Final Report Abstract
The propagation of current waves along stochastic transmission lines inside of resonators was investigated. Three main approaches were considered. The Method of Symmetrical Line in a resonator, allows obtaining an exact analytical solution for a straight symmetrical line having an arbitrary set of loads. It is also applicable for a set of perpendicular lines. The stochastic properties of the line are created by random values of the lumped loads, by small stochastic deviation from the straight geometry or by a stochastic position of the line. All results can be obtained using the Green's function of the system. The second approach, the Method of Analytical Regularization, leads to an approximate Green's function for the transmission line in a resonator by splitting the resonator Green's function in a singular and a regular part. This TL Green's function can be applied for the stochastic investigations of finite lines. The third method is the Transmission Line Super Theory. The propagation of current waves in a transmission line in any linear environment can be reduced to the solution of Telegrapher's-like equations, that parameter matrix contains properties of the transmission line as well as of the environment (resonator in our case). A parameter matrix was found for the symmetrical line and a variant of perturbation theory was used for calculations. The developed techniques allow fast statistical investigations using numerical or iteration methods. The average value of the transmission coefficient for the current, its variance and PDF was calculated. Using the principle of maximum entropy it could be shown, that the PDF can be approximated by the Beta distribution. As a main result of the research it could be shown that the current wave in the resonator can pass through the stochastic transmission line due to the possibility of signal propagation not only along the transmission line, but also due to multiple reflections from the walls of the resonator. This is in contrast to the case of a stochastic line in free space, which leads to a complete reflection of the wave in the event of sufficient stochastization. This result was also proofed for several models.
Publications
- "Electromagnetic coupling to thin wire structures inside resonators", European Electromagnetics Symposium EUROEM 2016, 11-14 July 2016, London, UK
S. Tkachenko, J. Nitsch, R. Rambousky, R. Vick
(See online at https://doi.org/10.1109/APEMC.2016.7523000) - "High Frequency Coupling with Stochastic Transmission Line in Rectangular Resonator", Asian Electromagnetic Symposium ASIAEM, Bangalore, 22-24 July2017
S. Tkachenko, J. Nitsch, R. Vick
(See online at https://doi.org/10.1155/2018/4150217)
