Predavanje: Propagation of Current Waves in Stochastic Transmission Lines

09. rujna 2016.

od 10:00 do 12:00

A302, Predavaonica

S. Tkachenko, University of Magdeburg, Germany

Investigation of the propagation of currents and voltages along different wiring structures is one of the main groups of problems in electromagnetic compatibility. In praxis often electrical parameters of the transmission lines are known only statistically (e.g. in cars, aircraft, satellites, etc.). A usual approach to solve such problems includes the following three steps: numerical generating of the stochastic geometry of the line, numerical solution of corresponding TL- or full – wave equations for each configuration and averaging the statistical ensemble. On the other side, the application of direct numerical methods to solve stochastic problems is very time consuming and only describes a specific case of distribution with fixed parameters.

In the present research we investigated propagation of current waves along stochastic transmission lines using analytical methods. As the researched quantity we choose the “reflection-transmission coefficients” for current waves, which are connected with the transfer matrix and usual scattering S- matrix. Two models were considered.

In the first model we investigated transmission line with stochastic geometry, which are described by classical Telegrapher’s equations for an inhomogeneous line. Both cases of weak and strong scattering were considered. For the case of weak scattering a perturbation theory was used. For the strong scattering a general theory developed earlier for the stochastic scattering was used. Equations for the PDF and lower moments of the investigated values were obtained. The results are model-independent and can be expressed in terms of the pair correlation function of the deviation of the vertical coordinate of the line from its mean. To do more obvious the obtained results a model of the Fourier series with stochastic (the Gaussian) coefficients was developed.

 

The interesting results of this theory are the following: if the region of stochastic non-uniformity is long enough, the line reflects the incident wave with probability one, due to multiple re-reflections of the wave in internal sub-regions of the line. However, for some realizations the amplitude of current waves can essentially increase in some regions in comparison to the average value, but on the whole, the current wave is reflected from the stochastic line. This physical phenomenon is known as a dynamical localization of scattered waves in the randomly layered media.

At the same time, a current wave propagating along an inhomogeneous transmission line radiates, which also leads to damping of the wave amplitude. Moreover, in the regions of dynamical localization, the radiation losses (as any other losses) essentially increase. An important issue here is the consideration of the “competition” of the stochastic and radiation decay of the amplitudes of current.

However the attempts to consider this effect numerically (by Full Wave TL Theory or by direct numerical method, i.e., MoM) do not deliver results in a relative short time for a necessary number of statistical samples (10000-100000).

By this reason, we consider the second model of a stochastic transmission line which yields results in a reasonable time. This line is realized as a chain of equal lumped loads arranged stochastically. (The model also can describe the TL with short-range non-uniformities). During the calculation one has to define the scattering matrix for a non-uniformity only once for all series of the statistical treatment (for each frequency). We have obtained lowest statistical moments for the reflection and transmission coefficients and its PDF. It was examined for which parameter values the stochastic or radiation attenuation dominated the current waves.

 

Sergey V. Tkachenko (M’07–SM’12) was born in Moscow, Russia, in 1958. He received the M.S. and Ph.D. degrees in mathematical and theoretical physics from the Moscow Engineering and Physics Institute MEPhI (now National Research Nuclear University MEPhI), Moscow, Russia, in 1981 and 1987, respectively.

 

From 1986 to 1989, he was a Researcher and a Senior Researcher with the Department of Electromagnetic Compatibility, State Radio Research and Development Institute, Moscow. In 1993, he spent eight months as an Invited Researcher at the Swiss Federal Institute of Technology, Lausanne, Switzerland (EPFL). From 1996 to 1999, he worked with the LRE EPFL within a framework of the European INTAS Project 94-3939 “Electromagnetic Compatibility of Interconnection Cables Subject to Interferences.” Since 2000, he has been an Invited Researcher with the Institute for Fundamental Electrical Engineering and EMC Otto-von-Guericke University, Magdeburg, Germany. He is an author or coauthor of more than 150 scientific papers published in peer-reviewed journals and presented at international conferences. He is co-editor (together with F. Rachidi) of the book Electromagnetic Field Interaction with Transmission Lines: From Classical Theory to HF Radiation Effects (Southampton, U.K.: WIT Press, 2008). This book was translated in Chinese language in 2012. He is an elected EMP Fellow (2008, for theoretical investigation of high-frequency electromagnetic field coupling to transmission lines in different environments). His research interests concern applied electromagnetics and electromagnetic compatibility, in particular electromagnetic field coupling to complex wiring structures, also inside cavities, mainly, using analytical techniques.

Dr. Tkachenko, together with J. Nitsch, has received the Best HPE Paper Award four times (best basic paper for the years 2002–2003, 2006–2007, 2008–2009, and 2014-2016 (together also with R.Rambousky) correspondingly).