High Frequency Stochastic Properties of Transmission Lines
Final Report Abstract
The propagation of the current waves along stochastic transmission lines was investigated using the statistical properties of the reflection and transmission coefficients. This problem is important for different aspect in electrical engineering, including considerations of cabling in cars, aircrafts, etc. An analytical consideration of the problem is important, because the results do not depend on the specific stochastic model. Two main approaches were considered. The first one is applied for the continued transmission line with stochastic geometry for the low frequencies, where the classical transmission line approximation is applicable. The weak and the strong scattering were considered. In case of weak scattering the PDF of the reflection coefficient and its statistical moments have a simple Gaussian form. For the case of strong scattering a general theory developed earlier for the Schrödinger equation with stochastic potential was applied. The PDF and the moments of the distribution of the absolute values of the reflection and transmission coefficients were formulated. In both cases the result is evaluated from the pair correlation function of the coordinate deviation. To obtain results in the explicit form a model (“Fourier-Gauss”) for the stochastic geometry of the transmission line was developed. Numerical calculations carried out by the method of transfer matrix (developed earlier in our works) have shown a good agreement with analytical theory. This approach is not applicable for the high frequencies, when the radiation of the line is important, because the basic classical transmission line equations are not valid. For this case an application of the Full–Wave Transmission Line Theory (FWTL), developed earlier, looks reasonable. However, using these equations leads to a cumbersome calculation and does not allow to obtain analytical answers in the explicit form or to make the required number of statistical tests (~104 to 105). Therefore, another approach was developed, a transmission line with small scale, randomly arranged scatterers. This model is applicable for a transmission line with local non-uniformities. The scattering coefficient of each non-uniformity can be found by a simple model. Again, the two cases of the weak and strong scattering were considered analytically and by the method of transfer matrices. The moments and the PDF of the reflection and transmission coefficients as well as the “competition” between stochastic and radiation processes were investigated. The numerical simulations and the measurements showed a good agreement with the theory. The most important result of the research is the realisation that a current wave cannot penetrate through a very long stochastic line even in case of missing conductive or radiation losses. This result was yielded by both of the two considered approaches and is practically important.
Publications
- “Propagation of Current Waves along a Transmission Line with Stochastic Geometry“, Book of Abstracts EUROEM 2012, Toulouse, p.46
S. Tkachenko, J. Nitsch and R. Vick
- “Singularity Expansion Method (SEM) for Long Terminated Transmission Lines”, Proceedings of 10th International Conference on Electromagnetics in Advanced Applications (ICEAA 13), September 9-13, 2013 - Torino, Italy
S. Tkachenko, J.Nitsch, R. Vick, F. Rachidi and D. Poljak
- „Propagation of Current Waves along a Transmission Line with Randomly Located Non-Uniformities“, Proceedings of 10th International Conference on Electromagnetics in Advanced Applications (ICEAA 13), September 9-13, 2013 - Torino, Italy
S. Tkachenko, H.-J. Scheibe, X. Wang, R. Vick
