The low-voltage power distribution network is considered today as a serious candidate to provide residential customers with a high-speed access to communication services such as Internet. Outdoor Power-Line Communications (PLC) systems represent an alternative to the other classical 'last-mile solutions' such as ADSL, cable modems, or wireless access systems. We developed an accurate powerline channel simulation tool based on the Multiconductor Transmission Line theory. This tool is able to predict the end-to-end channel responses on the basis of the multiconductor cable structure and the network topology. Then the issue of optimal resource allocation in a multiuser environment was addressed in the light of the Multiuser Information Theory. Simultaneously active users are in competition for the limited resources that are the power (constrained by electro-magnetic compatibility restrictions) and the bandwidth (in the range of 1 to 10 MHz for outdoor PLC). The concept of multiuser balanced capacity was introduced to characterize the optimal resource allocation providing the maximum data rates with fairness constraints among the subscribers. The optimal PLC system was shown to require the shaping of the signal spectrum in the transmitters, and successive decoding in the receiver. A generic multiple access scheme based on Filter Banks (FB) was proposed, which offers the required spectral shaping with limited degrees of freedom. Classical multiple-access techniques (TDMA, CDMA, OFDMA) can be obtained by selecting the appropriate FB. The Minimum-Mean-Square-Error Decision-Feedback Joint Detector was shown to approach the performance of the optimal successive decoding receiver. Finally, the robustness of the proposed system against channel estimation and timing synchronization errors was addressed. The problem of multiuser timing synchronization was introduced, and practical multiuser timing error detectors were proposed.

An analytical solution for the coupled telegrapher’s equations in terms of the voltage and current on a homogeneous lossy transmission line and multiconductor transmission line is presented. The resulting telegrapher’s equation solution is obtained in the form of an exact time domain propagator operating on the line voltage and current. It is shown that the analytical equations lead to a stable numerical method that can be used in the analysis of both homogeneous and inhomogeneous transmission lines. A numerical dispersion relation is derived proving that this method has no numerical dispersion down to the two points per wavelength Nyquist limit. Examples are presented showing that exceptionally accurate results are obtained for lossy single and multiconductor transmission lines. The method is extended to represent the general solution to Maxwell’s differential equations in vector matrix form. It is shown that, given the electromagnetic field and boundary conditions at a given instant in time, the free space time domain propagator and corresponding dyadic Green’s functions in 1-, 2-, and 3-dimensions can be used to calculate the field at all subsequent times.

Neste trabalho, são caracterizadas as soluções do tipo ondas planas e modais de modelos matemáticos referentes à teoria de linhas de transmissão, com e sem perdas, e à teoria de vigas, modelo de Timoshenko e modelo não local de Eringen. Os modelos são formulados matricialmente, e as ondas em questão são determinadas em termos da base gerada pela resposta matricial fundamental de sistemas de equações diferenciais ordinárias de primeira, segunda e quarta ordem. A resposta matricial fundamental é utilizada numa forma fechada que envolve o acoplamento de um número finito de matrizes e uma função escalar geradora e suas derivadas. A função escalar geradora é bem comportada para mudanças em torno de frequências críticas e sua robustez é exibida através da técnica de Liouville. As ondas modais são decompostas em termos de uma parte que viaja para frente e uma parte que viaja para trás. Essa decomposição é utilizada para fornecer matrizes de reflexão e transmissão em descontinuidades e condições de contorno. No contexto das linhas de transmissão são consideradas uma junção de linhas com impedâncias características diferentes ou uma carga em uma extremidade da linha. Na teoria de Timoshenko são consideradas uma fissura ou condições de contorno em uma das extremidades. Exemplos numéricos com descontinuidade são considerados na viga. Na teoria de linhas de transmissão exemplos com multicondutores são considerados e observações são realizadas sobre a decomposição das ondas modais. No modelo não local de Eringen, para vigas bi-apoiadas é discutida a existência do segundo espectro de frequências. / Plane type solutions and modal waves of mathematical models, which refer to transmission lines theory, both lossless and lossy, and to beam theory, using both Timoshenko and nonlocal Eringen models, are being characterized in this work. The models are formulated in matrix form, and the waves are determined in terms of matrix basis generated by fundamental matrix response of systems of ordinary differential equations of first, second and fourth order. The fundamental matrix response is used in the closed-form, which involve the coupling between a number finite of matrices of a generating scalar function and its derivatives. The generating scalar function is well behaved for changes around critical frequencies and its robustness is exhibited through the Liouville technique. Modal waves are decomposed in forward and backward parts. This decomposition is used for providing reflection and transmission matrices when dealing with discontinuities and boundary conditions. In the context of transmission lines junction of lines with different characteristic impedances or a load at one end of the line are being considered. In Timoshenko’s theory the crack problem or boundary conditions at one end are also being considered. Numerical examples with discontinuities are considered in the context of beams. Numerical examples with discontinuities and boundary value problems were approached using modal wave decomposition. In transmission line theory examples with multiconductors are considered and observations are made about decomposition of the modal waves. In the nonlocal of Eringen model, for bi-supported beams, the existence of the second frequency spectrum is discussed.

Neste trabalho, são caracterizadas as soluções do tipo ondas planas e modais de modelos matemáticos referentes à teoria de linhas de transmissão, com e sem perdas, e à teoria de vigas, modelo de Timoshenko e modelo não local de Eringen. Os modelos são formulados matricialmente, e as ondas em questão são determinadas em termos da base gerada pela resposta matricial fundamental de sistemas de equações diferenciais ordinárias de primeira, segunda e quarta ordem. A resposta matricial fundamental é utilizada numa forma fechada que envolve o acoplamento de um número finito de matrizes e uma função escalar geradora e suas derivadas. A função escalar geradora é bem comportada para mudanças em torno de frequências críticas e sua robustez é exibida através da técnica de Liouville. As ondas modais são decompostas em termos de uma parte que viaja para frente e uma parte que viaja para trás. Essa decomposição é utilizada para fornecer matrizes de reflexão e transmissão em descontinuidades e condições de contorno. No contexto das linhas de transmissão são consideradas uma junção de linhas com impedâncias características diferentes ou uma carga em uma extremidade da linha. Na teoria de Timoshenko são consideradas uma fissura ou condições de contorno em uma das extremidades. Exemplos numéricos com descontinuidade são considerados na viga. Na teoria de linhas de transmissão exemplos com multicondutores são considerados e observações são realizadas sobre a decomposição das ondas modais. No modelo não local de Eringen, para vigas bi-apoiadas é discutida a existência do segundo espectro de frequências. / Plane type solutions and modal waves of mathematical models, which refer to transmission lines theory, both lossless and lossy, and to beam theory, using both Timoshenko and nonlocal Eringen models, are being characterized in this work. The models are formulated in matrix form, and the waves are determined in terms of matrix basis generated by fundamental matrix response of systems of ordinary differential equations of first, second and fourth order. The fundamental matrix response is used in the closed-form, which involve the coupling between a number finite of matrices of a generating scalar function and its derivatives. The generating scalar function is well behaved for changes around critical frequencies and its robustness is exhibited through the Liouville technique. Modal waves are decomposed in forward and backward parts. This decomposition is used for providing reflection and transmission matrices when dealing with discontinuities and boundary conditions. In the context of transmission lines junction of lines with different characteristic impedances or a load at one end of the line are being considered. In Timoshenko’s theory the crack problem or boundary conditions at one end are also being considered. Numerical examples with discontinuities are considered in the context of beams. Numerical examples with discontinuities and boundary value problems were approached using modal wave decomposition. In transmission line theory examples with multiconductors are considered and observations are made about decomposition of the modal waves. In the nonlocal of Eringen model, for bi-supported beams, the existence of the second frequency spectrum is discussed.

Диплом посвящен описанию методики моделирования системы передачи данных на симметричных линии передач. Приведена методика построения моделей систем в программной среде NI AWR Design Environment. Производится разбор этапов построения модели. / Diploma is dedicated to the describe method of modeling of transmission system build upon symmetric transmission lines. Method of modeling in NI AWR Design Environment been presented. An extensive explanation of modeling process is given.