Some Properties of Impulse Response of Distribution Networks With Periodic Tree-Type Topology

Abstract

The main motivation for this paper was to investigate certain asymptotic properties of impulse response in periodic treetype distribution networks owed to the network topology alone, regardless of ohmic losses or material dispersion normally present in practical situations. The research was performed using theoretical analysis of Dirac impulse propagation through a model network, with a focus on topology-related features. Several numerical examples were designed to illustrate the meaning of the main conclusion, namely that the very topology of any tree-type network leads to an impulse response in which amplitudes of individual pulses decay rapidly with their respective delays after the leading impulse. On the other hand, it was not a goal of this research to design any practical tool for network-response calculation. The very fact that impulse response decays rather quickly after the train of the first few impulses does not mean that the calculation of these first few is by any means simple. The frequency-domain network-analysis methods in case of a complex distribution network with a tree-like topology seem to have practical advantages over the impulse-response calculation techniques, especially because the effects of ohmic losses and material dispersion would have to be included in any model constructed for realistic simulations, and in the authors' experience, this can be done more easily in frequency-domain-based models.

Stochastic modeling of signal propagation in power‐line communication networks

“…Although these ‘ghost’ pulses carry negligible power (Figure ), this is still a good warning that aliasing is something one should not forget. Apart from the aliasing‐caused premature pulses, the impulse response shows very quick decay of received pulse power with time, which is consistent with findings presented in .…”

“…All these features make PLC channel modeling rather hard to do. There have been a number of published articles, reporting valued research results and models developed in that field . Such models can be broadly categorized in the following way:In relation to basic modeling approach, there can betime‐domain‐based models andfrequency‐domain‐based models.As for the network dynamics modeling, there can be four types of models:static deterministic,static stochastic (or quasi‐static stochastic),dynamic deterministic, anddynamic stochastic.…”

“…Sabolic et al . studied topology‐related phenomena of the time‐domain network response in . (Quasi)‐periodical structures can be found, for example, in most of office buildings, homes, and so on.…”

“…Theoretical modeling in time domain is, in principle, possible. However, computational issues are so big that the expected results are probably not worth the effort, as indicated in .…”

Modeling and measurement of cross‐talk transmission between coupled lines

“…A technical area where this work can be practically implemented is, for example, power‐line communication systems (PLC) . A brief review of PLC channel modeling can be found in author's previous work published in this journal .…”