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The purpose of this paper is to analyze the properties of indoor power line communications channels when they are used for broadband transmission. It will be shown that these channels exhibit a short-term variation, due to the fact that high-frequency parameters of electrical devices depend on the instantaneous amplitude of mains voltage. This phenomenon leads to a channel model proposal based on a linear periodically time-varying system and cyclostationary random noise. A measurement system, designed to capture these time variations in real power networks, and some of the most significant results obtained with it, are presented. In addition, a statistical analysis of the measurements performed in several indoor power line scenarios is included, so that the relevance of time variations in actual channels can be evaluated.