This paper proposes a new analysis for very long transmission lines of RS485 control networks for building facilities. Our method presents closed-form equations for superposition of reflected signal waveforms propagating between terminals of the transmission line. Our analysis is able to handle not only one-to-one basic line but also complex transmission lines with a branch. Signal waveforms by our analysis for complex transmission branch lines without terminators are compared with waveforms by computer simulations. Our waveform analysis is enough effective for preliminary investigation on severity of waveform distortions in the branched transmission lines of a building in planning.

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