analysis theory [@Pozar]. We show that an equivalent mixed-mode transmission matrix [@4287166] can be derived from the MTRL model of each branch. Moreover, all the devices that cannot be physically modeled due to their complex geometrical and circuit structure (couplers, sockets, etc…) can be still represented by an equivalent mixed-mode transmission matrix (MMTM). The chain rule of transmission matrices finally allows the cumulative analysis of the network properties. Therefore, the herein proposed approach allows the development of a bottom-up PLC channel model that accounts for both conducted and radiated fields, which significantly extends state-of-the-art PLC channel models presented in the literature [@versolatto2011an].

This paper is organized as follows. In , we derive the radiation model for a two-wire transmission line and introduce the MTRL. In , we explain how mode conversion is caused by the discontinuities in power line networks, and how this affects both the radiation and the communication. is dedicated to the explanation of the mixed-mode transmission theory. Its application to the representation of single devices and the extension to power line networks is presented in . Measurements results are reported in and conclusions follow in .

Radiation losses in Power Lines {#sec:radiation}
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The classical TL theory 