## 2 Theoretical Frame and Materials
### Theoretical Frame  
The previous documents mentioned regarding single-cable transmission in Section 1 considered frequencies of transmission above 50 MHz (higher than the ones we worked with in this first demonstration stage for our PV-PLC system), whose current distribution is expected to be flowing superficially or in a thin layer close to the surface of the cable (skin effect), with propagation described to be carried out by a surface wave whose phase velocity is c (the speed of light). Our direct measurements of the phase velocity over a line of single PV cable at a frequency of 20 MHz showed speeds around 0.6 c, closer to what is observed in typical coaxial cables [14], even when the propagation mode is different in our single-cable medium (TM) than the one in coaxial cables (TEM). The lower frequency used in our single-cable support suggests that the current distribution flows in a thicker layer inside the conductor, and the influence of the material lowers the phase velocity with respect to the previously mentioned Sommerfeld surface wave. As a result, the single-cable analogy applied to the PV plant cable cannot allow us to assume the same propagation mode described in Section 1, and since our aim with this document is not to establish a theoretical background but to develop a practical approach for implementing a working PLC system specific for PV plants, we assumed the measured phase velocity of 0.6 c and tried to start from a simple model to characterize our system. The influence of the topology of the physical wiring in the previous literature on PLC systems for PV strings is not usually discussed, probably because the low-frequency carriers proposed do not show limitations related to higher frequencies, such as interferences or resonance issues. Some previous works use an open line topology [7; 15; 16] and some others propose a current loop topology [17]. The frequencies are normally in the order of 100 kHz or less, that is to say, considering the assumed phase velocity (0.6 c) wavelengths are around 1800 m, much bigger than the usual length of the string. With this work, we try to explore the possibility of setting the carriers of higher frequencies (from 1 MHz on), analysing the effects of the increased frequency and offering a practical solution, which inevitably leads to considering the physical topology of the wiring. In a single PV string, the power wires starting from a combiner box return to the same box after connecting the modules in series. In essence, it is easy to establish a circular communications path by means of a capacitor connected between the two cables arriving at the combiner box and to bypass capacitors connected through each PV module. This allows for a cable loop configuration to be a communications physical support for a single string. The choice of a closed-loop configuration for the signal path has several advantages for communications purposes. This topology sets all the points along the circular line at the same level regarding attenuation, so differences in reception levels are reduced to a minimum and it allows for a resonance condition to be established for the signal along the loop, since there is a natural reactive impedance associated with a cable loop depending on the relationship between the wavelength and the physical length of the loop, which can be compensated for by some added lumped reactive impedance, leaving only a low-resistance path for the signal. Adding the ring topology proposed to the aforementioned assumption about phase velocity = 0.6 c, a simple propagation model can be considered.