**3. Results**

Figure 7 shows the action of the compensation described, where a 20-m-long loop was kept in resonance at 9.5 MHz initially with the corresponding control voltage of 5 V. Then, the length of the loop was shortened to 15.10 m, and with the resonance control electronics off, the resonance frequency was displaced to 11.1 MHz. If we then switched on the electronics, the control voltage was readjusted by the MCU to get the resonance back to 9.5 MHz. All the electronics described above could work to keep the resonance condition on any of the two modes described in Section 2. The S21 modulus was measured with a VNA connected in series with the loop, the tuning circuit and a 50-ohm load. Maximums show the frequencies of minimal attenuation of the propagation along the (loop)-(tuning circuit) chain. The black trace corresponds to the 20 m cable with a control voltage of 5 V in the tuning circuit, where the maximum is over the chosen carrier frequency (9.5 MHz). The blue solid trace corresponds to a variation in the loop length from 20.00 m to 15.10 m with no change in control voltage, and the new maximum is over 11.1 MHz and the carrier (9.5 MHz) is attenuated from |S21| = 0.228 to 0.100. The blue dashed trace corresponds to the new loop length (15.10 m) after the tuning circuit action for compensation, leading to a control voltage of 0.9 V, and the maximum is back over the carrier at 9.5 MHz.

**Figure 7.** Effect of microcontroller action to retune the loop, in response to variations in cable distance.

During the current distribution measurements in the one-wavelength loop presented before (Figure 2), with an exciting signal of 10 volts in amplitude, the absolute voltages measured across the current sensor were between 70 and 330 mV, which, considering that the sensor sensibility is 10 Volts/Amp, indicates averaged current amplitude values in the order of 200 mA. This suggests that with much lower exciting voltages, communication with reasonable SNRs is possible due to loop resonance, making simpler and low-cost transceivers conceivable.

As a validation of the current levels present in the short-loop configuration (1 ⁄4 wavelength), measurements were made over an experimental setup composed of a cable loop 20 m long with ten capacitors and ten small toroidal transformers distributed evenly in series simulating the bypass capacitors and the transceiver inductively coupled and installed within each PV module in a real installation. The toroidal transformers had a transformation ratio of 30:1 with the secondary connected to the loop, and their inductances were adjusted to form with the bypass capacitors LC resonators at the carrier frequency, in such a way that the transceivers were LC resonators at the same frequency as the loop resonance. The control electronics were also placed in series with the loop. A carrier frequency of 1 MHz was chosen, fulfilling the condition of a loop shorter than <sup>1</sup> ⁄4 wavelength, and was injected in the primary of one of the transformers with an amplitude of 5 volts, simulating a transmission from one of the transceivers towards the others. The voltage amplitude measurements at the primaries of the ten transformers receiving the signal are shown in Table 2.


**Table 2.** Voltage amplitude measurements of the <sup>1</sup> ⁄4 wavelength configuration.

#### **4. Conclusions and Future Works**

An analysis of a ring topology as physical support for a PLC system specially intended for PV strings has been presented, proposing that pushing this loop to resonance optimises the reception levels along the cable. Previous works on this subject had proposed resonant circuits for coupling to the line; we added here to this feature the possibility of working with the whole loop under resonance, improving even more the signal levels along the line. In addition, the conditions needed for the levels to be reasonably equalised has been derived. Control electronics have been designed to keep the communications signal path on resonance, making the system flexible and able to self-adapt to different specific installations or changes within the same setup. As this check and adaptation to resonance is a task that does not need to be accomplished continuously (it would be enough to execute it once per day), the MCU that controls all the communications in a final application could be the same, allowing a lower-cost system.

The insertion of transmission (TX) and reception (RX) circuits along the loop shows reactive impedances (inductive or capacitive coupled to the line) or even small resistances, consequently modifying the resonance condition on the loop; nonetheless, our tests have shown that the addition of the compensation reactance supplied by the circuit described before is able to return the loop to the optimal working point of resonance. The approach here presented is useful as a starting point for further research that could determine the precise influence of lumped impedances along the loop in the communications performance, but for moderate reactances in the TX/RX circuits (enough for signal injection and recovery), the compensation circuit is enough, with only small deviations compared to the behaviour of the raw cable loop.

Two options regarding the relationship between the loop length and the wavelength have been presented: a loop with one wavelength perimeter and a loop with <sup>1</sup> ⁄4 wavelength perimeter or less. The measurement levels in the loop have shown the possibility of working with relatively low signal levels without compromising the SNR in both options, allowing the design of cheaper and simpler transceivers. The main line of research from our results must be to explore and test for future work the ways proposed to excite the travelling wave mode in the one wavelength loop, which in essence could suppose a great leap forward for equalising the signal levels working at carrier frequencies over 5 MHz, leading to baud rates close to or even over 1 Mbps (depending on the spectral efficiency of the modulation scheme chosen), keeping all the advantages of working in resonance.

**Author Contributions:** Conceptualisation, J.I.M.-A. and L.H.-C.; methodology, J.I.M.-A., V.A.G., M.S.M.W. and L.H.-C.; validation, J.I.M.-A., V.A.G., M.S.M.W., J.G.F.C. and L.H.-C.; formal analysis, J.I.M.-A. and M.S.M.W.; investigation, J.I.M.-A., V.A.G., M.S.M.W., A.R.-P., D.F.-M., F.J.S.-P. and L.H.- C.; writing—original draft preparation, J.I.M.-A., M.S.M.W., S.G.-S. and L.H.-C.; writing—review and editing, J.I.M.-A., J.G.F.C., S.G.-S. and M.S.M.W.; supervision, L.H.-C.; project administration, L.H.-C.; funding acquisition, J.I.M.-A. and L.H.-C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by the Universidad of Valladolid with the predoctoral contracts of 2020 cofunded by Santander Bank. This study was supported by the Universidad of Valladolid with ERASMUS+ KA-107.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
