# Influence of Random Modulated Power Converter on G3 Power Line Communication
## 5 Results and Discussion
### Effects of Random Number Update Rate and Modulation Index  
In this section, the effects of the RNUR and the modulation index of a randomly modulated power converter on the G3-PLC system are investigated. The RNUR of the random number (see Appendix A) plays a significant role on signal transmission because, with the higher RNUR of the random number, the pulse position of the RPWM changes rapidly. The modulation index determines how much the pulse position could be varied with respect to the switching period. CE reduction is proportional to the modulation index because higher value result in higher reduction of the CE peak. Indeed, the maximum pulse position variation, \(\Delta_{max}\), should be:  
\[\Delta_{max}\leq(T-d) \tag{9}\]  
Based on the results obtained in Section 5.1, to analyze the effects of the RNUR of the random number and the modulation index, three switching frequencies are chosen, in which one is around the intermediate frequency of the G3-PLC (60 kHz) where maximum disturbance due to random modulation is registered (see Section 5.1) and the other two are out of the frequency band of the G3-PLC (10 kHz and 100 kHz). A range of RNUR and modulation index values are considered to assess the performance of the G3-PLC. Figure 10 shows the FER obtained when the switching frequency of the randomly modulated converter is 60 kHz, and the RNUR and the modulation index take values in the intervals 0.16-100% and 5-20%, respectively. The obtained result shows that the FER is directly proportional to both the RNUR and the modulation index. The FER increases when the RNUR and the modulation index increase. This result further confirms that there is a trade-off between EMI reduction and coexistence, i.e., increasing the modulation index helps in reducing the peaks of the converter CE (see Figure 11). However, it causes more disturbance to the G3-PLC. The Channel Capacity of the G3-PLC with respect to the RNUR and the modulation index is depicted in Figure 12. The Channel Capacity exhibits significant reduction when both the RNUR and the modulation index are increased. The reduction with the RNUR  
Figure 10: FER of the G3 PLC measured with different values of RNUR and modulation index of the RPPM modulated DC-DC converter at 60 kHz switching frequency. is significant for large values of the modulation index. Conversely, for small modulation indexes, limited variations are observed. These results are also confirmed in terms of Channel Capacity Loss, as shown in Figure 13. Normally, the Channel Capacity Loss also increases with an increase in both the RNUR and the modulation index. Figure 11: CE of the DC-DC converter measured with different values of the modulation index at 20 kHz switching frequency and at 33% RNUR. Figure 12: Channel Capacity of the G3 PLC measured with different values of the RNUR and the modulation index of the RPPM modulated DC-DC converter at 60 kHz switching frequency. The performance of the G3-PLC for switching frequencies outside the PLC bandwidth are shown in Figures 14 and 15, respectively, confirming an increase in the FER when both the RNUR and the modulation index increase. However, the amount of variation in Figures 14 and 15 is insignificant compared to the results in Figure 10.  
Figure 14: FER of the G3 PLC measured with different values of the RNUR and the modulation index of the RPPM modulated DC-DC converter at 10 kHz switching frequency. Figure 13: Channel Capacity Loss of the G3 PLC calculated with different values of the RNUR and the modulation index of the RPPM modulated DC-DC converter at 60 kHz switching frequency. Therefore, it is possible to conclude that the RNUR and the modulation index of a randomly modulated power converter play a significant role in affecting the G3-PLC only when the switching frequency of the power converter overlaps with the bandwidth of the G3-PLC and is negligible for switching frequencies out of the bandwidth of the G3-PLC.