## 3 Results and Discussion
### Tests with SAR Converters with Four Chassis  
In the second stage of this phase, the tests focused on the analysis of the SAR type converters with the distribution as presented in Figure 4.  
In this phase, we analysed the results obtained with the box-and-whisker plots (Figure 19) as well as the type of distribution with the non-parametric probability density (Figure 20). For the measurements with three and four chassis, a sequence of 50-75 m and 50-75-10 m was chosen. With two chassis, the results with 50 m and 75 m conductors were compared. It was observed that the average errors were approximately 3 \(\upmu\)s. This was primarily due to the externally connected LEM LV-25 voltage transducers at each of the NI-9215 inputs. In this second test, it was observed that the phase errors were only attributable to the SAR converters and to the synchronisation technique with TSN. The input signal for the two channels derived from the same transducer output. Figure 21 compares the tests with two chassis for two different configurations. With 50 m and 75 m Ethernet cables, the length of the conductor had very little influence. In total, 95% of the measurements were below 100 ns and 100% were below 140 ns. In both cases, optimal results were obtained. In total, 95% were below 80 ns and 100% were below 100 ns. With the probability density curves, we still observed that the distributions were not Gaussian, but all four curves for the test type in Figure 22 shared the same type of symmetry. Again, anomalous behaviour was observed. The estimator approximated the response to a curve with values less than zero. It is considered very likely that some values in the time series were erroneous. Figure 21: Box diagram for SAR with an LEM. Figure 20: Distribution density with two LEMs. In comparing the results in Tables 7 and 8, the time response of the LV25 LEMs can be perfectly appreciated, which is around 3 \(\upmu\)s. It is very reasonable to use CADDOCK Electronic's high-precision resistor divider technology to guarantee uncertainty levels very close to those obtained in Table 8. This technique to attenuate the voltage deriving from the supply network is the one used by the NI-9242 modules. A comparison of the results in Table 6 for the Sigma-Delta converters with those obtained for the SAR converters in Table 8 shows that the latter had a lower variance and standard deviation. The data were more clustered around the mean but this degree of dispersion did not affect the quality of the timing system because 95% of the values were below 100 ns. They were adequate for the objective set from the beginning. Moreover, the response of the LV-25 LEMs was within the admissible tolerance range for a timing system that is required to meet the \(\upmu\)PMU standard. This set of results guarantees compliance with the specifications of the synchro-phasor standard and ratifies the expectations of the TSN standard, which includes among its specifications a guaranteed resolution of at least 1 \(\upmu\)s for the synchronisation of multiple devices connected to a conventional Ethernet network. Tests with National Instruments' technology not only guarantee this level of synchronism but can also claim that values in the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Test: 50 Hz and 230 Vpp with Sampling Fs = 50 kS/s**} \\ \cline{2-5}
**2 LEM Phase Errors (ns)** & \multicolumn{4}{c}{**16-bit SAR Converters with 2 LEMs**} \\ \cline{2-5}  & **Chassis 1–2:** & **Chassis 2–3:** & **Chassis 1–2–3:** & **Chassis 1–2–3–4:** \\  & **A0–50 m-B0** & **B0–75 m-C0** & **A0 50 m 75 m C0** & **A0 50 m 75 m 10 m C0** \\ \hline Mean & 3082.5 & 2991.4 & 3069.7 & 3032.0 \\ \hline Median & 3085.1 & 2991.5 & 3068.1 & 3032.4 \\ \hline Variance (\(\sigma^{2}\)) & 6021.9 & 1371.2 & 5438.4 & 4304.5 \\ \hline Standard Deviation (\(\sigma\)) & 77.6012 & 117.0998 & 73.7458 & 65.6089 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Phase errors for SAR converters. Tests with two LV-25 LEMs.