## 3 Results and Discussion
### Tests with Two Modules with 16-bit SAR Converters and Two Chassis  
This set of tests were carried out to demonstrate that it is possible to use a 16-bit SAR converter type to replace the 24-bit Sigma-Delta converters while maintaining accuracy and precision in accordance with the requirements of the synchro-phasor standard. It is  
Figure 8: Probability density for Sigma-Delta converters. Figure 7: Box-and-whisker plot for Sigma-Delta converter tests. very important to note that in this case, no voltage transducers were used to estimate the quality of the synchro-phasor. A high-quality signal from a Tektronix AFG3022B was used to generate a waveform similar to that obtained from a transducer with an appropriate transformer ratio. The choice of external transducers is a topic that will be studied in the second part of this paper. Figure 9 shows the equipment involved in the tests for the SAR-type converters. A 50 Hz, 20 Vpp sine wave signal was applied simultaneously from a signal generator. This signal was connected to the input of each of the devices and the deviation in the phase measurements of both the C0 and D0 inputs of the modules under test was calculated. In the same way as in the previous tests, the phase difference between two consecutive channels of the same C-module was measured. Secondly, a test was carried out to determine the phase error between two channels of the C and D modules under test. The two modules were inserted into the same cDAQ-9185 chassis. The phase shifts from Channel-C0 and Channel-D0 were measured. In the third test, captures were made with different cDAQ-9185s. Modules C and D were plugged into Slot1. The two chassis were synchronised with the TSN standard. The test allowed for verifying the synchronism for the simultaneous sampling of 20 Vpp voltages with 2 and 10 m Ethernet cables. Figure 10 shows how almost all the time series data were below 80 ns, while Figure 11 shows the types of distribution of the tests with TSN synchronisms concerning the reference tests in the same chassis. As can be seen in both figures, there is a larger dispersion, but the central positions of the distributions (medians) were below 50 ns. Figure 9: Configuration using 16-bit SAR converters without sensors. Table 4 shows the accuracy of SARs integrated in a module with four channels, which is equivalent to a median of Me = 10.3 ns with a variance of \(\sigma^{2}\) = 82.3 ns, notably much higher than that of the Sigma-Delta modules. When the channels were in different slots and in modules C and D, average errors of Me = 14.95 ns and a variance of \(\sigma^{2}\) = 113.71 ns were obtained. The same table shows the responses when capturing with different chassis and Ethernet cable lengths of 2 and 10 m. The medians obtained were of very high quality, with values of 25.63 ns and 30.72 ns, but with a dispersion represented by variances of \(\sigma^{2}\) = 168.43 ns and \(\sigma^{2}\) = 185.66 ns. These are very good results with a consistent response depending on the length of the conductors. The results with the Sigma-Delta converters in the previous section served as a reference to estimate whether the phase measurements of the 16-bit SAR converters met the requirements of the synchro-phasor standard. The results in Table 4 were very similar to those obtained with the 24-bit Sigma-Delta converters in the previous section, but it is necessary to estimate the uncertainty levels for their integration in a distributed instrumentation system. Again, we used the box-and-whisker plot to identify where 95% of the samples were concentrated. Figure 11: Histograms for phase measurements with SAR modules. Figure 10: Time series of the four SAR converter tests. As depicted in Figure 12, when measuring with two consecutive channels, the measurements were below 38 ns for 95% and below 60 ns for 100%. The results corroborate the manufacturer's specifications concerning the phase error between channels. The TSN tests showed two limits at 95% depending on the length of the cable.