## 3 DAC Integral/Differential Nonlinearities--New Normalized Error Vector Metrics
### Monte Carlo Simulations of Key Properties of the INL, DNL, IEV, DEV eDAC Metrics  
In this subsection we verify essential features of the INL, DNL, IEV, DEV eDAC metrics theoretically treated heretofore in Section 3, presenting Monte Carlo simulations based on the same ensemble of 1500 BiWgt UNIP PAM4 eDACs with \(B=3\), C = 8, as already used in the simulations in 2.9. Here we randomly extract five eDACs out of the 1500 eDACs ensemble, drawing five random realizations of the corresponding source vectors, \(\mathbf{I}\), satisfying Proposition 1, (five mutually independent Gaussian random vectors, each with independent components with means and variances per (94), with parameters as defined in the simulations in Section 2.9). We then work out the five resulting output currents \(\mathbf{J}\), by acting onto the five drawn \(\mathbf{I}\) vectors with the \(8\times 3\) UNIP BiWgt code matrix. For each of the resulting five output UNIP constellations, \(\mathbf{J}\), we evaluate the INL, DNL, IEV, DEV vectors, and have these vector metrics depicted in Figures 7-10. Overviewing the four figures presented in Figure 7, 5 INL curves are assembled together and so are 5 DNL curves. Figure 8 piles 5 IEV curves together and 5 DEV curves together. Figure 9 associates each of the five INLs with its corresponding IEV. Figure 10 associates each of the five DNLs with its corresponding DEV. Elaborating, Figure 7 verifies Corollary 8, visualizing the skew-centrosymmetry of the INL, the centrosymmetry of the DNL and the fact that the INL is \"pinned\" to zero values at its two extreme (LSL and MSL) samples. Figure 8: Monte Carlo simulations (**left**) IEV, (**right**) DEV for five UNIP BiWgt eDACs with randomly drawn source currents, verifying the symmetries of the IEV and DEV metrics. Figure 7: Monte Carlo simulations of (**left**) INL, (**right**) DNL for five eDACs with randomly drawn source currents, verifying the symmetries of the INL and DNL metrics. The colors of the various jagged lines represent distinct sample paths of the random process. Figure 9: Monte Carlo simulations of the INL (dashed, blue curves) and IEV (solid, orange curves) of each of the 5 BiWgt UNIP PAM8 eDACs (randomly selected out of the eDACs ensemble) the 5 INL curves of which were already plotted in Figure 7(left). Here, plotting the INL and IEV together for each of the five eDACs enables discerning the distinct qualities of these metrics, in particular the pinning to zero of the INL at the two extreme samples (the LSL and MSL) vs. a trend of increased deviation of the INL from zero, as the index c increases, consistent with the variance of the eDAC zero-mean output current component actually linearly increasing with the index c (Theorem 4). Next transitioning from the INL, DNL to the corresponding IEV, DEV metrics, Figure 8 is the counterpart of Figure 7, presenting the respective IEV and DEV for the same five randomly drawn BiWgt UNIP PAM4 eDACs. Visually comparing the INL and IEV graphs (Figure 7(left) vs. Figure 8(left)) it is apparent that the UNIP IEV is no longer skew-centrosymmetric, and in particular it is no longer pinned to zero at the MSL index (\(c=8\)) (though it is pinned to zero at the LSL index (\(c=1\)). In fact, the general statistical trend of the IEV is to rise in absolute value as the index \(c\) increases, consistent with our analytical model in Theorem 4 indicating that for unbiased UNIP eDACs as the index \(c\) increases, the variance of the IEV linearly increases. Evidently, these are just 5 IEV realizations out of the entire statistical ensemble but the variance growth tread trend is already visible.