# NBTI and Power Reduction Using an Input Vector Control and Supply Voltage Assignment Method
## 4 Experiment and Discussion
### Result and Discusion
The results are shown in Figure 8.  
In Figure 8, the x-axis represents the different power constrains for the ILP formulation in Ref. [27], and the y-axis is the ratio of \(P_{\text{dyn}}\) and \(P_{\text{leak}}\) between the SVA + IVC #3 method and the SVA + IVC #4 method. Figure 8 shows that, for the different circuits, the co-optimization ILP formulations with different power constrains can obtain the optimal leakage and dynamic power reduction result. For example, the power reduction result is optimal for an c880 circuit when the constrain is 30%. However, for the c3540 circuit, the optimal result can be obtained when the constrain is set to 10%. Therefore, it is inconvenient to find the best parameter for the co-optimization ILP formulation in Ref. [27]. In comparison, our proposed ILP formulation can obtain the only optimal input vector that can help the SVA method save power dissipation conveniently. Finally, we implement a 5000 times Monte Carlo simulation to find input vectors for the circuit. We calculate the \(P_{\text{leak}}\) and \(P_{\text{dyn}}\) of the SVA in ten years when these randomly selected input vectors are used in standby mode. The simulation setting is the same as the above section. We compare the power dissipation of SVA + MC with our proposed SVA + IVC #3 method. The result is shown in Table 9.  
Table 9 shows that the proposed IVC #3 method can find the optimal input vector and help the SVA save more leakage power than the input vector obtained by MC simulation. Since the dynamic power \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Circuit**} & \multicolumn{2}{c}{**SVA + MC (\(\mu\)W)**} & \multicolumn{2}{c}{**SVA + IVC \#3**} \\ \cline{2-5}  & \(P_{\text{leak}}\) (\(\mu\)W) & \(P_{\text{dyn}}\) (\(\mu\)W) & \(P_{\text{leak}}\) (\(\mu\)W) & \(P_{\text{dyn}}\) (\(\mu\)W) \\ \hline c432 & 8.37 & 17.93 & 7.95 & 17.90 \\ c880 & 18.21 & 41.55 & 16.67 & 41.51 \\ c1908 & 22.67 & 49.79 & 21.61 & 49.51 \\ c2670 & 32.76 & 76.67 & 30.98 & 77.78 \\ c3540 & 51.93 & 102.13 & 49.39 & 101.23 \\ c5315 & 83.11 & 196.66 & 75.08 & 195.59 \\ c7552 & 102.21 & 273.18 & 100.16 & 278.71 \\ c85378 & 58.82 & 115.74 & 55.46 & 117.43 \\ s9234 & 87.18 & 153.23 & 78.22 & 153.20 \\ s13207 & 129.53 & 205.18 & 115.67 & 204.49 \\ Avg. & 7.26\% & \(-0.22\%\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Leakage and dynamic power of SVA using an input vector found by Monte Carlo (MC) simulation and the IVC #3 method. Figure 8: Leakage and dynamic power of SVA for the c880 and c3540 circuits when using the input vector obtained by the co-optimization method in Ref. [27] under different power constrain settings. (**a**) c880 circuit; (**b**) c3540 circuit. is strongly dependent on the circuit's supply voltage in the active mode, the impact of NBTI-induced \(V_{dd}\) change on power dissipation is great. As shown in Figure 6, the result of NBTI mitigation by MC simulation is close or even better than the result by the proposed IVC #3 method, so the best result of the dynamic power for SVA + MC is close to the dynamic power of the SVA + IVC #3 method. Finally, the \(P_{\text{dyn}}\) and \(P_{\text{leak}}\) of the SVA method for the c880 and c3540 circuits when using the input vector obtained by MC and the three IVC methods are illustrated in Figure 9, respectively. In Figure 9, the x-axis and y-axis represent the leakage and dynamic power of the SVA method, respectively. Point A (the rectangular point) and B (the triangle point) correspond to the result of SVA + IVC #1 and SVA + IVC #2, respectively. Point C (the star point) represents the result of our proposed SVA + IVC #3 method. The small asterisk point represents the leakage and dynamic power of the SVA method using the input vector obtained by MC simulations. The iteration number for MC simulation is 100,000.