# NBTI and Power Reduction Using an Input Vector Control and Supply Voltage Assignment Method
## 4 Experiment and Discussion
### Result and Discusion
The histograms in Figure 7 show that, for both circuits, the \(P_{\text{leak}}\) of SVA + IVC #2 and SVA + IVC #3 increase faster than that of SVA + IVC #1. However, for the c432 circuit, the leakage power in standby mode that corresponds to IVC #1 is much higher than that corresponding to the other two ILP formulations at the starting time (0 year), which makes it still the highest after some iterations of \(V_{dd}\) adjustment. Therefore, the \(P_{\text{leak}}\) of SVA + IVC #1 is higher than that of SVA combined with IVC #2 and IVC #3, as shown in Table 5. In contrast, although the initial leakage power that corresponds to the input vector found by IVC #2 is also the lowest for the c7552 circuit, the \(P_{\text{leak}}\) of SVA + IVC #2 is the highest for the c7552 circuit. The reason for this phenomenon is that the frequency of \(V_{dd}\) adjustment for SVA + IVC #2 is much faster than for SVA + IVC #1 and IVC #3 because of the severe delay degradation in standby mode, and makes its corresponding leakage power also increase fast as shown in Figure 7b. Finally, we can see that the input vector obtained by our proposed co-optimization ILP formulation can provide a balanced tradeoff between NBTI and leakage, so that both specifications are near optimal, and it can help the SVA save more leakage power than the ILP formulation for a single effect. Moreover, we have analyzed the power dissipation of the SVA method when \(R_{AS}\) is 0.01 and 1.0, and the results are shown in Tables 6 and 7, respectively. Tables 5-7 show that the power reduction result of the SVA method is dependent on both the input vector in standby mode and the \(R_{AS}\) value. First, compared with the SVA + IVC #1 method, our proposed SVA + IVC #3 method can save more leakage power, at the cost of a small increase of dynamic power. Second, when \(R_{AS}\) decreases, the advantage of our proposed SVA + IVC #3 method over the SVA + IVC #2 method on power reduction becomes high. For example, when \(R_{AS}\) is 0.01, the SVA + \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Circuit**} & \multicolumn{2}{c}{**SVA + IVC \#1 (\(\mathbf{\mu}\)W)**} & \multicolumn{2}{c}{**SVA + IVC \#2 (\(\mathbf{\mu}\)W)**} & \multicolumn{2}{c}{**SVA + IVC \#3 (\(\mathbf{\mu}\)W)**} \\ \cline{2-7}  & \(P_{\text{leak}}\) & \(P_{\text{dyn}}\) & \(P_{\text{leak}}\) & \(P_{\text{dyn}}\) & \(P_{\text{leak}}\) & \(P_{\text{dyn}}\) \\ \hline c432 & 8.52 & 17.26 & 7.65 & 17.89 & 7.38 & 17.34 \\ c880 & 17.87 & 39.61 & 15.70 & 41.00 & 15.26 & 39.99 \\ c1908 & 21.96 & 47.77 & 20.38 & 48.63 & 19.92 & 47.85 \\ c2670 & 33.42 & 75.29 & 29.16 & 76.30 & 28.67 & 75.29 \\ c3540 & 47.73 & 97.61 & 47.13 & 100.59 & 45.33 & 97.62 \\ c5315 & 78.50 & 187.71 & 71.68 & 192.41 & 68.39 & 188.02 \\ c7552 & 97.77 & 266.61 & 104.12 & 287.98 & 90.81 & 267.39 \\ s5378 & 58.49 & 113.37 & 52.63 & 115.76 & 51.17 & 113.57 \\ s9234 & 82.45 & 147.05 & 74.47 & 150.14 & 72.26 & 148.23 \\ s13,207 & 127.09 & 197.03 & 109.01 & 200.94 & 105.96 & 197.17 \\ Avg. & 13.54\% & \(-0.31\%\) & 4.28\% & 2.69\% & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Leakage and dynamic power of SVA combined with different ILP formulations (\(R_{AS}=0.01\)). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Circuit**} & \multicolumn{2}{c}{**SVA + IVC \#1 (\(\mathbf{\mu}\)W)**} & \multicolumn{2}{c}{**SVA + IVC \#2 (\(\mathbf{\mu}\)W)**} & \multicolumn{2}{c}{**SVA + IVC \#3 (\(\mathbf{\mu}\)W)**} \\ \cline{2-7}  & \(P_{\text{leak}}\) & \(P_{\text{dyn}}\) &  
IVC #3 method can save 4.28% more leakage power on average than that of SVA + IVC #2. However, when the \(R_{AS}\) is 1.0, our proposed method can only save 0.03% more leakage power. The reason for this phenomenon is that when the \(R_{AS}\) is small, the ratio of standby mode in the whole lifetime becomes high; the advantage of the input vector found by IVC #1 and IVC #3 on NBTI mitigation becomes more distinct over the input vector obtained by IVC #2.