# NBTI and Power Reduction Using an Input Vector Control and Supply Voltage Assignment Method
## 4 Experiment and Discussion
### Result and Discusion
Therefore, the frequency of \(V_{dd}\) adjustment for the SVA method when using the input vector found by IVC #3 is much slower than that of IVC #2, which in turn helps the SVA + IVC #3 method save more leakage and dynamic power than that of the SVA + IVC #2 method. In Ref. [27], [PERSON] et al. have proposed a kind of co-optimization method for NBTI and leakage reduction. This co-optimization ILP formulation is named IVC #4 in the following section. Their method constructed an ILP formulation to find the minimum NBTI-induced delay degradation with different power constraints. In this paper, we also use IVC #4 to find the input vector and analyze the power reduction result of the SVA method when using these input vectors. First, the ILP formulation for leakage minimization and the modified version of ILP formulation for leakage maximization are generated as per the design flow in Ref. [27]. Then, we find the potential best and worst leakage power for the circuit by solving these formulations. Second, a set of power constrains can be built with 10% steps of the leakage power compared to the potential minimum value. With each constrain, an ILP formulation for NBTI mitigation is generated, and the result of these ILP formulations are input vectors, which can obtain the minimum NBTI-induced aging and satisfy the leakage power constrain. Finally, we use each of these ten input vectors in standby mode and apply an SVA to compensate for the performance aging. At the end of the circuit's lifetime, we calculate the average leakage and dynamic power of an SVA when using each input vector. Suppose \(P_{\text{leak},i}\) and \(P_{\text{dyn},i}\) is the leakage and dynamic power of an SVA corresponding to input vector \(i\). \(P_{\text{leak},min}\) and \(P_{\text{dyn},min}\) is the potential minimum leakage and dynamic power for all of the ten input vectors. Then we define \(E_{i}=P_{\text{leak},i}/P_{\text{leak},min}+P_{\text{dyn},i}/P_{\text{dyn},min}\) for each input vector \(i\), and the minimum \(E_{i}\) is considered as the optimal result on power reduction for each circuit when using IVC #4. The leakage and dynamic power of the SVA method when using the input vector found by IVC #4 and our proposed IVC #3 method is shown in Table 8.  
From Table 8, we can see that compared with the IVC #4 method, our proposed method can save more leakage power dissipation during a circuit's lifetime, at the cost of a slight increase in dynamic power. Moreover, the design procedure of our proposed method is much simpler than that in Ref. [27], which demonstrates the advantage of our method. In addition, we implement a simulation on c880 and c3540 circuits to investigate the leakage and dynamic power change of the SVA method when using the input vector obtained by IVC #4 under \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Circuit**} & \multicolumn{2}{c}{**SVA + IVC \#4 in Ref. [27]**} & \multicolumn{2}{c}{**the proposed 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 & 7.95 & 17.90 & 7.95 & 17.90 \\ c880 & 16.91 & 41.51 & 16.67 & 41.51 \\ c1908 & 21.65 & 49.51 & 21.61 & 49.51 \\ c2670 & 31.49 & 77.78 & 30.98 & 77.78 \\ c3540 & 49.92 & 101.73 & 49.39 & 101.23 \\ c5315 & 76.19 & 195.38 & 75.08 & 195.59 \\ c7552 & 100.21 & 278.69 & 100.16 & 278.71 \\ s5378 & 56.17 & 117.32 & 55.46 & 117.43 \\ s9234 & 80.48 & 153.20 & 78.22 & 153.20 \\ s13,207 & 117.51 & 204.41 & 115.67 & 204.49 \\ Avg. & 1.16\% & 0.02\% & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Leakage and dynamic power of SVA method using input vector found by Ref. [27] and the proposed ILP formulation. different power constrains in detail. In order to observe the change more precisely, the leakage and dynamic power results of SVA + IVC #4 are normalized to the power results obtained by the proposed SVA + IVC #3 method.