# NBTI and Power Reduction Using an Input Vector Control and Supply Voltage Assignment Method
## 4 Experiment and Discussion
### Result and Discusion  
First, we compare the NBTI and leakage reduction results of different IVC methods. We define \(P_{\text{leak}}\) and \(P_{\text{dyn}}\) as the average leakage power and average dynamic power during the overall lifetime of the circuit, respectively. In the first step, three kinds of ILP formulations are constructed and their corresponding optimal input vectors are found. Then, the corresponding delay degradation \(\Delta D\) and leakage power \(P_{\text{leak}}\) for these input vectors in ten years is calculated, and the result is shown in Table 4.  
The delay degradation \(\Delta D\) that corresponds to the input vector obtained by the IVC #1, IVC #2, and IVC #3 methods is shown in column two to four, respectively. The corresponding leakage power \(P_{\text{leak}}\) of these three IVC methods is shown in column five to seven, respectively. From Table 4, we can obtain the following conclusions: first, IVC #1 and IVC #2 can find the optimal \(\Delta D\) or \(P_{\text{leak}}\) minimization result, respectively. However, because only one issue is considered in generating the co-optimization ILP formulation, the reduction result for the other issue is not satisfactory. The proposed ILP formulation considers both effects, and can reduce \(\Delta D\) and \(P_{\text{leak}}\) at the same time. For instance, compared with IVC #1, our proposed IVC #3 method can achieve a 13.15% improvement in \(P_{\text{leak}}\) reduction at the cost of a 0.69% \(\Delta D\) increase on average. On the other hand, compared with IVC #2, our proposed method can decrease \(\Delta D\) by 8.32% on average, at the cost of a 2.01% increase in leakage power. As shown in Table 4, the results of the three ILP formulations are different tradeoffs between NBTI and leakage. In the following section, we combine these different IVC methods with the supply voltage assignment, which is a subsequent method after the input vector is determined. In most modern systems, the devices will periodically switch between the active and standby mode, and the circuit's delay degradation is dependent on the ratio between the active and standby modes (\(R_{AS}\)) according to Equations (1)-(6). In some industrial applications, the circuit works under a predefined routine, and the \(R_{AS}\) is a fixed value during its lifetime. However, the \(R_{AS}\) value in some other applications will change randomly. In order to simplify the experimental setting, we assume that the \(R_{AS}\) is fixed, and analyze the NBTI and power reduction results of the combination method when \(R_{AS}\) is set to different values. In our future work, we will further analyze the results of our proposed method when the \(R_{AS}\) changes randomly. First, we use three kinds of ILP formulation IVC #1, IVC #2, and IVC #3 to determine the input vector that satisfies the NBTI minimization, leakage minimization, and co-optimization requirements, respectively. Then, the input vector is used in standby mode and the ratio between the active mode and the standby mode is assumed to be 0.1. Afterwards, an SVA method that uses the input vector obtained by IVC #1, IVC #2, and IVC #3, respectively, is applied to compensate for the NBTI-induced performance degradation. The \(V_{dd}\) update cycle for the SVA method is five days, and the resolution for \(V_{dd}\) adjustment is 20 mV. The above process is repeated until the end of the circuit's lifetime. Then, the average leakage and dynamic power of the circuit in ten years is calculated.