Approximation-Based Implementation for a Minimum Energy Point Tracking Algorithm over a Wide Operating Performance Region

This paper refers to an optimal pair of the supply and the threshold voltages, which minimizes the energy consumption under the given delay constraint, as a minimum energy point (MEP). This paper proposes an approximation-based implementation method for an MEP tracking algorithm over a wide operating performance region. The key point is that the accuracy required for determining the MEP is not high. Even if the MEP estimated by the algorithm differs by a few tens of millivolts in comparison with the actual MEP, the energy loss introduced by the estimation error is small. Therefore, the complexity for determining the MEP can be reduced by approximating complex operations such as the logarithmic or the exponential functions in the MEP estimation algorithm, which leads to hardware-Isoftware-efficient implementation. Measurement results based on a 32-bit RISC-V processor fabricated in a 65-nm process technology show that the energy loss introduced by the proposed approximation is less than 1% in comparison with the MEP operation. When the MEP tracking algorithm is implemented in software, the MEP estimation time is reduced from 1 ms to 13 $\mu \mathrm{s}$. When implemented in hardware, the proposed method can reduce the area of an MEP estimation circuit to a quarter.