Approximation-Based System Implementation for Real-Time Minimum Energy Point Tracking over a Wide Operating Performance Region

This paper refers to the optimal voltage pair, which minimizes the energy consumption of LSI circuits under a target delay constraint, as a Minimum Energy Point (MEP). This paper proposes an approximation-based implementation method for an MEP tracking system over a wide voltage region. This paper focuses on the MEP characteristics that the energy loss is sufficiently small even though the voltage point changes near the MEP. For example, the energy loss is less than 5% even though the estimated MEP differs by a few tens of millivolts in comparison with the actual MEP. Therefore, the complexity for determining the MEP is relaxed by approximating complex operations such as the logarithmic or the exponential functions in the MEP tracking algorithm, which leads to hardware-/software-efficient implementation. When the MEP tracking algorithm is implemented in software, the MEP estimation time is reduced from 1ms to 13µs by the proposed approximation. When implemented in hardware, the proposed method can reduce the area of an MEP estimation circuit to a quarter. Measurement results of a 32-bit RISC-V processor fabricated in a 65-nm SOTB process technology show that the energy loss introduced by the proposed approximation is less than 2% in comparison with the MEP operation. Furthermore, we show that the MEP can be tracked within about 45 microseconds by the proposed MEP tracking system.