A Necessary and Sufficient Condition of Supply and Threshold Voltages in CMOS Circuits for Minimum Energy Point Operation

Abstract

Scaling supply voltage (V_DD) and threshold voltage (V_th) dynamically has a strong impact on energy efficiency of CMOS LSI circuits. Techniques for optimizing V_DD and V_th simultaneously under dynamic workloads are thus widely investigated over the past 15 years. In this paper, we refer to the optimum pair of V_DD and V_th, which minimizes the energy consumption of a circuit under a specific performance constraint, as a minimum energy point (MEP). Based on the simple transregional models of a CMOS circuit, this paper derives a simple necessary and sufficient condition for the MEP operation. The simple condition helps find the MEP of CMOS circuits. Measurement results using standard-cell based memories (SCMs) fabricated in a 65-nm process technology also validate the condition derived in this paper.