A Methodology for Datapath Energy Prediction and Optimization in Near Threshold Voltage Regime

In this article, we propose a method for sizing an arbitrary combinational datapath to minimize its energy consumption. Our method involves deriving expressions for the components of energy consumption at both the stage and path levels. In this work, we identify overshoot energy (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E_{\text {OS}}$ </tex-math></inline-formula>) consumption as a previously unreported component contributing to energy consumption, particularly significant in the near/sub-threshold voltage regime. We determine that this <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E_{\text {OS}}$ </tex-math></inline-formula> consumption is proportional to the input and output transition times and size of a logic gate at a particular stage of a datapath. We also observe that, for a given number of stages (N) and path effort, the total energy consumption is optimized when the stage effort (f) in a datapath is kept constant. Based on our observations and derivations of all the energy components and the requirement for a constant “f” in the datapath, we develop a method to minimize the energies of a logic circuit while maintaining the timing closure requirement. We determine that the non-critical paths (NCPs) must be sized to a minimum “f” while maintaining the timing requirements. We verified our models on several ISCAS and EPFL benchmark circuits with an average reduction of 28.1% (41.2%) and 19.2% (28.4%) in energy consumption [figure of merit (FoM)], respectively. The proposed methodology predicts the total energy consumption at a stage and path level of N-stage logic, with only one-time SPICE simulation on a single stage, with a maximum error of 1.3% and 1.62%, respectively, against SPICE simulations. The simulations are performed in Synopsys HSPICE environment with ST Microelectronics 65 nm CMOS and 28 nm FDSOI technology nodes, resulting in a very good agreement with the developed methodology.