Energy-optimal voltage model supporting a wide range of nodal switching rates for early design-space exploration

This paper explores the models of the energy-optimal voltage (V
_OPT
) of near/sub-threshold digital VLSI circuits with a focus on the support for a wide range of nodal switching rates. The previous models can estimate the V
_OPT
of the circuits having relatively high nodal switching rates (V
_{OPT, H}
), but can become inaccurate in finding the VOPT of the circuits having low nodal switching rate. In this work, therefore, we develop the models for finding (i) the V
_OPT
of the circuits having low nodal switching rates (V
_{OPT, L}
) and (ii) the critical nodal switching rate point (α
_crit
) below which the V
_{OPT, L}
should be used. The models are verified with inverter chains and sub-threshold 10-transistor SRAM arrays in SPICE-level simulation. The model takes only process technology parameters to estimate V
_OPT
s, and can be suitable for early-stage design-space exploration.