Assessing the Impact of Temperature and Supply Voltage Variations in Near-threshold Circuits using an Analytical Model

In this paper, we develop an analytical model based on Enz Krummenacher Vittoz (EKV) current equations to assess the impact of temperature and supply voltage (V-DD) variations in circuits operating in near-threshold voltage (NTV) regime. Using the proposed model, we derive parameters that can be optimized to reduce the impact of these variations on devices operating in the NTV regime and highlight the dominant role of the inversion coefficient of the EKV equations. Further, we show that, instead of operating circuits such as a CMOS inverter very close to the threshold voltage (V-TH), it is beneficial to operate these circuits 3-4kT/q above the V-TH. At these voltages, the impact of the temperature variations on the delay is minimized and the impact of V-DD variations on delay is 0.7x lower than when operated at V-DD = V-TH. Additionally, compared to the super-threshold operation, the power consumption reduces by 5x and the delay increases by 5x. The results presented in this paper can be employed in estimating the increase in the time margins required when a circuit is migrated from the super-threshold operation to the near-threshold operation.