Modeling phase noise and jitter in subthreshold region and assessing the randomness performance of CMOS ring oscillators

This paper analyzes the phase noise and jitter issues for random number generation in the weak inversion operating region of CMOS Ring Oscillators (RO) with the purpose of increasing the randomness of a RO. To the best of our knowledge, this is the first study on modeling phase noise and jitter in subthreshold region and assessing the randomness performance in this region. Phase noise and jitter equations are derived. Furthermore, randomness equations are obtained from these equations and compared with the strong inversion counterparts to show the increase in randomness. Inverter-based Ring Oscillators (IbRO) and Differential Ring Oscillators (DROs) are examined. For design and analysis, 0.25µm standard CMOS process has been used with a supply voltage of 0.5V. Decreasing the supply voltage of IbRO from 2.5V to 0.5V results in 68.7 times increase in randomness and 1297 times reduction in energy. In DRO case, the same reduction in supply voltage results in 7.64 times increase in randomness and 51 times reduction in energy.