Modeling CMOS Ring Oscillator Performance as a Randomness Source

In order to maximize randomness of CMOS Ring Oscillators (RO) used in Random Number Generators (RNG), possibility of weak inversion operation of CMOS transistors is investigated. To predict weak inversion noise performance of RO, phase noise and jitter models of a CMOS RO in weak inversion operating region are obtained. Differential Ring Oscillator (DRO) and Inverter-based Ring Oscillator (IbRO) cases are both investigated. For each case, the model covers the flicker and the white noise component of phase noise and jitter. The derived models are verified by measurement results. 0.25 m standard CMOS process has been used with a supply voltage of 0.7 V for DRO and 0.5 V for IbRO. Furthermore, phase noise and jitter behavior of a CMOS RO in strong and weak inversion region are compared through analytical models, simulations, and measurements. Even though white noise component of phase noise uses two different models for weak and strong inversion regions of operation, these two models exhibit continuity. Flicker noise component in weak inversion is much lower than the one in strong inversion, which also reduces the corner frequency. For a fair comparison of randomness performances, a randomness parameter is defined and randomness equations are derived for each case.