Characterization of Oscillator Phase Noise Arising From Multiple Sources for ASIC True Random Number Generation

This paper presents an analytical study together with an oscillator phase measurement technique to assess the magnitude of the five most prevalent noise types found in free-running oscillators, intended for use in true random number generation. The noise types under study range from white thermal-to flicker-and random walk noise, acting either on the oscillator phase or frequency. A time domain study establishes an analytical connection between the oscillator excess phase variance and the accumulation time length. A variance model that characterizes the phase measurement method is developed, taking into account that one noise type will dominate over all other handled noise types within a specific measurement interval. Additionally, this model considers the effects of both test setup induced variance and quantization noise. The measurement method utilizes a differential approach based on Delay Chains (DCs) and is implemented using a 65nm Complementary Metal-Oxide-Semiconductor (CMOS) technology. A time resolution less than 100 ps could be achieved, effectively lowering the quantization noise floor and allowing to examine jitter accumulation at a time scale down to 30 ns. Measurement results show that typical CMOS ring oscillators are predominantly affected by flicker noise, creating long-term dependencies between the generated period jitter. This observation might in turn invalidate the popular assumption of mutual independence between successive oscillator periods, made in many true random number generator stochastic models. A noise corner is observed at the lower end of the measured accumulation time interval, below which thermal noise becomes dominant over flicker noise, and consecutive period jitter can be considered mutually independent again.