Numerical Simulation of Clock Error, Given Allan Variance

Thomas J. Blenk Jr.

Abstract: As systems become more complex and aim to achieve high performance through optimization, system clock attributes continue to play an increasing critical role in overall system performance. When attempting to predict system performance, it is extremely important to use realistic, accurate, and hardware representative clock models. Unfortunately, including a clock model in modeling and simulation environments is often an afterthought, and modeling and simulation practitioners will default to simple Markov stochastic models due to the complexity of accurately modeling a random process representing a unique hardware solution. By exploiting the relationship of the time domain Allan Variance representation of a random process and the frequency domain power spectral density (PSD), we can create a realistic representative model given only an Allan Variance. This is extremely convenient as the Allan Variance is a commonly used method of evaluating clock performance, and is provided by many clock manufacturers. Several key motivations drove the design of the proposed solution. First, the solution must be easily understandable to execute without an in-depth knowledge of timing devices. Second, the solution must be easily integrated into existing models while minimizing additional computation burden, and therefore requires the ability to pre-compute the frequency behavior of a clock for an entire simulation run. Lastly, the proposed solution yields a unique and independent random process for each trial enabling Monte-Carlo type analysis. This paper proposes and evaluates a simple process meeting the aforementioned key motivations for taking any Allan Variance curve and generating a random process that closely approximates the original.
Published in: Proceedings of the 53rd Annual Precise Time and Time Interval Systems and Applications Meeting
January 25 - 27, 2022
Hyatt Regency Long Beach
Long Beach, California
Pages: 87 - 95
Cite this article: Blenk, Thomas J., Jr., "Numerical Simulation of Clock Error, Given Allan Variance," Proceedings of the 53rd Annual Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California, January 2022, pp. 87-95.
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