Non-linearity analysis of stochastic time-to-digital converter

Stochastic TDCs excel in high resolution at narrow dynamic ranges by employing comparators which have their decision influenced by PVT variations. As the functionality relies on these variations, a transfer function akin to the Gaussian distribution ensues, which is non-linear. We propose a theoretical derivation of the non-linearity analysis and use it to find the stochastic TDC´s effective resolution and optimal dynamic range. Software and circuit Monte Carlo simulations are conducted in support of the theoretical findings, where the circuit employs comparators implemented in 180nm CMOS technology.