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.