An Analysis of Stochastic Self-Calibration of TDC Using Two Ring Oscillators

This paper presents a theoretical analysis of the stochastic calibration of TDC using two ring oscillators. Designers of TDC with the calibration function have to decide the design parameters to guarantee the convergence of error and valid calibration time. The basic theory of the calibration is useful to decide these parameters and the policy on the calibration design. The performance of the stochastic calibration depends on the design parameters, the frequencies of the two ring oscillators, the number of the stages, the buffer delay, and so on. This work analyzes explicitly the relation between these parameters and the performance of the calibration with simulation-based analysis. Simulation results reveal that the convergence of the calibration is guaranteed when both of the cycles of the two ring oscillators are the prime cycles. The histogram of each bin converges to the corresponding buffer delay value in a well-behaved manner, the DNL measurement error decreases monotonically in proportion to the increase of the number of the times of the measurement. In other words, the required number of the measurement times is in proportion to the required accuracy of calibration. This result is applied to the calibration of VDL-based TDC, too.