On the differential nonlinearity of time-to-digital converters based on delay-locked-loop delay lines

A theoretical analysis of the effects of the delay-line differential nonlinearity (DNL) on the typical performance parameters of high-resolution time-to-digital converters (TDCs) based on delay-locked-loop (DLL) delay lines has been developed. The theoretical study is based on the knowledge of the delay-line nonlinearity values that can be measured, with the desired precision, by means of a statistical code-density test. In particular, the effects on the TDC time resolution and error standard deviation curve as a function of the measured time interval are investigated. An a posteriori linearization technique, consisting in a proper correction of the TDC readouts, is then analyzed and its advantages are theoretically demonstrated. Finally, the theoretical results are superimposed on experimental data coming from a real TDC. The measured deviations from the ideal behavior are thus justified and can just be ascribed to the delay-line nonlinearity.