Theory of TDC Operation

This chapter addresses theoretical aspects of time-to-digital converters. First the basic shape of a TDC input–output characteristic is explained. The quantization error that arises from the mapping of a continuous into a discrete signal domain is revisited. Linear and non-linear imperfections of a TDC, namely offset and gain error as well as differential and integral non-linearities, are explained. Dynamic performance figures are motivated on the basis of analog-to-digital converters. The difference between ADC and TDC measurement is discussed. The interrelation between the single tone experiment of ADCs and the single shot experiment for TDCs is derived. An effective number of bits is defined for TDCs based on a single shot measurement. Therewith, an ADC compliant figure of merit is defined for TDCs. Local (process) variations are a critical issue for high resolution time-to-digital converters. Variations hit TDCs in the buffer tree of the stop signal, the delay-line, and the comparators. The susceptibility of each of these components is analyzed individually. Finally, the particular variation effects are combined.