time-to-digital converter

A time-to-digital converter (TDC) is an integrated circuit that measures the time interval between two electrical events and outputs the result as a digital value. One event typically arrives at a start input, the other at a stop input; the TDC counts the elapsed time with nanosecond or picosecond resolution and encodes it as a binary word. This serves applications where you need precise numerical records of when something happened, not just that it happened.

The circuit works by feeding the time interval into a chain of delay elements or a ring oscillator, then counting how far the pulse propagates before the stop signal arrives. Higher-frequency oscillators yield finer time resolution, but at the cost of power consumption and silicon area. Most modern TDCs are built into larger systems on chip (SoCs), though standalone versions exist for laboratory and test equipment. Typical resolutions range from 10 picoseconds to a few hundred picoseconds, with measurement windows from nanoseconds to microseconds depending on the design.

TDCs appear wherever event timing matters: in time-of-flight (ToF) sensors for distance measurement, positron emission tomography (PET) scanners, time-tagged photon detectors, radar systems, and particle physics experiments. They also handle precise frequency measurement by capturing the arrival times of repeated pulses. In mass spectrometry and lidar, accurate time-to-digital conversion directly affects spatial and mass resolution.

Sources of error and design tradeoffs

Practical TDCs suffer from integral nonlinearity (INL) and differential nonlinearity (DNL), where delay stages do not behave identically. Temperature drift and supply voltage variation alter the propagation delays, shifting calibration. Dead time, the minimum interval the converter can resolve, sets a lower bound on measurable intervals. Designers reduce these effects through careful layout, thermal compensation, and calibration circuits that map actual delays against ideal values. Trade publications and datasheets often specify DNL and INL in fractions of a least significant bit (LSB).

The name reflects the function plainly: time (the quantity measured) to digital (the output form). Unlike an analog-to-digital converter (ADC), which digitizes a continuous voltage, a TDC converts the domain of time itself into a number. This distinction matters in the lab and in design specifications, because the two devices solve different problems and impose different constraints on the rest of the signal chain.