different numbers of counted clock pulses and (see picture). These occur with probabilities with the fractional part of . The value for the time interval is then obtained by Measuring a time interval using a coarse counter with the averaging method described above is relatively time consuming because of the many repetitions that are needed to determine the probabilities and . In comparison to the other methods described later on, a coarse counter has a very limited resolution (1ns in case of a 1 GHz reference clock), but satisfies with its theoretically unlimited measuring range. Fine measurement In contrast to the coarse counter in the previous section, fine measurement methods with much better accuracy but far smaller measuring range are presented here. Analogue methods like time interval stretching or double conversion as well as digital methods like tapped delay lines and the Vernier method are under examination. Though the analogue methods still obtain better accuracies, digital time interval measurement is often preferred due to its flexibility in integrated circuit technology and its robustness against external perturbations like temperature changes. The counter implementation's accuracy is limited by the clock frequency. If time is measured by whole counts, then the resolution is limited to the clock period. For example, a 10 MHz clock has a resolution of 100 ns. To get resolution finer than a clock period, there are time interpolation circuits. These circuits measure the fraction of a clock period: that is, the time between a clock event and the event being measured. The interpolation circuits often require a significant amount of time to perform their function; consequently, the TDC needs a quiet interval before the next measurement. Ramp interpolator When counting is not feasible because the clock rate would be too high, analog methods can be used. Analog methods are often used to measure intervals that are between 10 and 200 ns. These methods often use a capacitor that is charged during the interval being measured. Initially, the capacitor is discharged to zero volts. When the start event occurs, the capacitor is charged with a constant current I1; the constant current causes the voltage v on the capacitor to increase linearly with time. The rising voltage is called the fast ramp. When the stop event occurs, the charging current is stopped. The voltage on the capacitor v is directly proportional to the time interval T and can be measured with