The time interval measurement accuracy of WaveMaster series oscilloscopes is expressed in the form: ±((0.06 * Sample Interval) +(1 ppm of measured interval)). This specification reflects the two major sources of uncertainty in time measurements on digital oscilloscopes. The second component (1 ppm of the measured interval) represents the uncertainty due to the scope's timebase. The WaveMaster Series of oscilloscopes incorporates a 1 ppm timebase. This is the most accurate oscilloscope timebase available. This component affects longer time intervals. For instance, if you measure a 1 GHz clock (1 ns period) the uncertainty due to the timebase is 1 fs.

The first component of the time interval accuracy (0.06 * Sample Interval) is related to the scope's measurement interpolator and timebase short term stability. The timebase, in the case of the LeCroy scopes, is a minor contributor to uncertainty. The interpolator is simply a software component that measures the location in time at which the signal crosses a given threshold value. Given the maximum sampling rate available, 20 GHz, interpolation is necessary in most cases. Interpolation is automatically performed in the scope when three or fewer samples exist on any given edge. Interpolation is not performed on the entire waveform. Rather, only the points surrounding the threshold crossing are interpolated for the measurement. To find the crossing point, a cubic interpolation is used, followed by a linear fit to the interpolated data. This is shown in Figure 1.

The accuracy of the interpolation is dependent on many factors. The key factors are the transition time of the signal, the sampling rate, vertical noise, and the effective vertical resolution. Figure 2 shows a typical calculation, using a simple model, for a signal with a 300 ps edge sampled at 20 GS/s using an 8 bit digitizer. The signal amplitude is 80% of full scale. The relationship between the vertical resolution and time resolution is:

$$Δt = Δv/ dv/dt$$

Where | **Δt** - time uncertainty |

| **Δv** - amplitude uncertainty |

| **dv/dt** - slope of the transition |

For a vertical uncertainty of 1 l.s.b. (1/256 of fullscale) and based on the slope of 0.8 of full scale over 6 samples (300 ps @ 50 ps/sample) the equivalent time uncertainty works out to:

$$Δt = (1/256) / (0.8/6) = 0.03 sample periods

Since the sampling period is 50 ps the uncertainty for this measurement is 1.5 ps. This timing uncertainty applies to any single measurement.

Most measurements of this type are not made in isolation. Multiple measurements allow users to study the variation in measured values. As in all measurements, the uncertainty of the mean of the measured values decreases with multiple measurements. For Gaussian distributions the uncertainty in a measurement decreases as the square root of the number of measurements. So, repeating the measurement 100 times yields an improvement of 10 times in the accuracy of the sample mean. The graph in figure 3 shows the results of 20 sets of measurements of the period@ level parameter on a 700 MHz squarewave. Each set of measurements was performed on an acquisition that included 35,000 cycles. This would reduce the specified uncertainty to the order of 16 fs. The measurement was correlated with a frequency counter which is plotted on the same axis. Note that the scope measurement is well within the normalized specification limits and is in good agreement with the counter measurements. Note that the horizontal scale on the graph is 20 fs per division.

The use of sampled data does not limit timing measurement accuracy to the sampling period. Timing measurements on properly sampled waveforms can be measured with resolution in the order of picoseconds with statistical accuracy of the mean value down into the tens of femtosecond range.