Solution
There are several contributors of error for a delta time/two edge separation measurement: noise, jitter, clock accuracy, etc. Though this specification is not published, it can be calculated using the following formula:
An explanation for this formula is given as follows:
- The portion under the radical determines the RMS Jitter for the edge measurements.
- SlewRate1 and SlewRate2 are the slew rates, in V/s, for each edge being measured respectively.
- Random Noise, or RMS Noise is the noise introduced to the measurement by the digitizer. This can be found in the specifications, and has the units V rms.
- Random Noise / Slew Rate = Jitter (of measured edges)
- Clock Jitter is a specification that can be found in the device documentation
- Typically the units are specified in fs rms.
- Timebase Accuracy can also be found in the device specifications.
- Timebase Accuracy, in ppm, is the accuracy of the onboard Reference Clock.
- This can be improved by importing a more accurate Reference Clock.
- The reading is the expected or measured separation between the two edges being measured, indicated by SlewRate1 and SlewRate2.
Typically, a two-edge separation measurement is performed when the edge being measured crosses a specified threshold voltage. For measurements taken over short time intervals (on the order of nanoseconds), the calculated error is usually dominated by random noise, unless the Digitizer’s sample rate is not high enough to represent the edges accurately. If the sample rate is insufficient, we must rely on interpolated data to determine when the edge crosses the threshold voltage, which will introduce additional error.
When the acquired edges are sufficiently sampled (i.e. >4 samples on the edge), then interpolation can be performed to improve the measurement accuracy. Interpolation allows us to determine the edge threshold value with sub-sample accuracy. The Resample Waveforms (single shot) VI can interpolate the measured waveforms. It is recommended to use the “FIR filter” interpolation mode.
The following is an example of the error calculation of a two-edge separation measurement, being performed on a PXIe-5186, with a Vertical Range of 1Vpp, and 50 ohm input impedance.
Slew Rate: 0.65V/ns
PXIe-5186 RMS Noise*: 3.5 mV rms (50 ohm, 1V)
Sample Clock Jitter*: 500 fs rms
Time Base Accuracy*: 25 ppm
Reading: 5ns
* Denotes values taken from the device specifications. For the PXIe-5186, a link to this documentation can be found below in the related links.