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The components of uncertainty vary depending on which test is running. The E Series device calibration procedure runs up to three main tests, depending on which device you are calibrating. Each test takes different uncertainty components into account. After Calibration Executive calculates all the components of uncertainty, the components are converted to a 1-sigma normal distribution, then combined using the root-sum-square method. The combined standard uncertainty is then multiplied by an appropriate coverage factor, taking degrees of freedom into account, to arrive at the reported expanded uncertainty of measurement, which corresponds to a coverage probability of approximately 95%.
This section describes the components of counter uncertainty in the E Series device calibration procedure. You must manually calculate final expanded counter uncertainty at a 95% confidence level based on the manufacturer’s specifications for the counter and your own Type A calculations. Enter this value when the procedure prompts you for it. A suggested final expanded uncertainty value is computed as follows:
where
where 10 is the number of measurements taken.
Type B uncertainty can be calculated as shown in the following example, which measures a 5 MHz square wave signal (which has negligible trigger error) with a one second gate time. This example is for an HP53132A counter with a high-stability oven that was calibrated three days ago.
where
Number of Samples is 200,000 (because frequency > 200 kHz)
Gate Time is 1 second
Time Base Error is Temp. Stability × (3 Days × Daily Aging Rate)
t_{acc} is the timebase accuracy of the counter (from the hardware documentation)
t_{jitter} is the jitter specification of the counter (from the hardware documentation)
t_{res} is the rms resolution of the counter (from the hardware documentation)
= 2.5 × 10^{–9} + 3 × (5 × 10^{–10})
= 4.0 × 10^{–9}
= [±4.0 × 10^{–9} ± 1.96 × (2.01 × 10^{–12} + 3 × 10^{–12})] × 5 MHz
= (±4.0 × 10^{–9} ±9.8 × 10^{–12}) × 5 MHz
= ±20.05 mHz
The following table contains the names and descriptions of the components of analog input uncertainty in the E Series device calibration procedure.
Uncertainty Component | Description |
---|---|
Calibrator uncertainty | Retrieved from the calibrator uncertainty text file. |
Resolution uncertainty of the E Series device | where Resolution of DUT is the range of the E Series device divided by the number of levels in the ADC. The term in the denominator results from assuming a rectangular distribution of probabilities of the measurement values. |
Type A uncertainty |
where 10,000 is the number of measurements taken. |
Leads, wiring, and calibration fixture | Insignificant compared with other uncertainty components. |
The following table contains the names and descriptions of the components of analog output uncertainty in the E Series device Calibration Executive procedure.
Uncertainty Component | Description |
---|---|
DMM uncertainty | Retrieved from the DMM uncertainty text file. |
Resolution uncertainty of the E Series device |
where Resolution of DUT is the range of the E Series device divided by the number of levels in the digital-to-analog-converter (DAC). The term in the denominator results from assuming a rectangular distribution of probabilities of the measurement values. |
Type A uncertainty |
where 10 is the number of measurements taken and 1.06 accounts for the t-distribution. |
Leads, wiring, and calibration fixture | Insignificant compared with other uncertainty components. |
Note If you use the recommended test equipment and follow the test conditions guidelines, the vast majority of the uncertainty for the analog input tests is due to the resolution uncertainty of the ADC on the E Series device. The majority of the uncertainty for the analog output tests is due to the resolution uncertainty of the DAC on the E Series device. Other uncertainty components are negligible compared to these components. |