Uncertainties Using & Calculating Uncertainties for Electrical Measurement

Expressing Uncertainty of Measurement All measurements, even the most accurate, have an unknown inaccuracy or doubt. The is known as the UNCERTAINTY As there is always an uncertainty with any measurement we need to estimate this amount. We also need to calculate our confidence in the estimate of uncertainty, which is how sure we are that the true value is within the uncertainty we have estimated.

Expressing Uncertainty of Measurement As an example we may measure 1 Volt and be 95% confident that we are within 10uV

Expressing Uncertainty of Measurement UNCERTAINTY vs. ACCURACY There is no connection between these terms. Uncertainty is purely the unknown in any measurement. Accuracy or Tolerance is the difference between the desired value and the actual measured value.

Expressing Uncertainty of Measurement Example With a digital watch with 1 second resolution this resolution will limit the best uncertainty to which you can tell the time (ie. 1 second), however the watch itself may only be accurate to a few minutes.

Expressing Uncertainty of Measurement There are many sources of uncertainty in any measurement which need to be combined using statistical techniques to give a total. Different types of uncertainty need to be treated differently to obtain an accurate estimation.

Expressing Uncertainty of Measurement To calculate uncertainty you must first identify all the sources of error, estimate the size of the contribution from each source and also decide on the type of uncertainty for each source. There are two types of uncertainty Type A – Based on using statistics e.g. repeated readings Type B – Based on other factors e.g. manufacturers specifications

Sources of Uncertainty in Electrical Measurements. Imported Uncertainty Drift of reference instrument Temperature effects Lead and thermal errors (DC volts) Rounding errors due to resolution Repeatability Noise Self heating of high current shunts

Imported Uncertainty Imported uncertainty is taken directly from the certificate issued by the laboratory which calibrated the reference instrument. The probability distribution is ‘NORMAL’

Drift of reference instrument Drift of reference instrument can be either taken form historical data on the instrument or from the manufacture specification for stability. If the drift with time can be predicted it is possible to use a corrected figure for the actual value of the reference with a reduced figure for drift. However it is more normal to use an ‘un corrected’ figure. The probability distribution is ‘Rectangular’.

Temperature Effects The effect of temperature on many modern instruments is often very small, and in many cases the instruments specification covers a band of temperature without any further addition. Some reference standards for example resistors the Temperature coefficient may be quite important. The figure for TC can be taken from the manufactures spec or measured. The probability distribution is ‘Rectangular’.

Lead and thermal errors (DC volts) Thermal emf can be difficult to evaluate. With a little care and correct leads it is normal for thermal EMF to be less than 1uV, or even 0.5uV which is a figure often used in calculations. The probability distribution is ‘Rectangular’.

Resolution of Measurement It is firstly important to understand that there is a big difference between the resolution of a measuring instrument and that of a reference source. A source, such as a standard resistor may have no resolution at all, but can still be very accurate, while for a measuring instrument resolution is essential to achieve accuracy. It is only necessary to include measurement resolution in the uncertainty calculation. Note if a DMM is used to compare say two resistors then the resolution must be entered twice. The probability distribution is ‘Rectangular’

Combining Uncertainties It is normal these days to use a spread sheet, in Excel, taking a template from M3003. Use column 1 for a description of source of uncertainty Use column 2 for the value of uncertainty usually in ppm Use column 3 for a description of type of Probability distribution Use column 4 for the divisor, 2 for a normal dist, for rect Use column 5 for a coeficient used to convert say millvolts to microvolts Use column 6 = column2(value) x column4(divisor) x column5(coeff) Use the sum of square to total column 6 to get the Combined Standard Uncertainty To obtain the Expanded uncertainty (K=2, 95% Confidance) multiply the result above by 2. Then round to 2 significant places.

Expressing Uncertainty of Measurement Example

Using ProCal to calculate Uncertainties ProCal use three key elements to dynamically calculate uncertainties as the test is run 1) A table with imported uncertainties and calibrator specifications 2) A laboratory procedure incorporating additional factors such as lead /connection errors etc. 3) The noise / flicker which can be input at the time of test

Set Up Instrument Spec and Imported Uncertainties Use Proset, select instrument Traceability in the file menu. Select the Instrument required Select the ‘uncertainties button to access the table Enter the data, note default table exists for 2000 Series

Set Up Procedure Template Use ProSet, select ‘laboratory procedures’ in the file menu. Select the Instrument required Select the procedure spreadsheet template say for DC voltage Enter the parameters to be calculated, note the imported and reference specification will always be added automatically. Note the procedures for the main functions of the calibrator are Installed as default

Set Up Calibration Procedure Use ProEdit, edit a procedure and go to the ‘Instruments’ tab. Check the calibration instrument, lab. Procedure and uncertainty line. If a Transmille calibrator is in use these items will be set automatically, without having to be selected.

Calibrating An Instrument Use ProCal, run a calibration Input the reading and select / enter the noise / flicker in the drop down box displayed. If required, click on the UNCERT button to view the uncertainty calculation.

Where to Get More Information UKAS ( National Physical Laboratory Transmille Ltd (