UncertaintiesUncertaintiesUsing & Calculating Uncertainties for Electrical Measurement

Expressing Uncertainty of Expressing Uncertainty of Measurement 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 anymeasurement we need to estimate thisamount. We also need to calculate ourconfidence in the estimate of uncertainty, which ishow sure we are that the true value is within theuncertainty we have estimated.

Expressing Uncertainty of Expressing Uncertainty of MeasurementMeasurementAs an example we may measure 1 Volt andbe 95% confident that we are within 10uV

Expressing Uncertainty of Expressing Uncertainty of MeasurementMeasurementUNCERTAINTY vs. ACCURACYThere 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 Expressing Uncertainty of MeasurementMeasurementExampleWith a digital watch with 1 second

resolutionthis resolution will limit the best uncertaintyto which you can tell the time (ie. 1 second),however the watch itself may only beaccurate to a few minutes.

Expressing Uncertainty of Expressing Uncertainty of MeasurementMeasurementThere are many sources of uncertainty in anymeasurement which need to be combinedusing statistical techniques to give a total.

Different types of uncertainty need to betreated differently to obtain an accurateestimation.

Expressing Uncertainty of Expressing Uncertainty of MeasurementMeasurementTo calculate uncertainty you must firstidentify all the sources of error, estimate thesize of the contribution from each source andalso decide on the type of uncertainty foreach source.There are two types of uncertainty Type A – Based on using statistics

e.g. repeated readings

Type B – Based on other factorse.g. manufacturers specifications

Sources of Uncertainty in Sources of Uncertainty in Electrical Measurements.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 UncertaintyImported 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 instrumentDrift 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 EffectsTemperature 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 Lead and thermal errors (DC volts)(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 MeasurementResolution 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 UncertaintiesCombining 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, 1.732 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 Expressing Uncertainty of MeasurementMeasurementExample

Using ProCal to calculate Using ProCal to calculate UncertaintiesUncertainties

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 Set Up Instrument Spec and Imported UncertaintiesImported 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 TemplateSet 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 ProcedureSet 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 InstrumentCalibrating 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 InformationWhere to Get More Information

UKAS (www.UKAS.co.uk)National Physical LaboratoryTransmille Ltd (www.transmille.com)