Uncertainties of resistors temperature coefficients - Measurement ...

MEASUREMENT SCIENCE REVIEW, Volume 7, Section 1, No. 3, 2007NN2⎛⎞⎜2 ⎛ ⎞N TnT ⎟n⎜ ∑ ∆ − ⎜∑∆ ⎟⎟n=1n 1uA() u⎝ ⎝ = ⎠β =⎠y.detTUsing temperature coefficients as correction coefficients for resistor values suggests determination ofuncertainties of these values. For the resistors below 1 kΩ these uncertainties are about 1-3% ofcoefficient value. For higher resistances uncertainties increases, but radius of curve also increases. Fig.3.1 - 3.2 shows dependence of normalized resistance on temperature. For higher resistances type Auncertainty of β doesn’t have any influence on the results. It’s caused by flattening of the curve. Itsuggest, that type A uncertainty of β coefficientshould be used only for resistors with parabolictemperature characteristic. Resistance dependenceon temperature is an individual quantity of eachresistor. Results of type A uncertainty calculationsfor 6 measurement points are show in table 1.Increasing of measurement point will results withimproving approximation accuracy.2,0E-06Table 1.Type A uncertainties of temperaturecoefficientsR Ω u A (α) 1/K u A (β) 1/K0,00003(7b)100 7,89623E-09 1,84735E-0910 6 4,94877E-07 1,13894E-071,0E-060,000020,000010,0E+00-1,0E-06-8,0 -6,0 -4,0 -2,0 0,0 2,0 4,0 6,0 8,00-0,00001-6,0 -5,0 -4,0 -3,0 -2,0 -1,0 0,0 1,0 2,0 3,0r wr w-0,00002-2,0E-06-0,00003-0,00004-3,0E-06-0,00005-4,0E-06-0,00006-0,00007-5,0E-06∆T w K∆T w KFig. 3.2 Temperature characteristic for 100 Ω resistorFig. 3.2. Temperature characteristic of 1 MΩ resistor4. Type B uncertainty of temperature coefficientsType B uncertainty comes from non-statistical measurement analysis. The main influence for itsvalue has accuracy of temperature and resistance measurements. From (1) one can write2r − β∆Tα = , (8a)∆Tr −α∆T(8b)β = .2∆TStandard uncertainties of these coefficients can be written as follows2⎛ dα⎞ 2 ⎛ dα⎞ 2u SB( α ) = ⎜ ⎟ u ( ∆T) + ⎜ ⎟ u () r , (9a)⎝ d∆T⎠ ⎝ dr ⎠22(9b)⎛ dβ⎞ 2 ⎛ dβ⎞ 2u SB( β ) = ⎜ ⎟ u ( ∆T) + ⎜ ⎟ u () r .⎝ d∆T⎠ ⎝ dr ⎠Uncertainty of normalized resistance is the uncertainty of R(∆T)/R(T=23):uR( ∆T)uRrel= , (10)R( ∆T )and overall type B relative uncertainty can be written in form of sum225