Simulation of temperature dependence measurements of resistance measures by SVD

Abstract

One of the important characteristics of high-precision resistance measures is the temperature dependence of resistance. Since this dependence is generally non-linear, it is most often approximated by a second-degree polynomial.
 Polynomial coefficients: resistance of the measure at a reference temperature (T0= 20 °C or 23 °C) R0, a coefficient characterizing the linear dependence of resistance on temperature a, and a coefficient characterizing the quadratic dependence of resistance on temperature b are determined experimentally by measuring the resistance of the measure RT at different temperatures T and by solving the resulting system of equations.
 To increase accuracy, multiple measurements are performed, which results in a redefined system of equations allowing solutions to be found by various methods.
 The paper considers the solution of a redefined system of linear equations using the SVD (singular value decomposition) method, if the inaccuracy of measurements of RT and T is caused by random factors. To simulate random factors, random values distributed according to the normal law were used.
 The SVD method was implemented using the MATLAB software package.
 The paper presents some results from simulating the process of measuring the temperature dependence of resistance measures.