Thermometric characteristics approximation of germanium film temperature microsensors by orthonormal polynomials

Approximations of thermometric characteristics of germanium film temperature microsensors are presented using a mathematical approach based on their expansion with orthonormal polynomials. A weighted orthonormal polynomial expansion method (OPEM) is applied, involving the experimental errors of calibration test data at every point. The thermometric functions R(T) and T(R) of resistance and temperature are described in the whole temperature range (1.7-300 K) and in three subintervals (1.7-20, 20-150, and 150-300 K). The absolute, relative, and specific sensitivities of the sensor, as well as the main approximation characteristics, are discussed. The OPEM is extended to obtain a mathematical description of R(T) and T(R) functions by usual polynomial coefficients calculated by orthonormal ones. A comparison between maximal relative deviations of R(T) and T(R) three-interval approximations, correspondingly, by usual and orthonormal polynomials, is presented. Numerical results of the approximation parameters of these type of temperature sensors are shown in the figures and tables. (c) 2005 American Institute of Physics.