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FITTING CURVE METHOD IN ACCELERATED MICROCALORIMETER MEASUREMENTS

FITTING CURVE METHOD IN ACCELERATED MICROCALORIMETER MEASUREMENTS. Introduction. The paper presents a comparison between the methods applied in the data computation when starting from experimental results obtained in accelerated microcalorimetric measurements.

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FITTING CURVE METHOD IN ACCELERATED MICROCALORIMETER MEASUREMENTS

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  1. FITTING CURVE METHOD IN ACCELERATED MICROCALORIMETER MEASUREMENTS

  2. Introduction • The paper presents a comparison between the methods applied in the data computation when starting from experimental results obtained in accelerated microcalorimetric measurements. • Beside a simple exponential function, usually for an integrative first order system, other two functions are discovered by nonlinear curve fitting algorithms starting from the same experimental data.

  3. The microcalorimeter and its load

  4. Instrumentation set-up used in data acquisition

  5. Long-time classical measurement method

  6. 2.50E-05 e M 2.30E-05 2.10E-05 Thermopile output voltage (V) 1.90E-05 e m T SW 1.70E-05 1 91 181 271 361 451 Time (min) Accelerated-Measurements Method Figure 3. Microcalorimeter output waveform resulted by accelerated-measurements method for a time constant  = 38 minutes and a switching time TSW = 90 minutes.

  7. A. First-order system assessment method

  8. B. Nonlinear fitting law method Table 1. Fitting coefficients sets for 6 experimental data cycles and 90 points/set. Table 2. Goodness parameters associated with the fitting coefficients sets.

  9. Nonlinear fitting law method Figure 4. Extrapolated microcalorimeter output waveform resulted by nonlinear fitting law method applied in accelerated-measurements method for a time constant  = 30.45 minutes, a switching time TSW = 90 minutes and an extrapolation time interval of 305 minutes.

  10. C. Nonlinear fitting law method Table 3. Fitting coefficients sets for sum of two exp. fitting function and the same experimental data. Table 4. Goodness parameters associated with the new fitting coefficients sets.

  11. Nonlinear fitting law method Figure 5. Extrapolated microcalorimeter output waveform resulted by nonlinear fitting law method applied in accelerated-measurements method for time constants 1 = 29.06 minutes and 2 = 4.47 minutes, a switching time TSW = 90 minutes and an extrapolation time interval of 305 minutes.

  12. Comparison of the results Table 5. Results and quality parameters for different computation methods in microcalorimeter measurements.

  13. Conclusions • The efficiency of the fitting method can not be proved by uncertainty improvement but the changes in the wanted value can change the result of a key comparison. • The chosen computation method in accelerated microcalorimeter measurements it allows to decide the switching time interval and the number of data per every period. • An adaptive automated measuring system can change the switching time in a manner which will lead to an adequate uncertainty. • However, the manly part of the uncertainty is from microcalorimeter calibration step and accelerated measurement not appear as being enough accurately. • In this kind of measurement, the measurement time is never enough long and a good correction can be done by a suitable curve fitting method.

  14. References 1. Fantom A. E., Radiofrequency & microwave power measurement, Peter Peregrinus Ltd., London, 1990. 2. IEEE Standard Application Guide for Bolometric Power Meters, IEEE Standards 470-1972. 3. Brunetti L., Vremera E., "A new microcalorimeter for measurements in 3.5-mm coaxial line", IEEE Trans. Instrum. Meas., 52, 2, 320-323, (2003). 4. Vremera E., Brunetti L., Broadband Coaxial Microcalorimeter Efficiency Determination Based on Thermal Simulation and Vector Network Analyzer Measurements, Bul. Inst. Politehnic, Iaşi, XLVIII (LII), 3-4, 65-76, Electrotehnică, Energetică, Electronică (2002). 5. Brunetti L. and Vremera E., New Calibration Method for Microcalorimeters, IEEE Transaction on Instrumentation and Measurement, 54, 2, 684-687 (2005). 6. Vremera E., Brunetti L., "Improvement of Microcalorimeter Measurements through Data Correction", Proc. of 16-th IMEKO TC4 Symposium, Athena-Greece, pp. 260-265, 2004 7. Brunetti L. and Vremera E., CIPM Key Comparison CCEM-RF-K10CL: Power in the coaxial PC 3.5mm line system, IEN Technical Report, Torino, 636 (2001). 8. Brunetti L., Oberto L., Vremera E., Recent Evolutions of the Microcalorimeter Technique, Proceedings of the XXIXth URSI, New-Delhi, India, A01.8(01763).pdf, 2005. 9. Clauge F. R., A Method to Determine the Calorimetric Equivalence Correction for a Coaxial Microwave Microcalorimeter, IEEE Transaction on Instrumentation and Measurement, 43, 3, 421-425 (1994). 10. EA –4/02: Expression of the Uncertainty of Measurement in Calibration, December 1999

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