Comparison of Thermistor Linearization Techniques for Accurate Temperature Measurement in Phase Change Materials

Comparison of thermistor linearization techniques for accurate temperature measurement in phase change materials This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 J. Phys.: Conf. Ser. 307 012009 ( Download details: IP Address: The article was downloaded on 02/10/2012 at 01:40 Please note that terms and conditions apply. View the table of contents for this issue, or go to the jo
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  Comparison of thermistor linearization techniques for accurate temperature measurement inphase change materials This article has been downloaded from IOPscience. Please scroll down to see the full text article.2011 J. Phys.: Conf. Ser. 307 012009( details:IP Address: article was downloaded on 02/10/2012 at 01:40Please note that terms and conditions apply.View the table of contents for this issue, or go to the  journal homepage for more HomeSearchCollectionsJournalsAboutContact usMy IOPscience    Comparison of thermistor linearization techniques for accurate temperature measurement in phase change materials S B Stankovic 1,3  and P A Kyriacou 1,2,3   1  School of Engineering and Mathematical Sciences, City University London,  Northampton Square, London EC1V 0HB, UK 2  E-mail:   Abstract . Alternate energy technologies are developing rapidly in the recent years. A significant part of this trend is the development of different phase change materials (PCMs). Proper utilization of PCMs requires accurate thermal characterization. There are several methodologies used in this field. This paper stresses the importance of accurate temperature measurements during the implementation of T-history method. Since the temperature sensor size is also important thermistors have been selected as the sensing modality. Two thermistor linearization techniques, one based on Wheatstone bridge and the other based on simple serial- parallel resistor connection, are compared in terms of achievable temperature accuracy through consideration of both, nonlinearity and self-heating errors. Proper calibration was performed  before T-history measurement of RT21 (RUBITHERM® GmbH) PCM. Measurement results suggest that the utilization of serial-parallel resistor connection gives better accuracy (less than ±0.1°C) in comparison with the Wheatstone bridge based configuration (up to ±1.5°C). 1. Introduction Recent years have witnessed an increasing development of alternative energy technologies. One of the main objectives in this area can be achieved through application of phase change materials (PCMs) for reduction of energy consumption. Thermal characterization of PCMs is essential prior to any profound utilization of these materials. Current methods for the investigation of thermo-physical properties of PCMs (e.g. differential scanning calorimeter – DSC) show significant drawbacks especially in terms of the limited sample size [1] [3]. Therefore, the measurements in this study were performed through implementation of the method specifically designed for the investigation of PCMs, the temperature history (T-history) method [3]. Since PCMs are able to store/release large amounts of heat in a narrow temperature range of few degrees, the accurate thermal investigation of these materials is of key importance. However, the majority of the T-history studies in the literature have not emphasized the accuracy of temperature measurements [3]-[8]. Also, it must be taken into an account that sensors for measurements inside the PCM samples need to be small in order to reduce the interference with the phase change process. Consequently small thermistors (model Newark MA100GG103A) were selected for this investigation [9]. 3  The research funding was provided by Engineering and Physical Sciences Research Council (EPSRC).   1   Thermistor’s nonlinearity and self-heating errors are the biggest problems in any temperature application. Several linearization techniques have been developed over the years based on voltage divider or bridge circuits, discrete active elements, and different software solutions [10] [11]. In this  paper two techniques based on the Wheatstone bridge design and simple serial-parallel resistor circuit are compared in terms of achievable temperature accuracy. T-history based characterization of RT21 PCM (RUBITHERM® GmbH) specimen with the expected phase change temperature range between 18°C and 23 °C requires measurements in the range from 11°C to 30 °C [12]. Hence, the thermistor characteristic was linearized in the range from 10°C to 39 °C in order to meet application requirements. Firstly, the linearization methods were theoretically evaluated through calculations of temperature-output voltage dependencies and absolute errors introduced by linearization circuits. Subsequently calibration was performed in 1 °C step temperature  program from 10 °C to 39 °C and calibration curves were determined along with the absolute errors. Finally, T-history measurement on RT21 PCM and distilled water as a reference material was  performed. 2. Materials and methods 2.1. Temperature sensors Since the sensors used for temperature measurements in PCMs need to be small, a negative temperature coefficient (NTC) MA100GG103A thermistor model with a 2 mm diameter probe and a 28 wire gauge was used [9]. The temperature dependence of the thermistor resistance  R t is given by the table of resistances with the nominal resistance of 10k  Ω  at 25 °C. Its operating range is from 0 to 50 °C. Therefore, linearization was performed for the range between 10°C and 39 °C due to indicated application requirements. 2.2. Linearization circuits The principle of thermistor linearization circuit is to provide relatively linear dependency between temperature and the circuit’s output voltage. In addition to linearization the main goal of this study were accurate temperature measurements. The first design goal was to minimize the thermistor self-heating error Δ T   to 0.05 °C. This error defines the value of thermistor maximum permissible   current  I  max  as indicated by equation (1): (1) where C   represents thermistor dissipation constant. Critical value (in air) of this constant for the selected thermistor is 2.5·10 -3   mW  /°C.  R t,min  represents the minimal thermistor resistance in the operating temperature range. The second design goal was to keep the supply voltage V  CC   equal to the standard value of 5V in order to minimize the circuit’s power dissipation. Nonlinearity error is determined by appropriate temperature-output voltage curve fitting. The first (linear) and the third (cubic) order polynomial fitting equations were determined. The first linearization circuit is more common and based on Wheatstone bridge (WB) (see figure 1). Since the Wheatstone bridge is just a form of a voltage divider the maximum permissible thermistor current defines the value of resistor  R 3  and automatically determines the shape of temperature-output voltage curve and nonlinearity error. The values of the two other resistors determine the output voltage range, but do not affect the shape of the temperature-output voltage linearization curve. On the other hand, the second linearization circuit, based on simple series-parallel resistor connection (Ser_Par) in figure 2, is more flexible since the self-heating error condition only determines the value of a single resistor (here  R 1 ) in the connection. Additional resistor (  R 2 ) in this configuration allows shaping of temperature-output voltage curve in order to minimize the nonlinearity error and achieve better accuracy in the particular temperature range.   2   The value of resistor  R 2 (in figure 2) was determined by equating the second temperature derivative of temperature-output voltage transform function with zero in order to determine the linear region of the transform function. VCC5VR115k Ω 1%R224k Ω 1%NTC_Thermistor 10k Ω 25 °CU1AOP497FP 321141 VEE-5VR325k Ω 1%U2AOP497FP 321141 U3AOP497FP 321141  OUTPUT R57.5k Ω 1%R415k Ω 1%Rf 15k Ω 1%Rg7.5k Ω 1% VaVbVaVb VEE-5VVCC5VVCC5VVEE-5VVCC5V   Figure 1.  Wheatstone bridge thermistor linearization circuit. VCC5VR150k Ω 1%R210k Ω 1%NTC_Thermistor 10k Ω 25 °CU1AOP497FP 321141 VEE-5V OUTPUT VCC5V   Figure 2.  Serial-parallel resistor thermistor linearization circuit. 2.2.1. Theoretical evaluation of temperature-output voltage dependencies The temperature-output voltage dependency was calculated for both linearization circuits based on the temperature-thermistor resistance characteristic. Calculations were performed for a temperature range  between 10°C and 39 °C. MATLAB® code was developed to determine linear and cubic order  polynomial fitting equations of calculated curves [13]. The absolute errors between real and fitted temperature values were calculated (see figure 3 and figure 4). Figure 3.  Theoretical absolute error values when using linear fitting for WB and Ser_Par linearization circuits. Figure 4.  Theoretical absolute error values when using cubic fitting for WB and Ser_Par linearization circuits. 2.2.2. Practical evaluation of temperature-output voltage dependencies Prior to PCM T-history measurements proper sensor calibration for the two linearization circuits was  performed. Each sensor was subjected to 1 °C step temperature program from 10 °C to 39 °C. The calibration measurement was performed in a thermally controlled environment. Data acquisition  performed utilising a NI 6212 USB 14-bit DAQ card at a sampling rate of 10Hz [14]. Recorded output voltage data were evaluated at known temperatures (10 °C to 39 °C in 1°C step) and the calibration curves were determined. Once again, the calculation of absolute errors between expected and fitted measured temperature data was evaluated based on MATLAB® linear and cubic calibration curve fitting equations [13].   3

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