An Optimal Linearization Method of Parameter Design for NTC Thermister Interface Circuit

Transcription

1 6 International Conference on Mechanics Design, Manufacturing and Automation (MDM 6) ISBN: An Optimal Linearization Method of Parameter Design for NC hermister Interface Circuit Yan-Ju WANG,a, Li-Kun YANG,b, Hui-Long JIN,c, Peng GAO,d, Shu-Jing ZHANG,e,* Electronic Department of HeBei Normal University, Shijiazhuang, China, 53 a yjwang3@63.com, b yl73@63.com, c jhl98@hebtu.edu.cn, d churchillgp@63.com, e shujing_zhang@yeah.net *Corresponding author Keywords: NC thermister, Nonlinearity compensation, Interface circuit, Parameter design. Abstract. he thermister based temperature measurement scheme is widely applied for its low cost, strong stability and well flexibility. As the property between resistance and temperature is nonlinear, the practical application of thermister usually relies on the method of table loo-up. Inevitably, that leads to the problems of poor versatility and large memory cost. Based on the analyses of resistance and temperature property, we propose an optimal linearization method of parameter design for NC thermister interface circuit in this paper. he proposed approach is simple, but has a good linearity and high sensitivity. est results are given to support the theoretical analyses and conclusions. Introduction hermistor is a ind of sensitive element which is made of semiconductor materials. Its advantages include small volume, high sensitivity, fast reaction-rate, high resolution and so on [,]. he temperature coefficient is negative for NC thermistor. It can convert the change of temperature directly into that of electricity [3,4]. Consequently, the NC thermistor is widely used in modern industry for temperature measurement and in the compensation circuit of temperature [5,6]. But because of the nonlinear nature of NC thermistor, the interface circuit should be linearly compensated according to actual needs in the design process of circuit. hen we can acquire the signal transfer characteristic of optimal linearization. In this paper, we propose an optimal linearization method of parameter design for NC thermister interface circuit basing on the theoretical analyses of resistance and temperature property. his simple approach has a good linearity and high sensitivity. est results are given to support the theoretical analyses and conclusions. he Characteristic Analysis of NC hermistor he relationship between resistance and temperature of the NC thermistor can be described by the following equation: B B R R exp( ) ()

2 Where R expresses the resistance when the thermistor s temperature is and exp represents the exponential function. is also referred to as the temperature of balance point. According to the definition of temperature coefficient of resistance, it is easy to get that: B ( dr d Ae ) B t B R d Ae d () Eq. shows that the temperature coefficient t of NC thermistor is negative and it decreases with the square of temperature. hat is to say, the period of low temperature is more sensitive than that of the high temperature. herefore, the NC thermistor is often used in the measurement of low temperature. he constant B can be obtained through experiments. If the resistances R and R under temperatures and have been measured, and then we can calculate B by the following equation: ln R ln R B. (3) Generally, the value of B is between 5K and 6K for the NC thermistor. he Optimization of Parameter Design for NC hermister Interface Circuit he ey problem is selecting a best fitting line in order to achieve the optimal linearization of interface conversion circuit for NC thermistor. he analyses of optimal linearization are mainly based on the circuit equations. According to the practical operating conditions and requirements, we can choose a balance point temperature and then use aylor series to analyze the circuit equations. In order to obtain a larger range of linear outputs, we generally choose the midpoint of the input temperature range to correspond the midpoint of the output range. Let the quadratic term coefficient of aylor series be zero, thus we can acquire the best parameters under the optimal linearization. Fig. is a typical voltage divider circuit for thermistor. Its circuit equation can be described by: U ( ) R R R E. (4) R R U ( ) Figure. he voltage divider circuit for temperature measurement.

3 Eq.4 demonstrates that the relationship between output voltage U ( ) and temperature is nonlinear. herefore, we need to linearize the circuit and design the best circuit parameters to obtain the linear output. B R In the characteristic equation of thermistor (i.e. Eq. ), let x, b, r. hen R we can get the normalized characteristic equation by: R rx ( ) r exp b( ) R x (5) U In the circuit equation (i.e. Eq. 4), let ( x). hen the normalized circuit equation can E be expressed as: ( x) R R R r( x) R R (6) Assuming the temperature of balance point is, namely, x. If the normalized circuit equation is expanded with aylor series at the balance point, that is x ( ) ( x) ( x) ( x) (7) 3 3 And the expansion coefficients can be gained as: ( x) x r R R R, br ( r ), br - r - b - r, 3 b. Let, we can get:

4 b B r, R R b B Ignoring the nonlinear errors which are larger than the third order, we can describe the linear fitting equation as: x ( ) ( x ) (9) he maximum relative linear error can be described as: (8) b 3 ( x) ( x ) () his method can be used to determine the value of according to the actual needs of temperature precision. Selecting the appropriate thermistor can determine the optimal linearization parameters for gain compensation circuit. Experiment and Analysis Suppose we use the MF5 beaded glass-sealed semiconductor thermistor, and its material constant B is about 36.7 K. he input voltage E is equal to 3V in Fig.. If the testing range of temperature measurement is -4, thus 93K, R( ) We can get that R by Eq. 8. Finally, it can be derived that the fitted output voltage U L ( ).57.38( 93) by Eq. 5, Eq. 6 and Eq. 9. In the same way, if the testing temperature range is 6-, 353K, R( ). 99. hus we can get that R. 668 and U L ( ).8.( 353). (K ) able. Results during -4 and R (Ω) U(V) U L (V) ΔU(V) (K) R (Ω) U(V) U L (V) ΔU (V)

5 Results of the fitted output voltage U L and its theoretical value U as well as the nonlinear error ΔU during -4 and 6- are listed in able where R can be obtained from the sensor manual and the theoretical output voltage U can be calculated by Eq. 4. Results of the fitted output voltage U L and its theoretical value U can be compared more directly by Fig.. Moreover, the nonlinear errors during -4 and 6- are presented in Fig U L (V) U (V) U L (V) U (V) (K) (K) Figure. Comparisons of the fitted output voltage and its theoretical value (V) (K) Figure 3. Comparisons of the nonlinear errors. Fig. 3 shows that the nonlinear errors are significantly reduced when temperatures are close to the balance point temperature. Additionally, we can seen the nonlinear errors of -4 are smaller than those of 6-. his demonstrates that the higher the temperature range is, the smaller the nonlinear error is. hat is to say, our proposed optimal linearization parameter design method is more suitable to the higher temperature range in NC thermister interface circuit.

6 Summary In this paper, we introduce an optimal linearization method for the NC thermistor interface conversion circuit. We carry out the linearization analysis and design by setting the quadratic term coefficient of aylor series to be zero for circuit equations in the balance point. In the practical application, the following points are worth noting: ) We should select the appropriate interface circuit, according to the practical application conditions and requirements. ) he choice of balance point temperature generally corresponds to the midpoint of the input temperature range. 3) he nonlinear error still exists for our proposed method. And the nonlinear error becomes larger, if the temperature is more far from the balance point. In the practical application, we can adopt the method of taing multiple measuring points and approaching with multiple sections of lines. Acnowledgement his research was financially supported by the National Natural Science Foundation of China (Grant No. 6568), Science and echnology Commission of Hebei Province (Grant No. 59D,F658), Educational Commission of Hebei Province (Grant No. QN545, Z57) and the Doctor Foundation of Hebei Normal University (Grant No. L5B9). References [] A.A. Khan, Linearization of thermister thermometer. International Journal of Electronics, 36 (987) [] A.A. Khan, M.A. Al-uraigi, A.R.M. Alamoud, A novel wide range linearization approach for thermistor thermometer, IEEE ransactions on Instrumentation and Measurement. IM-36 () [3] Carl Renneberg, orsten Lehmann, Analog Circuits for hermistor Linearization with Chebyshev-Optimal Linearity Error, 8th European Conference on Circuit heory and Design, August 6-3, 7, Sevilla, Spain. [4] Ayushi Srivastava, Vaishnavi A.R.S.N, Mahesh Prasad. M., Rama Rao. P. and K.V.L. Narayana, Development of hermistor Linearization Circuit based on Modified 555 imer using LabVIEW. International Journal of Computational Engineering Research. () [5] K.V.L. Narayana, Bhujanga A. Rao, A Novel Method of Linearizing hermistor Characteristic Using Voltage Controlled Oscillator, Sensors & ransducers. () [6] N.M. Mohan, V.J. Kumar, P. Sanaran, Linearising dual slope digital converter suitable for a thermistor, IEEE ransactions on Instrumentation and Measurement. 6 () 55-5.