A Log Amplifier Based Linearization Scheme for Thermocouples

Sensors & TransducersVolume 100January 2009www.sensorsportal.com ISSN 1726-5479Editor-in-Chief: professor Sergey Y. Yurish, phone: +34 696067716, fax: +34 93 4011989, e-mail: editor@sensorsportal.comEditors for Western EuropeMeijer, Gerard C.M., Delft University of Technology, The NetherlandsFerrari, Vittorio, Universitá di Brescia, ItalyEditors for North AmericaDatskos, Panos G., Oak Ridge National Laboratory, USAFabien, J. 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Sensors & Transducers Journal, Vol. 100, Issue 1, January 2009, pp. 1-10Sensors & TransducersISSN 1726-5479© 2009 by IFSAhttp://www.sensorsportal.comA Log Amplifier Based Linearization Schemefor Thermocouples1 Nikhil MONDAL, 2 A. ABUDHAHIR, 3 Sourav Kanti JANA,1 Sugata MUNSHI and 3 D. P. BHATTACHARYA1 Electrical Engineering Department, Jadavpur University, Kolkata-700032, India2 National Engineering College, Kovilpatti-628503, India3 Physics Department, Jadavpur University, Kolkata-700032, IndiaFax: +913324146184E-mail: sugatamunshi@yahoo.comReceived: 22 October 2008 /Accepted: 19 January 2009 /Published: 26 January 2009Abstract: This paper presents a new analog linearization circuit for thermocouple temperature sensors.The proposed circuit employs the linearizing action inherent in logarithmic operation, as well as theratiometric property of op-amp based logarithmic amplifier compensated against variation in ambienttemperature. Numerical and PSPICE simulation studies have been carried out using the standard datafor T, J and G type thermocouples. Encouraging results have been obtained. Copyright © 2009 IFSA.Keywords: Thermocouple, Temperature-sensor, Linearization, Log-Amplifier1. IntroductionThermocouples are long being used as temperature sensors in different fields of Science andTechnology. In view of the advantages of thermocouples over other temperature sensors [1-3], it isobvious that there should be considerable effort in developing more and more improved techniques forprocessing thermoelectric signals. Two important issues in the conditioning of thermocouple signalsare cold junction compensation (CJC) and Linearization of the transfer relation. While CJC is aproblem unique to this class of transducers, the problem of linearization is universal. The problem ofcold junction compensation has been given due importance by the investigators over years and avariety of techniques have been developed [4-7].1

Sensors & Transducers Journal, Vol. 100, Issue 1, January 2009, pp. 1-10The generalized software based linearization techniques for transducers [8-10] can also be used forthermocouples, but in the literatures, the results of such applications have seldom been reported. Thereare however few exceptions [11, 12]. So far as hardware based schemes are concerned, although it istrue that there are commercially available hardware modules, e.g. SCM7B47 modules fromDATAFORTH, which perform both CJC and linearization for thermocouples, in the researchpublications one rarely comes across issues in the development of linearizing circuits forthermocouples. Principles of hardware based linearizing schemes developed for other sensors can ofcourse be utilized for thermocouples. It is however worth mentioning that the issue of linearization asapplied to thermocouples in general, is further complicated due to the fact that that the refractory metalthermocouples meant for measurement of very high temperatures have transfer characteristics that arenot only extremely nonlinear, but are also non monotonic.Rapid development of digital computer and microprocessor based systems, combined with theirdwindling prices, have resulted in wide spread use of computer based measurement systems where theproblem of transducer nonlinearity is tackled by software packages. Although it is generally true thatcomputational algorithms for linearization have better performance compared to hardware methods,there are also exceptions [13]. Moreover, even with slashed prices of computer based systems,hardware based linearizers are by and large still cheaper. Hardware linearization methods can also beused to supplement the software techniques. As an example, linearization of a transducer signal by ahardware method followed by a simple form of software linearization, e.g. by means of a ROM lookuptable combined with linear interpolation, may yield better results than those obtained solely bysome other complex algorithm.This work presents a newly devised log-amplifier based circuit for linearizing thermocouple signals. Ithas originated from the knowledge that linearization is inherent in logarithmic operation, and this iswhy varieties of log- circuits are already in use for linearization of different transducer characteristics[13]. In the present work the task of linearization has been further facilitated by utilizing theratiometric property of op-amp based temperature-compensated logarithmic amplifier. Computationaland PSPICE based studies have been carried out using the manufacturer’s data for T and J typethermocouples that have decent linearity, and also for G type thermocouple that has an extremely nonlineartransfer characteristic, to assess the performance of the proposed linearizing scheme.2. Theory for Proposed Linearizing CircuitThe output of the temperature compensated log amplifier [14] shown in Fig. 1, isV1Vo = Aoln , (1)Vwhere Aο = AKTa /q , q = 1.6 x 10 –19 C is the magnitude of the charge of electron,k= 1.38×10 −23 J / K is the Boltzmann’s constant and T a is the ambient temperature in Kelvin. It isconvenient at this point to assume the ‘standard’ ambient temperature of 25 °C (298 K), which iswidely used in specifying semiconductor properties.To linearize analog transducer signals, equation (1) can be modified as2VINVo= Aoln , (2)VRe f2

Sensors & Transducers Journal, Vol. 100, Issue 1, January 2009, pp. 1-10whereV IN = V 1 = E (T) + E (3)andVRe fE K=2. (4)1+K 1+Kr( T ) V = + E( T )Here, T is the temperature being measured, E(T) is the analog output voltage signal from thethermocouple (after cold junction compensation) and E is the constant dc voltage used to ensure thatV o (0) = 0. E r is a dc voltage and K is a constant. By selecting the appropriate values for linearizingconstants ‘K’ and E r , the linearity of the signal E(T) can be improved.Fig. 1. Practical Form of Logarithmic Amplifier.Then, equation (2) can be written as∴( 1+K ){ E( T ) + E}⎛⎞⎜E ⎟rVo( T ) = AoIn⎜⎟(5)⎜ 1+KE( T ) ⎟⎝Er⎠In order to satisfy the condition V o (0)=0, assuming that E(0)=0, the value of E should be so selected tofulfill the conditionErE = (6)1+K3. Determination of Optimum Values of K and E rThe normalized deviation of V o (T) Vs. T characteristic from linearity is defined as3

Sensors & Transducers Journal, Vol. 100, Issue 1, January 2009, pp. 1-10( E , K,T )where T f denotes the full-scale value of T.DrVVo( E , K,T )o= − , (7)r( E , K,T )The optimal values of E r and K can be reached by numerically minimizing the sum-squared deviation‘S’, given in equation (8), with respect to E r and K.S =N∑n=1D2r( E K,)rT nfTTf, , (8)where N denotes the number of values (T 1 ,T 2 ,etc.) of T, considered for computation.The optimum values of linearizing coefficient K and dc voltage E r and the values of scaling constant Afor the different thermocouples and for different temperature ranges have been determined andtabulated in Table 1. A has been calculated, considering that numerical value of V o (T f ) in mV shouldbe equal to T f. It can be seen that the value of K required is negative.Table 1. Optimum values of ‘k’ and reference voltage ‘e r ’ and values of 'a' for different thermocouples.Thermo-CoupleTypeTemp.RangeKE rmVEmVV o (T f )mVE(T f )mVACopper –Constantan0 o C – 300 o C - 0.209 11.1 14.032 300 14.86 10.972(T – Type) 0 o C – 400 o C - 0.198 12.8 15.96 400 20.87 12.548Iron Constantan 0 o C – 300 o C - 0.352 18.1 27.932 300 16.32 13.704(J – Type) 0 o C – 760 o C - 0.01 258.1 260.707 760 42.92 189.255Tungsten –Tungsten 26%Rhenium400 o C –2300 o C- 0.084 3.804 4.15 2300 38.325 21.069(G – Type) 1000 o C –2300 o C- 0.132 6.515 7.50 2300 38.325 26.7444. Circuit DiagramA circuit is proposed that may be used for linearization when the value of K required is negative, andis shown in Fig. 2.4

Sensors & Transducers Journal, Vol. 100, Issue 1, January 2009, pp. 1-10The salient features of the findings of the study undertaken, are summarized below:1. From Table 3, it can be observed that for T-type, the maximum % error and RMS % error aresubstantially reduced to about 1/50 of their original values in the two different temperature ranges0 o C to 300 o C and 0 o C to 400 o C. In the case of J-type, for the temperature range 0 o C to 300 o C, thesequantities are reduced to same extent as in T-type. However in the range 0°C to 760 o C, thereduction in the interested quantities are small (1/4 of the original values) due to the wide range oftemperature considered for computation. For G-type, it can be seen that the maximum and RMS%deviation can be reduced approximately to 1/5 of their original values for 400ºC to 2300 o C. Overthe range 1000 o C to 2300 o C, the reduction is approximately to 1/10 of the original values.2. The performance of the log-amplifier based linearizing circuit is excellent when used for T-typethermocouple. The non-linearity with the present scheme is within. ± 0.01% over 0°C to 300°C and± 0.1% over 0°C to 400°C. The performance is substantially better than that of a software methodintroduced by Bolk [11] which yields a nonlinearity of ± 0.36% over 0°C to 300°C. It is noteworthythat Bolk had proved that his method gives better results than the interpolation techniques.3. The performance of the log-amplifier based linearizing circuit is excellent when used for T-typethermocouple. The non-linearity with the present scheme is within. ± 0.01% over 0°C to 300°C and± 0.1% over 0°C to 400°C. The performance is substantially better than that of a software methodintroduced by Bolk [11] which yields a nonlinearity of ± 0.36% over 0°C to 300°C. It is noteworthythat Bolk had proved that his method gives better results than the interpolation techniques.4. When used for type-J thermocouple, the performance of the proposed linearizer is also brilliant. Thenon-linearity is within ±0.04% and ±0.55% over 0 o C to 300 o C and 0 o C to 760 o C respectively. Theerror value achieved with Bolk's method lies within ±0.29% over 0 o C to 300 o C.5. When applied to type-G thermocouple, the logarithmic circuit, as expected, yields inferior results.The results with the proposed log-amplifier based contender are not satisfactory compared to thesoftware methods indicated below. From 1000 o C to 2300 o C, the non-linearity with the presentscheme lies within ±0.53% of full-scale, which is ±12.2 o C. The RMS deviation is 0.365%, whichcorresponds to 8.28 o C. It is worth mentioning that the RMS deviations obtained by Attari et al. [12]using linear interpolation, quadratic interpolation, polynomial interpolation and by an ANN method,are 2.11 o C, 1.27 o C, 10.54 o C and 1.06 o C respectively even over a wider temperature range of250ºC to 2150ºC.6. ConclusionA low-cost log-amplifier based linearizing circuit has been proposed for thermocouple temperaturesensors. It has been shown that its performance when employed for thermocouples with monotonicthermo-emf vs. temperature characteristics is better than some of the common software linearizersused for these thermocouples.For the G-type thermocouple, the performance of the proposed linearizer is not satisfactory comparedto that of software methods. Therefore, for temperature measurement using G-type thermocouple, thelog circuit can be used only for high temperature applications, provided that linearity of transfercharacteristic can be sacrificed to a certain extent, in exchange of the low cost of the linearizer. Forcomputer based measurement systems employing G-type thermocouple sensor, the log circuit may alsobe used as a first stage linearizer, and the final linearization may be carried out by some simple9