Linearization of the Output of a Wheatstone Bridge for Single Active Sensor. Madhu Mohan N., Geetha T., Sankaran P. and Jagadeesh Kumar V.

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1 Linearizatin f the Output f a Wheatstne Bridge fr Single Active Sensr Madhu Mhan N., Geetha T., Sankaran P. and Jagadeesh Kumar V. Dept. f Electrical Engineering, Indian Institute f Technlgy Madras, Chennai , India Ph: vjk@iitm.ac.in Abstract: The utput f a Wheatstne bridge with nly a single active resistive sensr is inherently nnlinear. A generalized feedback cmpensatin scheme is presented in this paper that prvides a linear utput fr a Wheatstne bridge with nly a single active resistive sensr, even fr large variatins in the resistance f the sensr. Simulatin studies and experimental verificatins establish the efficacy f the prpsed linearizatin technique. The prpsed methd is best suited fr single active resistive sensrs invlving Resistive Temperature Devices (RTD) and piezresistive type sensrs pssessing large range f variatin. I. Intrductin The Wheatstne bridge is a simple and ppular signal cnditining circuit fr resistive sensrs such as Strain gages, RTD, and piezresistive sensrs [1]. The typical frm f a Wheatstne bridge circuit with a single active sensr is given in Fig. 1. The resistance R f the sensr can be expressed as R =R (1± k x), where x is the parameter being S S 0 measured, R is the nminal value f the resistance f the sensr (when x is zer) and k is the sensitivity f the sensr and 0 can be either psitive (fr RTD) r negative (fr sensrs with negative temperature cefficient f resistance, such as R 1 R 1 V B v 0B A v 0A = A v 0B R 0 R S = R 0 (1±kx) Figure 1 Wheatstne Bridge fr a single active Resistive Sensr thermistrs). Since the utput f the bridge will be small, the same is amplified with the help f an instrumentatin amplifier f gain A. The utput v B f the bridge shwn in Fig. 1 in terms f the bridge excitatin vltage V B is given by kx v = V B B 1, (1) ( ) kx 1 ( 1 ) where = R / R. It is easily seen that the utput f the bridge is a nnlinear functin f the measurand x [], [3]. The 1 0 nnlinearity can be reduced t a large extent by the chice f and the maximum value f kx [4]. Resistive sensrs such as metallic strain gages have lw maximum permissible values fr kx (~ 0.1), thus minimizing the nnlinearity. Nnlinearity can als be made insignificant, by chsing a large value fr. The utput f the bridge shwn in Fig. 1, fr varius values f, is given in Fig.. It can be bserved frm Fig. that large values f imprve linearity but the sensitivity f the bridge is reduced, resulting in lw bridge utput and hence lw reslutin. Fr resistive sensrs like the

2 = 5 = 10 = Output (V) = 1 = Nnlinearity % Input (kx) Figure Output f the single active sensr Wheatstne Bridge Pt100, the platinum resistance temperature device (RTD), the value f kx can be as large as 3 [5] and hence even with a f 10, the nnlinearity will be much mre than depicted in Fig., where the maximum value f kx is chsen t be 1. Thus the Wheatstne bridge, thugh simple, cannt prvide a perfectly linear utput fr a single active sensr, especially if the sensr pssesses large variatin in kx. Attempts have been made t linearise the bridge using psitive feedback cmpensatin [6],[7] but they invlve specific applicatin designed chips and are expensive. Mrever, they are limited t a narrw dynamic range f the RTD. Even ICs which have been specifically designed fr Strain Gage / RTD type f sensrs require external cmpnents as well as iterative prcedures fr linearising the transducer utput in additin t manual peratin t determine the sense f the feedback [8]. We nw present a nvel, generalized feedback scheme that perates n the utput f the Wheatstne bridge f Fig. 1 and prvides a final utput that is linearly prprtinal t the measurand x. II. Feedback Cmpensatin Scheme The prpsed scheme is shwn in Fig. 3. The utput f the bridge v is amplified by an instrumentatin amplifier f gain A t btain the final utput v. A part f the utput, say β ( β B v < 1 ) is added t a reference vltage V R, emplying a unity gain adder and the utput f the adder prvides the bridge excitatin V B. Then, V B = V R β v 0 Σ V R R 1 R 1 v 0B A v 0 R 0 R 0 (1 ± kx) β v 0 Figure 3 Feedback cmpensatin fr linearising the utput f a Wheatstne bridge with a single active resistive sensr

3 resulting in Rearranging equatin (3) we get: v = Av = AV B kx 1 and V=Vβv, () kx B R 0 ( ) 1 ( 1 ) B v =A v =(V β v )A B R 0 kx (1) kx 1 (1) kx kx v Aβ v =V A 0 R (1) kx (1) kx 1 1 (1) ( 1 ) (3) (4) Equatin (4) simplifies t v 1 =V Ak R (1 ) x (5) kx 1 (1 Aβ (1 ) If the attenuatin factr β is chsen such that A β is made equal t v =V Ak R x (6) (1 ) Equatin (6) implies that the feedback scheme f Fig. 3 prvides an amplified utput, linearly prprtinal t the parameter (1 ) x that is being sensed by the resistive sensr, prvided the feedback is adjusted such that Aβ =. T determine the efficacy f the prpsed methd, simulatin and experimental studies were carried ut as detailed next. (1 ) III. Simulatin Studies The entire circuit shwn in Fig. 3 was simulated using the circuit layut and simulatin sftware, OrCAD (v9.0). A resistr having a nminal value R 0 f 100 Ω and kx varying frm 1 t 1 was chsen t simulate the perfrmance f the resistive sensr. The INA101 served as the instrumentatin amplifier while the OP07 was used fr realizing the summer and the vltage fllwers. The reference vltage f 1. V was btained with the help f a precisin Vltage Reference then Output (V) = 5 = 10 = 0 = 1 = Maximum Nnlinearity (%) Input kx Figure 4 Simulated Output f the single active sensr Wheatstne bridge with the prpsed feedback cmpensatin

4 Dide LM The results f the simulatin are prtrayed in Fig. 4. Figs. and 4 clearly illustrate that the prpsed scheme prvides a linear utput and cnsiderably reduces the nnlinearity, that wuld therwise be present in the utput f the Wheatstne Bridge. IV. Experimental Setup The circuit shwn in Fig. 3 was set up using fftheshelf cmpnents and breadbarded. The INA101 frm Burr Brwn (nw Texas Instruments) was used fr the instrumentatin amplifier and the OP07 was the pamp f chice fr the summer and vltage fllwers, mainly due t its lw input ffset vltage (~5μV), easy availability and affrdability. The LM3851. Reference Vltage Dide frm Natinal Semicnductr Crp. was emplyed fr generating the reference vltage. The sensr resistance was simulated using a precisin resistance bx ranging frm Ω (Mdel V441 frm Ott Wlff Berlin, Germany), having an accuracy f 0.001%. The bridge was set up t simulate the cnditins f = 1 and 0. The utput acrss the bridge was carefully measured using a 6½digit multimeter (HP34401A). The ambient temperature was maintained at 5 C, t nullify any change in the resistances due t temperature variatins. The results btained are pltted in Fig. 5 and the nnlinearity in bth the cases indicated Maximum Nnlinearity (%) Output (mv) = Input (kx) = Figure 5 Output f the prttype fr tw different values f V. Cnclusins A feedback cmpensatin scheme fr linearising the utput f a Wheatstne Bridge has been presented in this paper. Results indicate that the circuit utlined in the paper significantly reduces the nnlinearity in the utput f the bridge, using easily available, fftheshelf, inexpensive cmpnents. It is t be emphasised that the reductin in nnlinearity is due t the nature f the cmpensatin emplyed and that further imprvement in perfrmance can be achieved if cmpnents with better specificatins and tlerances are used. Further wrk needs t be carried ut t determine the limits f peratin f the circuit as well as t determine and quantify ptential surces f errrs in the circuit. References [1] Debelin E.O., Measurement Systems Applicatin and Design, McGrawHill Publicatins, Furth Editin,1990. [] PallasAreny R. and Webster J.G., Sensrs and Signal Cnditining, Vl. I, nd Ed., Jhn Wiley and Sns, New Yrk, Nv. 000 [3] Webster J.G., (Ed), The Measurement, Instrumentatin and Sensrs Handbk, CRC Press, Flrida, 1999 [4] Dyer S.A.,(Ed), Survey f Instrumentatin and Measurement, Jhn Wiley and Sns, New Yrk, 001

5 [5] Fraser R.E., Prcess, Measurement and Cntrl Intrductin t Sensrs, Cmmunicatin, Adjustment and Cntrl, PrenticeHall Inc., NJ, 001 [6] Maxim Crpratin Applicatin Nte AN3450, Psitive Analg Feedback cmpensates Pt100 Transducer, available nline at (last accessed June 8, 008) [7] Bacharwski W., A precisin interface fr a Resistance Temperature Detectr (RTD), Natinal Semicnductr Crpratin, 008 available nline at (last accessed June 8, 008) [8] Analg Devices, High Perfrmance, Ecnmy Strain Gage/RTD Cnditiners (B30/31), Linear Prducts Handbk, April 1988, pp. 11/7111/76.