EFFECT OF 'OVERLAPPING' VOLTAGE CONTACTS IN PLANAR ...

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18 Medwm side Fig 1 One-sxded PHT with several kinds of voltage contacts A overlappmg upper contact, 3 overlappmg lower contact, C bulge contact, D point contact, * drrectlon of mltlal M,, + dlrectlon of the current In the next section a description of the mathematical model 1s aven, which IS generally apphcable Next, the experimental verlflcatlon 1s described and fmally the results are presented m a number of diagrams Mathematical model of the planar Hall transducer In this description of the model we consider a conflguratlon with only one Hall voltage contact Such a conflguratlon may be part of the one-sided dual sensor suggested by Flultman or may be used m the ways depicted in Fig 2 (‘smgle’ one-sided PHT) In these sltuatlons the disturbing MR compo- nent 1s neutralized and only m the latter (voltage-dmven mode) situation is there a constant zero-field offset The voltage-dnven mode 1s used in the computations because of better correspondence with the integral equation mentioned above, as ml1 be shown below The change of the current by the MR effect 1s only a few per cent We consider the stmpe axis as the X-axes and the width duectlon as the y-axis The ferromagnek resistance anlsotropy can be expressed with [3] E=pJ or J = oE (1) m which p and (T are tensors In many apphcatlons the magnetxzatlon m the stripe 1s mhomogeneous (demagnetlzmg effects, mhomogeneous fields) m the y-dlrectlon, thus o IS a function of y and has to be calculated first [4] Fig 2 ‘Single’ oneslded PHT and response m a homogeneous field, two posslbllltles are presented to neutralize the MR voltage
Figure 3 shows the rectangular permalloy stripe with two dnve voltage leads and one overlappmg Hall contact In order to solve the problem, the stnpe LS represented by a matnx of node-pomts We define the Hall voltage on the node-points as the difference between the potentials w&h the magnetic field on and off, The distance between the node-pomts m the honzontal and vertical dlrectlons can be arbltranly chosen Further, we know that E=-_VU and V*J=O (3) Expression (3) IS the contmulty equation used by many authors to solve sumlar problems by denvmg the different& equation Another approach 1s to use the integral form of eqn. (3) that IS derived by using Gauss’s theorem $Jmnds=Oj $uVu*nds = 0 (4) We apply eqn (4) to contours around every node-point, except the ones that are part of the overlappmg contact (see A, B, C and D m Fig. 3) We also apply eqn (4) to the contour around all of the overlap node-points (see E m Fig. 3). There are special boundary condltlons for the node-points at the edges a Neumann condltlon for the upper and lower edges (B), and a Dmchlet condltlon for the left and nght edges (C) Both condltlons apply to node-pomts m the corner (D) We calculate #UP u*n ds by defmmg the potential function u m every triangle by means of the potentials on the angular pomts (see A m Fig. 3) In this way we get a number of finite difference equatrons that can be solved dvectly v&h the help of a computer, together with the set of equations that follow from the fact that all overlap node-pomts have an equal potential (m matnx form* Au = b) With the calculated potentials u it 1s possible to compute the current JX (eqns (1) and (2)) m order to normalize the output mth respect to the current of a PHT w?thout overlap (an overlapping contact decreases the resistance and as a result mcreases J, ) 1 Volt - r ----f--_- Fig 3 A PHT represented by a matrur of node-pomts (see text) 1 0 - Volt -0 19 (2)
Page 1: Sensors and Actuators, 4 (1983) 17
Page 5 and 6: fields (such as the earth’s magne
Page 7 and 8: Fmally, the resolution of four PHT

EFFECT OF 'OVERLAPPING' VOLTAGE CONTACTS IN PLANAR ...

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