sensors Article
Modelling of a Hall Effect-Based Current Sensor with an Open Core Magnetic Concentrator Ivan Yatchev 1, *, Mehmet Sen 1,2 , Iosko Balabozov 1 and Ivan Kostov 1 1 2
*
Faculty of Electrical Engineering, Tehcnical University of Sofia, 1000 Sofia, Bulgaria;
[email protected] (M.S.);
[email protected] (I.B.);
[email protected] (I.K.) Vocational School of Technical Sciences, Uludag˘ University, 16059 Nilufer/Bursa, Turkey Correspondence:
[email protected]; Tel.: +359-2-965-3873
Received: 11 February 2018; Accepted: 16 April 2018; Published: 19 April 2018
Abstract: The present paper deals with the modelling of a Hall effect current sensor with open core magnetic concentrator. 3D magnetic field modelling is carried out using the finite element method (FEM) and Comsol Multiphysics software. Two rectangular core constructions are considered. Different geometric parameters of the magnetic concentrator are varied and their influence on the sensor characteristic is studied, with the aim of reducing the dependence on the output signal on the distance to the conductor. Of the studied parameters, core window length leads to the most significant change in the sensor characteristic. Future work can include the optimization of the sensor construction. Keywords: current sensors; Hall effect; 3D FEM; magnetic concentrator
1. Introduction Current sensors based on the Hall effect are widely used in different applications and are the subject of increasing interest in recent years [1–4]. The output signal of sensors without a magnetic core strongly depends on the distance between the conductor and the Hall sensor, and different approaches are used for eliminating this dependence [5–7]. Where possible, constructions with magnetic cores are used [8,9]. Commercially available current measuring apparatus based on Hall effect sensors usually include a closed magnetic core with a small gap where the Hall sensor is placed. In some specific cases, though, the employment of closed cores as magnetic concentrators is not possible due to the construction of the system where the current to be measured flows. Different geometries of Hall sensors working in current mode are studied in [10]. To prove the accuracy of COMSOL models, they make comparison with results achieved from a model implemented in Verilog-A software. In [11], various schemes of magnetic biosensors that are used for the identification of a wide spectrum of biological, physical, and chemical agents are presented. By numerical simulations using the finite element method (FEM), bending-induced stress effects on ultrathin cross-shaped magnetic sensors are analyzed in [12]. One application of this type of sensors is electronic or tactile skin. In [13–15], different arrays of Hall sensors working in current mode are studied, and electronic interfaces that are used with sensors are presented. To improve the characteristics of the magnetic sensors in [16,17], optimal design solutions are studied and an optimal geometry of the Hall plate is proposed. In fixed arrangements, the sensor could be easily calibrated for any type of magnetic concentrator and also for coreless design. In nonfixed arrangements, though, especially in the case when a closed core concentrator is not practically realizable, open core magnetic concentrators could be employed, thus reducing the error in the current measurement due to an error in the distance measurement.
Sensors 2018, 18, 1260; doi:10.3390/s18041260
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Sensors 2018, 18, x 2 of 11 In the present paper, 3D FEM modelling of the magnetic field in a Hall effect-based current sensor with Sensors 2018, 18, x an introduced magnetic concentrator of open core type is carried out with the aim of reducing 2 of 11 the In the present paper, 3D FEM modelling of the magnetic field in a Hall effect‐based current dependence of the output signal on the distance between the conductor and the Hall plate. This can sensor with an introduced magnetic concentrator of open core type is carried out with the aim of In the present FEM modelling of sensor the magnetic field in a Hall effect‐based current give the opportunity ofpaper, further3D design of a current with preliminary estimated error due to the reducing the dependence of the output signal on the distance between the conductor and the Hall sensor with an introduced magnetic concentrator of open core type is carried out with the aim of deviation of the conductor position. plate. This can give the opportunity of further design of a current sensor with preliminary estimated
reducing the dependence of the output signal on the distance between the conductor and the Hall error due to the deviation of the conductor position. plate. This can give the opportunity of further design of a current sensor with preliminary estimated 2. Studied Constructions error due to the deviation of the conductor position. 2. Studied Constructions Two constructions of the magnetic core of the current sensor are considered: a rectangular C-core
with 2. Studied Constructions one Two air gap for the Hall sensor (referred to the as construction with one air gapa or concentrator constructions of the magnetic core of current sensor are considered: rectangular one air gap for the Hall sensor (referred to as construction with one air gap or with C‐core one Two airwith gap), and a rectangular magnetic core with two air gaps: one for the Hall sensor constructions of the magnetic core of the current sensor are considered: a rectangular and concentrator with one air gap), and a rectangular magnetic core with two air gaps: one for the Hall one additional airone gap, onthe theHall opposite (referred to as construction air gaps C‐core with air placed gap for sensor leg (referred to as construction with with one two air gap or or sensor and one additional air gap, placed on the opposite leg (referred to as construction with two concentrator with two air gaps). concentrator with one air gap), and a rectangular magnetic core with two air gaps: one for the Hall air gaps or concentrator with two air gaps). sensor and one additional air gap, placed on the opposite leg (referred to as construction with two
2.1. Construction with One Air Gap air gaps or concentrator with two air gaps). 2.1. Construction with One Air Gap
The construction consists of two ferromagnetic legs, which on the one end are linked with a third 2.1. Construction with One Air Gap The construction consists of two ferromagnetic legs, which on the one end are linked with a leg with anleg airwith gap,an where the where Hall plate is placed (Figure 1).(Figure The dimensions given ingiven the figure are in third The air gap, the Hall plate is placed 1). the The dimensions in the construction consists of two ferromagnetic legs, which on one end are linked with a millimeters. The Hall plate is also included in the model (inside the air gap) and its dimensions figure leg are with in millimeters. Hall plate is plate also included the model (inside the air given gap) and its are third an air gap, The where the Hall is placed in (Figure 1). The dimensions in the considered to be 0.24 × 0.24 × 0.1 mm. dimensions are considered to be 0.24 × 0.24 × 0.1 mm. figure are in millimeters. The Hall plate is also included in the model (inside the air gap) and its dimensions are considered to be 0.24 × 0.24 × 0.1 mm.
Figure 1. Construction with one air gap. Figure 1. Construction with one air gap.
Figure 1. Construction with one air gap.
2.2. Construction with Two Air Gaps
2.2. Construction with Two Air Gaps
2.2. Construction with Two Air Gaps The construction with two air gaps (Figure 2) is similar to the one in Figure 1, but a fourth leg
The construction two air gaps (Figuregap 2) is to the one inwhere Figure 1, Hall but aplate fourth with The construction with two air gaps (Figure 2) is similar to the one in Figure 1, but a fourth leg a second gap with is introduced. The second is similar greater than the one the is leg with alocated and is large enough in order to allow passing a conductor through it. second gap is introduced. The second gap is greater than the one where the Hall plate is located with a second gap is introduced. The second gap is greater than the one where the Hall plate is and islocated and is large enough in order to allow passing a conductor through it. large enough in order to allow passing a conductor through it.
Figure 2. Construction with two air gaps. Figure 2. Construction with two air gaps.
Figure 2. Construction with two air gaps.
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3. FEM Modelling Sensors 2018, 18, x 3. FEM Modelling
The finite element method is used for modelling the magnetic field of the two constructions. The 3. FEM Modelling The finite element method is used for modelling field of The the two constructions. Comsol Multiphysics program [18] has been employedthe formagnetic this purpose. AC/DC module and The finite element method is used for modelling the magnetic field of the two constructions. The Comsol Multiphysics program [18] has been employed for this purpose. The AC/DC module Magnetic Fields and Electric Currents interfaces have been used. For computation of the Hall plate The Comsol Multiphysics program [18] has been employed for this purpose. The AC/DC module and Magnetic Fields and Electric Currents interfaces have been used. For computation of the Hall output voltage, the approach employed in [19] has been used. and Magnetic Fields and Electric Currents interfaces have been used. For computation of the Hall plate output voltage, the approach employed in [19] has been used. The finite element analysis is carried out for the 10 A value of the current in the conductor and plate output voltage, the approach employed in [19] has been used. The finite element analysis is carried out for the 10 A value of the current in the conductor and different parameters of the magnetic concentrator. Results for the magnetic flux density distribution The finite element analysis is carried out for the 10 A value of the current in the conductor and different parameters of the magnetic concentrator. Results for the magnetic flux density distribution for one variant of the two considered constructions are shown in Figures 3 and 4. different parameters of the magnetic concentrator. Results for the magnetic flux density distribution for one variant of the two considered constructions are shown in Figures 3 and 4. for one variant of the two considered constructions are shown in Figures 3 and 4.
Figure 3. Flux density distribution for the construction with one air gap.
Figure 3. Flux density distribution for the construction with one air gap. Figure 3. Flux density distribution for the construction with one air gap.
Figure 4. Flux density distribution for the construction with two air gaps. Figure 4. Flux density distribution for the construction with two air gaps.
Figure 4. Flux density distribution for the construction with two air gaps. Although the inner dimensions of the concentrator with two gaps is greater than for the one Although the inner dimensions of the concentrator with two gaps is greater than for the one with one gap, the flux density is greater due to introducing the leg with a second gap. with one gap, the flux density is greater due to introducing the leg with a second gap. Although the inner dimensions of the concentrator with two gaps is greater than for the one with In order to estimate the effect of introducing the magnetic concentrator, the dependence of the In order to estimate the effect of introducing the magnetic concentrator, the dependence of the one gap, the flux density is greater due to introducing the leg with a second gap. magnetic flux density in the Hall plate (volume integral average) on the distance to the conductor for magnetic flux density in the Hall plate (volume integral average) on the distance to the conductor for construction magnetic is shown Figure 5a. In Figure 5b,c, same In order to without estimatea the effectconcentrator of introducing the in magnetic concentrator, thethe dependence construction without a magnetic concentrator is shown in Figure 5a. In Figure 5b,c, the same dependence is shown for the constructions with concentrators with one and two gaps. Both of the magnetic flux density in the Hall plate (volume integral average) on the distance to the dependence is shown for the constructions with concentrators with (without one and concentrator) two gaps. Both relationships are close to a linear one, while for the coreless design the 5b,c, conductor for construction without a magnetic concentrator is shown in Figure 5a. In Figure relationships are close to a linear one, while for the coreless design (without concentrator) the dependence is strongly nonlinear. the same dependence is shown for the constructions with concentrators with one and two gaps. dependence is strongly nonlinear. Relative values of the flux density are used in order to allow comparison between the different Both relationships are close to a linear one, while for the coreless design (without concentrator) the Relative values of the flux density are used in order to allow comparison between the different curves. dependence is strongly nonlinear. curves.
Relative values of the flux density are used in order to allow comparison between the different curves.
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(a)
(b)
(c) Figure 5. Dependence of the flux density on the distance to the conductor (a) no magnetic Figure 5. Dependence of the flux density on the distance to the conductor (a) no magnetic concentrator; concentrator; (b) concentrator with one gap; (c) concentrator with two gaps. (b) concentrator with one gap; (c) concentrator with two gaps.
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The influence of different geometric parameters has been studied for both constructions. The varied parameters are shown in Figure 6a,b. In addition to the distance between the Hall plate and 4. Results for the Influence of Different Parameters the conductor (denoted by d), the parameters subject to variation are window length (l), window height The influence of different geometric parameters has been studied for both constructions. The (h), and eccentricity (e) of the conductor with respect to the central line. For the case of the concentrator varied parameters are shown in Figure 6a,b. In addition to the distance between the Hall plate and with two gaps, the size gap2by ofd), thethe additional airsubject gap is to also varied.are window length (l), window the conductor (denoted parameters variation The other geometric parameters are fixed, as follows: height (h), and eccentricity (e) of the conductor with respect to the central line. For the case of the -
concentrator with two gaps, the size gap2 of the additional air gap is also varied. coreThe other geometric parameters are fixed, as follows: cross section is of size 7 × 7 mm;
accommodating the Hall plate is 1.5 mm; -air gap core cross section is of size 7 × 7 mm; diameter is 2 mm. -conductor air gap accommodating the Hall plate is 1.5 mm; conductor diameter is 2 mm.
(a)
(b)
Figure 6. Parameters subject to variation for the two constructions: (a) construction with one air gap;
Figure 6. Parameters subject to variation for the two constructions: (a) construction with one air gap; (b) construction with two air gaps. (b) construction with two air gaps.
4.1. Construction with One Air Gap
4.1. Construction with One Air Gap
Three parameters have been varied for the construction with one air gap: the length l and height
h of the window and deflection of the conductor from the central symmetry line e. Three parameters have been varied for the construction with one air gap: the length l and height The dependence of the magnetic flux density B in the Hall plate (volume integral average) on h of the window and deflection of the conductor from the central symmetry line e. the distance between the conductor and the Hall plate for different parameter values are shown in The dependence of the magnetic flux density B in the Hall plate (volume integral average) on Figures 7–9. For better comparison of the different characteristics, the flux density in the Hall plate is the distance between the conductor and the Hall plate for different parameter values are shown in presented in relative units with respect to its maximal value Bmax, which is obtained in the plate at Figures 7–9. For better comparison of the different characteristics, the flux density in the Hall plate is the minimal considered distance (10 mm) between the conductor and the Hall plate. presentedCore in relative units with respect to its maximal value Bmax, which is obtained in the plate at the window length has a significant influence on the flux density–distance relationship, minimal considered distance (10 mm) between the conductor and the Hall plate. leading to about 30% difference between the flux density for the first and the last value of the length Core window length at the largest distance. has a significant influence on the flux density–distance relationship, leading to about 30% difference flux density for the first and the conductor last value from of the length at the Variations of between the core the window height and deflection of the the central symmetry largest distance.line do not lead to significant change in the characteristics (about 4–6% at the largest distance). of the core window height and deflection of the conductor from the central symmetry Variations line do not lead to significant change in the characteristics (about 4–6% at the largest distance).
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Figure 7. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 7. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 7. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 7. Dependence of the flux density on the distance to the conductor for the concentrator with one gap and different window lengths l. one gap and different window lengths l. one gap and different window lengths l. one gap and different window lengths l.
Figure 8. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 8. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 8. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 8. Dependence of the flux density on the distance to the conductor for the concentrator with one gap and different window heights h. one gap and different window heights h. one gap and different window heights h. one gap and different window heights h.
Figure 9. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 9. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 9. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 9. Dependence of the flux density on the distance to the conductor for the concentrator with one gap and different conductor deflections in the transversal direction e. one gap and different conductor deflections in the transversal direction e. one gap and different conductor deflections in the transversal direction e. one gap and different conductor deflections in the transversal direction e.
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4.2. Construction with Two Air Gaps 4.2. Construction with Two Air Gaps 4.2. Construction with Two Air Gaps Four parameters have been varied for the construction with two air gaps. In addition to the Four parameters parameters have been varied varied for for the the construction construction with with two two air air gaps. In addition addition to to the the Four In parameters varied for thehave casebeen of one air gap, the value of the additional airgaps. gap is also varied. parameters varied for the case of one air gap, the value of the additional air gap is also varied. parameters varied for of thethe case of one air the value of the additional air gap also varied.and Hall The dependences relative fluxgap, density on the distance between theis conductor The dependences of the relative flux density on the distance between the conductor and Hall The dependences of the relative flux density on the distance between the conductor and Hall plate for different parameters of this construction are shown in Figures 10–13. plate for different parameters of this construction are shown in Figures 10–13. plate for different parameters of this construction are shown in Figures 10–13. For this construction, both sizes of the core window (length and height) influence the sensor For this this construction, construction, both both sizes sizes of of the the core window (length (length and and height) influence the sensor sensor For coresecond window performance. Regarding the influence of the air gap, as it height) can be influence expected,the the lowest performance. Regarding the influence of the second air gap, as it can be expected, the lowest performance. Regarding the influence of the second air gap, as it can be expected, the lowest dependence on the distance features the construction with the smallest value of the second air gap. dependence on the distance features the construction with the smallest value of the second air gap. dependence on the distance features the construction with the smallest value of the second air gap. ForFor comparison, in Figure 13, the dependence of the construction with the closed core is also given. comparison, in Figure 13, the dependence of the construction with the closed core is also given. For comparison, in Figure 13, the dependence of the construction with the closed core is also given. ForFor this construction, the window length and height have more influence on the dependence on this construction, the window length and height have more influence on the dependence on For this construction, the window length and height have more influence on the dependence on thethe conductor position, leading to changes of 13% and 10%, respectively. The variation of the other conductor position, leading to changes of 13% and 10%, respectively. The variation of the other the conductor position, leading to changes of 13% and 10%, respectively. The variation of the other twotwo studied parameters results in less than 5% change in the characteristic. studied parameters results in less than 5% change in the characteristic. two studied parameters results in less than 5% change in the characteristic. AllAll thethe obtained characteristics with open corecore magnetic concentrators, though, feature an almost All the obtained characteristics with open core magnetic concentrators, though, feature an obtained characteristics with open magnetic concentrators, though, feature an linear dependence on the distance between the conductor and the Hall plate. almost linear dependence on the distance between the conductor and the Hall plate. almost linear dependence on the distance between the conductor and the Hall plate.
Figure 10. Dependence of the flux density on the distance to the conductor for the concentrator with Figure 10.10. Dependence distanceto tothe theconductor conductorfor forthe theconcentrator concentrator with Figure Dependenceofofthe theflux fluxdensity density on on the the distance with two gaps and different window lengths l. two gaps and different window lengths l. two gaps and different window lengths l.
Figure 11. Dependence of the flux density on the distance to the conductor for the concentrator with Figure Dependenceofofthe theflux fluxdensity density on on the the distance with Figure 11.11. Dependence distanceto tothe theconductor conductorfor forthe theconcentrator concentrator with two gaps and different window heights h. two gaps and different window heights h. two gaps and different window heights h.
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Figure 12. Dependence Dependence of of the the flux flux density density on on the the distance distance to to the the conductor conductor for for the the concentrator concentrator with with Figure 12. Figure 12. Dependence of the flux density on the distance to the conductor for the concentrator with two gaps and different conductor deflections in the transversal direction e. two gaps and different conductor deflections in the transversal direction e. two gaps and different conductor deflections in the transversal direction e.
Figure 13. Dependence Dependence of of the the flux flux density density on on the the distance distance to to the the conductor conductor for for the the concentrator concentrator with with Figure 13. Figure 13. Dependence of the flux density on the distance to the conductor for the concentrator with two gaps and different values of the second air gap (gap2). two gaps and different values of the second air gap (gap2). two gaps and different values of the second air gap (gap2).
4.3. Results for Different Values of the Measured Current 4.3. Results for Different Values of the Measured Current 4.3. Results for Different Values of the Measured Current For estimation of the influence of the value of the current on the output voltage signal from the For estimation of the influence of the value of the current on the output voltage signal from the For estimation of the influence of the value of the current on the output voltage signal from the Hall plate, the output signal has been computed for different values of the current, varying the latter Hall plate, the output signal has been computed for different values of the current, varying the latter Hall plate, the output signal has been computed for different values of the current, varying the latter from 10 to 40 A. computations have been out using the approach in [19] from 1010 A. The The computations have carried been carried carried out the in approach in construction [19] for for the the from toto 40 40 A. The computations have been out using theusing approach [19] for the construction with two air gaps and value of the second gap of 5 mm. construction with two air gaps and value of the second gap of 5 mm. with two air gaps and value of the second gap of 5 mm. In Figure 14, the dependence of the Hall plate output voltage Vhall on the current I for different In Figure 14, the dependence of the Hall plate output voltage Vhall on the current I for different In Figure 14, the dependence of the Hall plate output voltage Vhall on the current I for different distances to the conductor is given. In Figure 15, the same family of curves has been presented as the distances to the conductor is given. In Figure 15, the same family of curves has been presented as the distances to the conductor is given. In Figure 15, the same family of curves has been presented as the dependence of the Hall plate output voltage on the distance to the conductor for different currents. dependence of the Hall plate output voltage on the distance to the conductor for different currents. dependence of the Hall plate output voltage on the distance to the conductor for different currents. The obtained results give the possibility of the difference in the The obtained obtained results results give possibility of estimating estimating the maximal maximal difference the output output The give thethe possibility of estimating the maximal difference in the in output signal signal when varying the distance from the conductor to the Hall plate from 10 to 40 mm. This signal varying when varying the distance the conductor to the Hall plate from 10 to This 40 mm. This when the distance from thefrom conductor to the Hall plate from 10 to 40 mm. maximal maximal difference is less than 24% for all currents. maximal difference is less than 24% for all currents. difference is less than 24% for all currents. The linearity of the obtained dependencies could be used as an objective function in a future The linearity of the obtained dependencies could be used as an objective function in a future The linearity of the obtained dependencies could be used as an objective function in a future optimization. Having the best linear fit of the characteristics (Hall plate output voltage relative to the optimization. Having the best linear fit of the characteristics (Hall plate output voltage relative to the optimization. Having the best linear fit of the characteristics (Hall plate output voltage relative to distance of the distance of the conductor conductor to to the the Hall Hall plate), plate), it it will will be be possible possible to to design design aa current current sensor sensor with with preliminary estimated current error with respect to the distance error. preliminary estimated current error with respect to the distance error.
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the distance of the conductor to the Hall plate), it will be possible to design a current sensor with preliminary estimated current error with respect to the distance error. Sensors 2018, 18, x 9 of 11 Sensors 2018, 18, x
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Figure 14. Dependence the plate voltage Vhall on the current for different distances to the Figure 14. Dependenceof theHall Hall plate voltage Vhall on the current for different distances to Figure 14. Dependence of ofthe Hall plate voltage Vhall on the current for different distances to the conductor. the conductor. conductor.
Figure 15. Dependence of the Hall plate voltage Vhall on the distance to the conductor for four Figure 15. Dependence four Figure 15. Dependence of of the the Hall Hall plate plate voltage voltage Vhall Vhall on on the the distance distance to to the the conductor conductor for for four different currents. different currents. different currents.
5. Conclusions 5. Conclusions 5. Conclusions Computer models for the constructions of Hall effect‐based current sensors with additional Computer models for the constructions of Hall effect‐based current sensors with additional models concentrators for the constructions of Hall effect-based current of sensors with additional open open Computer core magnetic are created. The employment an open core magnetic open core magnetic concentrators are created. The employment of an open core magnetic core magnetic concentrators are created. The employment of an open core magnetic concentrator leads concentrator leads to an almost linear dependence of the output signal on the distance between the concentrator leads to an almost linear dependence of the output signal on the distance between the to an almost linear dependence of the output signal on the distance between the conductor and the conductor and the Hall plate. The influence of changing different geometric concentrator parameters conductor and the Hall plate. The influence of changing different geometric concentrator parameters Hall plate. The influence of changingof different geometric concentrator estimated for two is estimated for two constructions the magnetic concentrator of parameters rectangular isshape, showing a is estimated for two constructions of the magnetic concentrator of rectangular shape, showing a constructions of the magneticof concentrator oflength rectangular shape, showing a more significant influence more significant influence the window and height. The dependence of the Hall plate more significant influence of the window length and height. The dependence of the Hall plate of the window length and height. The dependence of the Hall plate output voltage on the distance to output voltage on the distance to the conductor has been obtained for different values of the current, output voltage on the distance to the conductor has been obtained for different values of the current, the conductor hasof been obtained for values ofThis the current, and estimation of its linearity can and estimation its linearity can different be performed. linearity can be the subject of further and estimation of its linearity can be performed. This linearity can be the subject of further be performed. This linearity can be the subject of further optimization with the aim of the design of optimization with the aim of the design of a current sensor with an open core magnetic concentrator optimization with the aim of the design of a current sensor with an open core magnetic concentrator a current sensor with an open core magnetic concentrator for nonfixed arrangements. for nonfixed arrangements. for nonfixed arrangements. Acknowledgments: Financial support Uludag University for covering costs of open access Acknowledgments: Financial support from from Uludag University for covering costs of open access publishing is Acknowledgments: Financial support from Uludag University for covering costs of open access greatly acknowledged. publishing is greatly acknowledged. publishing is greatly acknowledged. Author Contributions: I.Y., M.S. and I.B. performed the computer modelling, I.Y., M.S. and I.K. Author Contributions: I.Y., M.S. and I.B. performed the computer modelling, I.Y., M.S. and I.K. analyzed the results, I.Y. wrote the paper. analyzed the results, I.Y. wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.
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Author Contributions: I.Y., M.S. and I.B. performed the computer modelling, I.Y., M.S. and I.K. analyzed the results, I.Y. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
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