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ASM Science Journal, Volume 7(1), 2013and we only focused on the behavior of certain parametersat different physical characteristics of the coil structure.RESULTS AND DISCUSSIONThe output of a fluxgate is actually induced voltage atsensing coils and given as:V ind = NA dBdt (1)The complexity of Equation 1 is increased to takeinto account the magnetizing and demagnetizing of themagnetic core (Ripka 2001). Equation 1 then becomes:V ind = NA µ o H o(1 – D) dµ(t){1 + D[µ(t) – 1]} 2 dt (2)where, H o is outside of the core magnetic field while D isthe demagnetizing factor.However, in this study, magnetic core is excluded toreduce the complexity. With the exclusion, the structuredesign of the three-dimensional coils resembles thesolenoid. Hence, basic equations related to the inducedvoltage of the solenoid can be applied.Based on Faraday's law of induction, induced voltage,V ind can be determine as follows:V ind = – N dFdt (3)and also,V ind = – L dIdt (4)where, L is the inductance, with current, I and number ofturns, N. Magnetic flux is denoted as Ф. It can be seenthat, the induced voltage is directly proportional to theinductance, and number of turns.Magnetic energy in a coil is given as:E m = LI22 (5)Physical characteristics of the three-dimensionalcoil structure are: width of the coil; distance betweensuccessive coils; and gap between the top and bottomcoils. Simulations were done based on the three physicalcharacteristics of the coils.Width of CoilIn this part, only the width of the coil is varied andparameters such as inductance and magnetic flux densityare determined. Table 2 summarizes simulation settings forthis part.The resulting plot between inductance, magnetic energyand magnetic flux density against varying width of coil isshown in Figure 3. It can be seen that inductance decreasesas the width of the coil increases.There is an obvious explanation. As the width of the coilincreases, the cross-section of the coil also increases. Thisleads to higher conductivity, less resistance and inductance.Magnetic energy is half the values of inductance whenTable 1. Simulation process steps.StepStep 1Step 2Step 3Step 4Step 5ProcessGeometry modelingThickness: 20 µmInitial width: 50 µmInitial distance: 50Initial gap: 40 µmModule and application settingAC/DC moduleMagnetostatic applicationPhysics settingsSub-domainBoundaryMeshSolve30
N. Sulaiman and B.Y. Majlis: Physical Characteristics of Three-dimensional Coil Structure for MEMS MagnetometerTable 2. Width of coil simulation settings.Physical characteristicsDescriptionWidth of coil Varying dimensions (20, 30, 40, 50, 60, 70, 80) µmDistance between successive coils Constant at 50 µmGap top and bottom coil Constant at 40 µmCurrentConstantly at 1 Acurrent I is kept constant, therefore it follows the samepattern as inductance plot.Magnetic flux density is simulated at point X betweenthe top and the bottom coil. The illustration can be seen inFigure 4.As the width of the coil increases, the magnetic fluxdensity at point X also increases. This is because the areawhere point X is located becomes nearer to the coil, andhence increases the magnetic flux density value.Distance Between Successive CoilDistance between successive coils is varied while othersare kept constant. Table 3 summarizes simulation settings.Figure 5 shows the resulting plot between inductance,magnetic energy and magnetic flux density against varyingdistance between successive coils.From the plot, inductance, magnetic energy andmagnetic flux density decreases with the increase ofdistance between successive coils.Increase in the distance between successive coils denotesincrease in the distance between turns. This results in lessflux linkage between coils and causes less inductance.Magnetic flux density as simulated at point X of Figure4, decreases due to the distance between successive coilsincreases. The further point X from the coil, the less fluxdensity becomes.Gap between the Top and Bottom CoilThe gap between the top and bottom coil is varied toobserve the effects on inductance and magnetic flux density.The simulation settings are shown in Table 4. Figure 6shows the plot between inductance, magnetic energy andmagnetic flux density against the gap between the top andbottom.Both inductance and magnetic energy increases as thegap increases. When the gap between the top and bottomcoils increases, so does the diameter of the winding. Theincrease in the winding diameter A, causes the increase ininductance based on the following basic Equation 6.L = N2 µAl (6)Magnetic flux density at the same point X decreases asthe gap increases. This is mainly because point X becomesfurther from the coil as the gap increases.CONCLUSIONThe physical characteristics of three-dimensional coils havebeen investigated using FEM software. The changing ofthe dimension size of the coil had an effect on inductance,magnetic energy and magnetic flux density.In this work, the inductance value increased as thegap between the top and the bottom coils and the widthof the coils was increased. While inductance decreasedas the distance between successive coils increased. Highinductance was preferable however it was not the solecondition to the performance of fluxgate magnetometer.The increase in coil width had a positive effect inincreasing the magnetic flux density but at the same timeit decreased the inductance and magnetic energy. Increasein the width of the coil also meant an increase in theoverall space-area of the occupied device which defeatedthe purpose of miniaturization of devices. With theseconflicting requirements, moderation in coil design wasnecessary.Based on the investigation and having moderation inmind, the following was proposed:• The width for coils could be 30 µm – 50 µm;• The distance between successive coils could be 40 µm –60 µm. Since the distance contributed towards the areasize of the device, moderation is significant;• The gap between the top and bottom coils could be 40µm – 60 µm.31
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