# A 3-Axis Miniature Magnetic Sensor Based on a Planar Fluxgate Magnetometer with an Orthogonal Fluxguide

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## Abstract

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## 1. Introduction

## 2. Design of the Fluxgate Magnetometer

#### 2.1. Tri-Axis Fluxgate Sensor with an Orthogonal Fluxguide

^{−4}H/m, respectively.

**Figure 1.**(

**a**) Conceptual schematic of the planar fluxgate structure with an orthogonal fluxguide; (

**b**) the PCB-based tri-axis fluxgate magnetometer. Note that all pick-up coils are implemented on the back side of the PCB.

#### 2.2. Design and Analytic Simulation of the Fluxgate Magnetometer

^{®}SV 2-D simulator software (Ansoft Corporation., Pittsburgh, PA, USA, 2002) to model and analyze the visualization of magnetism. First, let us verify the sensing principle of the planar fluxgate only with a cruciform core, and the cross-section along the core is shown in Figure 2. For the detection of X-axis (or Y-axis) magnetic fields, the magnetic flux lines are assumed to be parallel to the axial direction of the magnetic core, as depicted in Figure 2a. It can be visibly seen that magnetic flux lines may exhibit convergence or divergence near the ends of the core, and more importantly, a number of flux lines are concentrated or squeezed into the interior of the core until they deviate into air (or vacuum) at the other end. This phenomenon helps generate a variation of the vector field intensity magnitude and flux density around both core ends and this thus can be converted to voltage induced by two pick-up coils beneath them. It is noted that the parallel flux lines near the up and bottom surface of the core may generate the same sensing directions for the corresponding pick-up coils in X-axis due to the fluxguiding (or flux concentration) effect. By implementing a X-Y sensing circuit, one can sum up the induced voltage of two pick-up coils and successfully obtain the vector magnitude of magnetic fields in X-axis (or Y-axis). On the other hand, the Z-axis flux lines, as observed in Figure 2b, are applied to pass through the magnetic core without any flux concentration effect occurred in it. Therefore the planar fluxgate is considered merely sensitive to the in-plane field vectors.

**Figure 2.**Flux line diagrams illustrate the sensing principle of the planar fluxgate only with a cruciform core and the cross-section is along the longitudinal core: (

**a**) in X-axis sensing direction; (

**b**) in Z-axis sensing direction.

**Figure 3.**Flux line diagrams illustrate the sensing principle of the planar fluxgate with a cruciform core and an orthogonal fluxguide, and the cross-section is along the longitudinal core: (

**a**) in X-axis sensing direction; (

**b**) in Z-axis sensing direction.

Condition | Under a X-Axis Field (50 G) | Under a Y-Axis Field (50 G) | Under a Z-Axis Field (50 G) | Non-Orthogonality (%) | ||
---|---|---|---|---|---|---|

Measurement | ||||||

Pick-Up Voltage V_{x}(X-axis sensing mode) | 2.21 (V) | 5.6 (mV) | 16.8 (mV) | 0.25 (X-Y plane) | 0.76 (X-Z plane) | |

Pick-Up Voltage V_{z}(Z-axis sensing mode) | 16.4 (mV) | 16.1 (mV) | 204 (mV) | 8.04 (X-Z plane) | 7.89 (Y-Z plane) |

_{e}is the external dc field, µ

_{d}is the time-dependent permeability and B

_{i}(t) is the magnetic flux density in the longitudinal course of the i-th magnetic core [26]. Equation (1) argues that the output voltage from all pick-up coils is associated with the number of coil turns N, external dc fields H

_{e}and the derivative of permeability µ

_{d}. Also, the time-dependent permeability µ

_{d}is comparable to the gradient of the B-H curve of the core material, and in consequence the higher it is, the greater the output voltage is. Besides, demagnetization factor D is considered dominant in building up the induced voltage. As one knows, demagnetization factor is mainly related to the aspect ratio of core diameter (or width in this study) to core length. Accordingly, a narrow and long magnetic core featuring a smaller aspect ratio can considerably reduce demagnetization effect and thus raise the voltage in Equation (1). Apart from the use of a high-permeability core, it is also essential to optimize the dimensional configurations of the planar coils and the magnetic core for responsivity enhancement and power reduction in consideration of demagnetization effects.

#### 2.3. Simulation and Analysis for Excitation Coils and Core Magnetization

^{®}(ANSYS, Inc., Canonsburg, PA, USA), it is imperative to find the locally optimal dimension in terms of the metal wire width of the excitation coils for the proposed fluxgate. Therefore, we simulate and evaluate the distribution of magnetic flux density (B) along the axis of the magnetic core while core magnetization and sensor excitation are fulfilled. To investigate design diversity of the copper excitation coils, the following parameters are modulated for simulations: (1) metal wire width = 0.1–0.5 mm with a 0.1 mm interval; (2) metal wire gap = 0.1–0.5 mm with a 0.1 mm interval; and (3) excitation current = 0.1–0.5 A with a 0.1 A interval. Next, some key constants and variables are given: (1) Cu metal resistivity = 17 μΩ-m; (2) core (2714 A) permeability = 80,000 H/m; and (3) core length (single rod) = 40 mm and core width = 2 mm. It can be seen that numerous simulations were carried out by a combination order, and one can acquire the induction trend excited by the excitation coils. For example, assuming a uniform excitation current through the coils, one of the series simulation results provided in Figure 4 indicates the theoretical magnetic flux density along the core length with respect to various Cu metal wire width from 0.1 mm to 0.5 mm when metal wire gap is 0.1 mm and excitation current is 0.5 A. From the comprehensive simulations, it is reveled that the maximum value of magnetic flux density appears to occur near the middle position of the half-core, and the influence of various metal wire gaps on the magnetic flux density can be trivial. Thus, by considering the overall sensor dimensions and PCB processing feasibility, the miniature fluxgate is fabricated to have an excitation coils with 0.35 mm in wire gap as well as wire width for further device analysis later.

**Figure 4.**The theoretical magnetic flux density along the magnetic core vs. the distance from the core junction with respect to various wire width.

**Figure 5.**The theoretical magnetic flux density along the longitudinal core vs. the distance from the core junction with respect to various core width.

**Figure 6.**A 3-D model of a planar excitation coils and its simulated result with a 2-mm cruciform ferromagnetic core under the excitation current of 5 A.

**Figure 7.**A 3-D modeling and simulation result of a tri-axis planar device with a 2-mm cruciform ferromagnetic core and a fluxguide (

**left**); The variation of magnetic flux density along the core is also available and the magnetic fields in Z-axis is 40 A/m (

**right**).

## 3. Device Characteristic Results

#### 3.1. Responsivity Measurement of the Fluxgate

**Figure 9.**In-plane sensor responsivity (e.g., X-axis) vs. the excitation current at 25 kHz and 50 kHz, respectively.

**Figure 10.**The orthogonal sensor responsivity (i.e., Z-axis) vs. the excitation current at 25 kHz and 50 kHz excitation frequencies, respectively.

#### 3.2. Orthogonality Analysis of the Axes

#### 3.3. Noise Measurement and Frequency Response

**Figure 11.**Field noise spectra of the magnetometer with 2-mm core width under different excitation frequencies in X- and Z-axis: (

**a**) at 25 kHz; (

**b**) at 50 kHz.

**Figure 12.**Comparison of the maximum field noise spectral density results under different excitation frequencies in X- and Z-axis.

**Figure 13.**The frequency response result of the fluxgate with regard to the external field frequency.

#### 3.4. Linearity Characterization and Geomagnetic Fields Detection

_{e}.

**Figure 15.**The geomagnetic measurement results of the planar fluxgate magnetometer as an electric compass under a excitation frequency of 25 kHz.

**Figure 16.**The error distribution of geomagnetic measurement for the in-plane axes with respect to the azimuth angle.

## 4. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Lu, C.-C.; Huang, J. A 3-Axis Miniature Magnetic Sensor Based on a Planar Fluxgate Magnetometer with an Orthogonal Fluxguide. *Sensors* **2015**, *15*, 14727-14744.
https://doi.org/10.3390/s150614727

**AMA Style**

Lu C-C, Huang J. A 3-Axis Miniature Magnetic Sensor Based on a Planar Fluxgate Magnetometer with an Orthogonal Fluxguide. *Sensors*. 2015; 15(6):14727-14744.
https://doi.org/10.3390/s150614727

**Chicago/Turabian Style**

Lu, Chih-Cheng, and Jeff Huang. 2015. "A 3-Axis Miniature Magnetic Sensor Based on a Planar Fluxgate Magnetometer with an Orthogonal Fluxguide" *Sensors* 15, no. 6: 14727-14744.
https://doi.org/10.3390/s150614727