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Quasi-Static Current Measurement with Field-Modulated Spin-Valve GMR Sensors^{ †}

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methods and Experiments

#### 2.1. Design of the GMR-Based Device

#### 2.2. Sensing Principles

_{0}. When an external field (H) is applied along the pinning direction of the sensing elements, the resistance of sensing elements decreases, which is indicated by the solid dot in the R-H curves in Figure 2a. The response of an ideal spin-valve GMR element to the applied field can be simulated with the following empirical formula [14]:

_{eff}= H + H

_{in}± H

_{c}is the effective field for positive and negative sweep, H

_{in}is the shift in operation point due to the unbalanced coupling between magnetic layers, H

_{s}is the nominal saturation field, H

_{c}is the coercivity, and R

_{0}is the resistance at zero effective field. The reduction in the resistance of sensing element results in an increase in the output of GMR bridge, which can be simulated by the following formula derived from (1):

_{ab}(H) are generally non-linear and hysteretic when H

_{c}is non-zero, and V

_{cc}denotes DC bias voltage of the GMR bridge. An example of the simulated R(H) curve using Equation (1) fit to the experimental data is available in [14], and the typically simulated V

_{ab}(H) curves using Equation (2) at zero and non-zero applied field are given in Figure 2b. The parameters used are: H

_{app}= 0 and 1.2H

_{s}, H

_{mod}= 3.5H

_{s}, H

_{c}= 0.5H

_{s}, H

_{in}= −0.065H

_{s}, and r = 10%. It was assumed that V

_{ab}is not a function of modulation frequency. The nonlinearity and remaining hysteresis can be eliminated by applying an AC modulation field to modulate the output of the GMR bridge sensor. The simulated time trace (V

_{ab}) and DC level output (V

_{out}) of the GMR bridge under a modulation field of H

_{exc}= H

_{mod}sin(ωt) is shown in Figure 3, where H

_{mod}denotes the amplitude of modulation field, ω = 2π/T is the angular frequency, t is the time, and T is the period of the excitation waveform. The maximum time rate of change of the modulation field is in proportion to the modulation amplitude:

_{app}induced by the test current is applied, the total external field is H = H

_{app}+ H

_{exc}, which results in a shift in the V-H curve shown in Figure 2b. For a small external field H

_{app}= ΔH, the zero-crossing points of the time trace are shifted in time by:

_{s}. In this case, the applied field induces a shift in the V-H curve by ΔH, as shown in Figure 2b, while the linear H-t relation is shifted by Δt, as shown in the bottom of Figure 3a. As previously mentioned, the change in the DC level of V

_{ab}due to ΔH can be calculated as V

_{out}:

_{0}is the zero-field level and V

_{max}= V

_{ab}(∞) is the saturation voltage of a spin-valve bridge. The averaged output levels under different external DC fields are shown as the horizontal dashed lines in Figure 3. With a positive applied field of H

_{app}= 2H

_{s}, the time duration that V

_{ab}stays at the maximum level (V

_{max}) becomes longer, resulting in an elevated average DC level (V

_{out}). With a negative applied field of H

_{app}= −0.2, the V

_{out}becomes negative. The simulation results imply that V

_{out}has a bipolar response to the applied field. The change in output level is determined by the last term in (5), where 4V

_{max}Δt corresponds to the approximate area of the shaded regions of the V-t plot in Figure 3. The harmonic spectrum with and without an applied field is given in Figure 3b, which indicates that the second harmonic has a maximum sensitivity to the applied field H

_{app}.

_{max}ΔT approximates the yellow-shaded areas, similar to the simulation results. From (5), the average output voltage in a small-signal mode is found to be proportional to the applied field ΔH as follows:

_{r}is the relative permeability, l

_{c}is the path length of magnetic circuit in the core, and l

_{g}is the air gap length. Given μ

_{r}≈ 10

^{3}, l

_{c}≈ 100 mm, and l

_{g}= 3 mm, Equation (8) reduces to H ≈ NI/l

_{g}. This relation applies to the modulation field (H

_{exc}), as well as the external field (H

_{app}) induced by the current I to be detected by the GMR sensor. For H

_{exc}, N = 50 is the number of turns of the excitation coil, and hence, H ≈ 200I, in units of Oe/A. For H

_{app}, the current under test passes through the long conductor at the center of the C-shaped core, and hence, N = 1, so the relation becomes H ≈ 4I in units of Oe/A.

#### 2.3. Measurement Experiment

## 3. Results and Discussions

#### 3.1. Demodulated Sensitivity

#### 3.2. Frequency Dependence

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematics of the current sensor: (

**a**) GMR sensor with a C-shaped ring-core made of ferrite; (

**b**) wiring of the spin-valve chip mounted on assembled printed-circuit boards; (

**c**) schematic layout of a spin-valve GMR bridge sensor with a flux concentrator.

**Figure 2.**(

**a**) Equivalent circuit of a spin-valve GMR bridge sensor with two shielded resistors for reference. (

**b**) Voltage-field (V-H) curves of a GMR sensor simulated by using Equations (1) and (2) with and without an applied magnetic field.

**Figure 3.**Analytic model for the modulated output of a GMR spin-valve bridge sensor: (

**a**) Time trace of voltage output (V

_{ab}) and DC level (V

_{out}). The excitation waveform is also shown at the bottom for comparison, where t is the time and T denotes the cycle time. (

**b**) Harmonic spectrum of V

_{ab}with and without an applied field.

**Figure 4.**(

**a**) Observed time traces of a GMR sensor; (

**b**) V-H curves of the direct output for a GMR sensor.

**Figure 6.**(

**a**) Transfer curves of the GMR current sensor at modulation currents of 11, 22, 34, and 45 mA. The vertical dashed lines indicate the range of maximum nonlinearity less than 2%. (

**b**) The sensitivities with respect to various modulation currents.

**Figure 7.**Dependence of the modulation frequency on (

**a**) the maximum sensitivity and (

**b**) 1-Hz current noise.

**Figure 8.**Current noise spectra under 1-kHz and 50-kHz modulation fields under the maximum sensitivity condition.

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**MDPI and ACS Style**

Jeng, J.-T.; Trinh, X.-T.; Hung, C.-H.; Lu, C.-C.
Quasi-Static Current Measurement with Field-Modulated Spin-Valve GMR Sensors. *Sensors* **2019**, *19*, 1882.
https://doi.org/10.3390/s19081882

**AMA Style**

Jeng J-T, Trinh X-T, Hung C-H, Lu C-C.
Quasi-Static Current Measurement with Field-Modulated Spin-Valve GMR Sensors. *Sensors*. 2019; 19(8):1882.
https://doi.org/10.3390/s19081882

**Chicago/Turabian Style**

Jeng, Jen-Tzong, Xuan-Thang Trinh, Chih-Hsien Hung, and Chih-Cheng Lu.
2019. "Quasi-Static Current Measurement with Field-Modulated Spin-Valve GMR Sensors" *Sensors* 19, no. 8: 1882.
https://doi.org/10.3390/s19081882