# A Feedback Method to Improve the Dynamic Range and the Linearity of Magnetoimpedance Magnetic Sensor

Authors: Dongfeng He
Journal: Journal of Sensors
 (2019)

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## Abstract

We developed a high-sensitivity magnetoimpedance magnetic field sensor using a FeCoSiB amorphous wire and a coil wound around it. The amorphous wire had the diameter of 0.1 mm and the length of 5 mm. The magnetic field resolution of about 20 pT/√Hz was achieved. But the dynamic range of the magnetoimpedance magnetic field sensor was only about ±0.7 Gauss, which was not enough for some applications, such as the defect evaluation of steel plate. The linearity of the system was also not good when big magnetic field was applied, which will cause some noise when the system is used in unshielded environment. We developed a feedback method to improve the dynamic range and the linearity of the magnetic field sensor. The operation point of the magnetic field sensor was fixed by sending a feedback current to the coil. Using the feedback method, the dynamic range was improved from ±0.7 Gauss to ±10 Gauss and the linearity was also improved over 100 times better. An eddy current testing system using the magnetic sensor was developed, and the crack defects in steel plate and in 3D-printed titanium alloy plate were evaluated.


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## Body

## 1. Introduction

Room temperature-sensitive magnetic sensors have been developed and used in various areas of communication, geological exploration, medical diagnostics, nondestructive evaluation (NDE), and security control [1–10]. These sensors are normally operated in unshielded environment with big background interferences, such as the power line interference. To measure the small signal in the big background interferences, good linearity of the sensing system is important. Otherwise, the big background interferences may cause the distortion of the signal and increase the noise of the system.For the NDE application of magnetic sensor, some ferromagnetic material samples may produce strong magnetic fields and cause the saturation of the magnetic sensors. Feedback methods are often used to increase the dynamic ranges of magnetic sensors and improve the linearity of magnetic sensors [11–13].Using the (Fe0.06Co0.94)72.5Si12.5B15 (FeCoSiB) amorphous wire with the diameter of 0.1 mm and the length of 5 mm, we developed a high-sensitivity magnetoimpedance (MI) sensor [14]. There was no electrical connection with the amorphous wire. The DC bias current and the AC current flow in the coil directly. In this paper, we present our new results of the high-sensitivity MI sensor and a feedback method to improve the dynamic range and the linearity of the magnetic sensing system. We also constructed the eddy current testing (ECT) system with the magnetic sensor and used it to evaluate the crack defect of 3D-printed titanium alloy and steel plate.


## 2. MI Magnetic Sensor without Feedback

Figure1 shows the schematic block diagram of the MI magnetic field sensor made using the FeCoSiB amorphous wire and the driving circuit without feedback. The sensor element was composed of a FeCoSiB amorphous wire and a coil wound around it. Different from normal MI sensor, there was no electrical connection with the amorphous wire. To make it capable of measuring the applied DC magnetic field, DC bias current and AC bias current were used in the driving circuit. The inductor LD and the capacitors of C1 and C2 were used to isolate the DC bias current, the AC bias current, and the voltage signal across the coil. The magnetic sensor is used to measure the magnetic field along the direction of the amorphous wire.Figure 1
Schematic block diagram of the magnetic field sensor made using the FeCoSiB amorphous wire and the driving circuit without feedback.In our experiments, the length of the FeCoSiB amorphous wire was 5 mm and the diameter was 0.1 mm. The coil wound around the amorphous wire was 30 turns wrapped using a copper wire with a diameter of 0.1 mm. The diameter of the coil was about 0.6 mm. The DC bias current was about 50 mA, and the amplitude of the AC bias current was about 20 mA. The frequency of the AC bias current ranged from 100 kHz to 5 MHz, and maximum signal amplitudes were achieved when the frequency was between 1 MHz and 2 MHz. In this paper, we used the frequency of 1 MHz.Figure2 shows the B-H curve of the FeCoSiB amorphous wire and the principle of the MI magnetic field sensor. The DC bias current IDC in Figure 1 produced the DC magnetic field HDC, and the AC bias current IAC in Figure 1 produced the AC magnetic field HAC, VAC was the voltage across the coil wound around the amorphous wire. If HDC was small, the sensor element operated in the linear part of the B-H curve, the amplitude of VAC did not change with the external applied DC or low-frequency magnetic field. It could not be used to measure the DC magnetic field. If the DC bias current was increased and HDC was near to the saturation corner of the B-H curve, the amplitude of VAC changed with the external DC or low-frequency magnetic field.Figure 2
TheB-H curve of the FeCoSiB amorphous wire and the principle of MI magnetic field sensor.Figure3(a) shows the voltage signal when the external applied magnetic field was 0 Gauss. The signal amplitude was about 100 mV. Figure 3(b) shows the voltage signal when the external applied magnetic field was 1 Gauss. The signal amplitude was about 80 mV. The signal amplitude changed with the applied DC magnetic field.Figure 3
Voltage signal across the coil for different applied DC fields. (a) The signal when the applied field was zero. (b) The signal when the applied field was 1 Gauss.
(a)
(b)In the driving circuit shown in Figure1, the preamplifier with the gain of 30 dB was used to amplify the 1 MHz AC voltage signal. The demodulation was used to get the amplitude signal of the AC voltage signal, and the output voltage of Vout was used to measure the external DC or low-frequency magnetic field. We measured the output voltage changing with the applied external magnetic field. Figure 4 shows the results. For the applied external magnetic field between -0.7 Gauss and +0.7 Gauss, the magnetic field response of the magnetic sensor was nearly linear.Figure 4
Output voltage of the magnetic sensor without feedback changes with the applied external magnetic field.Figure5 shows the magnetic field noise spectrum of the magnetic sensor with amorphous wire. The magnetic field noise spectrum was measured in a three-layer permalloy shielding box. The peaks on the spectrum were the 50 Hz inference and its harmonics. The magnetic field resolution of about 20 pT/√Hz was obtained.Figure 5
Magnetic field noise spectrum of the magnetic sensor measured in a permalloy shielding box.To observe the distortion of the output signal of the magnetic field sensor, we applied a 30 Hz sine wave magnetic field to the sensor by putting the sensor in the centre of a Helmholtz coil, and the Helmholtz coil was connected with a 30 Hz sine wave current source. For the sensor without feedback, if the applied field was small and in the linear range of the magnetic field sensor, the distortion of the signal was small. Figure6 shows the output signal when the amplitude of the 30 Hz applied magnetic field was 0.2 Gauss (0.02 mT). If the applied field was big and exceeded the linear range of the magnetic field sensor, the distortion of the signal was big. Figure 7 shows the output signal when the amplitude of the 30 Hz applied magnetic field was 2 Gauss (0.2 mT).Figure 6
Output signal of the magnetic field sensor without feedback for the 30 Hz applied magnetic field with the amplitude of 0.2 Gauss (0.02 mT).Figure 7
Output signal of the magnetic field sensor without feedback for the 30 Hz applied magnetic field with the amplitude of 2 Gauss (0.2 mT).Figure8 shows the spectrum of the output signal for the 30 Hz applied magnetic field with the amplitude of 2 Gauss. Due to the signal distortion, the amplitudes of the harmonics were quite big.Figure 8
Output voltage spectrum of the MI magnetic field sensor without feedback for the 30 Hz applied magnetic field with the amplitude of 2 Gauss.Total harmonic distortion (THD) is normally used to evaluate the nonlinearity of magnetic sensing systems [15–17]. When a sinusoidal magnetic field is applied to the magnetic sensor, the THD of the output signal can be defined
(1)THD=A22+A32+⋯A1,where A1 is the signal amplitude of the fundamental frequency f; A2, A3, … are the amplitudes of the harmonics with the frequencies of 2f, 3f, …, which can be measured by a spectrum analyzer.Figure9 shows the experimental setup to measure the THD of the GMI sensor. The coil connected with the sine wave generator was used to produce the applied magnetic field. The harmonic distortion of the signal generated by the generator was below 5×10−4. A spectrum analyzer was used to measure the THD of the output signals of the MI magnetic field sensor. To measure the small harmonic signals accurately, the influence of fundamental frequency signal must be reduced. A resistance trimmer was used to suppress the fundamental frequency signal of MI sensor output. By this method, the influence of the harmonics of the input signal could also be reduced.Figure 9
Setup of nonlinearity measurement.In the measurement, the resistance of R1 was first adjusted to make the output of the MI magnetic field sensor be equal to the voltage of the sine wave generator; then, the resistance trimmer R2 was adjusted to cancel the fundamental signal of the sensor output. We estimated that the relative error of our measurement was about 10%.Figure10 shows the THD of the sensor without feedback for the 30 Hz applied magnetic field. It increased with the amplitude of the applied magnetic field.Figure 10
THD of MI magnetic field sensor without feedback for the 30 Hz applied magnetic field with different amplitudes.


## 3. MI Magnetic Sensor with Feedback

Magnetic feedback method is a good way to increase the linearity of magnetic sensor [18]. Figure 11 shows the block diagram of the MI magnetic field sensor with feedback. After the demodulation and an amplifier, an integrator was used. A feedback current produced by the output of the integrator and the feedback resistor RF was sent to the coil wrapped around the amorphous wire. The magnetic field produced by the feedback current automatically compensated the applied magnetic field. Thus, the operation point of the MI magnetic field sensor was fixed. By this way, the dynamic range and the linearity of the system can be dramatically improved. When the switch SW was off, the driving circuit operated in amplifier mode. The output voltage V of the amplifier responded to the magnetic field. When the switch SW was on, the driving circuit operated in feedback mode. A feedback current Vout/RF was produced, and the magnetic field produced by the feedback current was equal to the applied magnetic field. Thus, the output voltage Vout was proportional to the applied magnetic field.Figure 11
Block diagram of the MI magnetic field sensor and the driving circuit with feedback.Figure12 shows the output voltage of the MI magnetic field sensor with feedback changing with the applied external magnetic field. We can see that the linearity was very good for the applied external magnetic field between -10 Gauss and +10 Gauss. Compared with Figure 4, the dynamic range and the linearity were much improved.Figure 12
Output voltage of the magnetic sensor with feedback changes with the applied external magnetic field.With the feedback, the magnetic field resolution of the MI magnetic field sensor was similar with that of without feedback. To check the magnetic field resolution, a small 30 Hz magnetic field with the amplitude of about 2 nT was applied. Figure13 shows the output signal of the MI magnetic sensor. To remove the 50 Hz inference, the observation bandwidth was about 40 Hz.Figure 13
Output signal of the magnetic field sensor for the 30 Hz applied magnetic field with the amplitude of 2 nT.Figure14 shows the output signal of the MI magnetic field sensor with feedback when the amplitude of the 30 Hz applied magnetic field was 2 Gauss (0.2 mT); and Figure 15 shows the output signal when the amplitude was 20 Gauss (2 mT). The distortions of the signals were very small even for a strong magnetic field of 2 mT. The feedback method was effective to improve the linearity of the magnetic field sensor.Figure 14
Output signal of the magnetic field sensor for the 30 Hz applied magnetic field with the amplitude of 2 Gauss (0.2 mT).Figure 15
Output signal of the magnetic field sensor for the 30 Hz applied magnetic field with the amplitude of 20 Gauss (2 mT).Figure16 shows the spectrum of the output signal of the MI magnetic field sensor with feedback for the 30 Hz applied magnetic field with the amplitude of 2 Gauss. Compared with the spectrum of the output signal without feedback shown in Figure 8, the amplitudes of the 30 Hz harmonics were much small.Figure 16
Output voltage spectrum of the MI magnetic field sensor with feedback for the 30 Hz applied magnetic field with the amplitude of 2 Gauss.Using the setup shown in Figure9, we also measured the THD of the MI magnetic sensor with feedback for the 30 Hz applied magnetic field with different amplitudes. Figure 17 shows the results. For the amplitude of 1 Gauss, the THD of the signal with feedback was about 1.4×10−4, which was about 1% of the THD value without feedback. The linearity can be much improved using the feedback method.Figure 17
THD of MI magnetic field sensor with feedback for the 30 Hz applied magnetic field with different amplitudes.


## 4. Eddy Current Testing Using MI Magnetic Sensor with Feedback

Figure18 shows the block diagram of the ECT system using the MI magnetic field sensor with feedback. The excitation coil was 10 turns with the diameter of approximately 1 mm and was also wrapped around the FeCoSiB amorphous wire. The sine wave output of the lock-in amplifier was sent to the excitation coil to produce the excitation magnetic field. The excitation frequency was 20 kHz and the current amplitude was 20 mA. The amplitude of the magnetic field in the centre of the excitation coil was about 2 Gauss. The MI magnetic field sensor was used to measure the magnetic field produced by the eddy current in the sample. The sample was put on an X-Y stage for the scanning. Figure 19 shows the photo of the setup.Figure 18
Block diagram of the ECT system with amorphous wire magnetic sensor.Figure 19
Photo of the ECT setup.Figure20 shows the Ti-6L-4V titanium alloy sample fabricated by 3D laser printing. The size of the sample was 50×50×10mm. There were two surface flaws extending from the edges of the sample. The length of flaw a was about 13 mm with the depth of about 1.5 mm, and the width of flaw a was from 0.2 mm to about 10 μm. The length of flaw b was about 15 mm with the depth of about 5 mm, and the width of flaw b was from 0.3 mm to about 10 μm.Figure 20
Photo of titanium alloy sample fabricated by a 3D laser printer.Figure21 shows the ECT result using the amorphous wire magnetic sensor. The scanning area was 45mm×45mm and scanning step was 0.2 mm. The amplitude output signal of the lock-in amplifier was used to plot the 2D graph. The defects were displayed clearly.Figure 21
Scanning results by the ECT system with amorphous wire magnetic sensor.We also evaluated the defect in the steel plate using the ECT system. The thickness of the steel plate was 3 mm. In the steel plate, there was a small hole defect with the size of about 1.5 mm and the depth of about 2 mm. The steel plate produced a strong magnetic field of about 5 Gauss. The MI magnetic sensor with feedback could operate well during scanning. An excitation coil with the diameter of about 3 mm was used.The determination of the excitation frequency is an important factor in ECT, because the penetration of eddy current is limited by the skin effect. The skin depth is defined byδ=πfμσ−1/2, where δ is the skin depth, μ is the magnetic permeability, σ is the electrical conductivity, and f is the frequency. For the steel plate, the conductivity σ is about 2×106 S/m, the relative permeability is about 100, and the penetration depth is about 2.7 mm at the frequency of 170 Hz.To detect deep defect in the steel plate, a lower excitation frequency of 170 Hz was used. The amplitude of the excitation current was about 20 mA. Figure22 shows the defect signal of one scanning, and Figure 23 shows the 2D scanning results.Figure 22
One scanning signal of a defect in the steel plate.Figure 23
2D scanning result of the defect in the steel plate.


## 5. Conclusion

A feedback method was developed for the MI magnetic field sensor. Using the feedback method, the dynamic range of the MI sensor was improved from ±0.7 Gauss to ±10 Gauss, and the linearity of the magnetic sensing system was also improved. The THD of the output signal with the feedback was about 1% of the THD without feedback.If the MI sensor is used in an industrial environment, the amplitude of the 50 Hz line interference can be up to 1μT. For the MI sensor without feedback, the signal distortion caused by the nonlinearity is about 10 nT, which is big enough to influence the accuracy of the detection. For the MI sensor with feedback, the signal distortion is about 100 pT, which is close to the magnetic field noise of the GMI sensor and has less influence to the accuracy of the detection. Therefore, for the applications in the industrial environment, the MI sensor with feedback is necessary.We constructed the ECT system using the MI magnetic field sensor with feedback. Because of its big dynamic range, it can be used to evaluate defects in the steel plate. We will find more industrial applications for our magnetic field sensing system.



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*Source: 2413408-2019-12-12.xml*