# AC Current Sensor Based on Magnetoelectric Composites Transducers: Resonance Damping, Current Dynamic and Electric Field Disturbances

Raphaël Filâtre, Frédéric Mazaleyrat, Vincent Loyau

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Raphaël Filâtre, Frédéric Mazaleyrat, Vincent Loyau. AC Current Sensor Based on Magnetoelectric Composites Transducers: Resonance Damping, Current Dynamic and Electric Field Disturbances. IEEE Transactions on Magnetics, In press, 10.1109/TMAG.2024.3446910. hal-05056470

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# AC Current Sensor Based on Magnetoelectric Composites
Transducers: Resonance Damping, Current Dynamic and Electric
Field Disturbances

Raphaël Filâtre¹, Frédéric Mazaleyrat¹ and Vincent Loyau¹

¹SATIE CNRS UMR 8029, ENS Paris-Saclay, Université Paris-Saclay, 91190 Gif-sur-Yvette, France

In this paper, a current sensor based on a magnetoelectric (ME) composite realized by electrodeposition is presented. This ME sample is inserted in the gap of a toric flux concentrator associated with permanent magnets. The current dynamic and the current sensor bandwidth are studied. Then, mechanical damping allows the absorption of the mechanical resonance that affects the current measurement. Finally, a device is set up to test the sensor's immunity to electric field disturbances. An electronic based on charge preamplifiers connected in differential mode strongly attenuates these disturbances.

***Index Terms***—Magnetoelectric, damping, current sensor, electric field disturbances, bandwidth, resonance, electrodeposition

## I. INTRODUCTION

THE magnetoelectric (ME) effect is promising and has been studied for various applications, such as energy harvesters, magnetic sensors, current sensors, and wireless energy transmission. The extrinsic ME effect is preferred to the intrinsic one for these applications, requiring a magnetostri-ctive material mechanically coupled to a piezoelectric material.

In the actual energy transition context, power consumption and production will increase in the years to come, particularly due to automobile fleet electrification. It will increase requests for current sensors like Hall-effect, giant magneto-impedance, fluxgate sensors, etc. However, these sensors are expensive due to their relatively weak sensibility and complex electronics.

Some emerging sensor technologies, like current sensors based on magnetoelectric composites, have strong sensitivities and could solve this cost issue. Current sensing can be achieved with these materials because electric current cables create magnetic fields. The magnetostrictive material will be deformed when a magnetic field is applied, and the piezo-electric material will be deformed because of the mechanical coupling. Finally, a voltage will appear at the electrodes of the piezoelectric layer.

In the 2010s, the research on these current sensors was focused on obtaining a better ME effect using rare earth materials, like Terfenol-D [1]. These studies were generally conducted under a 50 Hz sine excitation in a laboratory with ideal conditions (no electric field disturbances). In recent years, other current sensor prototypes were proposed, some with self-biased materials, to measure 50 Hz currents [2] – [3] or DC currents [4]. Yet current sensors are often used in industrial applications in specific frequency ranges and specific current waveforms, such as triangular. Thus, a more general study of current sensors based on magnetoelectric composites is required to aim these applications. In 2018, Zhang et al. did so by proposing a gradient-type magnetoelectric sensor [5] with a bandwidth from 10 Hz to 170 kHz, a current dynamic up to 20 A, while studying noise impacts on the sensor. However, the sensor is based on Terfenol-D and requires

NdFeB magnets. Due to supply issues, rare earth materials need to be avoided. A study has been conducted to show that ferrites can lead to a similar ME effect [6]. Moreover, it has been shown in a previous study [7] that triangular and square wave signals may excite the material resonances, creating oscillations in the output voltage of the ME current sensor. These oscillations could be attenuated using a mixture with tungsten, as it was studied in backing materials for ultrasound probes [8].

This paper presents an AC current sensor with a simple electronic circuit for power electronics applications. Mechanical damping is proposed to limit the effect of the composite resonances on the current measurement, using polyurethane mixed with tungsten powder to coat the ME sample. Moreover, the sensor will be exposed to electric field disturbances, and it is necessary to study its immunity toward them. Thus, the sensor is tested in an electric field controlled environment. An electronic circuit based on charge preamplifiers connected in differential mode reduces these disturbances.

### A. Experimental methods

#### 1) Fabrication of the magnetoelectric sample

The mechanical resonances of the sample can be rejected to higher frequencies by miniaturizing the sample by using an electrodeposition technique advantageously, allowing the fabrication of ME samples with a surface of a few mm². Nickel has good magnetostrictive properties and has been chosen to be electrodeposited on each side of a PIC255 sample, which is a soft piezoelectric material bought from PI, already polarized and with electrodes already in place. These electrodes are useful for electrodeposition, and the ME voltage will be read between them.

A trilayer Ni/PIC255/Ni is obtained by deposing 150 µm of Nickel on each side of a PIC255 sample, which has a surface of 4 mm × 5 mm, a thickness of 0.5 mm. The magnetoelectric voltage $V_{ME}$ is obtained between the electrodes of the PIC255 sample.
## 2) ME characterisation

The ME effect of the sample is characterized by a transverse coupling coefficient $\alpha_{31}$ in L-T mode (magnetic field applied parallel to the plane of the sample, perpendicular to the piezoelectric polarisation), which depends on the DC magnetic field applied.

$$ \alpha_{31} = \left( \frac{\partial E}{\partial H_{AC}} \right)_{H_{DC}} \quad (1) $$

Where E is the measured electrical field, $H_{AC}$ is the alternative magnetic field applied. The sample's ME characteristic is obtained using an experimental setup in previous research [9] allowing the measure of $\alpha_{31}$ as a function of the DC magnetic field. The sample is inserted in the air gap of an electromagnet, which allows a change of the DC magnetic field applied to the sample. The AC magnetic field is produced by Helmholtz coils, and the ME voltage between the PIC255 electrodes is measured using a lock-in amplifier. The electric field is deduced by measuring the voltage and knowing the PIC255 sample thickness.

## 3) Current sensor prototype

To obtain a current sensor with the ME composite, a DC magnetic field is applied on the sample by permanent magnets to obtain an operating point around the maximum of the ME response (Fig.1a). A 3E27 toric flux concentrator is used, with an external diameter of 56 mm, an internal diameter of 32 mm, and a height of 18.5 mm. The Ni/PIC255/Ni sample is inserted in an 11 mm gap. The permanent magnets (barium ferrites) have a total volume of $10 \times 12 \times 18.5 \text{ mm}^3$ and are inserted in a diametrically opposed 12 mm gap.

Then, an electronic circuit based on charge preamplifiers in differential mode is connected to the electrodes of the ME sample. It allows for the reduction of electrostatic disturbances. The complete current sensor prototype is shown in Fig.1b.

<figure><img src="image_2.png" /><figcaption>Fig. 1. ME response of the ME sample and current sensor prototype</figcaption></figure>

The current dynamics are studied by measuring the THD (Total Harmonic Distortion) of the ME Voltage and the THD of the current as a function of the current at 1 kHz. The current is measured by a reference sensor (Tektronix A622) and an amplifier with a bandwidth from 20 Hz to 20 kHz, and a maximum current of 25 A is used for the tests. A winding of 24 turns is made around the toric flux concentrator to obtain a maximum current equivalent to 600 A turns.

## 4) Mechanical damping

Mechanical damping is realized to limit the effect of the material resonance on the sensor's bandwidth. The idea is

to find a mixture that can attenuate high frequencies without impacting the bandwidth. Polyurethane is a good candidate because it doesn't restrict the deformations of the ME sample too much. The addition of tungsten powder allows the acoustic waves created by the resonance of the sample to be dissipated more efficiently. Thus the mixture chosen for the mechanical damping is composed of polyurethane (Polurea GP040) and tungsten powder (12 µm grains). The Polurea GP040 required a mixture of a phase A and B with a mass ratio of 100:50. Before the mixture reticulation, the tungsten powder was introduced progressively while the solution was mixed. The next step is removing the air from the mixture using a vacuum pump. The solution is then poured into a mold, and the sample is immersed and maintained until reticulation. Finally, the sample is removed from the mold, and the total volume of the coated sample is $8 \times 6 \times 10 \text{ mm}^3$, which can easily be inserted in the gap of the flux concentrator. For each mixture realized, a load ratio is defined as:

$$ \tau = \frac{m_t}{m_p} \quad (2) $$

$m_t$ is the mass of tungsten and $m_p$ is the mass of polyurethane. Two PIC255 samples, with dimensions similar to those used for the ME trilayer (sides of 5 mm and a thickness of 0.5 mm), are used to test different load ratios. The first is immersed in a mixture with $\tau = 2.5$, the second with $\tau = 5$, and finally, the ME sample is coated with a resin with $\tau = 5$.

A comparison is made before and after the coating for the following experiments. The first experiment involves connecting the sample electrodes tested to an impedance analyzer after calibration to measure the real part of the impedance (R in $\Omega$). Thus, for each sample, the damping effect can be observed on the resonance peak, and the quality factor Q is calculated:

$$ Q = \frac{f_0}{\Delta f} \quad (3) $$

with $f_0$ the resonance frequency, and $\Delta f = f_1 - f_2$ is the resonance width. $f_1$ and $f_2$ corresponds to the frequencies at the maximum amplitude divided by $\sqrt{2}$.

Then, the current sensor is submitted to a current step response. The square current applied contained all the frequencies; thus, the mechanical resonances of the sample will be excited, and oscillations will appear on the ME voltage.

Finally, the sensor's transfer function with the electronic circuit is plotted. The gain is defined as follows:

$$ T_{ME} = \frac{V_{ME}}{22 \times I_m} \quad (4) $$

With $V_{ME}$, the ME voltage measured at the electronic output, $I_m$, the current measured with a reference current sensor (Tektronix TCPA300), and the winding turns have been changed to 22 instead of 24 in the THD measurement. Thus, the gain and the phase shift are plotted as a function of frequency.
<figure><img src="image_3.png" /><figcaption>Fig. 2. Device to produce electric field disturbances</figcaption></figure>

## 5) Electric field disturbances

Due to its capacitive behavior ($C \approx 1$ nF) on the electric output, the ME composite is very sensitive to ambient electric fields (60 Hz or 50 Hz, for example) and can detect them. The result is an unwanted "noise" voltage on the sample's output. An electronic circuit based on charge preamplifiers in differential mode is connected to the ME sample's output to eliminate such interferences. The last experiment tests the sensor response to these disturbances (Fig.2) with and without the electronic circuit. The sensor is put between two copper plates separated by 5.5 cm. An insulating layer is placed between the sensor and the bottom plate to avoid short circuits. A function generator connected to an amplifier supplies the copper plates with 200 V sinusoidal waves. The ME voltage is measured with a lock-in amplifier through a voltage bridge, which decreases the voltage reference of the lock-in to 1 V.

## B. Experimental results

### 1) Current sensor prototype

The THD of the magnetoelectric voltage $V_{ME}$ and the current measured by the reference sensor are plotted as a function of the current amplitude. The distortion of the reference sensor is negligible. Thus, the THD obtained with the current measured by the reference sensor corresponds to the amplifier's distortion and is small but not negligible compared to the distortion of the ME voltage. Depending on the applications, the THD standard may differ. For instance, if we set a THD threshold of 3 %, a 350 A current dynamic can be obtained. However, the current THD is included in the $V_{ME}$ THD, meaning that the THD of the ME sensor should be a bit smaller and the current dynamic a bit wider.

### 2) Mechanical damping

As described in the experimental methods section, each sample is characterized by the analyzer impedance (Fig.4). Then, the quality factor (Eq.3) is deduced from each curve by reading the resonance frequency and width, $Q_u$ is the quality factor before damping, and $Q_d$ is the quality factor after damping. For the PIC255 sample coated with $\tau = 2.5$, the quality factor after the coating is 7.35 times smaller than before (Table I). When $\tau$ is increased to 5 for the second PIC255 sample, the quality factor is reduced by 14.9, meaning the damping is improved by 2. However, it is difficult to obtain

<figure><img src="image_4.png" /><figcaption>Fig. 3. THD of $V_{ME}$ and the current $I$ as a function of the current amplitude, the current is measured with a reference sensor (Tektronix A622)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Real part of the impedance $R$ (in $\Omega$) as a function of frequency</figcaption></figure>

<table><caption>TABLE I
QUALITY FACTOR FOR EACH SAMPLE BEFORE AND AFTER DAMPING</caption><thead><tr><th></th><th>Q<sub>u</sub></th><th>Q<sub>d</sub></th><th>Q<sub>u</sub>/Q<sub>d</sub></th></tr></thead><tbody><tr><td>PIC255 with τ = 2.5</td><td>136</td><td>18.5</td><td>7.35</td></tr><tr><td>PIC255 with τ = 5</td><td>170.9</td><td>11.5</td><td>14.9</td></tr><tr><td>ME sample with τ = 5</td><td>76.6</td><td>6</td><td>12.8</td></tr></tbody></table>

a better damping because the mixture is too viscous when $\tau > 5$. The resin gave good results on the PIC255 samples. Thus, the mixture was created again with $\tau = 5$. This time, the quality factor is reduced by 12.8 instead of 14.9 with the PIC255. The difference could be that the resonance width is harder to read because the resonance peak is imperfect due to the nickel presence that changes the mechanical behavior at the interface with PIC255. Indeed, the nickel layers have their own resonance frequencies and are mechanically bonded to the PIC255 sample thanks to electrodeposition. Thus, there is mechanical stress at the interface, and the elastic compliances are different at the interface, which hinders the deformations of the piezoelectric phase.

Lastly, the step response of the sensor is studied (Fig. 5); the oscillations are strongly attenuated with the damping, and the time duration of the overshoot is smaller. The damping effect is also studied on the current sensor transfer function without electronics (Fig.6). The gain (Eq. 4) and the phase are plotted as a function of frequency with and without damping. It can be
<figure><img src="image_6.png" /><figcaption>Fig. 5. Damping effect on the sensor step response without electronic circuit</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. Damping effect on the transfer function of the sensor without electronic circuit</figcaption></figure>

observed that the gain doesn't change in the useful bandwidth, which goes from 100 Hz to 100 kHz. Moreover, the damping doesn't affect the phase, so it is a big advantage compared to electrical damping, which introduces a phase shift.

### 3) Electric field disturbances

The setup described in the previous section is applied, and a sinusoidal electrical field of 3636 V/m is applied to the sensor with and without electronics (Fig. 7). No current flows in the cable in the current sensor setup to only observe the pick-up voltage appearing on the sensor's output by antenna effect. It can be observed that the electronic circuit strongly reduces the effect of the electric field interference by a factor of 25.7 between 100 Hz and 1 kHz. The Signal-to-Noise Ratio of the sensor with the electronic circuit (SNR<sub>I</sub>) and without (SNR<sub>0</sub>) are studied to consider the electronic gain G. The ratio of the two SNRs is calculated Eq.5 with N<sub>0</sub> the noise of the sensor without electronic circuit, N<sub>1</sub> the noise of the sensor without, T<sub>ME</sub> the transfer function of the sensor without electronic circuit, I the measured current. Between 100 Hz and 1 kHz, the electronic gain is equal to 2.7 and N<sub>1</sub>/N<sub>0</sub> = 1/25.7. Thus, the SNR with electronics is 69 times bigger than the SNR without electronics.

$$ \frac{SNR_0}{SNR_1} = \frac{T_{ME}I}{N_0} \times \frac{N_1}{T_{ME}I.G} = \frac{N_1}{N_0.G} \quad (5) $$

<figure><img src="image_8.png" /><figcaption>Fig. 7. Electric field disturbances on the sensor with and without electronic circuit</figcaption></figure>

## II. CONCLUSION

A current sensor based on ME composites has been made. It has a bandwidth between 100 Hz and 100 kHz, a dynamic current of 300 A for a THD smaller than 3 %, and a sensitivity of 197 mV/mT. The mechanical damping realized is promising to improve the sensor's bandwidth and limit the resonance impact on the current measurement without introducing a phase shift. An "electronic damping" could be used in addition to the mechanical damping to improve the damping, but a phase shift will be introduced. Finally, a sinusoidal electrical field of 3636 V/m has been applied to the current sensor from 1 Hz to 10 kHz, with and without the electronic circuit. The electronic circuit based on charge preamplifiers connected in differential mode improved the SNR by 69 between 100 Hz and 10 kHz. The phase shift can be reduced, and the bandwidth can be increased by improving the electronic circuit.

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