Dependence of Modified Butterworth Van-Dyke Model Parameters and Magnetoimpedance on DC Magnetic Field for Magnetoelectric Composites

Abstract

This study investigates the impedance curve of magnetoelectric (ME) composites (i.e., Fe₈₀Si₉B₁₁/Pb(Zr_0.3Ti_0.7)O₃ laminate) and extracts the modified Butterworth–Van Dyke (MBVD) model’s parameters at various direct current (DC) bias magnetic fields H_dc. It is interesting to find that both the magnetoimpedance and MBVD model’s parameters of ME composite depend on H_dc, which is primarily attributed to the dependence of FeSiB’s and neighboring PZT’s material properties on H_dc. On one hand, the delta E effect and magnetostriction of FeSiB result in the change in PZT’s dielectric permittivity, leading to the variation in impedance with H_dc. On the other hand, the magnetostriction and mechanical energy dissipation of FeSiB as a function of H_dc result in the field dependences of the MBVD model’s parameters and mechanical quality factor. Furthermore, the influences of piezoelectric and electrode materials properties on the MBVD model’s parameters are analyzed. This study plays a guiding role for ME sensor design and its application.

1. Introduction

Magnetoelectric (ME) materials produce strong ME effects due to the mechanical coupling between magnetostrictive and piezoelectric materials, which has been studied intensively in both theories and experiments [1,2,3,4,5,6]. Such ME effects provide a promising candidate for the highly sensitive DC magnetic field sensor due to its significant variations with external direct current (DC) magnetic field. Dong et al. [7] presented a ME laminate under a constant drive of H_ac = 1 Oe, which can reach the limit of detection (LOD) for a DC magnetic field H_dc of 10⁻⁴ Oe. Sun et al. [2] reported a novel Nano-Electromechanical System (NEMS) AlN/FeGaB resonator with a high DC magnetic field sensitivity of 280 kHz/Oe and a LOD of 8 × 10⁻⁶ Oe. Liu et al. [8] demonstrated a highly sensitive DC magnetic field sensor with a LOD of 2 × 10⁻⁵ Oe. Martins et al. [9] showed a Metglas/poly(vinylidene fluoride)/Metglas magnetoelectric laminate with the sensitivity of 30 mV·Oe⁻¹ and resolution of 8 μ Oe for H_dc detection, and its correlation coefficient, linearity and accuracy values reached 0.995, 95.9% and 99.4%, respectively. Yao et al. [10] developed a Metglas/PMNT/Metglas laminate with the LOD of 10 × 10⁻⁵ Oe for H_dc detection. Wang et al. [11] also proposed a transformer-type magnetic sensor consisting of soft magnetostrictive alloy FeBSiC/piezoelectric ceramics Pb(Zr,Ti)O₃/FeBSiC heterostructure wrapped with both the exciting and sensing coils, which provided the maximum magnetic field sensitivity of 2.12 V/Oe and equivalent magnetic noise of 114 × 10⁻⁸ Oe/$\sqrt{\mathrm{HZ}}$ (at 1 Hz).

Meanwhile the material property and structure of ME composite have been researched intensively for the magnetic sensor application. As such, the field-dependent characteristics of piezomagnetic coefficient for magnetostrictive material [12], the effect of different magnetostrictive materials on the H_dc sensitivity [13,14,15,16], and the optimum structure of piezoelectric/magnetostrictive composite [17,18,19,20] etc. were reported. Additional to understanding the material property of ME composite, it is essential to study the equivalent electrical parameters of ME composite to further improve the DC magnetic sensor performance. However, few articles have reported and analyzed the H_dc dependence of equivalent electrical parameters based on the modified Butterworth–Van Dyke (MBVD) model of magnetoelectric material, even though this is crucial to guide the conditioning circuit design of the ME sensor. Hence, the exploration of electrical equivalent circuit for ME device in this study facilitates understandings of corresponding electrical resonance behavior, which is beneficial for the design and optimization of impedance matching circuits for ME devices. Additionally, this study is expected to guide the design of the magnetic-field-tuned ultrasonic transducer, which can effectively solve the problem of resonance frequency shift and impedance mismatch of the ultrasonic transducer. It is noted that the MBVD model characterizes the loss mechanisms more accurately compared to the conventional Butterworth–Van Dyke model by considering the effects of additional electrical losses and dielectric losses, which can model the measured results more accurately.

In this paper, we investigate the equivalent circuit of the ME sensor based on the MBVD model of PZT/FeSiB laminated composite. It is noted that Lead zirconate titanate Pb(Zr_0.3Ti_0.7)O₃ (PZT) exhibits the outstanding piezoelectric performance and high mechanical quality factor compared to other piezoelectric materials such as polyvinylidene fluoride (PVDF) and BaTiO₃ etc. Meanwhile, the FeSiB (International standard trademark Metglas-2605 S2) possesses a low saturation field and a strong magnetostrictive effect at low magnetic biases H_dc due to its ultrahigh magnetic permeability (i.e., the initial magnetic permeability of 45,000). Correspondingly, magnetostrictive material FeSiB and piezoelectric material PZT are utilized for the ME composite in order to obtain highly magnetic sensing capabilities. In this study, the electrical equivalent circuit parameters of the ME sensor are calculated with the electrical resonance characteristics of measured impedance. Furthermore, the dependences of magnetoimpedance and corresponding MBVD model’s parameters on DC magnetic field are measured and discussed. Such dependences are mainly attributed to the delta E and magnetostrictive effects of FeSiB and correspondingly varied PZT’s dielectric permittivity. Additionally, the effects of the piezoelectric materials and electrode material’s properties on the MBVD model’s parameters are analyzed. The study of electrical equivalent circuit facilitates the understanding of electrical resonance behavior for ME devices, and it plays a crucial role in the design of impedance matching circuits for ME devices. Meanwhile, the controllable impedance and dielectric permittivity of PZT/FeSiB ME composites with DC bias magnetic field have broad potential applications, such as tunable spin filters, storage devices, and magnetic sensor etc.

2. Experiment

The ME sensor consists of PZT/FeSiB laminated composite, where the sizes of magnetostrictive (FeSiB, supplied by Foshan Huaxin Microlite Metal Co., Ltd., Foshan, China) layer and the piezoelectric (PZT, produced by Zibo Yuhai Ceracomp Co., Ltd., Zibo, China) layer are 12 mm × 5 mm × 0.03 mm and 12 mm × 6 mm × 0.8 mm, respectively. First, the PZT plate and FeSiB ribbon are dipped in organic impregnant to clean them. Subsequently, the soft magnetic ribbon FeSiB is bonded with PZT plate by using epoxy glue. Here the West System 105/206 resin/hardener epoxy with a good mechanical property and a low viscosity is utilized to provide strong bondings among layers. The mixture ratio for the epoxy part ‘Resin’ and part ‘hardener’ is specified as 5:1 by the supplier. Then the PZT/FeSiB laminated composite is compacted in a vacuum bag and cured for 12 h at room temperature to further guarantee the strong bonding among layers. The thickness of the epoxy layers is controlled to be less than 5 μm with vacuum bagging techniques, which has been proved to negligibly affect the ME performance, according to previous research [19]. Considering the ease of fabrication and ME performance, the PZT/FeSiB laminated composite is designed to operate in the L–T (i.e., longitudinal–transverse) mode. That is to say, the FeSiB layer is magnetized along the longitudinal direction (i.e., length direction) since the demagnetizing field is much smaller along this direction. Meanwhile the silver electrodes of piezoelectric layer are at its top and bottom surfaces, and the PZT is poled along the transverse direction (i.e., thickness direction).

To measure the impedance of ME composite as a function of the external DC magnetic field H_dc, H_dc is applied along the longitudinal direction of FeSiB layer with a pair of electromagnets driven by a SR830 Lock-In Amplifier. Here the H_dc varies from 0 to 400 Oe, which is calibrated with a Gauss magnetometer (Lake Shore 455 DSP, Columbus, OH, USA). Additionally, when analyzing the dielectric characteristics of the ME sensor, an Impedance Analyzer (4194 A HP Agilent, Santa Clara, CA, USA) is used to measure the magnetoimpedance (Z) of ME composite with the excitation frequency ranged from 125 kHz to 155 kHz.

3. Results and Discussion

Figure 1 shows the impedance Z of the ME sensor as a function of electrical excitation frequency f when the varied DC bias magnetic field is applied along the length direction. As illustrated in the inset of Figure 1, the maximum and minimum impedance as a function of excitation frequency show a strong dependence on DC bias magnetic field.

It is known that the impedance of the ME sensor is defined by [21],

$$\mathrm{Z}=\sqrt{\frac{{\mu }_0{\mu }_{eff}}{{\epsilon }_0{\epsilon }_{eff}}}$$

(1)

where ${\mu }_{eff}$ and ${\epsilon }_{eff}$ are the effective relative permeability and permittivity, ${\mu }_0$ and ${\epsilon }_0$ are vacuum permeability and permittivity, respectively. The effective relative permittivity ${\epsilon }_{eff}$ can be represented as [22].

$${\epsilon }_{eff}={\epsilon }_r+d_{31,p}^2{E}_m\left[\frac{n_{pzt}{E}_{pzt}}{\left(1-n_{pzt}\right)E_m+n_{pzt}{E}_{pzt}}\frac{\tan \left(\frac{\pi f}{2f_s}\right)}{\frac{\pi f}{2f_s}}-1\right]$$

(2)

where ${\epsilon }_r$ is relative permittivity of piezoelectric material, d_31,p is the piezoelectric coefficient, f_s is the resonance frequency, $E_{pzt}$ and $E_m$ are the Young’s modulus of piezoelectric and magnetostrictive materials, respectively. $n_{pzt}$ and $1-n_{pzt}$ are the volume fractions of piezoelectric material PZT and magnetostrictive material FeSiB in the ME sensor, respectively.

By applying a DC bias magnetic field to the magnetostrictive material FeSiB, the magnetostriction is produced by FeSiB and transferred to the PZT layer through interfacial coupling. Meanwhile the magnetostrictive stress will also change the Young’s modulus $E_{m }$ of magnetostrictive material FeSiB and corresponding resonance frequency $f_s$. Correspondingly from the inset of Figure 1, the electromechanical resonance frequency f_s of the ME sensor shows a strong dependence on DC bias magnetic field H_dc. Specifically, the resonance frequency f_s of the ME sensor is determined by the geometrical dimensions and material parameters (i.e., Young’s modulus and mass density) of both piezomagnetic and piezoelectric materials, and is expressed as [12],

$$f_s=\frac{1}{2l}\sqrt{\frac{\overline{E}}{\overline{\rho }}}$$

(3)

where l is the length of the ME sensor, $\overline{\rho }$ and $\overline{E}$ are the average density and equivalent Young’s modulus of ME laminate, respectively. For the ME composite, $\overline{E}$ and $\overline{\rho }$ are determined by [6],

$$\overline{E}=\left(1-n_{pzt}\right)E_m+n_{pzt}{E}_{pzt}$$

(4)

$$\overline{\rho }=\left(1-n_{pzt}\right){\rho }_m+n_{pzt}{\rho }_{pzt}$$

(5)

where ${\rho }_{pzt}$ and ${\rho }_m$ are the densities of piezoelectric and magnetostrictive materials, respectively.

Here the Young’s modulus of magnetostrictive material FeSiB is given by [23],

$$E_m=\frac{\mathsf{\sigma }}{s^e+s^{me}}$$

(6)

where $s^e$, $\mathsf{\sigma }$,$s^{me}$ are the elastic strain, elastic stress and magnetoelastic strain, respectively. The magnetoelastic strain arises from the magnetic domain reorientation during the varied H_dc [24,25], which results in the change in effective Young’s modulus with H_dc. As a result, the shifts in corresponding resonance frequency (Equation (3)) with H_dc are observed.

According to Equations (1) and (2), the variations in the Young’s modulus $E_{m }$ of FeSiB and resonance frequency $f_s$ with H_dc also lead to the changes in effective relative permittivity and corresponding impedance with H_dc for ME composite. It is noted that the combination of magnetoresistance (MR) and the Maxwell–Wagner effect could also cause the magnetodielectric effect, according to the previous report [26]. However, for our asymmetric PZT/FeSiB laminate, piezoelectric material PZT is covered with the insulating epoxy glue at surface to prevent the current penetrating into the neighboring magnetic ribbon FeSiB. Hence, there is no giant magnetoresistance effect since the sensing current cannot go through the magnetic layers and, correspondingly, no spin dependent scattering phenomenon happens in the ferromagnetic layer. Furthermore, Castel et al. [22] have also reported that the magnetodielectric effect of BaTiO₃-Ni laminated composite could reach 10% near the resonance frequency at H_dc = 6 kOe and clarified that the magnetodielectric mechanism of their composites was based on the strain effect instead of the Maxwell—Wagner effect.

It is also interesting to find in Figure 2 that the maximum impedance Z_m at the antiresonance frequency (f_a) increases to a maximum value at H_dc = 30 Oe, and then decreases with further increasing H_dc, while the minimum impedance Z_n at the resonance frequency (f_s) varies in the opposite trend. Namely, Z_n decreases to a minimum value, and then increases with the increasing H_dc. This is mainly because the capacitance is directly proportional to dielectric permittivity, the minimum capacitance value at f_a results in the maximum impedance Z_m and the maximum capacitance value at f_s leads to the minimum impedance Z_n according to Equation (1).

In order to understand the trend of impedance as a function of DC magnetic field, the electromechanical (ME) sensor is characterized with a lumped-parameter equivalent circuit based on the MBVD model, as shown in Figure 3. To characterize the loss from the electrodes, the MBVD model adds two additional loss resistors (i.e., R₀ and R_s) to obtain a more accurate model compared with the standard Butterworth–Van Dyke model. It consists of two network branches in parallel, where R₀ represents the resistance associated with dielectric losses of the ME sensor, R_s represents the resistance associated with electrical losses of electrode, R_m denotes the resistance associated with mechanical losses, L_m and C_m denote the motional inductance and capacitance, C₀ represents the static capacitance formed between top and bottom electrodes of the ME sensor.

The analytical expression of impedance $Z\left(\omega \right)$ and the electrical admittance $Y\left(\omega \right)$ for MBVD model are given by [27,28],

$$Z\left(\omega \right)=R_s+\frac{(R_0+\frac{1}{j\omega C_0})(R_m+\frac{1}{j\omega C_m}+j\omega L_m)}{R_0+\frac{1}{j\omega C_0}+R_m+\frac{1}{j\omega C_m}+j\omega L_m}$$

(7)

$$Y\left(\omega \right)=\frac{1}{\frac{1}{\frac{1}{R_m+\frac{1}{j\omega C_{\mathrm{m}}}+j\omega L_m}+\frac{1}{\frac{1}{j\omega C_0}+R_0}}+R_s}$$

(8)

The series resonance frequency $f_s$ and antiresonance frequency $f_a$ can be expressed as [27,28],

$$f_s=\frac{1}{2\pi \sqrt{L_m{C}_m}}$$

(9)

$$f_a=\frac{1}{2\pi }\sqrt{\frac{C_m+C_0}{C_0{L}_m{C}_m}}=f_s\sqrt{\frac{C_m+C_0}{C_0}}$$

(10)

Using Equations (7), (9) and (10), the model parameter values of C₀, R₀, R_s, L_m, C_m and R_m are extracted from the measured Z.

Table 1. Parameters of the equivalent circuit model for ME resonator at H_dc of 30 Oe.

Model Parameters	Rm	Lm	Cm	R0	Rs	C0
values	88.3 Ω	30.2 mH	43.8 pF	20.8 Ω	60 Ω	1.08 nF

lists all the extracted model parameters. To verify the MBVD model for further design of the conditioning circuit, the simulation of the model is implemented with the electrical simulator Agilent ADS. Figure 4 presents the computed impedance Z and phase based on the extracted model parameters at H_dc = 30 Oe, which shows a good agreement with the measured data.

According to the measured Z with DC bias magnetic field H_dc, the corresponding equivalent circuit parameters (i.e., C_m, L_m, C_0, Q_s, R_s + R_m, f_s and f_a) are calculated and analyzed as a function of H_dc, as shown in Figure 5, Figure 6, Figure 7 and Figure 8, respectively.

Specifically, C_m and L_m are given by [27,28],

$$L_m=\frac{1}{8}\frac{\rho A{l}_t}{l_w^2}{\left(\frac{s_{11}^E}{d_{31}}\right)}^2=\frac{1}{8}\frac{\rho l{l}_t}{l_w}{\left(\frac{s_{11}^E}{d_{31}}\right)}^2$$

(11)

$$C_m=\frac{8}{\pi }\frac{A}{l_t}\frac{d_{31}^2}{s_{11}^E}=\frac{8}{\pi }\frac{l{l}_w}{l_t}\frac{d_{31}^2}{s_{11}^E}$$

(12)

where d₃₁, $s_{11}^E$, $\rho$, l_w, l_t and l are the piezoelectric coefficient, elastic compliance coefficient, density, width, thickness and length of the ME sensor, respectively. $A=l{l}_w$ is the plate area.

It is obvious that the the length l and elastic compliance coefficient $s_{11}^E$ have strong influences on the C_m and L_m according to Equations (11) and (12). Specifically, due to the stress-strain coupling of interlayers, the magnetostrictive strain produced by FeSiB under varying H_dc results in the change in the length $l$ and elastic compliance coefficient $s_{11}^E$ for piezoelectric material. As a result, the equivalent electrical parameters C_m and L_m of the ME sensor strongly depend on H_dc and vary in the opposite ways, as illustrated in Figure 5. This is due to the fact that L_m and C_m are proportional to ${\left(\frac{s_{11}^E}{d_{31}}\right)}^2$ and $\frac{d_{31}^2}{s_{11}^E}$, respectively.

Furthermore, C_m is proportional to the length l of composite, whereas it is inverse proportional to the elastic compliance coefficient. Since the Young’s modulus is the inverse of elastic compliance coefficient, C_m is determined by both the Young’s modulus E and length l. On one hand due to the stress-strain coupling of the interlayers, the length l increases quickly to a maximum value due to the large piezomagnetic coefficient d_33,m of FeSiB and then l reaches the saturation with further increasing H_dc. On the other hand, the Young’s modulus E of the magnetostrictive layer and, corresponding, ME composite decrease initially to a minimum value with the increasing H_dc, and then increases and reaches saturation at large H_dc when H_dc further increases [18]. When H_dc < 60 Oe, the magnetostriction does not attain to saturation, C_m is affected by both Young’s modulus and the length l. However, the effect of length l on C_m is more obvious than that of Young’s modulus due to the large d_33,m of FeSiB at the small H_dc, which causes C_m to increase with H_dc and reach a positive peak in low magnetic field H_dc = 60 Oe. When H_dc further increases above 60 Oe, the magnetostriction reaches saturation quickly; however, the Young’s modulus E still varies significantly and plays a dominant role in C_m. Currently, Young’s modulus E and corresponding C_m reach the local minimum values when H_dc further increases to 100 Oe, then C_m gradually increases and reaches saturation with further increasing H_dc due to the variation in E, as shown in Figure 5.

Meanwhile the static capacitance C₀ can be also expressed with the following expressions [28]:

$$C_0=\frac{{\mathrm{A}\mathsf{\epsilon }}_{\mathrm{r}}{\mathsf{\epsilon }}_0}{{\mathrm{l}}_{\mathrm{t}}}$$

(13)

where ${\epsilon }_r$ and ${\epsilon }_0$ are the relative dielectric permittivity and vacuum permittivity of the piezoelectric material, respectively.

When H_dc is applied along the longitudinal direction of the ME sensor, the magnetostrictive material FeSiB expands with the increasing H_dc, which changes dielectric permittivity of piezoelectric material due to the transferred magnetostrictive stress. Correspondingly, C₀ varies with the DC magnetic field since C₀ is strongly determined by the dielectric permittivity. Yao et al. [10] reported that the dielectric permittivity of Terfenol-D/PZT magnetoelectric composite at the resonant frequency decreased and then increased with increasing dc magnetic field. In this case, C₀ varies in a similar trend as function of H_dc since C₀ is proportional to the dielectric permittivity. Specifically, it is shown in Figure 6 that the static capacitance C₀ of the ME sensor first decreases with the increasing H_dc, and then gradually increases.

The R_m is used to characterize the mechanical loss, which is subject to energy loss in the ME sensor. It can be given as [28],

$$R_m=\frac{l_t^3}{8A{d}_{31}^2}=\frac{l_t^3}{8l{l}_w{d}_{31}^2}$$

(14)

$R_m$ is primarily determined by the length l. Correspondingly, the variations in the length l due to the magnetostriction of FeSiB cause the variation in $R_m$ with H_dc.

By analyzing the variation in equivalent circuit parameters (i.e., C_m, L_m, C_0, R_m etc.) with H_dc, it is found that the varying magnetostrictive strain of FeSiB with H_dc is the main reason for the H_dc dependences of equivalent circuit parameters. Furthermore, it is also noted that these equivalent circuit parameters depend on the actively vibrating area A, since R_m and L_m decrease with the enlarged area, whereas the capacitances C₀ and C_m increase with the enlarged area. Such relations are important for designing ME sensors.

Furthermore, the mechanical Quality factor (Q-factor) reflects the capability of the ME sensor to reserve mechanical energy and the corresponding loss of resonant circuit. Q is defined as the ratio of the stored energy to the dissipated energy per cycle during oscillation. According to Lakin’s method, the $Q_s$ at series resonance frequency $f_s$ and $Q_p$ at antiresonance frequency $f_a$ can be defined as [27,28],

$$Q_s=\frac{2\pi f_s{L}_m}{R_s+R_m}$$

(15)

$$Q_p=\frac{2\pi f_p{L}_m}{R_0+R_m}$$

(16)

On one hand, the smaller value of R_S is desired to improve the effective mechanical Quality factor $Q_s$ of the ME sensor, according to Equation (15). Since R_S represents the electrical loss of electrode, the type and quality of the electrode materials directly affect the $Q_s$ of the ME sensor. In this case, utilizing the electrode material with high acoustic impedance and low resistivity can reduce R_S and improve the effective electromechanical coupling coefficient of the ME sensor. On the other hand, Equation (16) predicts that the high $Q_p$ value can be obtained when the ME sensor possesses a low $R_0$. Since the dielectric losses R₀ of the ME sensor is mainly determined by the dielectric loss of piezoelectric material, it means the smaller dielectric loss results in the larger effective mechanical Quality factor $Q_p$ of the ME sensor. Additionally, from Equations (15) and (16), it is found that both $Q_s$ at resonance frequency and $Q_p$ at antiresonance frequency decrease with the increasing mechanical loss R_m. Hence, the mechanical loss R_m plays a primary role in the energy dissipations of the ME sensor.

Subsequently, the Q_s, Q_p and corresponding loss as a function of H_dc are experimentally investigated to verify and further understand the above theoretical analysis. It is known that R_m depends on the mechanical energy dissipation $tan{\delta }_{mech}$ of the ME sensor [28], while Q_s is inversely proportional to $tan{\delta }_{mech}$ [29]. When the DC magnetic field is applied, the mechanical energy dissipation R_s + R_m of magnetostrictive material FeSiB changes dramatically owing to the non-$180°$ domain wall motions. This results in the varied mechanical quality factor Q_s of the ME sensor with H_dc, as shown in Figure 7a. Specifically, the quality factor (Q_s) at the series resonance frequency $f_s$ decreases from 182 to the minimum value of 160 at the H_dc = 200 Oe and then gradually increases according to the MBVD model. Obviously, the variation in Q_s is mainly attributed to the magnetic mechanical loss associated with magnetic domain wall movement and material damping of FeSiB.

Furthermore, the trends of $Q_p$ and R₀ + R_m as a function of H_dc are similar to that of $Q_s$ and R_s + R_m, as shown in Figure 7b. However, the magnitude of antiresonance mechanical quality factor $Q_p$ ranges from 234 to 245.6, which is higher than the resonance mechanical quality factor Q_s. The differences between $Q_p$ and $Q_s$ were also reported by in previous literature [30,31]. Finally, the resonance frequency f_s and antiresonance frequency f_a of ME laminated sensor as a function of varied H_dc are investigated, as shown in Figure 8. Both f_s and f_a exhibit similar trends with H_dc, which increases with the increasing DC bias field. The obvious shifts of resonance frequency f_s and antiresonance frequency f_a with H_dc indicate that f_s and f_a of the ME sensor are adjustable by varying the DC bias magnetic field.

4. Conclusions

In summary, the impedance of the ME sensor (i.e., FeSiB/PZT composite) as a function of DC bias magnetic field is experimentally measured and theoretically analyzed. Meanwhile, the simulation results with the MBVD model of the ME sensor agrees with the measured impedance Z accurately. Specifically, the dependences of extracted MBVD model parameters and the magnetoimpedance effects of the ME sensor on H_dc are observed, which result from the varied magnetostriction and the mechanical energy dissipation of magnetostrictive material FeSiB with H_dc due to the corresponding delta E effect and magnetostrictive effect. Furthermore, the influences of piezoelectric materials property and electrode on the MBVD model parameters are analyzed. The analysis of MBVD model for ME composite is beneficial to the design of analog front-end circuits for the corresponding magnetic sensor, which could further improve the LOD.