Design and analysis of composite magnetic sensor based on GMM and SAW resonator

Magnetic field measurement has a wide range of applications in medicine, military, geology, etc., and is an important part of the modern measurement field. With the development of material technology, magnetostrictive materials are used as sensitive materials for magnetic field measurement and have become an important research topic in the field of magnetic sensing. B. Frank et al. evaporated a layer of magnetostrictive material on the optical fiber, and the optical path of light propagation in the optical fiber changed due to magnetostriction, which can obtain higher magnetic field measurement accuracy. However, this structure greatly destroys the stability of the polarization state of the light field in the optical fiber interferometer arm, thereby making the stability of the entire optical fiber weak magnetic field sensor worse. In 2005, N. Yoshiza-wa et al. studied the magnetic sensing structure of amorphous ferromagnetic thin ribbon and quartz/LiNbO3 composite, with a frequency/magnetic field sensitivity of up to 60 Hz/Oe, which can be used for geomagnetic field measurement. Dong et al. studied the composite of piezoelectric material and magnetostrictive material, using the magnetoelectric effect to measure the magnetic field, which can achieve an accuracy of more than 10-9T, but this magnetoelectric composite material is not suitable for measuring static magnetic fields.

This paper combines the GMM with extremely high magnetostrictive effect and SAW resonator, and uses the magnetic field to affect the large stress and strain generated by the GMM, which acts on the SAW resonator to affect its resonant frequency, thereby measuring the magnetic field. The sensor has a simple structure, low cost, is sensitive to magnetic fields, and can be used for static and dynamic magnetic field measurements. Since the SAW resonator itself can be used as a passive wireless sensor, the composite sensor can also be used as a passive, wireless magnetic sensor.

2 Composite sensing structure

Figure 1 is a schematic diagram of the composite structure of the SAW resonator and the GMM. The GMM, SAW resonator and the hard rigid material frame are in close contact under the action of the bolts and nuts. The frame also acts as a guide rail, limiting the deformation of the SAW resonator and Terfenol-D to only in the length direction. Adjusting the length of the bolt can adjust the prestress applied to the giant magnetostrictive material, so that it can obtain a larger magnetostriction in the magnetic field.

GMM uses Terfenol-D (Tb0.37Dy0.63Fe2) working in 33 mode. Under the action of magnetic field along the length direction, it will expand and contract in the same direction. Since both ends are tightened, the stress and strain of Terfenol-D material will cause the resonant frequency of SAW resonator to change. By detecting the change of resonant frequency of SAW resonator, the size of external magnetic field can be measured.

3 Theoretical Analysis

Taking the case where the contact surface between the GMM and the SAW resonator (SAWR) moves to the right when the GMM is stretched as an example, the force analysis is shown in Figure 2. F and F1 are the reaction forces of the fastening structure and the frame at both ends of the structure; CT, vT, TT, AT represent the force resistance, vibration velocity, internal stress and cross-sectional area of ​​the GMM respectively; Cs, vs, Ts, As are the force resistance, vibration velocity, internal stress and cross-sectional area of ​​the SAW resonator substrate; CTvT and Csvs are the resistance inside the material caused by vibration damping.

For GMM and SAW resonators, according to Newton's third law, we have

The force analysis of GMM and SAW resonator is carried out as a whole. According to Newton's second law,

In formula (2), mT and mS are the masses of GMM and SAW resonator respectively, and a is the acceleration. The strains of GMM and SAW resonator are sT=u/lT, ss=u/ls, and u is the displacement of the contact surface between GMM and SAW resonator. For SAW resonator, according to Hooke's law, ss=Ts/Es; for GMM, since only the stress and strain occurring along the length direction are considered, the scalar form of the piezomagnetic equation can be used to obtain

In the formula, H represents the magnetic field, ES and ET are the Young's modulus of SAW and GMM, and dm is the dynamic magnetostriction coefficient of GMM. From formulas (1) to (3), the vibration equation of the composite structure can be obtained as follows:

When the SAW resonator substrate material is deformed, the relationship between the change in its resonant frequency △f and the strain SS is:

Among them, fr0 is the free state resonant frequency of the SAW resonator, and R is the material constant. The transfer function H(s) of the magnetic sensor can be obtained by equations (4), (5) and Laplace transform. Let s = jω and substitute it to obtain the amplitude-frequency characteristic and phase-frequency characteristic of the composite magnetic sensor.

When the materials and device parameters in Table 1 are used, the amplitude-frequency response of the composite magnetic sensor can be obtained as shown in FIG3 .

Let f0 = 14.34 Hz, which is the cutoff frequency of the composite magnetic sensor. Therefore, the composite magnetic sensor is a low-pass system, which is suitable for measuring static or low-frequency dynamic magnetic fields.

When ω=0, that is, static magnetic field, the steady-state characteristic of the composite magnetic sensor is

Define a as the static sensitivity of the composite magnetic sensor. When the resolution of measuring the resonant frequency is constant, the larger the a value is, the higher the sensitivity and resolution of the magnetic sensor is. From formula (8), we know that the larger the dynamic magnetostriction coefficient dm is, the larger the length ratio lT/ls and the cross-sectional area ratio AT/As of the GMM and SAW resonator are, the higher the sensor sensitivity is. Using the data in Table 1, the theoretical value of a is 276.4 Hz/Oe.

4 Experimental testing

The static magnetic field changes from -1300 to +1300 Oe, and the experimental result curve is shown in Figure 4. As shown in Figure 4, the frequency change and the magnetic field size are approximately linear. Taking the entire magnetic field range [0, 1300] Oe for calculation, the sensitivity of the sensor reaches 123 Hz/Oe; if the magnetic field range [250, 550] Oe is taken for calculation, the sensitivity of the sensor can reach 190 Hz/Oe. In general, this sensitivity is higher than the 30 Hz/Oe of the amorphous ferromagnetic ribbon/LiNbO3 structure and the 60 Hz/Oe of the amorphous ferromagnetic ribbon/quartz structure in the literature [2].

5 Conclusion

Theoretical analysis and experimental tests show that the magnetic sensor composed of GMM and SAW resonator is a low-pass system with a cutoff frequency of about 14.34 Hz. When measuring static magnetic fields, the maximum sensitivity can reach 190 Hz/Oe. The sensor has a simple structure and low cost and can be used for static and dynamic magnetic field measurements.