Magnetic Flux Synchronous Motion Modulation for Improving the Low-frequency Magnetic Field Detection Limit of Magnetoresistive Sensor using MEMS Resonators

Abstract

IntroductionMagnetoresistive (MR) sensors increase explosively and are used widely in many fields due to its small weight, low power consumption, and high sensitivity, whereas the 1/f noise is larger in the low-frequency region and degrades the low-frequency magnetic field detection limit [1]. To reduce the impact of 1/f noise, MEMS-based magnetic flux concentrators (MFCs) are utilized to modulate the low-frequency field to a high-frequency region where the 1/f noise vanishes and improve the detection limit. MEMS-based MFCs consist of MEMS resonators vibrating with a high frequency and the high relative permeability magnetic film deposited on the surface of MEMS resonators, the combinations of them have been already tested and reported for high-frequency magnetic field modulation, resonance frequency detection, and 1/f noise of MR sensor cancellation [2-5]. When the MR sensor is integrated with MEMS-based MFCs and modulating the low-frequency magnetic field to the high-frequency region, the larger the modulation efficiency, the lower the detection limit. However, the modulation efficiency of existing modulation ways is not high, and the low-frequency magnetic field detection limit is low. To improve the low-frequency detection limit of the MR sensor, a new modulation way called synchronous motion modulation (SMM) is proposed.Theory of SMMSMM is evolved from gap-change modulation (GCM) [2]and vertical motion modulation (VMM) [3] with the highest modulation efficiency in the existing literature, as shown in Fig. 1. For GCM, the magnetic film deposited on the bottom of the piezoelectric cantilever resonator is static, and the MFCs deposited on the comb-driven resonator vibrate horizontally. But for VMM, the MFCs are static, and the magnetic film deposited on the bottom of the piezoelectric cantilever vibrates vertically. When the MFCs vibrate horizontally and the piezoelectric cantilever vibrates vertically, this is SMM, which modulates the magnetic flux in the position of the MR sensor to the high-frequency region. In this case, the direct current (DC) magnetic field will be modulated to an alternating current (AC) field and be measured by the MR sensor and bridge circuit.To compare the modulation efficiency of these three modulation ways, the vibration amplitude of comb-driven resonator is the same in SMM and GCM, the vibration amplitude of piezoelectric cantilever resonator is the same in SMM and VMM. The theoretical analyses show that the modulation efficiency of VMM increases with increasing amplitude and decreasing the initial height of magnetic film, but the modulation efficiency of GCM increases with increasing amplitude and decreasing the initial gap of MFCs. Additionally, the modulation efficiency of SMM is the sum of the modulation efficiency of VMM and GCM when two resonators have the same frequency and their phase difference is 180 degree.Validation and resultsTo demonstrate the theoretical analysis above, the finite element method (FEM) simulation is done. Assuming that the magnetic film and MFC with the same frequency of 10 kHz, the same amplitude of 10 um , and the phase difference of 180 degree, the results are shown in Fig. 2 (a). It is found that the DC magnetic field, 1 uT , is modulated into a high-frequency magnetic field, and the modulated magnetic field waveform is a slightly distorted high-frequency sine wave. The reason is that the modulated magnetic field has many harmonic components, but the amplitude of the first-order component and DC component is much larger than other components. The peak-peak amplitude of the modulated magnetic field of SMM is larger than that of GCM and VMM, the modulation efficiency of VMM, GCM, and SMM is 38.55%, 66.82%, and 100.31%, respectively, and the modulation efficiency of SMM is nearly equal to the sum of modulation efficiency of VMM and GCM.Additionally, the situations when the MEMS resonators vibrate from 1 um to 10 um with the step of 1 um are investigated, as shown in Fig. 2 (b). The results show that the modulation efficiency increases linearly with increasing the amplitude, and the SMM has the maximum modulation efficiency among three modulation ways. What's more, the theoretical values are coincident well with the simulated results, which demonstrates the utility of the theory.ConclusionTherefore, we can conclude that SMM can significantly improve the modulation efficiency of the MEMS-based MR sensor and improve the low-frequency magnetic field detection limit, and the amplitude of MEMS resonator as large as possible is desired. Of course, fabricating two MEMS resonators as like in this paper and synchronizing them are not easy, the current feasible method is to use MEMS bonding technology and an interface circuit based on a phase-locked loop. **