## 3 Results and Discussion
### Noise  
In addition to the sensitivity and linearity, the signal-to-noise ratio is also a key factor in assessing the performance of sensors in practical applications. The magnetic noise tests of our sensor were first carried out under different excitation frequencies and current amplitude conditions at 1 Hz in pT/Hz\({}^{1/2}\). As can be seen in Figure 8a, there exists a minimum noise value at 500 kHz when the excitation frequency is considered. This can be attributed to the change in the alternating current (AC) magnetic properties such as eddy current losses and demagnetization effect in the ferromagnetic layer toward variable driven frequencies. However, the noise level of our sensor clearly decreased with increasing excitation current amplitude because the melt-spinning ferromagnetic layer showed improved saturation with higher excitation current values (Figure 8b). Figure 8c presents the equivalent magnetic noise spectrum of the sensor for 70 mA peak excitation at 500 kHz frequency in a shielded environment. The measured magnetic noise is about 36 pT/Hz\({}^{1/2}\) at 1 Hz and the noise rms level is 215.68 pT within 0.1-10 Hz. Figure 8d shows the time-domain noise information of the sensor for four different external magnetic field values (0, 5 nT, 10 nT, 20 nT) under an excitation current amplitude of 70 mA and a frequency of 500 kHz, which corresponds to the minimum noise conditions according to Figure 8a-c. As shown in Figure 8d, evident stage differences in the sensor response were observed when the micro-fluxgate sensor was exposed to different external magnetic fields. The output curve of each magnetic field can be clearly distinguished, and a minimum external field of 5 nT can be clearly detected by our sensor, which indicates the superior resolution of our sensor. Although the resolution  
Figure 7: The permeing error of the sensor as a function of excitation current magnitude. level is still fairly large as compared to those of commercially used conventional fluxgate sensors, it is still very good for a magnetic sensor with microstructure. To the best of our knowledge, a compact micro-fluxgate sensor with such a high-resolution capability has not been reported anywhere else. Moreover, a comparison was made with respect to the performance of recently reported magnetic sensors and some commercialized sensors (as shown in Table 1). Compared with the sensors in most other studies, the results indicated that the micro-fluxgate sensor in this work possessed a wide linearity range and a relatively high sensitivity. Although the reported magnetoelectric composite (MC)-based sensor [31] or the commercial giant magnetoimpedance (GMI) sensor (Type DH) by AICHI Micro Intelligent Co., Ltd., Tokai, Japan [33] and commercial fluxgate sensor (Type uMag-01/02) by MEDA Co., Ltd., Tianjin, China [36] show higher sensitivity or resolution than ours, our sensor presents a great advantage over the linearity range performance. Actually, even when compared with certain commercial sensors [34; 35; 36; 37; 38], our sensor also exhibits an excellent comprehensive performance, especially in the linear range property. In addition, when compared with the commercialized system, the test system in our proposed work for determining our sensor is relatively simple and an open-loop circuit. In a previous study, [PERSON] et al. [39] and [PERSON] et al. [40] indicated that adding a feedback control unit into test system forms a closed-loop circuit, which may clearly improve the detection performance of a fluxgate sensor. This indicates that our sensor performance still had the potential to be further improved by operation circuit-loop optimization. Figure 8: (**a**) Effect of excitation frequency on the magnetic noise of the sensor; (**b**) Effect of excitation current value on the magnetic noise of the sensor; (**c**) The magnetic noise spectrum of the sensor up to 10 Hz for 70 mA peak excitation current at 500 kHz frequency; (**d**) Time-domain response of the sensor for four different external field values.