# Operating Point Self-Regulator for Giant Magneto-Impedance Magnetic Sensor

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## Abstract

**:**

## 1. Introduction

## 2. The Structure of GMI Sensor

#### 2.1. The Structure of Magnetic Detector

_{71.8}Fe

_{4.9}Nb

_{0.8}Si

_{7.5}B

_{15}amorphous wire is employed as the sensing elements with a length of 10 mm and a diameter of 30 μm. This wire is provided by the Advanced Technology & Materials Co. Ltd., Beijing, China. It is fixed on a printed circuit board with the silver conducting resin. Two solenoids (L

_{1}and L

_{2}) are fabricated by an enameled Cu wire wrapped around the column of bobbins which are made by polytetrafluoroethylene (PTFE). The winding number and the length of two solenoids are both 1050 turns and 50 mm respectively. The solenoids are used to generate the bias magnetic field. The amorphous wire is placed in L

_{1}, while a GMR sensor is placed in L

_{2}. The GMR sensor is used to measure the DC or quasi-DC components in external magnetic field. The amorphous wire and the GMR sensor have the same sensing direction. L

_{1}and L

_{2}are connected in series and designed to generate a same magnetic field, like Figure 1 depicted. The purpose of this design is to protect the amorphous wire from the electronic magnetic fields produced by the signal and power wires of the GMR sensor. When the amorphous wire and the GMR sensor are put in the same solenoid, the outputs and the power supply wires of the GMR sensor must be placed very close to the amorphous wire. This can cause disturbances in the measurement results of amorphous wire. The GMR sensor is a commercial spin valve sensor with the type of SpHDE that be produced by the SpinIC Co. Ltd., Shanghai, China. It has a resolution of 2.7 nT and a classical sensitivity of 28.58 mV/V/mT. The supply voltage is +3.3 V and the supply current is about 6.0 mA.

#### 2.2. The Design of GMI Sensor

#### 2.3. The Operating Point Self-Regulator and the Passive Phase-Lag Compensation Network

_{0}is the magnetic permeability of the vacuum, N and L are the winding number and length of the solenoids respectively, K

_{1}and K

_{2}are the gains of comparator and amplifier, R is the resistor that can regulate the current in V/I converter, S is the sensitivity of GMR sensor, and 1/(1 + as + bs

^{2}) is the transfer function of second-order low-pass filter.

_{1}[10]. In order to achieve an accurate operating point, the steady-state error of the feedback control system should be small. Thus the K

_{1}needs to be large when the system is stable. Nevertheless, an increase in K

_{1}results in an attendant decrease in the damping ratio of the system and therefore a more oscillatory response to a step input [20]. It means that the requirement of small steady-state error may cause fluctuations in the operating point when the external magnetic field is suddenly changing. In order to improve the performance of the operating point regulator and achieve an accurate and stable operating point, a phase-lag compensation network is added into the operating point regulator, like Figure 4 and Figure 5 show. The phase-lag network can provide an attenuation and increase the steady-state error constant of the feedback network [20]. There are two reasons for this compensation network in the design: firstly, the phase-lag network is utilized to increase the error constant and then reduce the steady-state error; secondly, the phase-lag network decreases the system bandwidth, which can suppress the high frequency noise. The phase-lag compensation network is depicted in Figure 6. Its transfer function G

_{c}(s) can be written as

_{2}C and α = (R

_{1}+ R

_{2})/R

_{2}, then Equation (3) is

_{2}is 100 and K

_{1}is adjustable; R is 392 Ω to provide a suitable current; a and b are 1.4142 and 1 respectively for a Butterworth second-order unity-gain low-pass filter. Therefore the uncompensated transfer function in Bode diagram is

_{1}should be larger than 50. With this value, the Bode diagram of uncompensated system can be drawn as Figure 7 shows. It is obviously that the uncompensated system is a minimum phase system because all its zeros lie in the left-hand s-plane. Then with the Nyquist stability criterion, the uncompensated system is always stable because its phase is bigger than −180° [20], and its phase margin is Φ

_{pm}= 11.5° at the crossover frequency ω

_{c}of 7.07. With its phase margin, the damping ratio ζ of the system is about 0.01 Φ

_{pm}= 0.115. With the known damping ratio, the percent overshoot for a unit step input of the system is [20]

_{pm}= 60°, thus the new crossover frequency ω

_{c}’ is located where Φ(ω) = −120°. The new crossover frequency ω

_{c}’ is about 1.48 as the Bode diagram shows. The attenuation necessary to cause ω

_{c}’ to be the new crossover frequency is equal to 26.4 dB. Both the compensated and uncompensated magnitude curves are an asymptotic approximation. Because the attenuation is 26.4 dB, thus 20 log(1/α) = −26.4 dB, and the α is 20.9. Therefore the zero is 20.9 below the crossover, or 1/τ = ω

_{c}’/20.9 = 0.07, and the pole is at 1/ατ = 0.0033. The compensated system is then

_{c}’ = 1.46 is Φ

_{pm}= 58.6°, which is the desired result.

## 3. Results and Discussion

#### 3.1. The Perfromance of the Operating Point Self-Regulator

#### 3.2. The Decision of the Operating Point

#### 3.3. The GMI Sensor with the Compensated Self-Regulating System

^{1/2}in the pass band. The noise level of SRS-based sensor is much higher than the fixed bias sensor, which is about 2.9 nT/Hz

^{1/2}from 0 to 5 Hz and about 1.6 nT/Hz

^{1/2}from 5 to 12 Hz. This comparison can prove that the feedback control on the operating point introduces noise into the GMI sensor. The proposed CSRS-based sensor has a much higher noise level than the fixed bias sensor at the range from 0 to 7 Hz, which is about 2 nT/Hz

^{1/2}, but the phase-lag compensator has attenuated its noise to the same level of fixed bias sensor in 7 to 15 Hz as presented in Figure 11. With this experiment, it can be found that the compensation network decreases the system bandwidth and then suppresses the high frequency noise in the GMI sensor introduced by the feedback control.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 8.**Time response to a step input for the uncompensated feedback control and the compensated feedback control.

**Figure 9.**Sensor output voltages versus the external magnetic field characteristics. The results show comparisons between excitations with (

**a**) different frequencies; (

**b**) different amplitudes; (

**c**) different DC bias.

**Figure 10.**Output characteristic curves of the GMI sensor, (

**a**) with the magnetic shield; (

**b**) without the magnetic shield.

Uncompensated System | Compensated System | |
---|---|---|

Controller | Gain, K_{1} | Phase-lag network |

Step overshoot | 72.2% | 4.2% |

Settling time (milliseconds) | 23 | 35 |

Steady-state error for step | 5.6% | 2% |

**Table 2.**The hysteretic characteristic of GMR sensor in an external magnetic field from 43 μT to 248 μT.

Magnetic Field (μT) | 43.4 | 62 | 80.6 | 99.2 | 117.9 | 136.5 |

Output (increase) (V) | 0.4346 | 0.5207 | 0.6086 | 0.699 | 0.7987 | 0.8890 |

Output (decrease) (V) | 0.435 | 0.5260 | 0.6125 | 0.7026 | 0.7989 | 0.8909 |

Magnetic Field (μT) | 155 | 173.7 | 192 | 210.9 | 229.5 | 248.1 |

Output (increase) (V) | 0.9827 | 1.0834 | 1.1790 | 1.2768 | 1.3773 | 1.4887 |

Output (decrease) (V) | 0.9843 | 1.0846 | 1.1833 | 1.2849 | 1.3834 | 1.4887 |

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**MDPI and ACS Style**

Zhou, H.; Pan, Z.; Zhang, D.
Operating Point Self-Regulator for Giant Magneto-Impedance Magnetic Sensor. *Sensors* **2017**, *17*, 1103.
https://doi.org/10.3390/s17051103

**AMA Style**

Zhou H, Pan Z, Zhang D.
Operating Point Self-Regulator for Giant Magneto-Impedance Magnetic Sensor. *Sensors*. 2017; 17(5):1103.
https://doi.org/10.3390/s17051103

**Chicago/Turabian Style**

Zhou, Han, Zhongming Pan, and Dasha Zhang.
2017. "Operating Point Self-Regulator for Giant Magneto-Impedance Magnetic Sensor" *Sensors* 17, no. 5: 1103.
https://doi.org/10.3390/s17051103