**7.3 Sensitivity**

The sensitivity of coil-less fluxgates strongly depends on the amplitude of the excitation current. However, while the sensitivity of traditional fluxgates increases if we use a bigger current, the sensitivity of coil-less fluxgates decreases. This means that the higher the excitation current is, the lower the sensitivity will result (Fig. 15). This can be clearly explained by considering the model of the sensor. By increasing the excitation current, the field energy associated to the circular magnetic field will also increase, causing the magnetization M to be tied more strongly to the excitation field in a circular direction, while the effect of anisotropy energy on the total energy of M will become progressively negligible.

By observing Fig. 15 one might think that the best working condition for coil-less fluxgates is obtained with an excitation current about 42÷43 mA, where the sensitivity is at its maximum. However, the excitation current must be high enough to fully saturate the wire, in order to lower the noise as well as to assure a wider linear range. Since an external field shifts the circumferential BH loop of the magnetic wire (Fig.13), the sensor will keep working regularly as long as the measured field is not too large to move one end of the BH loop out of saturation. If that were to happen, the linearity of the sensor would be lost. Therefore, it is recommended to keep the sensor working at a higher excitation current than the minimum current required to achieve saturation, although still not high enough to avoid significant loss of sensitivity.

Compared to traditional fluxgates a coil-less fluxgate has generally lower sensitivity. This is due to the fact that we pick up the circumferential flux with a virtual one-turn coil. While fluxgates with a pick-up coil can simply multiply the sensitivity by using a large number of turns, this is not possible for coil-less fluxgates.

Typical sensitivity for coil-less fluxgates based on a composite Cu-Permalloy wire is about 10 V/T. This value is significantly higher if a Co-based wire is used. In (Atalay et al., 2010) it is reported that a coil-less fluxgate obtained with a Co rich amorphous wire after 15 minutes joule annealing, which reaches sensitivity at about 400 V/T at 30 kHz. In (Atalay et. al, 2011)

field as shown in Fig. 13. The sensitivity of the sensor increases together with the increasing

M

The sensitivity of coil-less fluxgates strongly depends on the amplitude of the excitation current. However, while the sensitivity of traditional fluxgates increases if we use a bigger current, the sensitivity of coil-less fluxgates decreases. This means that the higher the excitation current is, the lower the sensitivity will result (Fig. 15). This can be clearly explained by considering the model of the sensor. By increasing the excitation current, the field energy associated to the circular magnetic field will also increase, causing the magnetization M to be tied more strongly to the excitation field in a circular direction, while the effect of anisotropy energy on the total energy of M will become progressively

HZ

Z

EA

By observing Fig. 15 one might think that the best working condition for coil-less fluxgates is obtained with an excitation current about 42÷43 mA, where the sensitivity is at its maximum. However, the excitation current must be high enough to fully saturate the wire, in order to lower the noise as well as to assure a wider linear range. Since an external field shifts the circumferential BH loop of the magnetic wire (Fig.13), the sensor will keep working regularly as long as the measured field is not too large to move one end of the BH loop out of saturation. If that were to happen, the linearity of the sensor would be lost. Therefore, it is recommended to keep the sensor working at a higher excitation current than the minimum current required to achieve saturation, although still not high enough to avoid

Compared to traditional fluxgates a coil-less fluxgate has generally lower sensitivity. This is due to the fact that we pick up the circumferential flux with a virtual one-turn coil. While fluxgates with a pick-up coil can simply multiply the sensitivity by using a large number of

Typical sensitivity for coil-less fluxgates based on a composite Cu-Permalloy wire is about 10 V/T. This value is significantly higher if a Co-based wire is used. In (Atalay et al., 2010) it is reported that a coil-less fluxgate obtained with a Co rich amorphous wire after 15 minutes joule annealing, which reaches sensitivity at about 400 V/T at 30 kHz. In (Atalay et. al, 2011)

anisotropy angle because the higher is the larger is HZ

H

H

HZ

Fig. 14. Working mechanism of coil-less fluxgates.

**7.3 Sensitivity** 

negligible.

significant loss of sensitivity.

turns, this is not possible for coil-less fluxgates.

a coil-less fluxgate based on a composite copper wire with Co19Ni49.6Fe31.4 electroplated shell is proposed. The sensitivity in this case is about 120 V/T at 20 kHz. Further research on different materials will show if even higher sensitivity will be achievable with other alloys.

Fig. 15. Output characteristic of coil-less fluxgates for different amplitudes of excitation current Iwire. The higher Iwire becomes, the lower the sensitivity of the sensor will be.

Sensitivity can be also increased with higher angles of helical anisotropy but we should keep in mind that saturation current also increases, and this will require a higher excitation current.

A drawback of coil-less fluxgates is that low sensitivity cannot be increased by using high gain amplification because the output voltage of the sensor includes large spurious voltage. This component of the voltage does not include a signal but contributes to enlarge its peak value, limiting the maximum amplification. The resistive part of the spurious voltage, due to the voltage drop on the wire's resistance can be easily removed by a classical resistive bridge. However, the inductive component of the voltage, given by the transition of the magnetization from one saturated state to the opposite, will be always present in the output. As previously explained, these peaks will be shifted by the external field to opposite directions, but they will continue to be present in the output. A technique proposed by (Butta et al., 2010a) is presented to remove the inductive peaks and obtain an output voltage that is null for no applied field and whose amplitude increases proportionally to it. The method is based on a double bridge with two sensing elements fed by current in opposite directions. In the output voltage, the positive peaks of the first wire will be compensated by the negative peaks of the second wire and vice versa. The sensitivity of the two wires must clearly point to opposite directions so that the sum of the voltage obtained with the opposite current will be the sum of the two signals rather than their difference.

### **7.4 Linearity**

A common technique used to improve linearity of magnetic sensors is to operate them in a closed loop mode, by generating a compensation field, which nullifies the measured field (Ripka, 2001). The pick-up coil is usually used for this purpose, because the compensating field must be generated at a low frequency, several orders of magnitude lower than the excitation frequency. Using the feedback mode, the working point of the sensor will always

Orthogonal Fluxgates 39


The following table summarizes several orthogonal fluxgates reported in the literature with their features and obtained performance. The proper choice for structure and operative parameters of orthogonal fluxgates can be made based on the application requirements and

> Fundamental mode

Amorphous wire

40 mA ac + 40mA dc

excitation 118 kHz 100 kHz 40 kHz 500 kHz 188 kHz 100 kHz

Offset -0.33V 48.2 mV

(gain 47) 0.51 V/T 20,000 V/T 850,000

1 Hz 10 pT/√Hz 95 nT/√Hz 0.11 nT√Hz

During this last decade, the research has been focused mainly on issues regarding orthogonal fluxgates, like noise reduction, increment of sensitivity, and simplification of the

Sasada. 2009 Zorlu, 2007 Paperno, 2004 Fan, 2006 Li, 2006 Goleman,

2nd harmonic (tuned)

Cu/Permall oy Wire

1 mm 20 mm 9 mm 18 mm 28 mm

m (squared) <sup>120</sup>m 20 m 16 m 125 <sup>m</sup>

x60 turns 400 1000 1000 250

10 mA rms sinusoidal

2nd harmonic (tuned)

16 glass coated amorphous wires

6 mA rms sinusoidal (each wire

2007

Fundamenta l mode

U-shaped amorphous wire

4 mA ac + 20 mA dc

at 10 Hz

V/T 1,600 V/T

finally mechanical stress, which is a typical source of noise.

Second harmonic

Planar Cu/Permallo y structure

2 planar coils

100 mA peak sinusoidal

consumption 8.1 mW 100 mW

sensors' configuration and development of wires with new structures.

Table 1. Comparison of several types of orthogonal fluxgates

available performances summarized here.

l mode

U-shaped amorphous wire

40 mm (20 mm sensitive length)

Diameter 120 m 16 m x 10

2 coils x1000 turns

8mA ac + 47 mA dc

Linear range ±25 T ±100 T

Resolution 215 nT 100 pT

Principle Fundamenta

Configuration

Length

N. of turns pick-up coil

Excitation Current

Frequency

Noise PSD @

Power

Sensitivity 350,000 V/T

**9. Future development** 

be around zero magnetic field and the output characteristic will be determined by the linear characteristic of the coil.

This method, however, cannot be used for coil-less fluxgates, since it has not a pick-up coil available for the generation of a compensating field (and if we add a compensation coil the sensor would not be coil-less anymore).

Therefore, the linearity of the coil-less fluxgate is an extremely important parameter, because the sensor will be used in an open loop mode. Fortunately, the coil-less fluxgate has a large linear range. In (Butta et al., 2010c) it is shown that a coil-less fluxgate with ±0.5% of full-scale non-linearity error in a ±50 µT measurement range. The non-linearity error is reduced to ±0.2% of full scale if we consider a ± 40 µT range. These values are comparable to the non-linearity of non-compensated parallel fluxgates (Kubik et al., 2009; Janosek & Ripka, 2009).

The high linearity of coil-less fluxgates comes from the working mechanism of the sensor, which is simply based on linear shifts of the circumferential BH loop. Non-linearity might be due to the non-uniformity of the helical anisotropy angle along its length. Further improvements of the manufacturing process can help make the anisotropy more uniform and improve the linearity of the sensor.
