**3.2 Excitation field inside the wire**

One of the main drawbacks of wire-based orthogonal fluxgates is that the excitation field is not uniform along the distance from the centre of the wire. This comes directly from Ampere's law. Let us consider a magnetic wire with uniform current distribution (i.e. we consider skin effect negligible). The excitation field H increases linearly from radius r=0, the centre of the core, to its maximum at the border of the wire (r=R). If we define HS as the

24 Magnetic Sensors – Principles and Applications

Besides the lack of an excitation coil, one of the main advantages of wire-core fluxgates is the diameter of the wire, usually very narrow (several tens of µm). A narrow diameter is advantageous not only for miniaturization, but also for improvement of spatial resolution in magnetic field measurement. Let us consider, for instance, a magnetic field HZ with constant gradient along the x direction, as shown in Fig. 5. Parallel fluxgates must use either a ring or a racetrack core to reduce the demagnetizing factor and compensate voltage peaks for zero measured fields. Such core has two sensitive sections in the measurement direction (namely A and B in Fig.5, left) which sense different fields HZA and HZB. The total field measured by

Parallel fluxgates rarely have a core narrower than 1÷2 cm, limiting the spatial resolution to such level. On the contrary, orthogonal fluxgates have the sensitive cross section of a single wire making it possible to measure the magnetic field HZ in the single spot, with resolution limited by the diameter. Since typical wires used for orthogonal fluxgates have diameters up to 100 µm, the spatial resolution of orthogonal fluxgates is two orders of magnitude better than conventional parallel fluxgates. To this extent, they were successfully employed for applications such as magnetic imaging. For instance, in (Terashima & Sasada, 2002) a gradiometer based on a wire-core orthogonal flux is presented. The gradiometer is used to measure magnetic fields emerging from a specimen of 3% grain oriented silicon steel, with steps of 50 µm (the diameter of the amorphous wire used as a core is 120 µm). Since the spatial resolution of the sensor is very high it was possible to measure the magnetic field emerging from a single domain, and then graphically represent the domain's topology of

Parallel fluxgates, based on PCB technology, with an ultra thin core (50 µm) have also been proposed (Kubik et al., 2007). In this case, the spatial resolution is remarkably improved in y

One of the main drawbacks of wire-based orthogonal fluxgates is that the excitation field is not uniform along the distance from the centre of the wire. This comes directly from Ampere's law. Let us consider a magnetic wire with uniform current distribution (i.e. we consider skin effect negligible). The excitation field H increases linearly from radius r=0, the centre of the core, to its maximum at the border of the wire (r=R). If we define HS as the

y x

HZB

Fig. 5. Spatial resolution in parallel (left) and orthogonal fluxgates (right).

HZA

**3.1 Spatial resolution** 

the sample.

the parallel fluxgate will be the average of HZA and HZB.

direction, but it is still poor in the x direction.

HZ

**3.2 Excitation field inside the wire** 

minimum field to saturate the material1, we observe that the inner part of the wire, for r<, where H<HS is not fully saturated. On the contrary, when we use a cylindrical core excited by a toroidal coil, then the whole core is equally saturated.

Saturation is a vital requirement for the proper working of a fluxgate, wherein only the outer saturated shell will contribute to fluxgate mode whereas the inner unsaturated part of the core will not act as a fluxgate. Most important, having the central part of the core unsaturated causes hysteresis in the output characteristic of the fluxgate. Indeed, if we apply an axial magnetic field to the wire this will magnetize the central part of the core in its direction. Since that part of the core is not saturated, the magnetization cannot be restored by the excitation field through saturation in the circumferential direction. The centre of the core will then naturally follow its hysteresis loop.

To this extent, it is very important to achieve the full saturation of the core to avoid the hysteretic behaviour of the sensor. Unfortunately, it is impossible to saturate the wire in its entire cross-section, since this would require an infinite current. Instead, we will always have an inner portion of the wire unsaturated.

Fig. 6. Magnetic wire with uniform current distribution. The magnetic field increases linearly within the wire and only the outer shell where H>HS is saturated.

Amorphous wires are often used as cores for orthogonal fluxgates. In this case, the wire has an inner cylinder with magnetization in the axial direction and a shell with radial or circumferential magnetization (Fig. 7) in case of positive or negative magnetostriction respectively (Vázquez & Hernando, 1996).

<sup>1</sup>The saturation field is clearly not a brick wall border. The amount of saturated material asymptotically increases when the magnetic field grows. Therefore, we cannot define a clear border between the saturated and unsaturated state. However, we can define a condition when the core can be considered saturated from a practical point of view. That occurs when any increment of the magnetic field does not cause any significant change in the working mechanism of the fluxgate.

Orthogonal Fluxgates 27

must carefully weigh the advantages of lager sensitivity given by a thicker magnetic shell against the disadvantages caused by an increment of current required for the saturation.

0 R

Rc

r

r

H

Hm

J

Fig. 8. Composite wire with copper core and magnetic shell. The current flows entirely

Skin effect, however, is not always negligible, especially when the sensor is operated at a high frequency in order to increase the sensitivity. In this case, the excitation current drains from the copper core to the magnetic shell, reducing the magnetic field in the magnetic shell. Depending on the actual current distribution, the magnetic field can strongly change. Numerical simulation is usually employed in order to predict the current distribution within composite wires (Sinnecker et al., 2002). The penetration depth strongly depends on the conductivity of both the conductive core and the magnetic shell as well as on the permeability of the latter. Therefore, a general value for a limit frequency to avoid draining the current to the magnetic shell cannot be given. Numerical simulation is suggested to

Finally, designers of orthogonal fluxgates should carefully choose their operating frequency. On the one hand, a higher frequency increases the sensitivity, which contributes to the reduction of noise, whereas on the other hand, a higher frequency can cause parts of the wire not to be completely saturated, incrementing the noise (besides the hysteresis and perming effect). The excitation frequency should be chosen as a compromise between these

A more complex structure has been proposed by (Butta et al., 2009a) to overcome the problem of the current draining to the magnetic shell due to the skin effect. This is carried out by putting a glass layer between the copper core and the magnetic shell. The glass layer provides electrical insulation, helping thus to keep the excitation current flowing entirely within the copper core, regardless of the operating frequency. Even if the skin effect should occur in the copper core, given Ampere's law, this does not affect the magnetic field

In order to manufacture a composite structure with glass insulation between the copper and the magnetic shell, glass coated copper wires are used as a base. Following this procedure, a

through the copper core so that the magnetic shell is fully saturated.

HS

predict current distribution within the wire.

generated from the copper's diameter.

two opposite effects.

**3.4 Glass insulation** 

In this case the central part of the core will never contribute to the fluxgate effect, which will be given only by the outer shell. The inner part of the core usually shows a bistable behaviour, which means that its magnetization will switch direction upon the application of an axial field larger than the critical field. A fluxgate base on such wires will be affected by the perming effect (i.e. shift of the sensor's output characteristic after the application of a large magnetic field) due to the switching of the magnetization in the central part of the wire.

Fig. 7. Cross-section of a magnetic wire with bamboo structure, in case of negative (left) and positive (right) magnetostriction.
