**2. Working principle**

A detailed explanation of the working mechanism of orthogonal fluxgates is given in (Primdahl, 1970) for the basic tubular structure proposed in (Alldredge, 1958).

Let us consider a tube of soft magnetic material as shown in Fig. 2a, exposed to a sinusoidal excitation field in the circumferential direction H (generated by a toroidal coil - not shown to simplify the drawing) and to an axial field HZ. The material is assumed to be isotropic with a simplified MH loop shown in Fig. 2b; the magnetization M lies between HZ and H in order to satisfy the minimum energy condition.

The core is a cylinder of soft magnetic material, with a toroidal excitation coil wound around it. The excitation current flows through the toroidal coil generating excitation H in the circumferential direction. The core is periodically saturated in the circumferential direction by H in opposite polarities. Finally, the output voltage is obtained with a pick-up coil as it was in the parallel fluxgate. Once more, when the external field Hdc is applied in the axial direction, even harmonics arise in the output voltage. In this case, the sensor is called an *orthogonal* fluxgate because the measured field Hdc is orthogonal to the x-y plane

Orthogonal fluxgates have been originally proposed in (Alldredge, 1952), both with a cylindrical core and a wire-core. Later, Schonsted proposed an orthogonal fluxgate based on a magnetic wire wound in a helical shape around a conductive wire carrying an excitation current (Schonsted, 1959). Several years later, orthogonal fluxgates appeared again in (Gise & Yarbrough, 1975) where the authors proposed an orthogonal fluxgate with a core obtained by electroplating a Permalloy film on a 6.3 mm diameter glass cylinder after the deposition of a copper substrate. The sensor showed large hysteresis, and it was later improved in (Gise & Yarbrough, 1977) with a core composed of a 3.2 mm diameter copper cylinder and of an electroplated shell on it. An orthogonal fluxgate based on a composite wire, manufactured with a conductive core and electroplated magnetic thin film (about 1 µm thick), was also proposed in (Takeuchi, 1977) after which orthogonal fluxgates were

From the early years, indeed, parallel fluxgates have been always preferred to orthogonal fluxgates because they usually offer better performances, especially lower noise. Thus, the

The development and improvement of techniques for the production of microwires obtained in the last decades (Vázquez et. al, 2011) have made it now possible to manufacture soft magnetic wires with an extremely narrow diameter (50-100 µm) and high permeability. Thanks to this, the principle of the orthogonal fluxgate has been rediscovered. For example, an orthogonal fluxgate sensor based on a glass covered Cobased alloy with a very narrow diameter was proposed in (Antonov et al., 2001) and a similar sensor with a Permalloy/copper wire was used as the core with a 20 µm diameter

Orthogonal fluxgates based on a microwire gained new popularity mainly due to the rising

A detailed explanation of the working mechanism of orthogonal fluxgates is given in

Let us consider a tube of soft magnetic material as shown in Fig. 2a, exposed to a sinusoidal excitation field in the circumferential direction H (generated by a toroidal coil - not shown to simplify the drawing) and to an axial field HZ. The material is assumed to be isotropic with a simplified MH loop shown in Fig. 2b; the magnetization M lies between HZ and H in

(Primdahl, 1970) for the basic tubular structure proposed in (Alldredge, 1958).

mainstream of research and development focused on parallel fluxgates.

requests for miniaturized sensors of magnetic fields.

order to satisfy the minimum energy condition.

where the excitation field H lays.

almost forgotten.

(Li et al., 2004).

**2. Working principle** 

The axial field is assumed to be much lower than the saturation field HS, therefore during the part of the period when H<HS the core is not saturated. Under these conditions, when H increases, then both the angle and the amplitude of M also increase, while the component of M in the axial direction MZ does not change because HZ is constant. However, when H reaches the amplitude where the total field is Htot=HS, then the core gets saturated; if H further increases, then the amplitude of M does not increase anymore and the only effect of H is to rotate M along the circumference which describes the saturation state (Fig. 2c). Under this condition MZ is not constant anymore but it starts decreasing as the M reaches the saturated state (Fig. 2e). As a result, a variation of the magnetic flux occurs in the axial direction and a voltage is induced in the pick-up coil (Fig. 2d).

Fig. 2. Working principle of orthogonal fluxgates.

Since the excitation field is sinusoidal the saturation is reached twice per period (i.e. in both the positive and negative directions). This means that the induced voltage will contain even harmonics of the excitation frequency, wherein the second harmonic is generally extracted by means of a lock-in amplifier to obtain the output signal. The amplitude of the induced voltage depends on MZ, which in turn is determined by HZ. Finally, the amplitude of the even harmonics gives us a measurement of the axial field HZ.

If the direction of HZ is reversed MZ becomes negative and the phase of the induced voltage is shifted by rad. This means that the orthogonal fluxgate is able to distinguish between positive and negative fields; usually, the real part of the second harmonic is used as an

Orthogonal Fluxgates 23

detailed characterization of the core's circular and axial magnetic properties is, therefore,

As previously mentioned, the availability of microwires suitable for the fluxgate cores gave

Fig. 4 shows the structure of an orthogonal fluxgate based on a magnetic wire core. The excitation current Iex is injected to the magnetic wire and generates a circumferential field

HZ

In this structure, the excitation coil is not required because the excitation field is generated by the current flowing through the wire. Therefore, the structure of the sensor is extremely simplified and the manufacturing of the sensor becomes easier. Even more importantly, the lack of an excitation coil makes it possible to significantly reduce the dimensions of the sensor. This plays strongly in favor of orthogonal fluxgates, because it makes them suitable

H

Fluxgates based on a microwire became popular also because during the last years the production techniques of magnetic wires have been subject of deep investigation. For example, in (Li et al., 2003) the effect of a magnetic field is shown during the electrodeposition of the NiFe film on a copper wire. By properly tuning the magnetic field's amplitude and direction it is possible to control the anisotropy direction (particularly useful for optimization of sensitivity and offset of the sensors) as well as to improve film uniformity, softness and grain size. Moreover, it has been shown that it is possible to strongly reduce the coercivity of electroplated Permalloy films as well as to increase their permeability by using pulse current instead of dc current for the electroplating process (Li et

Uniformity of the film is improved by a Cu seed layer sputtered on the Cu wire before electroplating because it minimizes the roughness of the surface, helping to reduce the coercivity. The effect of film thickness on the grain size, and finally on the coercivity, has also been studied in (Seet et al., 2006) where it is shown that grain size is lower for larger thickness. However, it is recommended to keep current density constant during the electroplating because if we use a constant current as the thickness increases, the current

always necessary before applying any model to the sensor.

H while a pick-up coil is wound around the wire as usual.

new popularity to the orthogonal fluxgate principle.

Fig. 4. Orthogonal fluxgate based on a magnetic wire.

al., 2006).

for current applications where high miniaturization is required.

density decreases, and this is shown to increase the grain size.

**3. Wire-core orthogonal fluxgates** 

Iex

output signal in order to take into account the phase of the voltage and to obtain an antisymmetrical function, which allows to discriminate the sign of the field.

### **2.1 Gating curve**

A gating curve is usually measured in order to understand how the flux is gated within the core of a fluxgate. We now consider a real MH loop as in Fig. 3b (without the simplification used in Fig. 2) and we derive the BZ-H curve that describes the gating occurring in the orthogonal fluxgate core. The amplitude of the peaks in the gating curve is proportional to HZ since they correspond to MZ out of saturation. Moreover, the position of the peaks is not constant. For a higher HZ the saturation is reached for a lower value at H, causing the distance between the peaks to decrease (Fig.3).

Fig. 3. Gating curves of an orthogonal fluxgate.

The peaks of the gating curve become negative for HZ<0 while no peaks appear when HZ=0. This means that the voltage induced in the pick-up coil is null for no measured field. This becomes extremely important when the sensor is operated in feedback mode with its working point kept around zero. In this case, the output voltage will be always around zero, making it possible to use high gain amplification to increase the signal-to-noise ratio.

### **2.2 Effect of anisotropy**

We must highlight that the model described above applies only if the magnetic core is isotropic or if it has circumferential anisotropy. In case of non-circumferential anisotropy the direction of magnetization M is determined not only by H and HZ but also by the anisotropy. In this case, the angle of M is obtained by minimizing the total energy of M, taking into account the field energy of H and HZ as well as the anisotropy energy (Jiles, 1991).

Non-circumferential anisotropy can in fact deviate the magnetization from the circumferential plane and give rise to an output voltage even for a zero measured field, significantly changing the gating curves. In such cases, a more detailed model that takes into account the effect of anisotropy should be used (Butta & Ripka, 2008b).

We should also note that in magnetic wires, the anisotropy direction and strength can significantly change according to geometric parameters and manufacturing methods. A

output signal in order to take into account the phase of the voltage and to obtain an anti-

A gating curve is usually measured in order to understand how the flux is gated within the core of a fluxgate. We now consider a real MH loop as in Fig. 3b (without the simplification used in Fig. 2) and we derive the BZ-H curve that describes the gating occurring in the orthogonal fluxgate core. The amplitude of the peaks in the gating curve is proportional to HZ since they correspond to MZ out of saturation. Moreover, the position of the peaks is not constant. For a higher HZ the saturation is reached for a lower value at H, causing the

The peaks of the gating curve become negative for HZ<0 while no peaks appear when HZ=0. This means that the voltage induced in the pick-up coil is null for no measured field. This becomes extremely important when the sensor is operated in feedback mode with its working point kept around zero. In this case, the output voltage will be always around zero,

M

BZ

H

H

We must highlight that the model described above applies only if the magnetic core is isotropic or if it has circumferential anisotropy. In case of non-circumferential anisotropy the direction of magnetization M is determined not only by H and HZ but also by the anisotropy. In this case, the angle of M is obtained by minimizing the total energy of M, taking into

Non-circumferential anisotropy can in fact deviate the magnetization from the circumferential plane and give rise to an output voltage even for a zero measured field, significantly changing the gating curves. In such cases, a more detailed model that takes into

We should also note that in magnetic wires, the anisotropy direction and strength can significantly change according to geometric parameters and manufacturing methods. A

making it possible to use high gain amplification to increase the signal-to-noise ratio.

account the field energy of H and HZ as well as the anisotropy energy (Jiles, 1991).

account the effect of anisotropy should be used (Butta & Ripka, 2008b).

symmetrical function, which allows to discriminate the sign of the field.

distance between the peaks to decrease (Fig.3).

Fig. 3. Gating curves of an orthogonal fluxgate.

**2.2 Effect of anisotropy** 

**2.1 Gating curve** 

detailed characterization of the core's circular and axial magnetic properties is, therefore, always necessary before applying any model to the sensor.
