**6.1 Working mechanism**

The structure of the sensor is identical to the wire-core orthogonal fluxgate; however a dc bias is added to the excitation current. The output voltage induced in the pick-up coil in this case will be at a fundamental frequency.

In order to understand the working mechanism underlying fundamental orthogonal fluxgates we can refer to Fig. 9. Since a dc bias is added to the excitation current, the resulting excitation field in the circumferential direction turns out to be as follows:

$$\mathbf{H}\boldsymbol{\phi} \mathbf{=} \mathbf{H}\_{\mathrm{dc}} + \mathbf{H}\_{\mathrm{ac}} \sin \left( 2 \cdot \boldsymbol{\pi} \cdot \mathbf{f} \cdot \mathbf{t} \right)$$

Fig. 9. Schematic diagram of the working mechanism of orthogonal fluxgate operated in fundamental mode.

The dc bias must be large enough to make the excitation field unipolar. As a result, magnetization won't reverse its polarity, as for a symmetrical bipolar excitation current with no dc bias. The magnetization M will oscillate between ±/2 in order to always satisfy the minimum energy condition, taking into account the field energy of H and HZ as well as anisotropy energy. In traditional fluxgates without the dc bias, the magnetization is reversed from positive to negative saturation and vice versa each period, thus the output voltage

Orthogonal fluxgates have been ignored in the past because they have higher noise than parallel fluxgates. This, in fact, moved the mainstream of research to focus on parallel fluxgates, since noise is one of the most important parameters for high precision magnetometers (other parameters such as linearity or sensitivity can be compensated to a large extent by proper design of electronics or sensors). Despite the fact that orthogonal fluxgates have recently gained new popularity due to their high spatial resolution and simple structure, their noise is still an issue for these kinds of sensors. Micro fluxgates are reported to have noise around units of nT/√Hz at 1 Hz, while wire core orthogonal fluxgates typically have 100÷400 pT/√Hz noise at 1 Hz. Without substantial reduction of

noise, orthogonal fluxgates cannot be considered competitive to parallel fluxgates.

An important step forward in the field of noise reduction in orthogonal fluxgates was made by Sasada, who proposed to operate the sensor in fundamental mode rather than in second

The structure of the sensor is identical to the wire-core orthogonal fluxgate; however a dc bias is added to the excitation current. The output voltage induced in the pick-up coil in this

In order to understand the working mechanism underlying fundamental orthogonal fluxgates we can refer to Fig. 9. Since a dc bias is added to the excitation current, the

H=Hdc+Hac sin (2 f t)

M

MZmin MZmax

Z

Fig. 9. Schematic diagram of the working mechanism of orthogonal fluxgate operated in

t

H

The dc bias must be large enough to make the excitation field unipolar. As a result, magnetization won't reverse its polarity, as for a symmetrical bipolar excitation current with no dc bias. The magnetization M will oscillate between ±/2 in order to always satisfy the minimum energy condition, taking into account the field energy of H and HZ as well as anisotropy energy. In traditional fluxgates without the dc bias, the magnetization is reversed from positive to negative saturation and vice versa each period, thus the output voltage

Hac HZ

resulting excitation field in the circumferential direction turns out to be as follows:

**6. Fundamental mode** 

harmonic mode (Sasada, 2002a).

case will be at a fundamental frequency.

H

Hdc

**6.1 Working mechanism** 

fundamental mode.

contains mainly a second harmonic. On the contrary, in the fundamental mode orthogonal fluxgate the dc bias does not allow the magnetization to reverse polarity but only to oscillate with the same frequency f of H. Therefore, the output voltage induced in the pickup coil by time varying MZ (component of M in Z direction) will be sinusoidal at a fundamental frequency.

At this point, we should point out that this sensor must be, after due consideration, classified as a fluxgate sensor, despite some similarities with other sensors. The magnetic flux within the core is indeed still gated; the sensor works at best, returning a linear and a bipolar response when the excitation field is large enough to deeply saturate the core, as typically found in fluxgates. The only difference between traditional fluxgates without dc bias and fundamental mode orthogonal fluxgates is that the flux is gated only in one polarity rather than in both polarities.

### **6.2 Offset**

So far we have not discussed the effect of anisotropy on the output voltage. The anisotropy contributes to determine the position of magnetization. For instance, if HZ=0 the resulting MZ is null only if =/2 (i.e. if anisotropy is circumferential). Contrarily, if the anisotropy is non circumferential (i.e. </2, as in Fig. 10) then MZ will be non-zero even for HZ=0 and M will lie between H and Ku (<</2). As a result, the output voltage due to time variation of MZ will be non-zero despite HZ=0. This means that the sensor's response will show an offset anytime the anisotropy is not circumferential.

Fig. 10. Non-circumferential anisotropy in a magnetic wire used as core for fundamental mode orthogonal fluxgates.

Unfortunately, non-circumferential components of anisotropy are typically found both in amorphous wires and composite Cu/Py wires. The output offset is therefore always expected in fundamental mode orthogonal fluxgates. In order to suppress the offset, a technique is proposed in (Sasada, 2002b). Sasada's method is based on the fact that the sign of the characteristic is reversed if the dc bias becomes negative, while the offset is unchanged. For HZ=0 the magnetization M will oscillate around 0' for positive dc bias and around 0'' for negative dc bias (Fig. 11). The projection of M on the Z axis will be identical because 0''=0'+ and Hac makes M rotate in the opposite direction according to the bias sign.

Orthogonal Fluxgates 33

This can be easily seen when analyzing the source of the noise. Typically, the noise of fluxgate sensors originates in the magnetic core. The reversal of magnetization from positive to negative saturation (and vice versa) involves domain wall movement, which is the origin of the Barkhausen noise. Since a pick-up coil detects time-variation of flux within the core, the Barkhausen noise will cause noise in the output voltage of the pick-up coil. Therefore, designers of fluxgates have chosen materials for the core, which are not only very easy to

This source of noise is dramatically reduced when a dc bias is added to the excitation current. If the bias is large enough to keep the core saturated for the whole period of the ac current Iac, then the magnetization is only rotated by Iac (Fig. 9) and no domain wall

Sensitivity, however, should also be considered when calculating the output noise in magnetic units. A higher dc bias Idc can significantly reduce sensitivity, because it increases the angle of magnetization M resulting in a lower projection of M on the longitudinal axis (i.e. the magnetic flux in the longitudinal direction is sensed by the pick-up coil). On the contrary, the sensitivity monotonically increases with the ac excitation current Iac (Butta et al., 2011) and therefore an increment of Iac can be useful to reduce the total noise even if a

The lowest noise of an orthogonal fluxgate in fundamental mode is then obtained selecting a pair of parameters Iac and Idc such that the sensitivity is large enough to minimize the noise but with the minimum value of the total current not too low, so as to avoid significant domain wall movement in the core. The optimum condition for noise reduction is obtained right before minor loops appear in the circumferential BH loop (Butta et al., 2011). Noise as low as 7 pT/√Hz at 1 Hz was obtained by optimizing excitation parameters, using the

The noise can be further reduced to 5 pT/√Hz at 1 Hz by using three-wire cores instead of a

As previously mentioned, orthogonal fluxgates based on microwires gained popularity due to the absence of the excitation coil, which help to simplify the manufacturing process. To this extent, the wire-core needs only a pick-up coil, which can be easily wound around it with an automatic procedure. However, the presence of a coil, even if it is simply a pick-up coil, can make the sensor unsuitable for applications where high miniaturization is required. A possible solution to this problem is to use planar coils manufactured on a substrate under the fluxgate core as in (Zorlu et al., 2006) although this solution has a more complicated structure, which needs an extra step in the manufacturing process. It would be better to have a fluxgate without any pick-up coil at all. This can be achieved with coil-less fluxgates

In a coil-less fluxgate, torsion is applied to a composite microwire with a copper core covered by a ferromagnetic layer, while an ac excitation current flows through the wire (Fig.

saturate but also present very smooth transitions between opposite saturation states.

movement occurs.

larger Iac could bring the core out of saturation.

single wire, in order to increase the sensitivity.

**7. Coil-less fluxgates** 

(Butta et al., 2008a).

**7.1 Structure of the sensor** 

magnetometer structure proposed in (Sasada & Kashima, 2009).

Fig. 11. Diagram of fundamental mode orthogonal fluxgates with positive and negative dc bias. The signal sensitivity is inverted changing the sign of dc bias but the offset is unchanged.

In order to suppress the offset we can periodically invert the dc bias and subtract the signals obtained with the positive and the negative bias. Since the sensitivity is reversed, by subtracting the characteristics we sum up the signals whereas the offset is cancelled given the fact that its sign is unchanged for both the positive and the negative bias.

The bias can be switched at a frequency much lower than the excitation frequency. For example, (Sasada, 2002b) suggests to invert the sign every 25 periods of excitation current. In this way we can reduce the effect of sudden transition from a saturation state to an opposite saturation state which could negatively affect the output noise of the sensor. To avoid the effect of bias switching on the noise we can exclude the period right before and after the transition. This can be easily done digitally (Weiss et al., 2010) or analogously using a fast solid state switch before the final low pass filter (Kubik et al., 2007).

It must be noted that all the proposed techniques require significant modification of the electronics both on the excitation side as well as on the signal conditioning circuit. While this slight complication in the electronics can be bearable for many magnetometers, it could be a non-negligible problem for applications such as portable devices.
