**3. Last and future developments**

### **3.1 Induction sensor bandwidth extension**

### **3.1.1 Dualband search-coil**

14 Will-be-set-by-IN-TECH

Fig. 12. NEMI of feedback flux amplifier: comparisons between analytic modelling & NEMI

It would be interesting to compare with other designs, as the one presented in (Grosz et al. (2010); Prance et al. (2000)) but this would require the recollection of datas describing the

When designers get their induction magnetometer. Some features of this magnetometer could be useful to know clearly what is measured. First of all, the transfer function and output noise will permit to know the dynamic and the noise equivalent magnetic induction. Next, the directionality of the magnetometer can be a key parameter in applications where the direction of the electromagnetic field must be determined accurately. Another key parameter, which is never mentionned, even if it is of great importance is the sensitivity to electric field. Induction sensors can be sensitive both to magnetic field and electric field and users must care about this last one to avoid to get wrong informations. The electric field sensitivity mechanism is symmetric to the principle of the induction sensor itself. In that case, the electric field will create a current through the wires of the sensor which will be amplify by the amplifier. An electrostatic shielding should surround the sensor and the cable until the preamplifier. This shielding must be refer to a potential (usually the ground), in the same time, this shielding (made of conductive surface) must avoid to allow circulation of eddy current (which would expel the magnetic field at frequency where the skin depth becomes smaller than the thickness of the conductive material). Finally the measurement of the electric field transfer function of the sensor could be an helpfull way to ensure the quality of the electrostatic shielding. As an example, we illustrate, on Fig. 13, a space induction magnetometer where the thermal blanket

reported in Seran & Fergeau (2005)

designs in the mentionned papers.

ensures also electrostatic shielding function.

**2.5 Calibration**

As mentionned previously, the signal from induction sensor decreases after the resonance frequency while NEMI increases whatever the electronic conditioning is. To bypass this drawback a mutual reducer made of ferromagnetic core is used between two windings Coillot et al. (2010) designed for contiguous frequency bandwidth. It allows to extend the frequency band of measurement using a single sensor. Adjusting a such dual band sensor is not an easy task and its use has sense mainly for applications where mass constraints are stringent.

### **3.1.2 Cubic search-coil**

An interseting way to reduce inductance of induction sensor and thus increase frequency resonance is presented in Dupuis (2005). It consists in implementing induction sensors on the edges of a cube 14.

In such configuration, each axis is constituted in 4 inductions sensors connected in "serie". Let us consider an induction sensor coil requiring a number of turns *N*. Each induction sensor of the cubic configuration will have *N*� = *N*/4 turns and, by connecting the single induction sensor in "serie", the total inductance will be proportionnal to 4 ∗ (*N*� )<sup>2</sup> instead of (4*N*� )2when the turns are mounted on the same core. Thus, the inductance will be 4 times lower. Since authors claim the capacitance value in the classical configuration and their cubic configuration is the same, the resonance frequency of the cubic induction sensor will be 2 times higher than for classical induction sensor allowing a desirable extend of the frequency range of use.

Fig. 15. Magnetic loop antenna description (reprinted with permission from Cavoit (2006).

Induction Magnetometers Principle, Modeling and Ways of Improvement 61

Let's compare the apparent permeability of a cubic induction sensor with the one of a single cylinder ferromagnetic core of 100mm lentgh and 4mm diameter. In the first case, the simplified formula 34 will lead to *μapp*−*<sup>x</sup>* = 450, this apparent permeability is 2 times higher

An efficient induction sensor combining a closed loop, in which magnetic field variations generates a current, and a current probe transformer to measure the current flowing trhough

This induction sensor designed for the frequency range from 100kHz up to 50MHz reaches

<sup>√</sup>*Hz*around 2MHz for a 1m\*1m square size.

A way to reduce size of induction magnetometer is presented in Grosz et al. (2010). It consists in integrating the electronic conditioning inside an hollow ferromagnetic core. They compensate the weak sensitivity of a short ferromagnetic core by using big magnetic concentrators. They try to take advantage of any free volume and they achieve extremely compact and efficient induction magnetometer at the price of a sophisticated mechanical

ASIC in CMOS technology designed for feedback flux induction sensor has been proposed by Rhouni et al. (2010). This miniature electronic circuit (photography of the chip on the left part of Fig. 16), is based on a differential input stage with big size input transistors (MP0 and MP1 on Fig. 16) which allow to reduce strongly the low frequency noise (1/f corner at 10Hz)

<sup>√</sup>*Hz* and *in* <sup>&</sup>lt; <sup>20</sup> *f A*/

<sup>√</sup>*Hz*,close to

the closed loop and feedback this current is presented in Cavoit (2006).

Copyright 2006, American Institute of Physics).

than the one of a single ferromagnetic core.

**3.2 Miniaturization of induction sensors**

**3.2.1 Integration of the electronics inside the sensor**

assembly they presented in Grosz et al. (2011).

usually encountered in MOS transistor.

**3.2.2 ASIC Application Specific Integrated Circuit**

The input noise parameters of this circuit are: *en* = 4*nV*/

the best amplifier while the size of the chip is only 2*mm* × 2*mm*.

**3.1.3 Magnetic loop antenna**

NEMI as low as 0.05 *f T*/

The presence of multiple resoncance beyond the main frequency resonance is not evoked and should be investigated.

The benefit on the apparent permeability value seems also interesting. That comes from the cubic shape which catch more flux. Let us give here a modelling first try.

We first consider cubic induction sensor consituted of ferromagnetic core of length *L* and diameter *d*. Because of the cubic shape the demagnetizing coefficient is the same in the 3 directions and we will have:

$$\rm N\_x + N\_y + N\_z = 1 \Rightarrow N\_x = N\_y = N\_z = \frac{1}{3} \tag{32}$$

Then, due the distributed ferromagnetic core on the edges, the flux The total flux caught by the cubic face Φ will be distributed between the four ferromagnetic core with a ratio corresponding to the surface ratio (*L*2/(4*d*2)). If we consider the x direction, we can derive from formula 8 the equation of the apparent permeability:

$$
\mu\_{app-x} = \frac{\mu\_r}{1 + N\_x \frac{4d^2}{L^2} \left(\mu\_r - 1\right)}\tag{33}
$$

For high values of relative permeability (*μ<sup>r</sup>* >> 1 & *Nx* <sup>4</sup>*d*<sup>2</sup> *<sup>L</sup>*<sup>2</sup> *μ<sup>r</sup>* >> 1), equation 33becomes:

$$
\mu\_{app-x} \simeq 3\frac{L^2}{4d^2} \tag{34}
$$

Fig. 15. Magnetic loop antenna description (reprinted with permission from Cavoit (2006). Copyright 2006, American Institute of Physics).

Let's compare the apparent permeability of a cubic induction sensor with the one of a single cylinder ferromagnetic core of 100mm lentgh and 4mm diameter. In the first case, the simplified formula 34 will lead to *μapp*−*<sup>x</sup>* = 450, this apparent permeability is 2 times higher than the one of a single ferromagnetic core.

### **3.1.3 Magnetic loop antenna**

16 Will-be-set-by-IN-TECH

The presence of multiple resoncance beyond the main frequency resonance is not evoked and

The benefit on the apparent permeability value seems also interesting. That comes from the

We first consider cubic induction sensor consituted of ferromagnetic core of length *L* and diameter *d*. Because of the cubic shape the demagnetizing coefficient is the same in the 3

*Nx* <sup>+</sup> *Ny* <sup>+</sup> *Nz* <sup>=</sup> <sup>1</sup> <sup>⇒</sup> *Nx* <sup>=</sup> *Ny* <sup>=</sup> *Nz* <sup>=</sup> <sup>1</sup>

Then, due the distributed ferromagnetic core on the edges, the flux The total flux caught by the cubic face Φ will be distributed between the four ferromagnetic core with a ratio corresponding to the surface ratio (*L*2/(4*d*2)). If we consider the x direction, we can derive

1 + *Nx* <sup>4</sup>*d*<sup>2</sup>

*<sup>μ</sup>app*−*<sup>x</sup>* � <sup>3</sup> *<sup>L</sup>*<sup>2</sup>

*<sup>μ</sup>app*−*<sup>x</sup>* <sup>=</sup> *<sup>μ</sup><sup>r</sup>*

<sup>3</sup> (32)

*<sup>L</sup>*<sup>2</sup> (*μ<sup>r</sup>* <sup>−</sup> <sup>1</sup>) (33)

*<sup>L</sup>*<sup>2</sup> *μ<sup>r</sup>* >> 1), equation 33becomes:

<sup>4</sup>*d*<sup>2</sup> (34)

cubic shape which catch more flux. Let us give here a modelling first try.

from formula 8 the equation of the apparent permeability:

For high values of relative permeability (*μ<sup>r</sup>* >> 1 & *Nx* <sup>4</sup>*d*<sup>2</sup>

Fig. 14. Cubic induction sensor.

should be investigated.

directions and we will have:

An efficient induction sensor combining a closed loop, in which magnetic field variations generates a current, and a current probe transformer to measure the current flowing trhough the closed loop and feedback this current is presented in Cavoit (2006).

This induction sensor designed for the frequency range from 100kHz up to 50MHz reaches NEMI as low as 0.05 *f T*/ <sup>√</sup>*Hz*around 2MHz for a 1m\*1m square size.

### **3.2 Miniaturization of induction sensors**

### **3.2.1 Integration of the electronics inside the sensor**

A way to reduce size of induction magnetometer is presented in Grosz et al. (2010). It consists in integrating the electronic conditioning inside an hollow ferromagnetic core. They compensate the weak sensitivity of a short ferromagnetic core by using big magnetic concentrators. They try to take advantage of any free volume and they achieve extremely compact and efficient induction magnetometer at the price of a sophisticated mechanical assembly they presented in Grosz et al. (2011).

### **3.2.2 ASIC Application Specific Integrated Circuit**

ASIC in CMOS technology designed for feedback flux induction sensor has been proposed by Rhouni et al. (2010). This miniature electronic circuit (photography of the chip on the left part of Fig. 16), is based on a differential input stage with big size input transistors (MP0 and MP1 on Fig. 16) which allow to reduce strongly the low frequency noise (1/f corner at 10Hz) usually encountered in MOS transistor.

The input noise parameters of this circuit are: *en* = 4*nV*/ <sup>√</sup>*Hz* and *in* <sup>&</sup>lt; <sup>20</sup> *f A*/ <sup>√</sup>*Hz*,close to the best amplifier while the size of the chip is only 2*mm* × 2*mm*.

**5. References**

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*Instruments* Vol. 77.

10(2): 255–260.

11(4): 1088–1094.

160(1-3): 329–332.

*App. Phys. Lett.* Vol. 98(10).

*Sensors and Actuators A* Vol. 91: 46–50.

Superieure de Cachan.

0): 351–357.

Aharoni, A. (1998). Demagnetizing factors for rectangular ferromagnetic prisms, *Journal of*

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Bozorth, R. & Chapin, D. (1942). Demagnetizing factors of rods, *Journal of Applied Physics* Vol.

Cavoit, C. (2006). Magnetic measurements in the range of 0.1-50mhz, *Review of Scientific*

Chen, D., Pardo, E. & Sanchez, A. (2006). Fluxmetric and magnetometric demagnetizing

Coillot, C., Moutoussamy, J., Lebourgeois, R., Ruocco, S. & Chanteur, G. (2010). Principle

Coillot, C., Moutoussamy, J., Leroy, P., Chanteur, G. & Roux, A. (2007). Improvements of the

Ferrieux, J.-P. & Forest, F. (1999). *Alimentations a decoupage - convertisseurs a resonance*, DUNOD. Grosz, A., Paperno, E., Amrus, S. & Zadov, B. (2011). A three-axial search coil magnetometer

Grosz, A., Paperno, E., Amrusi, S. & Liverts, E. (2010). Integration of the electronics and batteries inside the hollow core of a search coi, *Journal of App. Phys.* Vol. 107. Hayakawa, M. (2007). Monitoring of ulf (ultra-low-frequency) geomagnetic variations

Lebourgeois, R., Fur, C. L., Labeyrie, M. & Ganne, J.-P. (1996). Permeability mechanisms in

Lichtenberger, J., Ferencz, C., Bodnar, L., Hamar, D. & Steinbach, P. (2008). Automatic whistler detector and analyzer system, *Journal of Geophysical Research* Vol. 113. Lukoschus, D. (1979). Optimization theory for induction-coil magnetometers at higher frequencies, *IEEE Transactions on Geoscience electronics* GE-17(3): 56–63. Macedo, R., Cardoso, F. A., Cardoso, S., Freitas, P. P., Germano, J. & Piedade, M. S. (2011).

Moutoussamy, J. (2009). *Ph. D. Dissertation, Nouvelles solutions de capteurs a effet de*

Osborn, J. (1945). Demagnetizing factors of the general ellipsoids, *Physical Review* Vol. 7(No.

Pannetier, M., Fermon, C., le Goff, G., Simola, J. & Kerr, E. (2004). Femtotesla magnetic field

Pfaffling, A. (2007). Helicopter electromagnetic sea ice thickness estimation: An induction method in the centimetre scale, *Reports on Polar and Marine Research* 553. Popovic, R., Randjelovic, Z. & Manic, D. (2001). Integrated hall-effect magnetic sensors,

measurement with magnetoresistive sensors, *Science* (304).

Dupuis, J. (2005). Induction magnetometer, us patent 2005 0156601 a1.

associated with earthquake, *Sensors* Vol.7: 1108–1122.

factors for cylinders, *Journal of Magnetism and Magnetic Materials* Vol. 306(1): 351–357.

and performance of a dual-band search coil magnetometer : A new instrument to investigate fluctuating magnetic fields in space, *IEEE Sensors Journal* Vol.

design of search coil magnetometer for space experiments, *Sensor Letters* Vol. 5: 1–4.

optimized for small size, low power and low frequencies, *IEEE Sensors Journal* Vol.

high frequency polycrystalline ferrites, *Journal of Magnetism and Magnetic Materials*

Self-powered, hybrid antenna-magnetoresistive sensor for magnetic field detection,

*magnetoimpedance geante : Principe, Modelisation et Performances.*, Ecole Normale

*Applied Physics* Vol. 83(6): 3432–3434.

(n.d.a). (n.d.b).

Fig. 16. Design of a feedback flux amplifier ASIC (Fig. on the top : schematic of the ASIC circuit, Fig. on the left side: input noise measurement in *nV*/ <sup>√</sup>*Hz*, Fig. on the right : photography of the chip)

### **4. Conclusion**

The method presented in this chapter to modelize the induction sensor is based on basic knowledges that can be used to study other types of sensors: elektrokinetics model, noise contributions that must be inventoriated, the computation of the sensitivity... The analytical modelling helps the beginner to become familiar with the sensor and also to manipulate general principles. Even if new technologies can offer excellent performances, in many applications induction sensors remain the best way to achieve AC magnetic field measurements. They will continue to play a role both as induction sensor and combined with other technologies Macedo et al. (2011). One can notice that in some applications, induction sensors have been replaced by other kinds of sensors, like the well known example of Giant MagnetoResistance which have replace coil in the read head of hard disks. Another example is the replacement of the pick-up coil function (like magnetoresistance in squid Pannetier et al. (2004) but also in fluxgates). When the sensitivity does matter the induction sensors still remains an efficient solution. Induction sensors is maybe not the futur of magnetometers but a stone to build this futur.

### **5. References**

(n.d.a).

18 Will-be-set-by-IN-TECH

Fig. 16. Design of a feedback flux amplifier ASIC (Fig. on the top : schematic of the ASIC

The method presented in this chapter to modelize the induction sensor is based on basic knowledges that can be used to study other types of sensors: elektrokinetics model, noise contributions that must be inventoriated, the computation of the sensitivity... The analytical modelling helps the beginner to become familiar with the sensor and also to manipulate general principles. Even if new technologies can offer excellent performances, in many applications induction sensors remain the best way to achieve AC magnetic field measurements. They will continue to play a role both as induction sensor and combined with other technologies Macedo et al. (2011). One can notice that in some applications, induction sensors have been replaced by other kinds of sensors, like the well known example of Giant MagnetoResistance which have replace coil in the read head of hard disks. Another example is the replacement of the pick-up coil function (like magnetoresistance in squid Pannetier et al. (2004) but also in fluxgates). When the sensitivity does matter the induction sensors still remains an efficient solution. Induction sensors is maybe not the futur of magnetometers

<sup>√</sup>*Hz*, Fig. on the right :

circuit, Fig. on the left side: input noise measurement in *nV*/

photography of the chip)

but a stone to build this futur.

**4. Conclusion**

(n.d.b).


**Part 2** 

**Applications** 

