## 4 State of Art
### Magnetic Force Sensors
#### 4.3.2 Terfenol-D  
The first work combining Terfenol-D alloy with optical fiber sensors to measure static magnetic fields was reported by [PERSON] _et al_[50], see Figure 14. The magnetostrictive sensor with temperature compensation scheme was composed by two different alloys with similar thermal expansion coefficient, being one of them Terfenol-D and the other Monel 400. The mechanical expansion of both materials due to temperature and magnetic field variations was detected by the two FBGs attached. The spectral difference between the two Bragg wavelengths was proportional to the amplitude of the magnetostriction, and, the wavelength shift produced by the grating bonded to the non-magnetic alloy (Monel 400) was proportional to the temperature variation. **Figure 14.** Schematic diagram of the fiber sensor proposed by [PERSON] _et al_[50]. **Figure 13.** Experimental arrangement used for measuring electric current on high voltage systems. For applied magnetic fields smaller than 4.7 \(\times\) 10\({}^{-4}\) A/m (B \(<\) 60 mT) a linear response of the fiber sensor was verified. The spectral sensitivity in this range was independent of temperature, having a value of (2.31 \(\pm\) 0.05) \(\times\) 10\({}^{-5}\) nm/(A\({}^{2}\)m\({}^{-2}\)). In order to compensate the temperature effects in the FBG based on magnetostrictive materials, two simple techniques were demonstrated by [PERSON] _et al_. [65]. The first technique consisted of two FBGs placed perpendicular to each other and bounded onto a single Terfenol-D layer material. The second technique, two FBGs were stacked onto two different magnetostrictive bars (Terfenol-D and nickel) and physically parallel with each other. The materials used had similar thermal expansion coefficients but with magnetostrictive coefficients of opposite signs. The two techniques were capable of measuring the magnetostrictive effects with temperature insensitivity. The sensitivities due to the magnetic field were 2.44 \(\times\) 10\({}^{-4}\) nm/mT and 1.8 \(\times\) 10\({}^{-4}\) nm/mT, for the first and second techniques, respectively. An electric current optical sensor based on a passive prototype magnetostriction device for high power applications was developed and demonstrated by [PERSON] _et al_. [66]. The optical current sensor concept was achieved by attaching a piece of Terfenol-D to a FBG, thus producing mechanical strain that was proportional to the magnetic field amplitude. In order to obtain a linear response from the magnetostrictive alloy, the material was subjected to mechanical pre-stress and DC magnetic field bias tuning. The sensor had a linear electrical current range from 100-1,000 A, with a measured phase shift of 30\({}^{\circ}\) for a frequency signal at 60 Hz. [PERSON] _et al_. [67] demonstrated a magnetic field sensor based on dual FBG configuration consisting essentially in a rod of Terfenol-D attached to the optical fiber. One of the gratings was fixed on both ends of the magnetostrictive alloy, while the other was only attached on one point, being the other end free to move. The configuration of dual FBGs was employed for point measurement reference and for easy temperature compensation. The maximum sensitivity achieved was 0.018 nm/mT when the applied magnetic flux density was smaller than 70 mT. In 2006, [PERSON] _et al_. [68] presented a fiber optic AC current sensor for high voltage lines based on an uniform FBG mounted on a Terfenol-D piece. An innovative way of processing the optical signal from the sensing head allowed a simultaneous measurement of temperature and the AC current. The first physical parameter was coded on wavelength shift, while the second one was coded on the amplitude of the signal. The sensor could also operate at long distances with a capacity to be multiplexed. Also a sensor for simultaneous measurement of AC current and temperature was reported by [PERSON] _et al_. [69]. The device was composed of a magnetically biased Terfenol-D piece fixed to one FBG.