IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 1, JANUARY 2015 4000504 Magnetostriction Offset of Fluxgate Sensors Pavel Ripka, Mattia Butta, and Michal Pribil Faculty of Electrical Engineering, Czech Technical University in Prague, Prague 166 36, Czech Republic Magnetostriction is generally believed to cause excessive offset and noise in fluxgate sensors. We show that although the magnetostrictive core tapes are susceptible for offset instability, there is no simple direct mechanism for the generation of the second harmonic signal by magnetostriction. Offset and noise are caused by a variation of local core properties and mechanical stresses together with magnetoelastic coupling. Index Terms—Fluxgate sensor, magnetic sensor, magnetostriction. I. I NTRODUCTION W EINER [1] declared that magnetostriction causes excessive offset and noise in fluxgate sensors. This paper has become classical and widely accepted [2]. Since that time near-zero-magnetostrictive alloys have been used for fluxgate cores and not much further attention was paid to this topic. In the first part of this paper, we critically re-examine the theoretical description in [1] and show why we believe that it is not correct. According to our analysis, magnetostriction itself without dc field component cannot cause the second harmonic signal and therefore the offset. In Section II, we experimentally investigate the correlation between magnetostriction of the core material and offset or noise of the fluxgate sensor. For this paper, we prepared a series of electrodeposited fluxgate cores with the same geometry and different magnetostriction. We also describe experimental conditions, as both offset and noise strongly depend on the working point. We believe that this paper will help to understand problem, which was marked as unsolved in [3]. II. THEORY Weiner [1] has influenced generations of researchers and fluxgate designers. According to Weiner, periodic elongation of the sensor core caused by magnetostriction is a direct source of second harmonic. This signal cannot be distinguished from field- dependent signal and therefore causes sensor offset. The first reactions to Weiner’s theory was negative; Gordon et al. [4] attributed the dependence of noise on magnetostriction to indirect coupling of external stresses rather than by direct action of magnetostriction. Scouten [5] pointed out that magnetostriction should cause field-dependent signal rather than offset. This problem remained unsolved since then. Scouten has also shown using small search coils that sensor noise is a small-scale phenomenon compared with fluxgate mechanism. This indicates that the noise (and also the offset) is caused by random local isolated core volumes, which are not saturated by the excitation field in particular magnetization cycle. Manuscript received June 6, 2014; revised August 4, 2014 and August 12, 2014; accepted August 13, 2014. Date of current version January 26, 2015. Corresponding author: P. Ripka (e-mail: ripka@fel.cvut.cz). Digital Object Identifier 10.1109/TMAG.2014.2349171 Narod et al. [6] observed that minimum noise does not occur at alloys with zero magnetostriction, but at alloy with minimum core losses, which has both low saturation induction and coercivity. Nielsen et al. [7] selected and processed the core material to minimize magnetostriction. However, even the finest fluxgate cores developed for Oersted satellite project have significant magnetostriction, as they emit audible acoustic noise. First of all, we should highlight that the Weiner’s paper is based on wrong formulas: in [1, eqs. (2) and (7)], B and H should not be in absolute value. The first formula is derived from the induction law, which contains no absolute value. In the second case, dL depends on H 2 , which means that dL /dH should depend on H , not | H |. Weiner apparently misinterpreted Figs. 5 and 6 (which were taken from Bozorth and already contain absolute values of dL /dH ). As a result also in [1, eq. (8)] is wrong. Let us try to find offset sources related to global (i.e., constant in the whole volume of the core) magne- tostriction. Offset is second harmonic component of voltage induced at the sensor output when the measured field H dc is zero. Our description starts from the Faraday law. If we neglect the demagnetization effect, we can write for the induced voltage V i = − d  dt = d ( NAμ 0 μ r H ) dt = μ 0 N  HA d (μ r ) dt + H μ r d ( A) dt + Aμ r d ( H ) dt  (1) where the magnetic flux  depends on the field H , number of turns N , and time-dependent permeability μ r (t ), which is modulated by the excitation current. Here, also A(t ) is time- dependent due to the magnetostriction. The first term in (1) corresponds to the fluxgate effect, second term corresponds to magnetostriction, and third term corresponds to the induction effect. If the fluxgate has double- rod, racetrack, or ring core, most of the signal is suppressed by symmetry; however, this is irrelevant for the offset study, as the symmetry is never perfect. The core field H has two components: 1) ac excitation field H exc and 2) dc measured field H dc . If we search for magnetostrictive offset, we suppose that H dc = 0. We can also suppose that H = H exc contains no even harmonics. 0018-9464 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.