Fractional Modeling of the AC Large-Signal Frequency Response in Magnetoresistive Current Sensors

Abstract

Fractional calculus is considered when derivatives and integrals of non-integer order are applied over a specific function. In the electrical and electronic domain, the transfer function dependence of a fractional filter not only by the filter order n, but additionally, of the fractional order α is an example of a great number of systems where its input-output behavior could be more exactly modeled by a fractional behavior. Following this aim, the present work shows the experimental ac large-signal frequency response of a family of electrical current sensors based in different spintronic conduction mechanisms. Using an ac characterization set-up the sensor transimpedance function Z t ( jf ) is obtained considering it as the relationship between sensor output voltage and input sensing current, ( jf ) . The study has been extended to various magnetoresistance sensors based in different technologies like anisotropic magnetoresistance (AMR), giant magnetoresistance (GMR), spin-valve (GMR-SV) and tunnel magnetoresistance (TMR). The resulting modeling shows two predominant behaviors, the low-pass and the inverse low-pass with fractional index different from the classical integer response. The TMR technology with internal magnetization offers the best dynamic and sensitivity properties opening the way to develop actual industrial applications.

Frequency Response of MAPbI3 Perovskites for Photodetection Application

“…For this purpose, the particular shape of the pole requires to introduce a fractional capacitor, i.e., a capacitor with impedance Z = 1/((j 𝜔) N C), commonly used to model the electrical response of not pure electrical systems (vegetables, minerals…). [32] In the MAPbI 3 films under study, C 1 = 10 −8 -10 −7 s N1 Ω −1 , with N1 = 0.01-0.1, as deduced in Figure 2. [32] Since N1 is close to 0, the first RC network exhibits quasi-resistive behavior, wherein the deviations from a pure resistance reproduce decrease observed in the magnitude of I ph for frequencies below 10 kHz, see Figure 3.…”

“…[32] In the MAPbI 3 films under study, C 1 = 10 −8 -10 −7 s N1 Ω −1 , with N1 = 0.01-0.1, as deduced in Figure 2. [32] Since N1 is close to 0, the first RC network exhibits quasi-resistive behavior, wherein the deviations from a pure resistance reproduce decrease observed in the magnitude of I ph for frequencies below 10 kHz, see Figure 3. Thus, C 1 can be linked to the slow response in photocurrent introduced by shallow traps.…”

Sensors and Technologies in Spain: State-of-the-Art

“…In [ 52 ], the experimental AC large-signal frequency response of a family of electrical current sensors based in different spintronic conduction mechanisms is shown. The transimpedance sensor function is obtained considering it as the relationship between sensor output voltage and input sensing current.…”

Sufficient Criteria for the Absence of Global Solutions for an Inhomogeneous System of Fractional Differential Equations

“…The theory of fractional calculus provides useful mathematical tools for modeling several phenomena from Science and Engineering (see e.g., [1][2][3][4][5][6][7]). This fact has motivated researchers to investigate fractional differential equations in various directions including theory (existence and uniqueness of solutions [8][9][10], comparison principles [11,12], blow-up profile of solutions [13,14]), and numerical methods (see e.g., [15][16][17][18][19]).…”