## 3 Results and Discussion
### Evolution of the Microwave Scattering Properties in Co-Based MWs Linear Arrays
In contrast, the \(f_{\text{min}}\) is barely modified by this effect due to its electric dipole character (Equation (2)). To compare the evolution of the field-dependence of the \(S_{21}\) coefficient obtained from the three configurations, its relative variation (\(S_{21,\text{relative}}\)) is represented as a function of the DC applied magnetic field shown in Figure 5.  
\(S_{21,\text{relative}}\) is defined, as follows:  
\[S_{21,\text{relative}}(\%)=100\;\times\;\frac{\left|S_{21}\right|_{H\
eq 0\; \text{Oe}}\;-\;\left|S_{21}\right|_{H=0\;\text{Oe}}}{\left|S_{21}\right|_{H=0\; \text{Oe}}} \tag{6}\]  
For the configurations 1 and 2, a decreasing linear trend of the \(S_{21,\text{relative}}\) is found with the applied DC magnetic field. Increasing the number of Co-based MWs from 15 to 45 arranged in three linear array columns results in a moderate enhancement of the GMI effect with a maximum gain from \(\sim\)62% for configuration 1 to \(\sim\)67 % for configuration 2. In contrast, configuration 3 exhibits a decreasing logarithmic trend, reaching a large relative variation of \(\sim\)77%. Therefore, the GMI effect is more noticeable in the tandem system. The presented results show a high performance, obtaining a magnetic field-tunable microwave spectrum, but, also, it might be used as sensitive wireless sensors to remotely measure low strength magnetic fields. An advanced step of the variations in the microwave scattering spectra consists in applying an AC magnetic field to induce periodic changes in the internal structure of the MWs magnetic domains, in this case, modulated in time. The following study can be performed for any of the three configurations. As an example of application, a 17-Oe-amplitude magnetic field with a frequency of 10 Hz (near the saturation field) is applied to configuration 2. This relatively low strength magnetic field that is produced by the Helmholtz coils enables the magnetization to oscillate between a circumferential and axial direction periodically (Figure 6a). Figure 5: Representation of the \(S_{21,\text{relative}}\) as a function of the DC axial magnetic field from 1 to 17 Oe for the three linear array configurations represented in Figure 4a1–a3. Specifically, the maxima and minima of the AC magnetic field wave cause the magnetization to be saturated along the MW axis (upper plateau of the \(S_{21}\) coefficient). Instead, the zero values of this AC wave cause remanence state conditions (circumferential anisotropy) that correspond to the minima of \(S_{21}\) values. The GMI phenomena are notorious between two states, where the dynamic permeability change and that correspond to both the sharp negative and positive slopes of the modulated \(S_{21}\) signal around the minima. In addition, for a single wavelength of the displayed signature, its preferential anisotropy state is changed twice, because the hysteresis loop is symmetrical (Figure 2c). According to this, the modulation frequency (\(\hat{f}_{\text{modulation}}\)) of \(S_{21}\) parameter is twice the frequency of the applied magnetic field (\(f_{\text{HAC}}\)). The amplitude of the modulation (pulse depth) is given by the difference of the two magnetic states (\(\Delta S_{21}=\mid\!S_{21,\text{minimum}}\!\mid\!-\!\mid\!S_{21,\text{plateau}}\!\mid\!\)). The influence of \(\Delta S_{21}\) modulation is subsequently studied as a function of the thickness of polymeric slabs (\(\epsilon_{r}\)-3) up to 6000 \(\upmu\)m (\(t\)) overlapping on top of array platform configuration 2 (Figure 6b). The addition of different polymeric slab thicknesses causes a variation in the effective permittivity (\(\epsilon_{\text{eff}}\)) [2; 3; 37; 54], producing modifications in the \(f_{\text{min}}\) (Figure 6c). As the thickness of the layer increases, the \(f_{\text{min}}\) of the system decreases from \(\sim\)2.37 GHz to \(\sim\)2.07 GHz, being associated with an increase in the \(\epsilon_{\text{eff}}\) of the medium.