The effect of magnetic bias on dielectric spectra of composite sheets filled with Fe or Co-based microwires is studied experimentally and via simulation. The permittivity is measured using a free-space technique within the frequency band from 6 to 12 GHz. The bias is applied either parallel or perpendicular to the microwave electric field; the bias strength varies from 0 to 2.5 kOe. The composites with Fe-based wires reveal a single region of bias dependent permittivity under bias about 800-1000 Oe. The composites with Co-based wires reveal two such regions: the high-field region is close to that of composites with Fe wires, and the low-field region corresponds to the coercive field of Co wires (2-3 Oe). The high-field effect is related to the dependence of ferromagnetic resonance (FMR) parameters on bias; the low-field effect is related to the rearrangement of the domain structure of Co-based wires. The interference of magnetoimpedance and dipole resonance is analyzed, revealing the effects off wire length, diameter, parameters of magnetic resonance and composite structure. The results are considered in view of application to the problem of controlled microwave attenuation. Simulation shows that the narrower is the FMR spectrum and the higher is the admissible loss of a sheet in a transparent state, the wider is the dynamic range of attenuation control. The attenuation range of a lattice of continuous wires is smaller than that of a screen with identical wire sections, where the magnetoimpedance effect is amplified resonantly. At 15 GHz frequency the strength of the bias switching opaque sheet with Fe-based wires to the transparent state is about 2000 Oe. For 3 dB admissible loss, the range of attenuation control about 10 dB is feasible in a composite with aligned wire sections. If the aligned sections are distributed regularly, the loss in a transparent state is about 1 dB lower.
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