A two-layer dual-waveguide probe measurement geometry is proposed to nondestructively measure the complex permittivity and permeability of planar materials. The new measurement structure consists of two rectangular waveguides attached to a PEC flange plate that is placed against the material under test, followed by a known material layer backed by a PEC. The purpose for this new measurement geometry is to improve the permittivity results obtained using the existing dual-waveguide probe geometries, namely, the PEC-backed and free-space-backed geometries, by permitting a larger electric field into the material under test and increasing the field coupling between the two rectangular waveguide apertures. The theoretical development of the technique is presented extending the existing single-layer PEC-backed method to the proposed two-layer dual-waveguide probe method. The new measurement structure is theoretically analyzed by replacing the waveguide apertures with equivalent magnetic currents as stipulated by Love's equivalence theorem. Making use of the magnetic-current-excited two-layer parallel-plate Green's function and enforcing the continuity of the transverse magnetic fields over the waveguide apertures results in a system of coupled magnetic field integral equations. These coupled magnetic field integral equations are then solved for the theoretical reflection and transmission coefficients using the Method of Moments. The desired complex permittivity and permeability of the material under test are found by minimizing the root-mean-square difference between the theoretical and measured reflection and transmission coefficients, i.e., numerical inversion. Last, experimental results utilizing the new two-layer technique are presented for two magnetic shielding materials and subsequently compared to the existing PEC-backed and free-space-backed dual-waveguide probe geometries.
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