Novel dispersive modal approach for fast analysis of asymmetric coplanar structures on isotropic/anisotropic substrates

Reliable Nonuniform Discretization Algorithm for Fast and Accurate Hybrid Mode Analysis of Multilayered Planar Transmission Lines

“…As mentioned in [1,14,17], the Ŷ and Ẑ operators can be described in the form of diagonal matrices obtained from their spectral representation, thus Ẑ = Ŷ −1 . Their evaluation requires the involvement of a complete set of orthogonal basis functions ({|f n ⟩} n=0...N ) and the calculation of the mode admittances Y I n and Y II n of the respective upper and lower regions at the metallized interface (with N the number of modes).…”

“…As for the size of the resulted dispersion matrix, it will be of 4K × 4K, constituted of 16 submatrices for asymmetrical coupled microstrip [14] and coplanar lines [1], and of 2K × 2K, composed of 4 sub-matrices for the symmetrical case and for symmetrical/asymmetrical finline and microstrip structures [17]. Indeed, the size of the global dispersion matrix depends on the number of slots (or metallic strips), i.e., 2I max K × 2I max K for asymmetrical lines with 4I 2 max sub-matrices, where I max indicates the number of slots (or metallic strips) [17].…”

“…Several modeling methods have been proposed to address this issue. However, most of them suffer from large memory requirement and CPU time, particularly in characterizing asymmetrical planar lines in multilayer configurations [1]. Therefore, many numerical techniques have been retained to tackle propagation issues in multilayered structures such as the finite difference time domain (FDTD) method [2][3][4], spectral domain approach (SDA) [5][6][7], or multimode equivalent network (MEN) technique [8,9], to name a few.…”

“…The rationale behind such formalism is to describe, in a more convenient way, the boundary conditions of the electromagnetic fields at the interfaces [10][11][12]. In fact, this technique has been successfully used to analyze lossy transmission lines with finite metallization thickness [13], symmetrical/asymmetrical transmission lines including isotropic/anisotropic substrates [1,14], truncated substrates [15,16], and multilayered substrates [17,18]. Note that the proposed approach has been developed from the equivalent electrical circuit concept that allows converting the continuity relations of EM field expressions into current-voltage relationships [10,11], thus leading to the determination of a key parameter, i.e., the admittance/impedance operator [1,14].…”

“…In fact, this technique has been successfully used to analyze lossy transmission lines with finite metallization thickness [13], symmetrical/asymmetrical transmission lines including isotropic/anisotropic substrates [1,14], truncated substrates [15,16], and multilayered substrates [17,18]. Note that the proposed approach has been developed from the equivalent electrical circuit concept that allows converting the continuity relations of EM field expressions into current-voltage relationships [10,11], thus leading to the determination of a key parameter, i.e., the admittance/impedance operator [1,14]. Thanks to the relative simplicity of the considered equivalent circuit, there is no restriction on the number of layers, which, indeed, significantly extends this integral method to the analysis of generic symmetrical/asymmetrical planar transmission structures with an arbitrary number of layers.…”