Internal Network Boundary Condition Incorporated in TLM for Efficiently Modeling Thin Layer of Periodic Structures

It is a problem when modeling the thin layer of periodic structures with numerical method by directly discretizing the inner part, because the fine mesh applied to simulate the thin layer would result in great computational data. The internal network boundary condition (INBC) incorporated in the transmission line matrix (TLM) scheme is proposed in this paper, to avoid the directly discretization of the thin layer and achieve a high accuracy. The thin layer of periodic structure is regarded as an easily analyzed two-port network. Vector fitting approach is used to approximate the network parameters into a series of rational expressions with either real term or complex conjugate pole-residue pairs. The INBC equation with discrete-time form is derived and then incorporated in TLM scheme by introducing the approximate pole-residue pairs to the TLM update equation. Compared with the extremely fine-discretized TLM unit cell used to deal with the thin layer by the conventional TLM scheme, a much larger coarse TLM unit cell is accurate enough to be used to discretize the structure by the proposed method. Compared with the conventional TLM scheme, substantial savings in computational storage are achieved. A common frequency selective surface (FSS) structure is first analyzed for the validation of the method. Good agreement in scattering characteristics is observed in frequency domain between the proposed method and simulation by HFSS software. To further demonstrate the validity of the proposed method, an aperture-coupled resonator-based FSS is designed and fabricated. Good agreement among the S-parameters from the proposed method, simulation, and measurement is observed, verifying the accuracy of the proposed method.