Improving modal analysis of 1D-periodic lines based on the simulation of finite structures

The numerical analysis of ID-periodic waveguides and antennas can be performed through both approximate and rigorous methods. The latter ones are based on the full-wave solution of the electromagnetic problem in the minimal spatial period of the structure (the "unit cell") with Floquet conditions at its boundaries [1]. On the other hand, a well-known approximate method [2] is based on the description of the periodic waveguide as a cascade of cells, each characterized as a two-port network. Only one mode is assumed to be propagating along the unperturbed uniform waveguide, and a voltage and a current associated to it are defined at the boundary of each cell, i.e., at the ports of the relevant network. Since the Bloch waves propagating along the waveguide are modified simply through a complex factor between two adjacent ports, the associated voltage and current can be regarded as eigenvectors of the transmission matrix of each two-port network. Once the single cell is characterized through a simulation or a measurement, the dispersive analysis is then reduced to the algebraic problem of the study of the eigenvalues of a 2 × 2 complex matrix. This approach has proven to be very effective in microwave filtering applications for a long time, and has more recently been applied to radiation problems, in the framework of leaky-wave antennas [3] and metamaterial ID-periodic transmission lines [4]. Its drawback resides in the assumption that the characterization of the single cell is sufficient to model its behavior in a periodic environment; in other words, mutual coupling among the adjacent cells is neglected, possibly leading to inaccurate results. This is particularly true in radiative problems, especially when fine details of the dispersive behavior of the structures are considered. A solution of this problem could be the definition of new two-port networks, each made by a series of N adjacent unit cells, called here "W-macrocell". Instead of the circuit characterization in the minimal spatial period of the structure, the eigenvalue problem is formulated with respect to these new macrocells. As discussed in the following sections, this approach leads to the introduction of spurious eigenvalues, which should be carefully excluded from the analysis: a simple and effective method is proposed here to this aim, and is validated on a simple canonical frequency-selective device. © 2010 IEEE.