Modal characteristics of planar transmission lines with periodical perturbations: their behaviors in bound, stopband, and radiation regions

This work presents the modal characteristics of one-dimensional periodical transmission lines, including the microstrip with even-symmetric periodical perturbations, the microstrip on an electromagnetic bandgap (EBG) surface without via holes, and the electric-magnetic-electric (EME) microstrip, in the bound, stopband, and radiation regions. The Brillouin diagram, or the so-called k-β diagram, is employed to represent the dispersion characteristics of the periodical transmission lines. The matrix-pencil method is applied to analysis the surface currents J_s obtained by invoking the method of moment simulation, and the results are verified by the finite-element method analyzes. The complex modes in the form of +jα±β and -jα±β could be observed in the microstrip with even-symmetric periodical structure and form the stopband of the periodical microstrip. In the case study of the microstrip on the EBG surface, the complexity of the modal behaviors could be illustrated in the stopband. The complex mode pair in the form of +jα±β exists in the stopband. In the stopband of the EME microstrip, the complex mode in the form of +jα±β appears. Energy vanishes due to the space-wave leakages near the corner frequencies of the stopband of the microstrip on the EBG ground plane and the EME microstrip. The dispersion characteristics of three case studies exhibit the different modal behaviors although the scattering analyzes show the similar results in the passband, stopband, and radiation regions.