Dual-Period Impedance Loaded Transmission Line Model for Dispersion Relationship of Parallel Plates With Interdigital-Pin Bed of Nails

In this article, a dual-period impedance loaded transmission line model is established for the z-directed parallel plates with the x - and y -directed periodic interdigital-pin bed of nails. In the model, the y -directed periodicity is assumed to be smaller than the wavelength, and the height between two parallel plates is smaller than the half-wavelength. If so, for the periodic metallic nails in the yo\textit {z} plane, the zero-order Floquer's mode as a free wave exists in the structure, and the high-order modes as surface waves are tightly bound to the metallic nails. Thereby, the waveguide can be regarded as an x -direction transmission line alternately loaded by two types of periodic parallel impedances. Further, the dispersion equation is established to determine the passband and forbidden band through the imaginary part of the propagation constant. Especially if two kinds of parallel impedances are equal, the proposed theory can boil down to the existing dispersion model. Finally, based on the sinusoidal current distribution and the equivalent cross section assumptions, the calculus of variations is adopted to solve the analytical expression of the parallel impedance for the cylinder or rectangular nails. The simulations support the proposed theory, regardless of the periodic metallic rectangular and cylinder nails. Compared to the existing transverse resonance method, the proposed theory not only holds for interdigital (and noninterdigital) rectangular (and cylinder) nails but also shows a higher accuracy for the noninterdigital cylinder nails, greatly enriching the dispersion theory.