Abstract
This paper presents a modeling and an analysis of one-dimensional periodic structure composed of a cascade connection of N cells considered as infinite. The ABCD matrix representations with the Floquet analysis have been used to derive the dispersion relation and input impedance of infinite periodic structure. The transmission matrix for the N identical cascaded cells has been successfully used to obtain an efficient and easy-to-use formula giving the necessary number of cells such that they can be considered infinite. As an illustrative example, the formula is applied and verified to finite size TL periodically loaded with obstacles. Scattering parameters and the input impedance of the structure are expressed and plotted.
Highlights
A periodic structure consists fundamentally of a number of identical structural components “periodic elements” which are joined together end to end or side by side to form the whole structure [1,2]
The ABCD matrix representations with the Floquet analysis have been used to derive the dispersion relation and input impedance of infinite periodic structure
The study of the infinite periodic structure is reduced to a single unit cell, Floquet theorem is invoked and both dispersion diagram and input impedance are obtained
Summary
A periodic structure consists fundamentally of a number of identical structural components “periodic elements” which are joined together end to end or side by side to form the whole structure [1,2]. The study of the infinite periodic structure is reduced to a single unit cell, Floquet theorem is invoked and both dispersion diagram and input impedance are obtained. For the case of finite periodic structure we suppose that a finite structure with a very large number of unit cell, can be considered as an infinite structure, using the transmission matrix for the N identical cascaded cells, a condition of convergence of the finite structure to an infinite structure is concluded. This convergence condition helps to find the minimal number of unit cell necessary such that they can be considered infinite. Dispersion diagram, the stop and pass band property, the effect of changing geometrical parameters on the pass (stop) bandwidth, attenuation and phase constant are shown
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