Characteristics of Yagi arrays of two concentric loops with loaded elements

An expression for the phase velocity of the wave propagation along two concentric and loaded circular loop arrays is derived. The traveling wave idea is applied to derive a relationship for the wave propagation constant along the structure. The analysis is based on a "circuit theory" method which gives the dispersion relation in terms of the mutual impedances between a reference and the other elements in the array. In addition, Flouquet\´s theorem is used to account for the periodicity of the structure. The array operates at two separate passbands, which correspond to the traveling waves along the inner and the outer subarrays. It is found that for a given phase velocity of the traveling wave along the structure, a capacitive loading increases the operating frequency of the array. Furthermore, a capacitive loading of the inner array alone increases both the separation of the passbands and the bandwidth of the second passband. The excitation of finite arrays is also studied, and it is found that the gain and the input impedance characteristics are more superior when only the outer array is excited.