Antenna and wave theories of infinite yagi-uda arrays

An integral equation for the propagation constant along an infinitely long Yagi structure is derived by expanding the vector potential function for such an array in terms of the spatial harmonic solutions of wave theory. This equation is shown to be identical with the integral equation derived on the basis of array theory and transformed by the Poisson summation formula. With the identity of array theory and this new wave theory formation established, the wave theory is used to discuss allowed wave solutions and the physical characteristics required of dipoles in order that they support a wave solution. The fundamental integral equation is solved by means of the array theory of King and Sandler; the numerical results are found to agree quite well with previously published data. Finally, the problem of two parallel nonstaggered Yagi arrays is considered, and it is shown that the propagation constant of the composite structure either decreases or increases over that of the isolated array depending upon whether the symmetric or the antisymmetric mode is excited. Some peculiar effects are noted with respect to this antisymmetric solution, and these lead to the existence of conditions under which no unattenuated wave solution is possible. This is referred to as the "cutoff condition." Numerical results are achieved which agree very well with experimental data obtained as part of this research.