A UNIFICATION OF ANTENNA THEORY AND WAVE THEORY: INFINITE YAGI-UDA ARRAYS,
HARVARD UNIV CAMBRIDGE MASS CRUFT LAB
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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 formulation established, the wave theory is used to discuss allowed wave solutions, pass and stop bands, and the physical characteristics required of dipoles in order that they support a wave solution. An asymptotic evaluation of electric and magnetic fields is obtained. 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. The problem of two collinear Yagi arrays is formulated and conditions are found under which a current distribution which is symmetrical about the center of each dipole may be assumed.