An Accurate Model for Finite Array Patterns Based on Floquet Modal Theory

An accurate model for obtaining the radiation patterns of a finite array is presented. Using Floquet modal theory, the induced electric and magnetic fields on the apertures of all the elements of the array produced by an excited element are determined. Equivalence principle is then invoked to obtain the active element pattern (AEP) of the excited element. The AEP is found to vary substantially with the location of the element. In particular, the E-plane pattern of an element near the edge has a tilted beam, which is conspicuously different from that of the center element. The beam-tilt is explained from the “reverse phase” of a leaky wave in an array. Numerical results compare well with available measured data for open-ended waveguide and patch arrays. Also, a rigorous method of moment (MoM) analysis agrees favorably with the present model. One of the key features of the model is that it allows array pattern computation without much additional computational efforts. From array analysis, it is observed that the null depth at the blind spot is reduced as the array size shrinks and for very small arrays, the blind spot disappears. The scan loss is found to vary significantly with the array size particularly near the blind spot.