Position-modulated phased array-space factor considerations

The space factor of an element position-modulated array is expressed as an Anger function series for a general amplitude distribution. The behavior of the main lobe and the diffraction sidelobes for uniform excitation are presented in the form of universal curves. It is found that the nulls near the main lobe disappear for the modulation index above a critical value. The peak level of the grating plateaus and their shapes are given in terms of approximate expressions and are exactly determined computationally. The nature of the curves suitable for design of such arrays for a given scan range and permissible peak sidelobe level is given. An example shows that a high resolution beam may be obtained with a comparatively smaller number of elements than required by a uniformly illuminated periodic array. An exact-series summation formula for the directivity of nonuniformly spaced antenna arrays of isotropic elements is given. The directivity of the modulated array computed by this formula shows a smooth variation at the ends of the scan range in contrast to the sudden fall in the case of the periodic array.