Admittance analysis of nonuniformly spaced phased arrays of waveguide apertures in a ground plane

A general formulation for the analysis of a phased array of waveguide apertures in a common ground plane has been given for finite number of elements and nonuniform spacings based on network representation of the system. The analysis yields the radiation pattern, reflection coefficient, and aperture field in each waveguide. The pattern of an array of physically identical elements is expressed as superposition of patterns of infinite number of arrays. The formulation, when applied to single and two aperture cases, confirms the known results. It is then applied to investigate the properties of the element position modulated phased array of 15 rectangular waveguide apertures excited by uniform incident waves. Uniformly spaced arrays are also analyzed for comparison. The dominant mode and one higher order evanescent mode are included in the computations. The results show that the overall power reflection coefficient of the nonuniform array does not undergo any peaks over a wide scan range. It is concluded that the advantages of nonuniformly spaced arrays in suppressing grating lobes and eliminating blind spots are physically realizable.