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The fundamental limitation of superdirective antenna arrays was previously demonstrated through calculation of Chebyshev arrays. Those arrays are not optimum and have an extraneous parameter (sidelobe level). A new calculation is made using maximum directivity arrays and it is shown that log Q varies approximately linearly with directivity. A close fit to this behavior is given by log Q = π(G- G0). The π slope has been inferred from work of Rhodes but cannot be physically justified at this time.
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R.C. Hansen (1981) studied this question.
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