External and internal mutual impedance effects on the radiation patterns of circularly disposed arrays using antennafiers or passive monopoles

A theoretical analysis of circularly disposed receiving arrays of monopole or dipole elements is presented for general cases in which all the elements are purely passive or else all are integrated elements (antennafiers). The input impedances of the various ports of the beamforming network have arbitrary values in both cases. The effects of all (external) mutual impedances between any pairs of elements are included in the main analysis. Then by simply setting all of the external mutual-impedance coefficients equal to zero, they are automatically excluded in a separate analysis. Using the impedance coefficients in conjunction with two appropriate computer programs, we demonstrate, first, that the effects of all (external) mutual impedances on the normalized radiation pattern of the very broad-band practical arrays considered are negligible whether the high-input-impedance integrated amplifiers are present or not. This is true as long as the heights of the monopole elements are less than about 0.19 wavelength in the case of purely passive monopoles, and less than about 0.22 wavelength or 0.3 wavelength in the case of the particular amplifiers considered for numerical calculations when connected to monopoles of two different heights. Second, it is demonstrated that the effect of an impedance-mismatched beamformer on the normalized radiation patterns of the arrays considered first is not negligible. In particular, the effect of this beamformer mismatch on the normalized radiation pattern is often surprisingly noticeable even for an array containing the antennafiers that provide high effective isolation between the input and output terminals of their amplifiers under impedance-matched beamformer conditions.