Fundamental limitations in antennas

Four fundamental limitations in antennas have been identified in the areas of: electrically small antennas, superdirective antennas, superresolution antennas, and high-pin antennas. All exhibit roughly exponential increase in cost factors with performance increase beyond the robust range. This paper reviews these limitations. Electrically small antennas are analyzed via spherical mode theory, with the antenna enclosed in a virtual sphere. Minimum Q varies inversely as the cube of sphere radius in radian wavelengths when the radius is much less than the latter. This limits the achievable bandwidth. Superdirective apertures require a constraint; the optimization is generally intractable except for line sources. Superdirective arrays have spacing below half-wavelength, and for small spacings a constraint is desirable to limit Q, tolerances, efficiency, sidelobes, etc. This is accomplished by expressing constrained directivity as a ratio of two Hermilian quadratic forms, for which a solution exists. Array Q varies exponentially with directivity so only modest increases are practical. Superresolution arrays use maximum entropy processes to improve spatial frequency resolution for short samples (short arrays), analogous to spectral analysis processing. An amplitude-tapered autocorrelation function is extended by linear least square prediction and autoregression; the latter contributes filter poles. This extension is with minimum added information, hence maximum entropy. In contrast to superdirective arrays which are all zero functions, superresolution maximum entropy uses an all pole function. Results are dependent upon the sampling subarray size and upon signal/noise (S/N). Required S/N increases exponentially with inverse angular resolution. Achievable gain of high-gain reflector antennas is limited by cost of the structure. For random surface errors maximum gain is proportional to the mechanical tolerance ratio (antenna diameter/1σ tolerance) squared. Since cost increases rapidly with diameter and with tolerance ratio this comprises a gain limitation. Current best reflectors have maximum gain in the range of 90 to 100 dB.