An exact method, which is more straightforward than those previously published, is derived for the calculation of the minimum radiation Q of a general antenna. This expression agrees with the previously published and widely cited approximate expression in the extreme lower limit of electrical size. However, for the upper end of the range of electrical size which is considered electrically small, the exact expression given here is significantly different from the approximate expression. This result has implications on both the bandwidth and efficiency limitations of antennas which fall into this category.

A re-examination of the fundamental limits on the radiation Q of electrically small antennas

To address the need for fundamental universally valid definitions of exact bandwidth and quality factor (Q) of tuned antennas, as well as the need for efficient accurate approximate formulas for computing this bandwidth and Q, exact and approximate expressions are found for the bandwidth and Q of a general single-feed (one-port) lossy or lossless linear antenna tuned to resonance or antiresonance. The approximate expression derived for the exact bandwidth of a tuned antenna differs from previous approximate expressions in that it is inversely proportional to the magnitude |Z'/sub 0/(/spl omega//sub 0/)| of the frequency derivative of the input impedance and, for not too large a bandwidth, it is nearly equal to the exact bandwidth of the tuned antenna at every frequency /spl omega//sub 0/, that is, throughout antiresonant as well as resonant frequency bands. It is also shown that an appropriately defined exact Q of a tuned lossy or lossless antenna is approximately proportional to |Z'/sub 0/(/spl omega//sub 0/)| and thus this Q is approximately inversely proportional to the bandwidth (for not too large a bandwidth) of a simply tuned antenna at all frequencies. The exact Q of a tuned antenna is defined in terms of average internal energies that emerge naturally from Maxwell's equations applied to the tuned antenna. These internal energies, which are similar but not identical to previously defined quality-factor energies, and the associated Q are proven to increase without bound as the size of an antenna is decreased. Numerical solutions to thin straight-wire and wire-loop lossy and lossless antennas, as well as to a Yagi antenna and a straight-wire antenna embedded in a lossy dispersive dielectric, confirm the accuracy of the approximate expressions and the inverse relationship between the defined bandwidth and the defined Q over frequency ranges that cover several resonant and antiresonant frequency bands.

Impedance, bandwidth, and Q of antennas

By covering a metal ground plane with a periodic surface texture, we can alter its electromagnetic properties. The impedance of this metasurface can be modeled as a parallel resonant circuit, with sheet inductance L, and sheet capacitance C. The reflection phase varies with frequency from +/spl pi/ to -/spl pi/, and crosses through 0 at the LC resonance frequency, where the surface behaves as an artificial magnetic conductor. By incorporating varactor diodes into the texture, we have built a tunable impedance surface, in which an applied bias voltage controls the resonance frequency, and the reflection phase. We can program the surface to create a tunable phase gradient, which can electronically steer a reflected beam over +/- 40/spl deg/ in two dimensions, for both polarizations. We have also found that this type of resonant surface texture can provide greater bandwidth than conventional reflectarray structures. This new electronically steerable reflector offers a low-cost alternative to a conventional phased array.

Two-dimensional beam steering using an electrically tunable impedance surface

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.

Fundamental limitations in antennas

J J Adams ,[+] Prof J T Bernhard Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801, USA E-mail: jbernhar@illinoisedu Dr E B Duoss ,[+,++] T F Malkowski ,[+] Dr B Y Ahn , Prof J A Lewis Department of Materials Science and Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801 USA E-mail: jalewis@illinoisedu Dr M J Motala , Prof R G Nuzzo Department of Chemistry University of Illinois at Urbana-Champaign Urbana, Illinois 61801, USA [+] These authors contributed equally to this work [++] Presently at Lawrence Livermore National Laboratory, Center for Microand NanoTechnology, Livermore, CA 94550 USA

Conformal Printing of Electrically Small Antennas on Three‐Dimensional Surfaces

The physical limitations of omni‐directional antennas are considered. With the use of the spherical wave functions to describe the field, the directivity gain G and the Q of an unspecified antenna are calculated under idealized conditions. To obtain the optimum performance, three criteria are used, (1) maximum gain for a given complexity of the antenna structure, (2) minimum Q, (3) maximum ratio of G/Q. It is found that an antenna of which the maximum dimension is 2a has the potentiality of a broad band width provided that the gain is equal to or less than 4a/λ. To obtain a gain higher than this value, the Q of the antenna increases at an astronomical rate. The antenna which has potentially the broadest band width of all omni‐directional antennas is one which has a radiation pattern corresponding to that of an infinitesimally small dipole.

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L. J. Chu

Papers

Physical Limitations of Omni-Directional Antennas