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

A metamaterial paradigm for achieving an efficient, electrically small antenna is introduced Spherical shells of homogenous, isotropic negative permittivity (ENG) material are designed to create electrically small resonant systems for several antennas: an infinitesimal electric dipole, a very short center-fed cylindrical electric dipole, and a very short coaxially-fed electric monopole over an infinite ground plane Analytical and numerical models demonstrate that a properly designed ENG shell provides a distributed inductive element resonantly matched to these highly capacitive electrically small antennas, ie, an ENG shell can be designed to produce an electrically small system with a zero input reactance and an input resistance that is matched to a specified source resistance leading to overall efficiencies approaching unity Losses and dispersion characteristics of the ENG materials are also included in the analytical models Finite element numerical models of the various antenna-ENG shell systems are developed and used to predict their input impedances These electrically small antenna-ENG shell systems with idealized dispersionless ENG material properties are shown to be very efficient and to have fractional bandwidths above the values associated with the Chu limit for the quality factor without any degradation in the radiation patterns of the antennas Introducing dispersion and losses into the analytical models, the resulting bandwidths are shown to be reduced significantly, but remain slightly above (below) the corresponding Chu-based value for an energy-based limiting (Drude) dispersion model of the permittivity of the ENG shell

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Metamaterial-based efficient electrically small antennas

PCS (personal communication system) devices have become an important part of everyday life. The pressure to design small, lightweight, and user-friendly mobile-communication devices has increased accordingly, creating the need for optimal antennas for mobile applications. In this paper, we present some basic rules about electrically small antennas, give clues and guidelines about efficient antenna miniaturization, and, finally, show some examples of miniature antennas developed in our laboratory for practical applications.

PCS antenna design: the challenge of miniaturization

Fractal objects have some unique geometrical properties. One of them is the possibility to enclose in a finite area an infinitely long curve. The resulting curve is highly convoluted being nowhere differentiable. One such curve is the Koch curve. In this paper, the behavior the Koch monopole is numerically and experimentally analyzed. The results show that as the number of iterations on the small fractal Koch monopole are increased, the Q of the antenna approaches the fundamental limit for small antennas.

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The Koch monopole: a small fractal antenna

A method is presented for evaluating the Q of an antenna, where the Q is defined as in conventional network theory. The method consists of subtracting the energy density associated with the power flow from the total energy density, thus enabling the magnetic and electric reactive energy to be computed. Specific application of the method is made to the evaluation of the Q of spherical and cylindrical modes. It is verified that the Q becomes very large when the order of the mode exceeds k_{0}a where a is the radius of the sphere or cylinder on which the sources are located.

S. Rothschild

Papers

Evaluation of antenna Q