Minimum Q for Lossy and Lossless Electrically Small Dipole Antennas

Abstract

Abstract-General expressions for the quality factor (Q) of antennas are minimized to obtain lower-bound formulas for the Q of electrically small, lossy or lossless, combined electric and magnetic dipole antennas confined to an arbitrarily shaped volume. The lowerbound formulas for Q are derived for dipole antennas with specified electric and magnetic dipole moments excited by both electric and magnetic surface currents as well as by electric surface currents alone. With either excitation, separate formulas are found for the dipole antennas containing only lossless or "nondispersive-conductivity" material and for the dipole antennas containing "highly dispersive lossy" material. The formulas involve the quasi-static electric and magnetic polarizabilities of the associated perfectly conducting volume of the antenna, the ratio of the powers radiated by the specified electric and magnetic dipole moments, and the efficiency of the antenna.

Physical Bounds of Antennas

“…The D/Q and Q-factor limits for small electric dipole antennas composed of non-magnetic materials are well understood. There are several independent derivations that provide similar results [35,40,43,44,47,114,117,118], see also (5.4) and (6.6) for this case. In addition, many antenna designs are shown to perform close to the bounds, see [6,9,35,43,96] and Fig.…”

“…Yaghjian and Stuart derived similar bounds on the Q-factor in the limit of small antennas ka 1 using a different technique [118]. These latter bounds were generalized to electric and magnetic currents in [117], see also [73].…”

Physical Bounds of Antennas

“…Results similar to those introduced in the previous paragraph are derived by Yaghjian and Stuart [118] and using antenna current optimization [47], see also [111,114,117]. This bound is identical to that derived by Thal [110] for small spherical structures (4.5) with electric currents radiating as an electric dipole, i.e.,…”

“…14. The general case with electric and magnetic current densities is analyzed in [73,117] and show that electric polarizability dyadic in (6.6) is replaced with the sum of the electric and magnetic polarizability dyadics. The lower bound on the Q-factor for electric dipoles is e.g., [73,117] Q ≥ 6π k 3 max eig(γ e + γ m )…”

Fundamental Efficiency Limits for Small Metallic Antennas

“…Again, the diameter of the wire should be optimized to spread the current out as much as possible over the surface of the antenna, which in turn maximizes the radiation efficiency. In the future, more accurate bounds on the radiation efficiency can be derived for arbitrarily shaped antennas [40][41][42][43]. Furthermore, limitations on the radiation efficiency of magneto-dielectric loaded antennas can also be derived using a similar analysis, and the results should be compared to the limits of metallic antennas.…”