Stored energies in electric and magnetic current densities for small antennas

Abstract

Electric and magnetic current densities are an essential part of electromagnetic theory. The goal of the present paper is to define and investigate stored energies that are valid for structures that can support both electric and magnetic current densities. Stored energies normalized with the dissipated power give us the Q factor, or antenna Q, for the structure. Lower bounds of the Q factor provide information about the available bandwidth for passive antennas that can be realized in the structure. The definition of the stored energies that we propose is valid beyond the leading order small antenna limit. Our starting point is the energy density with subtracted far-field form which we obtain an explicit and numerically attractive current density representation. This representation gives us the insight to propose a coordinate independent stored energy. Furthermore, we find here that lower bounds on antenna Q for structures with e.g., electric dipole radiation can be formulated as convex optimization problems. We determine lower bounds on both open and closed surfaces that support electric and magnetic current densities.The here derived representation of stored energies has in its electrical small limit an associated Q factor that agrees with known small antenna bounds. These stored energies have similarities to earlier efforts to define stored energies. However, one of the advantages with this method is the above mentioned formulation as convex optimization problems, which makes it easy to predict lower bounds for antennas of arbitrary shapes. The present formulation also gives us insight into the components that contribute to Chu's lower bound for spherical shapes. We utilize scalar and vector potentials to obtain a compact direct derivation of these stored energies. Examples and comparisons end the paper. arXiv:1604.08572v2 [physics.class-ph]

Physical Bounds of Antennas

“…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].…”

“…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 )…”

“…The discussion is restricted to electric current densities and use of the stored energy expression (3.9) and (3.10). Magnetic current densities can in many cases lower the bounds on Q and can be analyzed using the stored energy expressions in [73,74].…”

“…The stored energies are also generalized to electric and magnetic currents [73,74] and lossy media [51].…”

Quality factor for lossy and lossless antennas

“…A secondary purpose of the paper is to correct the error, found by Jonsson and Gustafsson [3], that was made in the derivation of one of the main lowerbound formulas in [1] and resulted in that formula applying exactly to only ellipsoidal volumes. 1 The Q lower-bound formulas derived in this paper, like those in [1], are limited to electrically small antennas (ESAs) with ka .5, where a is the circumscribing radius of the antenna volume V a and k = ω/c = 2π/λ is the free-space wavenumber (with c being the free-space speed of light and λ the free-space wavelength).…”