Q factors for antennas in dispersive media

Abstract

Stored energy and Q-factors are used to quantify the performance of small antennas. Accurate and efficient evaluation of the stored energy is also essential for current optimization and the associated physical bounds. Here, it is shown that the frequency derivative of the input impedance and the stored energy can be determined from the frequency derivative of the electric field integral equation. The expressions for the differentiated input impedance and stored energies differ by the use of a transpose and Hermitian transpose in the quadratic forms. The quadratic forms also provide simple single frequency formulas for the corresponding Q-factors. The expressions are further generalized to antennas integrated in temporally dispersive media. Numerical examples that compare the different Q-factors are presented for dipole and loop antennas in conductive, Debye, Lorentz, and Drude media. The computed Q-factors are also verified with the Q-factor obtained from the stored energy in Brune synthesized circuit models.

Stored energies in electric and magnetic current densities for small antennas

“…The pure J e and the pure J m -terms are equal in structure (up to the constant η 2 ). For the integrand with purely electrical terms in (105) we find by inserting ( 16): We recall that (106) is part of the integrand in (105), we note that upon integration several of the above terms vanish by using (19) and (20). The first electrical non-vanishing contribution term in the integrand to P rad are of k 4 -order and have an integrand of the form:…”

“…The generalization in [19] and in the present paper includes electric and magnetic current-densities for arbitrary shapes. Antennas embedded in lossy or dispersive material has been considered in [20].…”

Optimal Currents on Arbitrarily Shaped Surfaces

“…It is also noteworthy to mention that, at the modest expense of introducing magnetic current [39], the formulation (2) can also be rewritten solely in terms of sources distributed on surfaces (thanks to the surface equivalence principle [39]) which significantly reduces evaluation time. Due to these properties, the source formulation is a popular choice for optimizations [20]- [22], [24], [25], [31]- [33], [40], [41] and this paper is no exception. This text therefore assumes J dV → J dS, switching the units of current density as Am −2 → Am −1 , i.e., to electric sources distributed on a surface.…”

“…In this paradigm, the continuous bilinear forms are transformed as J , LJ → I H LI, where I is the vector representation of the current density, L is the matrix representation of the operator L and super-index H represents the Hermitian conjugation. Within the community of applied electromagnetism, such a matrix representation can be dated back to the works of Harrington [43] and is, once again, becoming increasingly popular [25], [33], [40], [41].…”

“…The partial radiation intensity U (θ/ϕ) in spherical direction θ 0 or ϕ 0 is related to partial directivity [1] as where P rad is the radiated power (41) and…”