State‐space models and stored electromagnetic energy for antennas in dispersive and heterogeneous media

Abstract

Accurate and efficient evaluation of the stored energy is essential for Q factors, physical bounds, and antenna current optimization. Here it is shown that the stored energy can be estimated from quadratic forms based on a state‐space representation derived from the electric and magnetic field integral equations. The derived expressions are valid for small antennas embedded in temporally dispersive and inhomogeneous media. The quadratic forms also provide simple single frequency formulas for the corresponding Q factors. Numerical examples comparing the different Q factors are presented for dipole and meander line antennas in conductive, Debye, and Lorentz media for homogeneous and inhomogeneous media. The computed Q factors are also verified with the Q factor obtained from the stored energy in Brune synthesized circuit models.

A New Perspective on the Reactive Electromagnetic Energies and Q factors of Antennas

“…There are other methods to calculate the reactive energies [44]. A comprehensive comparison of them can be found in [32].…”

Physical Limitations of Phased Array Antennas

“…The above problem (29) with (and without) the optional constraints (30) and/or (32) is a quadratically constrained quadratic program (QCQP), which is a well-studied class of optimization problems. In the context of Q-factor optimization, see [20], [32], [49].…”

Q-Factor for Multiport Antennas and Achievable Bandwidth Estimation

“…where R and X are the real and imaginary parts of the input impedance Z, and R and X are their derivatives with respect to ω. Following [29], this can be generalized for multiport antennas as…”

“…We note that formula ( 14) differs from the one proposed in [29]. In order to have a formula that is consistent with the corresponding formula for single port antennas, we have added the derivative of the real part of the impedance matrix to the proposed formula (14).…”

“…This can be fairly accurate approximation at least for antennas with very small clearances in modern smartphones. Using this, the impedance-based Q-factor ( 14) can then be approximated as [29] Q…”