Stored Energies and Q-Factor of Two-Dimensionally Periodic Antenna Arrays

Abstract

The Q-factor for lossless 3-D structures with 2-D periodicity is here derived in terms of the electric current density. The derivation in itself is shape-independent and based on the periodic free-space Green's function. The expression for Q-factor takes into account the exact shape of a periodic element and permits beam steering. Both the stored energies and the radiated power, required to evaluate Q-factor, are coordinate-independent and expressed in a similar manner to the periodic electric field integral equation and can thus be rapidly calculated. Numerical investigations, performed for several antenna arrays, indicate fine agreement, accurate enough to be predictive, between the proposed Q-factor and the tuned fractional bandwidth, when the arrays are not too wideband (i.e., when Q ≥ 5). For completeness, the input-impedance Q-factor, proposed by Yaghjian and Best in 2005, is included and agrees well numerically with the derived Q-factor expression. The main advantage of the proposed representation is its explicit connection to the current density, which allows the Q-factor to give bandwidth estimates based on the shape and current of the array element.

Optimal Bandwidth Positions for a Terminal Embedded Antenna: Physical Bounds and Antenna Design

“…The induced current I 2 on Ω 2 is uniquely determined by (11). The induction matrix, C, thus effectively reduces all antenna quantities to smaller matrices acting on I 1 , through (12). The embedded region, as a part of the terminal, has a bound from below on the Q-factor that can be expressed in terms of the stored energies and total power as before but, now expressed in terms of the reduced matrices.…”

“…The choice of the embedded antenna position in (13) results in a partition of the impedance matrix into controllable and non-controllable parts and appear here in the matrix C, see (11). Consequently, all the matrices appearing in (13) depend on the antenna position through (12). Given the impedance matrix and the stored energy matrices for the entire device, it is a small additional effort to determine the new position matrices through (12), which makes the computation of the position-dependent quantities comparatively fast.…”

“…Consequently, all the matrices appearing in (13) depend on the antenna position through (12). Given the impedance matrix and the stored energy matrices for the entire device, it is a small additional effort to determine the new position matrices through (12), which makes the computation of the position-dependent quantities comparatively fast. The domain is decomposed into a 10 × 10 equidistant grid for the center positions x, y of the embedded antenna within the upper left symmetry-corner of the terminal.…”

“…[3] [8]. To determine the best antenna bandwidth, we use the stored energy Q-factor [9], which is known to provide an accurate estimation of the bandwidth for electrically small antennas [10], [11], see also [12][13][14] for periodic structures. The optimal antenna bandwidth can be increased, for example, by allowing a larger antenna size, or by adding a matching network beyond a tuning element in which the antenna together with the maching network has a wider bandwidth.…”

Improvement of Edge Brightening by Means of Q Factor Minimization in Circular Antenna Apertures: High Efficient Taylor-Like Patterns

“…For instance, Kwon and Pozar [10] reported antenna configurations involving arrays of dipoles with lengths from 0.15λ to 0.45λ. In the same line, but generalizing the study to a wider range of dipole lengths and overcoming the limit ka=1, more recent approaches can be found in the works of Ludvig-Osipov and Jonsson [11], [12]. Here, they calculated the Q factor and compared their results with MoM simulations in the framework of two-dimensional periodic arrays for both scenarios with and without ground plane.…”