Antenna Q and Stored Energy Expressed in the Fields, Currents, and Input Impedance

Abstract

Although the stored energy of an antenna is instrumental in the evaluation of antenna Q and the associated physical bounds, it is difficult to strictly define stored energy. Classically, the stored energy is either determined from the input impedance of the antenna or the electromagnetic fields around the antenna. The new energy expressions proposed by Vandenbosch express the stored energy in the current densities in the antenna structure. These expressions are equal to the stored energy defined from the difference between the energy density and the far field energy for many but not all cases.Here, the different approaches to determine the stored energy are compared for dipole, loop, inverted L-antennas, and bow-tie antennas. We use Brune synthesized circuit models to determine the stored energy from the input impedance. We also compare the results with differentiation of the input impedance and the obtained bandwidth. The results indicate that the stored energy in the fields, currents, and circuit models agree well for small antennas. For higher frequencies, the stored energy expressed in the currents agrees with the stored energy determined from Brune synthesized circuit models whereas the stored energy approximated by differentiation of input impedance gives a lower value for some cases. The corresponding results for the bandwidth suggest that the inverse proportionality between the fractional bandwidth and Q-factor depends on the threshold level of the reflection coefficient.

Physical Bounds of Antennas

“…Expression (3.6) is exact for the series RLCseries and often very accurate for antennas with Q 1. However, this expression can underestimate the Q-factor for multiple resonances [37,48,51,106].…”

“…Chu [14] and Thal [110] used circuit models of the spherical modes to determine the stored energy for spherical regions. Synthesized lumped-circuit models give an alternative method to estimate the Q-factor from the input impedance of antennas [37]. Collin and Rothschild [18] calculate the stored energy by subtraction of the energy density of the power flow giving Note that, in the far field,ê is perpendicular to r.…”

Physical Bounds of Antennas

“…6, assume that the stored energy can be determined accurately using (3.8), (3.9), and (3.10). There are initial investigations on the stored energy expressions [37,38,51,65] but much work remains before the stored energy is fully understood.…”

“…Accurate estimates of the fractional bandwidth (3.5) using Q Z require that the first order derivative |Z m | (linear term) dominates over the second and higher order derivatives. This requirement is not always met and there are synthesized cases with |Z m | ≈ 0 where Q Z overestimates the fractional bandwidth using (3.5) [37,48,51].…”

An Introduction to the Source Concept for Antennas

“…Geyi [9,Sec. 4] and later Vandenbosch [10] and Gustafsson [11] attempted to obtain stored electromagnetic energies directly from currents and their results lead to so-called measurable or observable energies since they are tightly connected to the frequency changes of an antenna's input impedance. Prior to this, observable energies were proposed by Rhodes [12], but he still relied upon using fields in space, not source currents.…”