927 research outputs found

### Maximum Gain, Effective Area, and Directivity

Fundamental bounds on antenna gain are found via convex optimization of the
current density in a prescribed region. Various constraints are considered,
including self-resonance and only partial control of the current distribution.
Derived formulas are valid for arbitrarily shaped radiators of a given
conductivity. All the optimization tasks are reduced to eigenvalue problems,
which are solved efficiently. The second part of the paper deals with
superdirectivity and its associated minimal costs in efficiency and Q-factor.
The paper is accompanied with a series of examples practically demonstrating
the relevance of the theoretical framework and entirely spanning wide range of
material parameters and electrical sizes used in antenna technology. Presented
results are analyzed from a perspective of effectively radiating modes. In
contrast to a common approach utilizing spherical modes, the radiating modes of
a given body are directly evaluated and analyzed here. All crucial mathematical
steps are reviewed in the appendices, including a series of important
subroutines to be considered making it possible to reduce the computational
burden associated with the evaluation of electrically large structures and
structures of high conductivity.Comment: 12 pages, 15 figures, submitted to TA

### Physical bounds and radiation modes for MIMO antennas

Modern antenna design for communication systems revolves around two extremes:
devices, where only a small region is dedicated to antenna design, and base
stations, where design space is not shared with other components. Both imply
different restrictions on what performance is realizable. In this paper
properties of both ends of the spectrum in terms of MIMO performance is
investigated. For electrically small antennas the size restriction dominates
the performance parameters. The regions dedicated to antenna design induce
currents on the rest of the device. Here a method for studying fundamental
bound on spectral efficiency of such configurations is presented. This bound is
also studied for $N$-degree MIMO systems. For electrically large structures the
number of degrees of freedom available per unit area is investigated for
different shapes. Both of these are achieved by formulating a convex
optimization problem for maximum spectral efficiency in the current density on
the antenna. A computationally efficient solution for this problem is
formulated and investigated in relation to constraining parameters, such as
size and efficiency

### Q factors for antennas in dispersive media

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 for electric and magnetic current densities

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 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.Comment: Minor updates to figures and tex

### Stored Electromagnetic Energy and Antenna Q

Decomposition of the electromagnetic energy into its stored and radiated
parts is instrumental in the evaluation of antenna Q and the corresponding
fundamental limitations on antennas. This decomposition is not unique and there
are several proposals in the literature. Here, it is shown that stored energy
defined from the difference between the energy density and the far field energy
equals the new energy expressions proposed by Vandenbosch for many cases. This
also explains the observed cases with negative stored energy and suggests a
possible remedy to them. The results are compared with the classical explicit
expressions for spherical regions where the results only differ by ka that is
interpreted as the far-field energy in the interior of the sphere. Numerical
results of the Q-factors for dipole, loop, and inverted L-antennas are also
compared with estimates from circuit models and differentiation of the
impedance. The results indicate that the stored energy in the field agrees with
the stored energy in the Brune synthesized circuit models whereas the
differentiated impedance gives a lower value for some cases. The corresponding
results for the bandwidth suggest that the inverse proportionality between
bandwidth and Q depends on the relative bandwidth or equivalent the threshold
of the reflection coefficient. The Q from the differentiated impedance and
stored energy are most useful for relative narrow and wide bandwidths,
respectively

### Bandwidth-Constrained Capacity Bounds and Degrees of Freedom for MIMO Antennas

The optimal spectral efficiency and number of independent channels for MIMO
antennas in isotropic multipath channels are investigated when bandwidth
requirements are placed on the antenna. By posing the problem as a convex
optimization problem restricted by the port Q-factor a semi-analytical
expression is formed for its solution. The antennas are simulated by method of
moments and the solution is formulated both for structures fed by discrete
ports, as well as for design regions characterized by an equivalent current. It
is shown that the solution is solely dependent on the eigenvalues of the
so-called energy modes of the antenna. The magnitude of these eigenvalues is
analyzed for a linear dipole array as well as a plate with embedded antenna
regions. The energy modes are also compared to the characteristic modes to
validate characteristic modes as a design strategy for MIMO antennas. The
antenna performance is illustrated through spectral efficiency over the
Q-factor, a quantity that is connected to the capacity. It is proposed that the
number of energy modes below a given Q-factor can be used to estimate the
degrees of freedom for that Q-factor.Comment: 13 pages, 17 figure

### Stored energies in electric and magnetic current densities for small antennas

Electric and magnetic currents are essential to describe electromagnetic
stored energy, as well as the associated quantities of antenna Q and the
partial directivity to antenna Q-ratio, D/Q, for general structures. The upper
bound of previous D/Q-results for antennas modeled by electric currents is
accurate enough to be predictive, this motivates us here to extend the analysis
to include magnetic currents. In the present paper we investigate antenna Q
bounds and D/Q-bounds for the combination of electric- and magnetic-currents,
in the limit of electrically small antennas. This investigation is both
analytical and numerical, and we illustrate how the bounds depend on the shape
of the antenna. We show that the antenna Q can be associated with the largest
eigenvalue of certain combinations of the electric and magnetic polarizability
tensors. The results are a fully compatible extension of the electric only
currents, which come as a special case. The here proposed method for antenna Q
provides the minimum Q-value, and it also yields families of minimizers for
optimal electric and magnetic currents that can lend insight into the antenna
design.Comment: 27 pages 7 figure

### Time-domain approach to the forward scattering sum rule

The forward scattering sum rule relates the extinction cross section integrated over all wavelengths with the polarizability dyadics. It is useful for deriving bounds on the interaction between scatterers and electromagnetic fields, antenna bandwidth and directivity and energy transmission through sub-wavelength apertures. The sum rule is valid for linearly polarized plane waves impinging on linear, passive and time translational invariant scattering objects in free space. Here, a time-domain approach is used to clarify the derivation and the used assumptions. The time-domain forward scattered field defines an impulse response. Energy conservation shows that this impulse response is the kernel of a passive convolution operator, which implies that the Fourier transform of the impulse response is a Herglotz function. The forward scattering sum rule is finally constructed from integral identities for Herglotz functions

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