Gerhard Kristensson

Impact of Matching Network on Bandwidth of Compact Antenna Arrays

We analyze the impact of the matching network on compact multiple-input multiple-output systems. Existing studies have found that the matching network has a significant influence on the performance of multiple antenna systems when the antennas are in close proximity. However, none has examined the wide-band case. In this paper, we investigate the wide-band performance of four different matching networks for multiple dipole antennas. The performance of the matching networks is given in terms of the bandwidths of correlation and matching efficiency, which are extensions of the single-antenna concept of bandwidth to multiple antenna systems. We also investigate the impact of the propagation conditions on the matching and bandwidth. For a uniform two-dimensional (2-D) angular power spectrum, we find that while individual-port matching can achieve in excess of 3% fractional correlation bandwidth for envelope correlation of 0.5 at an antenna separation of 0.01lambda, multiport matching is required for efficiency bandwidth to exist for a return loss of -6 dB. Moreover, even with multiport matching, both correlation and efficiency bandwidths decrease drastically at small antenna separations. At 0.01lambda, the correlation and efficiency bandwidths are 0.4% and 0.2%, respectively. Similar evaluations were performed for measured outdoor-to-indoor channels with moderate to small 2-D angular spreads. We find that the efficiency advantage of multiport matching over individual-port matching diminishes with decreasing angular spread

Physical limitations on antennas of arbitrary shape

In this paper, physical limitations on bandwidth, realized gain, Q-factor and directivity are derived for antennas of arbitrary shape. The product of bandwidth and realizable gain is shown to be bounded from above by the eigenvalues of the long-wavelength, high-contrast polarizability dyadics. These dyadics are proportional to the antenna volume and are easily determined for an arbitrary geometry. Ellipsoidal antenna volumes are analysed in detail, and numerical results for some generic geometries are presented. The theory is verified against the classical Chu limitations for spherical geometries and shown to yield sharper bounds for the ratio of the directivity and the Q-factor for non-spherical geometries.

Illustrations of New Physical Bounds on Linearly Polarized Antennas

A recent approach to physical bounds on antennas of arbitrary shape is numerically illustrated. In particular, physical bounds for antennas circumscribed by the rectangular parallelepiped, finite cylinders, and planar rectangles are presented. The bounds are verified against numerical results for various small antennas with excellent agreement.

Direct and inverse scattering in the time domain for a dissipative wave equation. Part 1: Scattering operators

This is the first part of a series of papers devoted to direct and inverse scattering of transient waves in lossy inhomogeneous media. The medium is assumed to be stratified, i.e., it varies only with depth. The wave propagation is modeled in an electromagnetic case with spatially varying permittivity and conductivity. The objective in this first paper is to analyze properties of the scattering operators (impulse responses) for the medium and to introduce the reader to the inverse problem, which is the subject of the second paper in this series. In particular, imbedding equations for the propagation operators are derived and the corresponding equations for the scattering operators are reviewed. The kernel representations of the propagation operators are shown to have compact support in the time variable. This property implies that transmission and reflection data can be extended from one round trip to arbitrary time intervals. The compact support of the propagator kernels also restricts the admissible set of transmission kernels consistent with the model employed in this paper. Special cases of scattering and propagation kernels that can be expressed in closed form are presented.

Constitutive relations, dissipation and reciprocity for the Maxwell equations in the time domain

The main goal of this paper is to establish general constitutive relations for the electromagnetic fields EBAR, DBAR, BBAR, and HBAR in a time domain setting. The four basic assumptions of the medium are linearity, invariance to time translations, causality, and continuity. These four assumptions imply that the constitutive relations are convolutions of the Riemann-Stieltjes type. A review of the classification of media in bianisotropic, biisotropic, anisotropic, and isotropic media, respectively, is made. Dissipation and reciprocity are defined and the constraints these concepts make on the constitutive relations are analyzed. Furthermore, an appropriate form of time reversal and functions of positive type are introduced and some consequences of these concepts are showed. (Less)

Direct and inverse scattering in the time domain for a dissipative wave equation. II. Simultaneous reconstruction of dissipation and phase velocity profiles

The one-dimensional inverse scattering problem for inhomogeneous lossy media is considered. The model problem involves electromagnetic wave propagation in a medium of unknown thickness with spatially varying conductivity and permittivity. Two inversion algorithms are developed in the time domain using data obtained from normally incident plane waves. These algorithms utilize reflection data from both sides of the medium, and one of them also uses transmission data. These algorithms are implemented numerically on several examples, one of which includes the effects of noisy data. The possibility of using one-sided reflection data and no transmission data is reviewed and analyzed.

A Floquet--Bloch Decomposition of Maxwell's Equations Applied to Homogenization

Using Bloch waves to represent the full solution of Maxwell’s equations in periodic media, we study the limit where the material’s period becomes much smaller than the wavelength. It is seen that for steady-state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the non-vanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.

Direct and inverse scattering in the time domain for a dissipative wave equation. III. Scattering operators in the presence of a phase velocity mismatch

The direct scattering problem for an inhomogeneous lossy medium is examined for the one‐dimensional case in which the phase velocity profile is discontinuous at the boundaries of the medium. Scattering operators (or impulse responses) and propagation operators are defined and equations that govern their behavior are developed. Knowledge of the scattering kernels for one round trip in the medium implies that the scattering kernels can be determined on any time interval. Numerical examples are presented. It is also shown that this scattering problem is reducible to one in which there are no phase velocity mismatches. This reduction provides considerable numerical advantage in the solution of the direct scattering problem. The inverse problem is examined in a companion paper.

Transient Electromagnetic Wave Propagation in Waveguides

This paper focuses on propagation of transient electromagnetic waves in waveguides of general cross section with perfectly conducting walls. The solution of the transient wave propagation problem relies on a wave splitting technique, which has been frequently used in direct and inverse scattering problems during the last decade. The field in the waveguide is represented as a time convolution of a Green function and the excitation. Some numerical computations illustrate the method. A new way of calculating the first precursor in a Lorentz medium is presented. This method, which is not based upon the classical asymptotic methods, gives an expression of the first precursor at all depths in the medium. The excitation of the waveguide modes for time dependent sources is also addressed.

The T matrix for acoustic and electromagnetic scattering by circular disks

The T matrix for scattering of waves by a circular disk is derived. Both the scalar (Dirichlet and Neumann boundary conditions) and the vector (perfectly conducting disk) cases are considered and the use of alternative choices for surface field functions is discussed in detail, and it is found that either type of the surface field representation is equally good for the disk case. Analytic expression of the farfield amplitude and total cross section is given in the low‐frequency limit for both plane‐wave incidence or a point source. Numerical results are presented for the two scalar cases as well as for the perfectly conducting disk. Finally, we give a computation of scattering from two parallel perfectly conducting disks.