In this paper, we study optimization of multi-tone signals for wireless power transfer (WPT) systems. We investigate different non-linear energy harvesting models. Two of them are adopted to optimize the multi-tone signal according to the channel state information available at the transmitter. We show that a second-order polynomial curve-fitting model can be utilized to optimize the multi-tone signal for any RF energy harvester design. We consider both single-antenna and multi-antenna WPT systems. In-band co-existing communication links are also considered in this work by imposing a constraint on the received power at the nearby information receiver to prevent its RF front end from saturation. We emphasize the importance of imposing such constraint by explaining how inter-modulation products, due to saturation, can cause high interference at the information receiver in the case of multi-tone signals. The multi-tone optimization problem is formulated as a non-convex linearly constrained quadratic program. Two globally optimal solution approaches using mixed-integer linear programming and finite branch-and-bound techniques are proposed to solve the problem. The achieved improvement resulting from applying both solution methods to the multi-tone optimization problem is highlighted through simulations and comparisons with other solutions existing in the literature.
Nanoparticles mixed with transformer oil can potentially increase the breakdown strength of the base liquid. Unfortunately, the basic physical mechanisms leading to such improvement are still not clear. This paper implements two existing theories to model the electrical conduction of cyclohexane with TiO2 nanoparticles in a needle to plane configuration. The generation and drift of carriers in the liquid are simulated by coupling the continuity equations for electrons, positive ions, negative ions, and nanoparticles with Poisson's equation for the electric field. The current-voltage characteristics are simulated and compared with the case of pure cyclohexane. The nanoparticles are modeled as either absorbers of electrons or as source of shallow traps in the fluid, according to the existing theories. The simulations show that the considered theories predict no significant effect of nanoparticles added to cyclohexane on the conduction current from a negative point electrode in steady state or under transient conditions.
A simplification of the Bogolubov-Hartree-Fock theory, which is a natural generalization of the traditional Hartree-Fock theory, is derived. This simplification allows to express the pairing interaction in terms of the one-particle density matrix for systems interacting by attractive pair potentials, such as the Newtonian gravitational potential.
A wideband switched beam antenna array system operating from 2 to 5 GHz is presented. It is comprised of a 4 × 1 Vivaldi antenna elements and a 4 × 4 Butler matrix beamformer driven by a digitally controlled double-pole four-throw RF switch. The Butler matrix is implemented on a multilayer structure, using 90° hybrid couplers and 45° phase shifters. For the design of the coupler and phase shifter, we propose a unified methodology applied, but not limited, to elliptically shaped geometries. The multilayer realization enables us to avoid microstrip crossing and supports wideband operation of the beamforming network. To realize the Butler matrix, we introduce a step-by-step and stage-by-stage design methodology that enables accurate balance of the output weights at the antenna ports to achieve a stable beamforming performance. In this paper, we use a Vivaldi antenna element in a linear four-element array, since such element supports wideband and wide-scan angle operation. A soft condition in the form of corrugations is implemented around the periphery of the array, in order to reduce the edge effects. This technique improved the gain, the sidelobes, and helped to obtain back radiation suppression. Finally, impedance loading was also utilized in the two edge elements of the array to improve the active impedance. The proposed system of the Butler matrix in conjunction with the constructed array can be utilized as a common RF front end in a wideband air interface for a small cell 5G application and beyond as it is capable to simultaneously cover all the commercial bands from 2 to 5 GHz.
This work introduces a wideband switched beam system for femtocell 5G base stations. The system consists of a 4 x 1 Vivaldi linear array and a 4 x 4 Butler matrix able to operate from 1.9-5.1 GHz. A soft surface is introduced along the outer edges of the vivaldi elements of the array for side lobes and back radiation suppression.
The scope of this article is to develop a modular radio-frequency (RF) energy-harvesting system for smart buildings that can act as a power source for sensing devices. Electromagnetic field-strength measurements at the main campus of the KTH Royal Institute of Technology in Stockholm, Sweden, were carried out to define the strength of the available ambient signals. Mainly two spectra were available for possible RF harvesting, i.e., two cellular bands [GSM1800 and third generation (3G)] and the 2.45-GHz Wi-Fi band. Based on these measurements, a modular approach for the system was adopted. The system is composed from two modules: 1) a Wi-Fi rectenna system composed of eight dual-polarized patch antennas and 16 rectifiers to produce eight differential voltage sources connected in series and 2) a cellular rectenna system composed of eight linear tapered slot antennas and eight rectifiers to produce four differential voltage sources connected in series. We propose an innovative multiple-input, single-output (MISO) wave rectifier that yields an efficient differential output. Both rectenna modules offer full azimuthal coverage and can operate either together or independently.
In this work an implementation of an ambient radio frequency harvesting system utilizing multiple input single output approach is demonstrated. Measurements of typical ambient radiation have been conducted with respect to power levels and frequency to determine which communication signals are suitable for harvesting. The measurement campaign showed that the WiFi frequency band at 2.45 GHz is a good candidate for indoors applications. A Greinacher voltage doubler is used for the rectification. A multiple input single output - MISO scalable scheme approach is implemented that is able to provide a DC differential output voltage. Simulated and experimental results proved the MISO rectenna to be an efficient scheme for RF harvesting.
Design of array antennas for satellite applications is always a trade-off between physical constrains and pattern requirements. In this paper, the focus is on the design of a large array antenna for earth coverage applications using spot beams. The array antenna has a diameter of 1 m and consists of circular polarized horn antennas positioned in a non-uniform grid. By using a binary coded genetic algorithm (BCGA) the desired element positions and their excitations are optimized to fulfill the pattern requirements. In addition thinning has been used to study the possibility of maintaining good antenna performance when reducing the number of elements. The proposed antenna design has robust side lobe level, beam width and gain; all remain virtually unchanged under a change of operating frequency +/- 7% and under lobe steering over earth +/- 8.8 degrees.
Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here, we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on the radiation quality factor (Q-factor) (maximizing single-resonance fractional bandwidth) but are far from reaching the associated physical bounds for efficiency. The relative performance of other canonical antenna designs is comparable in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design.
In this study, an experimental method has been investigated for efficient assessments of whole-body specific absorption rates (SAR) from radio base station antennas. Using surface amplitude measurements of the electric field components together with an integral equation technique, a method is obtained which is not biased to specific antenna designs or phantom shapes. For realistic material parameters, it has been found that only the amplitude of the tangential field components over the phantom boundary is needed to accurately assess whole-body SAR, which makes the proposed method well suited for integration with commercially available SAR measurement systems. The method has been validated with simulations and measurements. Compared with a volumetric scan, and for the cases investigated, the measurement time was reduced with a factor larger than 3 while keeping the relative error smaller than 8%.
In this paper we propose a novel 32 antenna port multiple-input-multiple-output (MIMO)-cube. The total volume of the cube is 320 x 320 x 120 mm(3) . On two faces, endfire radiating linear tapered slot antennas (LTSAs) are placed and on the remaining sides, a mix of both LTSAs and broadside patch antennas are placed. In total 16 LTSAs and 8 dual polarized patches are used. The LTSA is designed to operate at the GSM and 3G bands, from 1.7 to 2.3 GHz. A corrugation pattern is introduced along the edges of the LTSAs covering one face to increase directivity and decrease sidelobes. The LTSAs are placed in two different orientations in order to receive two polarisations. The patch antenna is dual band and dual polarized. It operates in the frequency bands 2.4-2.5 and 5.45-5.6 GHz where Wi-Fi communication is made. The spatial placement, with antennas on all sides of the cuboid, ensures full azimuthal coverage despite the high directivity of the antennas. Using different antennas on different faces of the cube further optimizes the volume efficiency of the cube for azimuthal coverage.
We study the long-time behavior of solutions to the Korteweg-de Vries-type equation partial derivative(t)u=-partial derivative(x)(partial derivative(2)(x)u+f(u)-b(t,x)u), with initial conditions close to a stable, b=0 solitary wave. The coefficient b is a bounded and slowly varying function, and f is a nonlinearity. For a restricted class of nonlinearities, we prove that for long time intervals, such solutions have the form of the solitary wave, whose center and scale evolve according to a certain dynamical law involving the function b(t,x), plus an H-1(R)-small fluctuation. The result is stronger than those previously obtained for general nonlinearities f.
A miniaturized tactical high power omni-directional antenna in HF/VHF Band is here proposed. The antenna has been designed for wideband frequency 5:1 (20-100 MHz) applications. In addition, tactical requirements such as weight, no ground-plane, windproof, and pressure-resistant have been satisfied in this antenna design. The proposed antenna has been designed with a maximum length of about 1m that is equal to a fifteenth of wavelength (lambda/15) in electrical size at 20 MHz. We have introduced a practical transformer to match the novel fork-shaped monopole antenna to 50 Omega. As a result, the antenna is matched by measured VSWR almost less than 3 over the whole frequency band. The antenna results in a good omni-directional radiation pattern without adding a ground plane. The antenna has been fabricated and its gain varies from -5 dBi to 0 dBi. A good agreement is achieved between measurement and simulation with 100W power handling. Simulation results of the antenna have been obtained by using both HFSS Ansoft Designer and Advanced Design System softwares.
This paper introduces a novel filtering approach that employs integrated periodic structures with a conventional Vivaldi antenna to achieve a fully integrated bandpass filtering antenna. The approach results in a wide out-of-band suppression, high passband selectivity, adjustable operational bandwidth, and low insertion loss. The proposed filtering approach maintains the original size of the conventional Vivaldi antenna (base antenna) without requiring additional modifications. To validate the approach, we present two filtering Vivaldi antennas: filtering antenna I (center frequency: 18GHz, fractional bandwidth: 21%, insertion loss: 0.32dB) and filtering antenna II (center frequency: 6.5GHz, fractional bandwidth: 12%, insertion loss: 0.6dB). Their wide out-of-band gain suppression (typically >= 15dB) covers the conventional Vivaldi antenna's frequency range (4-24GHz). A prototype of the filtering antenna I is manufactured. Its measurement results validate the proposed approach and show good agreement with the simulated reflection coefficient, realized gain, and radiation patterns. The features of the proposed filtering antenna approach, make it suitable for various applications requiring efficient frequency filtering.
In this paper, we propose a unit-cell element suitable designed for wide-angle scanning active phased array antennas. The design method utilizes the sub-array factor theory inside the unit-cell. The generalization shows that the unit-cell architecture can be applied to different elements to improve their embedded radiation pattern. The presented unit-cell is comprised of three similar radiating elements. It consists of one excited element and two unloaded/open passive parasitic ones. The 1 dB beamwidth of the embedded radiation pattern of the designed unit-cell with a miniaturized vivaldi element is around 130 degrees in the E-plane. It results in a gain reduction of -1.2 dB over +/- 60 degrees scan angles for a linear array. The total array factor of the proposed architecture is similar to the dense arrays with half-wavelength interelement distances and smaller (high-density array), with the same physical size. Another advantage is that the active impedance variation per scan angles has improved in comparison with half-wavelength arrays unit-cell. The number of excited ports is 1/3 of the equivalent high dense array with the same interelement distances. The whole aperture-size of the designed unit-cell is about half-wavelength in which there are three radiating elements with only one excited element.
This paper presents a novel method for analyzing and reducing the total coupled power in the Active Highly Integrated Phased Array Antennas (AIPAA), incorporating both the nonlinear impacts of the power amplifier (PA) transfer functions and the normalized scattering matrix. The proposed method introduces a new degree of freedom to reduce the coupling level utilizing two key factors: (i) the balance between the PAs’ transfer function gain and the coupled power difference to the PAs’ gate and drain/antenna ports, and (ii) the out-of-phase sum based on PAs’ transfer function phase response. The proposed method is theoretically demonstrated by accounting for all tones and also is subsequently simplified for the main tone. The method is practically validated by applying the method to a 1 × 5 AIPAA structure to reduce the total coupled power at its drain/antenna port. The results demonstrate a coupling reduction of −5 dB as an average with a maximum reduction of −20 dB, over a scan coverage of ±30∘ and 10% fractional bandwidth at 22 GHz for the center cell.
The goal of this design study is to determine the insertion-loss associated with a sequence of impedance-matching networks. These results are compared to the performance of direct integration of PA/antenna. In high-frequency, ≥ 20GHz, co-design of PA/antenna has as an important goal to remove any matching networks between the antenna and power amplifier by e.g. antenna shaping both to reduce the physical size and to improve the power added efficiency of the radio-front end. We determine the insertion-loss for matching a 2W GaN RF Transistor TGF2942 working in Class-A to a given real-valued load. This type of reference can serve as a benchmark to compare co-designed antenna performance. We also determine changes in power added efficiency and insertion-loss associated with changes in the physical size of a sequence of differently sized matching-network. The results are examined with respect to the electrical size, choice of material (dielectric attenuation), and given Z {mathbf{ant}} Z {mathbf{opt}}. In the reference case, we observe that direct matching may improve the power added efficiency by 10% for a 5% frequency bandwidth and by 6% at the center frequency.
In this communication, we propose a new wide-scan active direct-integrated 1×5 phased array antenna (AIPAA) for mm-Wave applications. The AIPAA's unit-cell comprises three K-band miniaturized tapered slot elements, a GaN high electron mobility transistor (HEMT) as a power amplifier (PA), a stability circuit, an input matching network (M.N.), and biasing components. The tapered slot antenna element is reshaped so that its input impedance closely matches the optimal load impedance of the HEMT (Zopt = 6 + j38 Ω at 22 GHz), which enhances the system efficiency. The peak-integrated PAs' power-added efficiency (PAEp) is ≥ 56 % with ≤ 9% variation over scan coverage (g±50°) at 1.5 dB power backoff from P1dB. The peak AIPAA system power-added efficiency (PAEs) is 51% with a peak array radiation efficiency of 92%. The relative frequency bandwidth with PAEp above 25% is between 9% and 13% over the scan range. The proposed AIPAA demonstrates less than 0.9 and 1 dB scanloss over the scan coverage in terms of antenna array gain and PAs' power gain (Gp), respectively. The peak PA-integrated array gain and EIRP at P1dB of 24 dBi and 51 dBm are achieved, respectively. The proposed AIPAA's size is 18 × 58 × 17 mm3 with a cell of 9.2 × 6.5 × 1.8 mm3. The measurements are in good agreement with electromagnetic and circuit co-simulation results.
In this paper, a novel omnidirectional array antenna based on Substrate Integrated Waveguide (SIW) technology is proposed. The proposed antenna is realized by removing some vias on one side of the narrow wall of a conventional SIW which results a slot antenna. The gain of an antenna with 8 slots is 9.5 dBi with a gain variation of 2 dB over 360 degrees. Besides, the antenna polarization is horizontal with the cross-polarization level of less than -40 dB in comparison with the co-polarization level. The bandwidth of 80 MHz at 6.66 GHz is achieved with the antenna's dimension of 300x22.86x1.575 mm(3). The measurement results of the antenna have a good agreement with the full-wave simulation results. The proposed antenna is well suited for 6 GHz wireless access applications due to the low cost, low complexity, simple integration, and high gain.
This work presents the design of a NB-IoT integrated antenna for LTE band 20 on a compact 50x30 mm terminal. The study will start from the Q factor limitation analysis and finish with a simulated prototype considering the different techniques to enlarge frequency bandwidth.
In time reversal acoustics (TRA), a signal is recorded by an array of transducers, time reversed, and then retransmitted into the configuration. The retransmitted signal propagates back through the same medium and retrofocuses on the source that generated the signal. If the transducer array is a single, planar (flat) surface, then this configuration is referred to as a planar, one-sided, time reversal mirror (TRM). In signal processing, for example, in active-source seismic interferometry, the measurement of the wave field at two distinct receivers, generated by a common source, is considered. Cross correlating these two observations and integrating the result over the sources yield the cross correlation function (CCF). Adopting the TRM experiments as the basic starting point and identifying the kinematically correct correspondences, it is established that the associated CCF signal processing constructions follow in a specific, infinite recording time limit. This perspective also provides for a natural rationale for selecting the Green's function components in the TRM and CCF expressions. For a planar, one-sided, TRM experiment and the corresponding CCF signal processing construction, in a three-dimensional homogeneous medium, the exact expressions are explicitly calculated, and the connecting limiting relationship verified. Finally, the TRM and CCF results are understood in terms of the underlying, governing, two-way wave equation, its corresponding time reversal invariance (TRI) symmetry, and the absence of TRI symmetry in the associated one-way wave equations, highlighting the role played by the evanescent modal contributions.
Calculating the mutual coupling between antennas on vehicles using full-wave simulations requires a vast amount of computer resources due to the electrical size of the structures. We therefore propose an alternative and approximate method to determine mutual coupling between antennas on vehicles for the case where there is line-of-sight (LOS) between the antennas. The proposed method is based on approximating the mutual coupling between LOS antennas on vehicles as near-field transmission between antennas in free space. We begin the analysis with a brief review of four methods for calculating the near-field free-space transmission. Of the investigated methods, we demonstrate that a nonsingular form of the near-field transmission integral originally proposed by Yaghjian (1982) is the most suitable for LOS antennas on vehicles. We introduce a modification to this method, in order to only use the antenna far-fields and geometrical separation to determine the mutual coupling. The comparison with full-wave simulations indicates that the proposed method has a good accuracy for LOS antennas. This paper ends with a full-scale mutual coupling calculation for two monopoles on an aircraft under LOS conditions, demonstrating a root mean square (rms) accuracy of 6 dB for frequencies up to 5 GHz, as compared with full-wave simulations.
The quality of small array antennas in airborne monopulse systems can be significantly reduced by the radome. We therefore present a convex optimization approach to minimize radome effects in monopulse arrays. This is achieved by using active element patterns in the optimization to determine the excitation weights. Simulation results for a BoR array with 48 elements and an extended hemispherical radome are presented. We demonstrate that it is possible to reduce the side-lobe level by 3.5 dB by taking radome effects into account in the optimization. This approach also results in an increased gain, particularly at large scan angles. Furthermore, the presented approach allows the monopulse slope to be indirectly specified as a design parameter. It is shown that the trade-off between the monopulse slope coefficient and the side-lobe level is approximately linear.
The four-quadrant monopulse array is widely used for direction of arrival (DOA) estimation. Errors in the angle estimate are introduced when installing the array on a platform, due to unwanted reflections in the platform, as well as reflection and refraction in the radome. These installation effects are captured in the installed element patterns, which can be computed using a number of computational electromagnetics methods. In this paper, we demonstrate that the error introduced in the DOA estimate can be determined from the installed element patterns. To illustrate how the method is used, we present results for two cases: (a) BoR-array without radome and (b) BoR-array with an extended hemispherical radome. The presented method can be applied for any installation configuration, as long as the installed element patterns can be computed.
Direction‐of‐arrival (DoA) estimation accuracy can be degraded due to installation effects, such as platform reflections, diffraction from metal edges, and reflections and refraction in the radome. To analyze these effects, this paper starts with a definition of the term installation error related to DoA estimation. Thereafter, we present a postprocessing method, which can be used to determine the DoA estimation accuracy for installed antennas. By computing synthetic signals from the installed far‐field data, it is possible to analyze the installation errors described above, in addition to analyzing array model errors. The method formulation is general, thus allowing generic array configurations, installation configurations, and direction‐finding algorithms to be studied. The use of the presented method is demonstrated by a case study of a wideband four‐quadrant array. In this case study, we investigate the installation errors due to a single‐shell radome. Thereafter, the effects of platform reflections are also analyzed, for an antenna placement in the tail of a fighter aircraft. Simulation results are presented for both the monopulse and the MUltiple SIgnal Classification direction‐finding algorithms.
We study solutions close to solitary waves of the pseudo-relativistic Hartree equation describing boson stars under the influence of an external gravitational field. In particular, we analyse the long-time effective dynamics of such solutions. In essence, we establish a ( long-time) stability result for solutions describing boson stars that move under the influence of an external gravitational field. The proof of our main result tackles difficulties that are absent when deriving similar results on effective solitary wave motions for nonlinear Schrodinger equations or nonlinear wave equations. This is due to the fact that the pseudo-relativisitic Hartree equation does not exhibit Galilean or Lorentz covariance.
We study the nonlinear equation i theta t psi = (root-Delta+m(2) - m) psi - (vertical bar x vertical bar(-1) * vertical bar psi vertical bar(2)) psi on R-3, which is known to describe the dynamics of pseudo-relativistic boson stars in the meanfield limit. For positive mass parameters, m > 0, we prove existence of travelling solitary waves, psi(t, x) = ei t mu phi(v)(x - vt), for some mu is an element of R and with speed vertical bar v vertical bar < 1, where c = 1 corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with v = 0). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions phi(v) H-1/2(R-3) as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type arguments. In addition to their existence, we prove orbital stability of travelling solitary waves psi(t, x) = e i t mu(v)(x - vt) and pointwise exponential decay of phi(v)(x) in x.
We study the behavior of solitary-wave solutions of some generalized nonlinear Schrodinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We consider solutions of the equations with a non-vanishing external potential corresponding to initial conditions close to one of these solitary wave solutions and show that, over a large interval of time, they describe a solitary wave whose center of mass motion is a solution of Newton's equations of motion for a point particle in the given external potential, up to small corrections corresponding to radiation damping.
Although, the stored electromagnetic energy of an antenna is used to determine the antenna Q, it is difficult to define the stored energy. The stored energy can be estimated from the input impedance of the antenna, the electromagnetic fields around the antenna, and the current densities in the antenna structure. These estimates are similar but not equal for all antennas. Here, the different approaches to determine the stored energy are discussed.
An antenna identity, derived from the forward scattering sum rule, shows that the partial realized gain of an antenna is related to the polarizability of the antenna structure. The partial realized gain contains the mismatch, directivity, efficiency, and polarization properties of the antenna. The antenna identity expresses how the performance depends on the electrical size and shape of the antenna structure. It is also the starting point for several antenna bounds. In this paper, the identity, its associated physical bounds, and computational aspects of the polarizability dyadics are discussed.
Physical bounds on the directivity Q-factor quotient and optimal current distributions are determined for antennas of arbitrary shape and size using an optimization formulation. A variational approach offers closed form solutions for small antennas expressed in the polarizability of the antenna structure. Finite sized antennas are solved using Lagrangian parameters in a method of moments formulation. It is also shown that the optimal charge density for a small antenna can be generated by several current densities. Numerical examples for small and large antennas are used to illustrate the results.
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.
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 energy expressions proposed by Vandenbosch for many but not all 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 the electrical size ka that is interpreted as the far-field energy in the interior of the sphere.
Time-reversal retrofocusing is used together with a gradient based inverse scattering algorithm to identify the material distribution in a cavity. The time-reversal retrofocusing algorithm designs input fields such that the field energy is concentrated to the region where the material is unknown at a specific time. After this time the field energy in the cavity decays rapidly.
The Q-factor of an antenna has been used to evaluate the maximum achievable bandwidth in small antennas. This capability has been extended to resonant periodic structures as well, enabling the maximum achievable bandwidth of specific element shapes to be evaluated for narrowband antenna arrays. In this paper, the sensitivity of the bandwidth to perturbations in the array element is studied for infinite periodic arrays above a ground plane.
We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.
A passive approximation problem is formulated where the target function an arbitrary complex-valued continuous function defined on an proximation domain consisting of a finite union of closed and bounded tervals on the real axis. The norm used is a weighted L-p-norm where 1 p <= infinity. The approximating functions are Herglotz functions nerated by a measure with Holder continuous density in an arbitrary ighborhood of the approximation domain. Hence, the imaginary and the al parts of the approximating functions are Holder continuous nctions given by the density of the measure and its Hilbert transform, spectively. In practice, it is useful to employ finite B-spline pansions to represent the generating measure. The corresponding proximation problem can then be posed as a finite-dimensional convex timization problem which is amenable for numerical solution. A nstructive proof is given here showing that the convex cone of proximating functions generated by finite uniform B-spline expansions fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in e convex cone of Herglotz functions which are locally Holder ntinuous in a neighborhood of the approximation domain, as mentioned ove. As an illustration, typical physical application examples are cluded regarding the passive approximation and optimization of a near system having metamaterial characteristics, as well as passive alization of optimal absorption of a dielectric small sphere over a nite bandwidth.
Quadratically constrained quadratic programming (QCQP) can be used to determine the best Q-factor for small antennas with constraints on the antenna efficiency. Constraints on the total directivity and a given front-to-back ratio can also be expressed as QCQP. Such problems are non-convex and hence challenging to solve. Their solution gives the best Q-factor available for any antenna within the considered volume. Thus, solutions to this type of problems provide a tool, which before the design can predict the best possible antenna performance within a given volume of a device. It is hence important to investigate methods to solve this class of QCQP problems. In this paper we compare and investigate two relaxation methods, the Lagrangian dual and semidefinite relaxation, to estimate lower bounds on the Q-factor. The former method is here reduced to solving a generalized eigenvalue-problem. Properties of the different relaxation methods are illustrated and compared. We focus in this paper on the Q-factor and its relation to efficiency, as expressed by the dissipation factor. However, these tools also apply to a larger class of problems including constraints on the directivity and other far-field conditions.
Constraints on the directivity reduce the available bandwidth of antennas. We develop here a formulation that determines the smallest Q-factor for an arbitrary shaped embedded antenna for a given partial or total directivity. An embedded antenna is an antenna that is located within a device often as part of a circuit board, where the main volume of the device is dedicated to non-antenna functions. We show that semi-definite relaxation can be used to predict the lowest Q-factor in an embedded antenna for a partial or a total directivity in a given direction, and that the bound is tight. The paper ends with an example.
Pareto-front optimization of antenna properties based on the stored energy approach are investigated in this paper with different methods. The goal is to study how bandwidth through the Q-factor depend on antenna design constraints. We consider two main methods, semi-definite relaxation and a dual-eigenvalue based method, applying them to the same optimization problem. The semi-definite relaxation methods tend to be easier to formulate and to solve than the eigenvalue-based method. The cost of the semi-definite relaxation comes in terms of a memory-intensive solution method.
We consider the nonlinear equation i partial derivative(t)psi = (root-Delta+m(2) - m)psi - (vertical bar x vertical bar(-1) * vertical bar psi vertical bar(2))psi on R-3 describing the dynamics of pseudo-relativistic boson stars in the mean-field limit. Recently this equation, with an external potential has been used to describe the dynamics of boson stars under the influence of an external gravitational field. This analysis makes one explicit critical assumption. To the above differential equation we call associate all energy function. The assumption is on the size of the kernel of the Hessian of the energy functional when it is linearized around a soliton, In this paper we provide a numerical indicator that the assumption is satisfied. To achieve this goal. we need to numerically calculate the soliton for a range of normalized frequencies as well as and the spectrum of the linearization around a soliton of the Euler-Lagrange equations describing the minimizer.
The equations for the electromagnetic field in an anisotropic media are written in a form containing only the transverse field components relative to a half plane boundary. The operator corresponding to this formulation is the electromagnetic system's matrix. A constructive proof of the existence of directional wave-field decomposition with respect to the normal of the boundary is presented. In the process of defining the wave-field decomposition (wave-splitting), the resolvent set of the time-Laplace representation of the system's matrix is analyzed. This set is shown to contain a strip around the imaginary axis. We construct a splitting matrix as a Dunford-Taylor type integral over the resolvent of the unbounded operator defined by the electromagnetic system's matrix. The splitting matrix commutes with the system's matrix and the decomposition is obtained via a generalized eigenvalue-eigenvector procedure. The decomposition is expressed in terms of components of the splitting matrix. The constructive solution to the question of the existence of a decomposition also generates an impedance mapping solution to an algebraic Riccati operator equation. This solution is the electromagnetic generalization in an anisotropic media of a Dirichlet-to-Neumann map.
An extension of directional wave field decomposition in acoustics from heterogenous isotropic media to generic heterogenous anisotropic media is established. We make a connection between the Dirichlet-to-Neumann map for a level plane, the solution to an algebraic Riccati operator equation, and a projector defined via a Dunford-Taylor type integral over the resolvent of a nonnormal, noncompact matrix operator with continuous spectrum. In the course of the analysis, the spectrum of the Laplace transformed acoustic system's matrix is analyzed and shown to separate into two nontrivial parts. The existence of a projector is established and using a generalized eigenvector procedure, we find the solution to the associated algebraic Riccati operator equation. The solution generates the decomposition of the wave field and is expressed in terms of the elements of a Dunford-Taylor type integral over the resolvent.