Delta-gap Source Research Articles

Characteristic Mode Formulation for Antennas With Waveguide Port Feeding Structures

In conventional characteristic mode (CM) theory, modal weighted coefficient (MWC) is often adopted to measure the interaction of CMs with external excitations. However, the MWC is only available in simple source models like plane wave incidence and the delta-gap source. In this letter, a CMs formulation is proposed for analyzing the radiation or scattering properties of antennas with practical waveguide port (WP) feedings. Owing to the energy-based derivation, the resultant CMs have a clear physical interpretation and forms an orthogonal set of current basis and far-field basis which can be used for modal decomposition. The following two benefits are obtained with the proposed method: first, it considers the influence of the feeding structures and can measuring the mode excitation level due to the more practical WP excitations; and second, the CMs solved from radiation and scattering problem are consistent, which provide the possibility to optimize the radiation and scattering performance of the antennas with the same set of CMs. Numerical examples are presented to illustrate the accuracy and effectiveness of the proposed CMs method in analysis of antennas with practical WPs.

Efficient Characteristic Mode Analysis for Radiation Problems of Antenna Arrays

The analysis for large-scale antenna arrays is a hot topic for design and optimization. In this paper, an efficient method for analyzing antenna arrays by using characteristic mode (CM) is proposed. In order to analyze common antennas composing of conductor and dielectric, the theory of CM is first introduced into the volume-surface integral equation. An auxiliary general eigen-equation is established to make the modes orthogonal. Furthermore, a source mode (SM) is constructed to modify the accuracy when using CMs to expand the currents excited by a delta gap source for antenna problems. To demonstrate the influence of antenna structures and excitations on the CM and SM, three antennas are analyzed and only a few modes are required to achieve a good accuracy. Due to the periodicity of antenna arrays, CMs can be served as entire-domain basis functions defined on one antenna element and reused to reduce the unknowns in the method of moments (MoM). Numerical results have shown that the proposed method can have a good agreement with the traditional MoM. Meanwhile, both the memory requirements and computational time of the proposed method can be significantly reduced.

Reply to “Comments on “Stored Energies and Radiation Q””

It will be shown that the comment [1] contains numerous errors, misconceptions, inaccuracies, false assumptions, misunderstandings and unjustified claims. The analysis of the comment is built on a false assumption that the terminal current of an antenna fed by a waveguide is independent of frequency. This false assumption arises from the misunderstandings on the basic theory of transmission lines and misconceptions of normalization for a linear system. As a result, all the equations obtained from the assumption in the comment are incorrect, and the related discussions are untruthful. The delta gap source modeling has been abused in the comment, and this is reflected in the numerical results in the comment that give rise to negative stored energy. The main results of the commented paper have been misinterpreted by the authors of the comment, and the related analysis is established on illogical reasoning. The comment fails to pinpoint any errors in the commented paper. Instead, it reveals that the main results obtained by the authors of the comment in their previous publication [2] are incorrect.

Efficient Antenna Modeling by DGTD: Leap-frog discontinuous Galerkin timedomain method

An essential characteristic for the accurate simulation of wideband antenna systems is the modeling of their intricate geometrical details, including the feeding ports. In this article, we describe a leap-frog (LF) discontinuous Galerkin (DG) time-domain (TD) method combined with an efficient local time-stepping (LTS) strategy to deal with the high contrast in the element sizes for the electromagnetic modeling of these kinds of structures. The traditional delta-gap source model and a realistic coaxial port model are revisited. Numerical examples are presented and validated with measurements and commercial software simulations to demonstrate the applicability of the proposed approach.

Convergence of Low-Frequency EFIE-Based Systems With Weighted Right-Hand-Side Effect

This paper addresses the convergence of the electric-field integral equation (EFIE)-based matrix systems with the right-hand-side effect. The role of the right-hand-side excitation in determining the convergence rate of the iterative solvers is found to be important or even crucial at low frequencies. The weighted contributions from different singular vectors are decided by not only the corresponding singular values but also the right-hand side. Based on this understanding, we investigate the low-frequency stabilized form of both EFIE and Calderon multiplicative preconditioner EFIE (CMP-EFIE) on capacitive problems. For the parallel-plate capacitor excited by the delta-gap source, the singular vectors with small singular values cannot be excited, and the charge currents on the capacitive surface dominate. Thus, the stability of the EFIE-based system can be achieved at low frequencies. Detailed spectral analysis and convergent results are carried out in order to capture the physical nature of the problems.

Comprehensive Study of the Spurious Effects on the Signal Guidance in Coplanar Waveguides

A study of the propagation characteristics and several signal integrity aspects of a conventional coplanar waveguide (CPW) is presented here. The study considers the bound and leaky modes supported by this structure up to high frequencies. The analysis of the dispersion characteristics of the structure is complemented with the study of the voltage excited along the line when fed by a delta-gap source of current. The results thus obtained allow us to discuss on the physical meaning of the modes and the relevance of the residual wave, which is key to link the practical role played by the different modal solutions with the spurious effects that may appear in the structure. The analysis of the eye-diagram performance also reveals that the signal integrity in CPW systems basically relies on the excitation of the parasitic fundamental coupled slotline mode as well as the high-frequency excitation of the continuous spectrum. These aspects have been studied in detail.

An Enhanced Gap Source Model

An enhanced gap source model is introduced by combination with Rao-Wilton-Glisson (RWG) basis functions. For decades, the stability of the delta gap source model remains a big problem. The RWG basis with triangulation and the feeding-edge model have been widely used in numerical analysis of antennas. Since the feeding-edge model uses a single RWG edge as the driving source and neglects the gap width effect, the resulting current undergoes sharp transition across the gap and thus the model is highly sensitive to the choice of the feeding edge. Consequently, the feeding-edge model suffers instability in calculations of current and input impedance. To circumvent these pitfalls, this enhanced gap source model uses multiple RWG edges and impulsive function to formulate the feeding behavior. This new gap source model exhibits significant improvements on both accuracy and stability. Numerical results are included to illustrate improved accuracy and stability of this new model by virtue of several typical antennas.

Reconsidering the Voltage-Gap Source Model Used in Moment Methods

To envision the delta-gap source as a physical gap of infinitesimal width may be confusing when the objective is to model an ideal voltage source of zero internal impedance. Also, rather than employing a spatially-extended impressed-source field to account for the actual feed geometry, we prefer to use a localized impressed-source field (ideal voltage source), and then explicitly model the feeding structure. A stationary formula for the input admittance is derived using the Lorentz reciprocity theorem. It is demonstrated that the current, voltage, and field relations are in accordance with the classical network theory. Despite this, we found a number of sign inconsistencies in the literature. We also prove that the input admittance as computed through a stationary formula (surface integration) equals the locally computed admittance at the feed point, provided that the electric-field integral equation (EFIE) has been discretized through Galerkin's scheme, in conjunction with a symmetric product for testing it.

Efficient, numerically robust characterisation of a large, double-loop antenna array

Arrays of circular, double-loops are treated via a semi-analytical technique, on the basis of a Method of Moments formulation. A Pocklington-type integral equation for the current is derived and discretised via a suitable set of basis functions. The matrix corresponding to the pertinent linear system is found to consist of circulant blocks. The system is therefore analytically solvable, and hence, potential ill-conditioning, encountered in large geometry cases, cannot possibly introduce any numerical instabilities to the calculations. Introduction of a delta gap source as excitation facilitates very efficient computation of the current and input admittance. The algorithm exploits almost exclusively elementary functions and yields results in terms of a set of rapidly convergent series, applicable to extremely large loops. Data for such loops are presented for the first time in literature. The method is expected to lead in the future to very efficient designs of multi-loop arrays.

Axially slotted antenna on a spheroid with an isorefractive coating

An algebraic solution is presented to the problem of radiation from an axisymmetric slot on a conducting prolate spheroid confocally coated with an isorefractive material, when the slot is excited by a delta gap source. The formulation of the problem is realized by expanding the electromagnetic field in each region in terms of spheroidal vector wave functions and a set of unknown expansion coefficients. Imposing the boundary conditions at the interface between the surface of the spheroid and the isorefractive coating, as well as that between the coating and the medium exterior to the coating leads to a set of simultaneous equations, the solution of which yields the unknown expansion coefficients. Numerical results are presented as normalized power patterns and radiation patterns for isorefractive materials, to show the effects of the coating on the radiation from the antenna.

Excitation of a Periodic Microstrip Line b>y an Aperiodic Delta-Gap Source

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The current excited by a delta-gap source on a periodically loaded microstrip line is studied by means of the array scanning method. The method requires the efficient solution of a large number of auxiliary Floquet-periodic subproblems, cast here in the form of an electric-field integral equation (EFIE) that has been discretized with the method of moments (MoM) in the unit cell. Numerical results are provided for a specific structure in both bound and radiative frequency ranges and are validated through independent codes. </para>

A Magnetic Frill Source Model for Time-Domain Integral-Equation Based Solvers

A magnetic frill source model developed for time-domain integral-equation-based solvers for accurate characterization of coaxially driven structures is presented. The MFS model is developed by representing the coax as a magnetic frill current, and the evaluation of the expressions for fields radiated by this current does not call for numerical differentiation of any kind. Also, the expression for the axial component of the electric field only calls for one-dimensional numerical integration. For model validation and demonstration of efficacy, the developed source model is incorporated into a marching-on-in-time (MOT) scheme for broadband characterization of coaxially-driven antenna structures comprised of arbitrarily shaped perfect electrically conducting surfaces and thin wires. The numerical results obtained from the MOT scheme incorporated with the developed source model are compared with values obtained by measurement, and with the traditionally used delta gap source model. Compared to the delta gap source model, the magnetic frill source model provides a relatively accurate characterization of the antenna structures over a wide band of frequency.

Radiation Characteristics of a Spheroidal Slot Antenna Coated with Isorefractive Materials

This paper presents an exact analytic solution to the problem of radiation from an axisymmetric slot antenna on a conducting prolate spheroid coated with an isorefractive material, when the slot is excited by a delta gap source. The problem is formulated by expanding the electromagnetic field in each region in terms of appropriate spheroidal vector wave functions and a set of unknown expansion coefficients, and imposing boundary conditions at the interface between the conducting spheroid and the isorefractive coating, as well as that between the coating and the medium outside the coating. This generates a set of simultaneous linear equations, the solution of which yields the unknown expansion coefficients. Results are presented in the form of normalized power patterns for conventional isorefractive materials as well as for isorefractive metamaterials, and for different slot locations, to show the enhancing effects of the coating on the radiation from the antenna.

Current on an Infinitely-Long Carbon Nanotube Antenna Excited by a Gap Generator

The current on an infinitely-long carbon nanotube (CN) antenna fed by a delta-gap source is studied using a Fourier transform technique. The CN is modeled as an infinitely-thin tube characterized by a semi-classical conductance, appropriate for the frequencies of interest considered in this work. The CN's current is compared with the current on solid and tubular copper antennas having similar or somewhat larger radius values. It is found that for radius values on the scale of nanometers, CNs exhibit smaller losses than cylindrical copper antennas having the same dimensions, assuming the bulk value of copper conductivity. When one assumes a more realistic, reduced copper conductivity that accounts for the nanoscopic radius of the wire, the advantage of the CN over a metallic wire is increased.

Novel Analytical Representations of the Continuous-Spectrum Current in Multilayer Stripline Structures

We consider a multilayer stripline structure excited by a delta-gap source and we study the continuous-spectrum current, which may be responsible of several spurious transmission effects such as interference with the quasi-TEM mode, undesired radiative effects, and crosstalk. In particular, a uniform asymptotic analysis of such continuous spectrum is presented, based on two alternative closed-form representations. Both representations are accurate also very close to the source and are valid inside a wide frequency range starting from DC. One formulation has a direct implementation, since it needs only knowledge of the spectral Green's function of the background structure. The other formulation requires knowledge of the exact complex (leaky) poles of the stripline Green's function and of their residues, but provides more physical insight since it gives quantitative information on the role of leaky waves in the continuous-spectrum representation in the entire considered frequency range. Numerical results which validate the accuracy and efficiency of the proposed approaches are provided at different frequencies for covered-microstrip structures with different strip widths.

Fast full-wave analysis of a cylindrical antenna using a single integral with an exact kernel

This paper presents a fast approach in the method-of-moments (MoM) analysis so as to obtain the nonuniform current distributions of cylindrical antennas with electrically large radii. An oblique incident field in its general form and a delta-gap source are considered in the formulation of nonuniform current distributions. In the Galerkin's MoM procedure, the Fourier cosine series is considered as the entire domain basis function series. In this formulation, the kernel is represented by a series of weighted spherical Hankel functions of the second kind and the convergence of this series is fast. As the result, the computation time is short. The Mathematica package is used to obtain and plot the current distributions along the cylindrical antennas.

High-frequency leaky-mode excitation on a microstrip line

The excitation of leaky modes (LMs) and the continuous spectrum (CS) on a microstrip line at high frequencies from a delta-gap source is studied. The delta-gap source models a practical source or discontinuity on the line. It is shown that the current excited from the source exhibits spurious effects at high frequencies due to the excitation of the CS (radiation spectrum), which may or may not be dominated by a physical LM, depending on the frequency range and the substrate permittivity. In some cases, the spurious effects are due to a physical LM, while in other cases the effects are due to the excitation of one or more residual-wave (RW) currents, which have not been previously studied for open microstrip lines. There are two types of RW currents: a free-space type and a surface-wave type. Depending on the frequency and the structural parameters, either of these may be the more dominant. At certain frequencies, weakly attenuated high-order LMs may also be excited, in which case spurious effects are observed out to large distances from the source.

Accurate model of arbitrary wire antennas in free space, above or inside ground

An accurate model of wire antennas in free space, above or inside lossy ground is presented in which the current is assumed to flow on the surface of the wire and the testing is also performed on the surface. To replace the traditional delta-gap source, a more accurate source model is developed by using the Huygens' principle. From this principle and reciprocity theorem, a variational formulation of the input admittance is derived. When the triangle function is chosen as both basis and weighting functions, all the elements of impedance matrix and source vector are formulated in closed forms, which can be rapidly computed. Several numerical results are given. Comparing with measured data, both the current distribution and input impedance by this model are more accurate than those of delta-gap model.

The influence of a top cover on the leakage from microstrip line

When a microwave integrated circuit is enclosed in a package, the top cover causes the transmission lines used in the circuit to become leaky at a lower frequency than otherwise. This effect is investigated in detail for microstrip line, and is found to be particularly dramatic. The leakage is strong enough to produce spurious effects that can ruin the performance of the circuit. The amplitude behavior is obtained by numerically solving for the current on a covered microstrip line due to a delta-gap source excitation. The results clearly show that a strong leaky mode (LM) is excited and that spurious effects due to the LM and from direct radiation from the source generally become more severe at higher frequencies and when the top cover is brought nearer to the strip.

Excitation of complex and backward mode on shielded lossless printed lines

In this paper, the surface current density excited by a delta-gap voltage source on shielded printed lines is computed and its modal decomposition analyzed. This analysis specifically aims to determine the practical excitation of complex and/or backward modes in this kind of structures. It has been found that complex modes in reciprocal structures are always excited in pairs whose propagation constants and amplitudes of excitation have the same imaginary part and opposite sign real part. The combination of the pair of complex modes gives rise to an evanescent mode whose amplitude is modulated by a sinusoidal function. Backward modes have also been found to be part of the modal spectrum excited by the source and, thus, in a frequency sweep, they appear after the attenuation constant of a pair of complex modes goes to zero.