Spectral Domain Method Research Articles

Analytical attenuation calculation of asymmetrical coplanar waveguide with finite‐extent ground planes for coplanar waveguide mode

AbstractIn this study, fast and new analytical formulations have been presented for correct loss calculations in asymmetrical coplanar waveguides (CPW) with finite‐extent ground planes for CPW mode. To generalize loss analysis for CPW mode, not only gaps but also finite ground planes are assumed as asymmetric. Moreover, dielectric thickness and ground plane widths are considered as finite for this transmission line. Another important concept presented in this article is that the proposed expressions are easily applicable for CAD platforms. Through the analyses, conformal mapping techniques (CMT) have been employed. The obtained results in this work have been compared with the results of other similar studies (spectral domain method, mode matching, etc.) available in the literature. These comparisons indicate that the expressions developed in this study are found to be more suitable for accurate calculations of loss as well as the characterization of asymmetrical CPW with finite‐extent ground planes. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2082–2087, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22709

A closed‐form solution to the asymptotic part of the MOM impedance matrix and the MOM excitation vector for printed structures on planar grounded dielectric slabs

AbstractIn the spectral domain method of moments (MoM) solution of printed structures on planar grounded dielectric slabs, the infinite double integrals which appear in the asymptotic parts of the MoM impedance matrix and the MoM excitation vector elements, have been previously transformed to one‐dimensional finite integrals, which have been numerically computed using the highly specialized “International Mathematics and Statistics Library” subroutines. In this paper, these one‐dimensional integrals are evaluated in closed‐form, resulting in an improved efficiency and accuracy for the rigorous investigation of printed antennas and complex millimeter and microwave integrated circuits. Numerical results in the form of mutual impedance between two expansion functions and input impedance of various microstrip antennas are presented to assess the accuracy of these closed‐form expressions. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 882–886, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22274

Hybrid-mode analysis of bilateral multilayered anisotropic CPW couplers

The dispersive characteristics of multilayered bilateral anisotropic coplanar couplers are determined using the spectral domain method. The dyadicadmittance Green's function is derived for both open and shielded couplers by extending the immittance-approach technique to multilayered structures via a recursive process that takes into account the anisotropy of the material. The number of dielectric layers is arbitrary and can be chosen by the designer. Explicit algorithms and numerical results are provided that describe the propagation characteristics of these structures for both electric and magnetic wall symmetries. The convergence and CPU times are also investigated.

EFFICIENT ANALYSIS OF FERROELECTRIC DEVICE FOR MICROWAVE PROPAGATION CHARACTERISTICS

ABSTRACT In this paper, we proposed a procedure to analyze a ferroelectric multilayer microstrip structure using the spectral domain method (SDM), which is used to find the microwave design parameters. In order to calculate the microwave characteristics of the proposed ferroelectric multilayer structure, propagation constant and effective permittivity are calculated from the SDM. The microwave design parameters of the proposed structure are optimized by using (1 + 1) evolution strategy (ES) combined with SDM. This novel numerical technique make it possible to take advantage of the high accuracy of the SDM as well as the high efficiency of the (1 + 1) ES.

VECTOR SPECTRAL-DOMAIN METHOD FOR THE ANALYSIS OF FREQUENCY SELECTIVE SURFACES

Standard spectral-domain method (SDM) is one of the popular approaches to analyze frequency selective surfaces (FSS). However, it is inherently incapable of handling normal incidence because of its dubious definition of excitation fields, reflection and transmission coefficients using z-component of vector potentials. Moreover, as far as the author knows, it has never been applied to analyze FSS with gangbuster arrays. In this paper, an improved SDM, the vector spectral-domain method, is presented. By proving the equivalence of the spectra of unit cell current and element current, the scattered field from FSS structures is formulated in terms of spectral- domain element current instead of spectral-domain unit cell current. Galerkin's method is applied to obtain the unknown induced surface current. Well-established definition of excitation fields, reflection and transmission coefficients is adopted. Extensive experimental validation has been conducted.

Full-wave analysis of single cylindrical striplines and microstriplines with multilayer dielectrics

In this paper, the spectral-domain method is used to calculate the propagation characteristics of cylindrical microstrip transmission lines. The problem is formulated using an electric field integral equation and the spectral-domain Green's function. The solutions of the field components are obtained in matrix forms, which facilitate the calculations of the Green's function and the power flowing over the lines. The Green's functions are obtained in terms of transition matrices over the dielectric layers. The obtained integral equation is solved by moment method using four kinds of basis functions. The convergence of the method is proven. Based on the power–current definition, a stationary expression for the characteristic impedance has been derived analytically. Numerical results of the effective dielectric constant and the characteristic impedance for various line parameters are calculated and analysed. The computed data are found to be in good agreement with results obtained using other methods. The formulation is then applied to covered microstripline, microstripline and stripline with air gaps, for which data are not found in the literature to date. The presented method is used to guide design of microstrip coil for magnetic resonance imaging. This method is also suitable for investigation of multiconductor strip lines. Copyright © 2006 John Wiley & Sons, Ltd.

Considerations for the efficient spectral evaluation of reaction integrals associated with separated domains

The authors address some aspects that have to be considered when using a recently proposed contour-deformation technique for the efficient numerical evaluation of reaction integrals arising in the spectral-domain method of moments for testing and expansion functions that exist on separated domains. The method is particularly efficient in the context of microstrip patch antenna elements and arrays where the testing and expansion functions can either be entire-domain functions on different antenna elements or where they are widely separated subdomain functions on the same or different antenna elements. However, the method becomes less efficient for testing and expansion functions that are not so widely separated. It is shown how the separation distance between the testing and expansion functions, in addition to substrate thickness, affects the behaviour of the reaction integrand and how the choice of a more suitable integration contour can simplify the numerical evaluation of the associated integral, especially for closely spaced testing and expansion functions on thick substrates, where the original method becomes less efficient. The minimum separation distance between the domains of the testing and expansion functions, that can be accommodated with this method, is also better defined.

2-D periodic leaky-wave Antennas-part II: slot design

The far-field radiation patterns of a two-dimensional (2-D) periodic slot leaky-wave antenna (LWA) are studied. The antenna consists of a two-dimensional periodic array of slots in a conducting plane that is printed on top of a grounded dielectric slab. The antenna is excited by a simple source such as a dipole inside the slab. Reciprocity along with the spectral-domain method is used to calculate the far-field pattern, and the radiation characteristics of the structure are investigated. A comparison between the present periodic slot LWA and a 2-D periodic patch LWA discussed in Part I is given to show the advantages of the slot antenna for certain applications. The slot LWA can achieve high directivity patterns, and a circularly-polarized version of the antenna can achieve good circular-polarization at broadside.

2-D periodic leaky-wave antennas-part I: metal patch design

The far-field radiation characteristics of a two-dimensional (2-D) periodic leaky-wave antenna (LWA) constructed from a periodic array of metal patches on a grounded dielectric substrate is investigated. A simple dipole source is used as the excitation. Reciprocity together with a periodic spectral-domain method of moments is used to calculate the far-field pattern. Design rules for the scan angle, the substrate dielectric constant, and the periodicity are provided. Finally, a comparison of the 2-D periodic LWA and a dielectric-layer LWA is given to show the similar performance of the two antennas.

Sparse representations of polyphonic music

We consider two approaches for sparse decomposition of polyphonic music: a time-domain approach based on a shift-invariant model, and a frequency-domain approach based on phase-invariant power spectra. When trained on an example of a MIDI-controlled acoustic piano recording, both methods produce dictionary vectors or sets of vectors which represent underlying notes, and produce component activations related to the original MIDI score. The time-domain method is more computationally expensive, but produces sample-accurate spike-like activations and can be used for a direct time-domain reconstruction. The spectral-domain method discards phase information, but is faster than the time-domain method and retains more higher-frequency harmonics. These results suggest that these two methods would provide a powerful yet complementary approach to automatic music transcription or object-based coding of musical audio.

Efficient analysis for nonlinear microwave characteristics of high-power HTS thin filmmicrostrip resonators

This paper investigates the nonlinear effects ofhigh-Tc superconducting (HTS) thin film in high-power applications. A nonlinear model forcomplex surface impedance has been proposed for the efficient analysis of the nonlinearityof HTS thin films. Further, using the developed model, analysis of HTS-MSR hasbeen done using the spectral domain method (SDM). The SDM formulation hasbeen modified to account for finite conductivity and thickness of HTS films byincorporating a complex resistive boundary condition. The results have been validatedwith the experiments performed with microstrip resonators (MSRs) based onYBa2Cu3O7−x (YBCO) thin films made by a laser ablation technique onLaAlO3 substrates, characterized for their characteristics, namely, resonant frequency and qualityfactor measured as a function of temperature and input RF power. A close agreementbetween the theoretical and measured results has been achieved validating the analysis.

Accurate Design of Finline Tapers for Millimeter Wave Applications

The design of nonuniform bilateral finlines on anisotropic substrates for millimeter wave applications is presented. The taper consists of a planar circuit with smooth variation of the slot width profile along the structure. The spectral domain method and Galerkin procedure are combined with the transmission line theory for studying the behavior of tapered bilateral finlines and evaluation of their design parameters. The influence of the substrate anisotropy on the propagation characteristics of these structures is also examined. This technique is general and can be applied to investigate a broad class of planar transmission line tapers.

Closed-form solutions for analysis of cylindrically conformal microstrip antennas with arbitrary radii

An efficient and accurate closed-form solution, based on the spectral-domain method of moments (MoM), is presented to analyze the characteristics of cylindrically conformal microstrip antennas with arbitrary radii. First, an algorithm that combines the recursive and the uniform asymptotic expansion method in different regions is developed to calculate the spectral-domain Green's functions for arbitrary dielectric coated cylinders accurately. Next, the integrands of the spectral integrals involved in MoM equation are partitioned into two parts, i.e., the fast oscillatory, slowly convergent part and the well-behaved part. Consequently, all of the integrals in MoM analysis can be categorized into two types. Through the Sommerfeld identity and its extension, these integrals are cast into closed-forms by using the nonlinear approximation method (generalized pencil-of-function method). In this method, any time-consuming numerical integration procedure is eliminated, which improves the computational efficiency drastically. Compared with the results from published references, the validity and accuracy of the method are demonstrated.

The Spectral Grid Method: A Novel Fast SchrÖdinger-Equation Solver for Semiconductor Nanodevice Simulation

A spectral-domain method is described for solving Schrodinger's equation based on the multidomain pseudospectral method and boundary patching. The computational domain is first divided into nonoverlapping subdomains. Using the Chebyshev polynomials to represent the unknown wave function in each subdomain, the spatial derivatives are calculated with a spectral accuracy at the Chebyshev collocation points. Boundary conditions at the subdomain interfaces are then enforced to ensure the global accuracy. Numerical results demonstrate that this spectral-domain method has an exponential accuracy and is flexible, and thus is an attractive method for large-scale problems. With only about four cells per wavelength, the results have an error less than 1% in our typical examples. For a typical quantum well, the method is about 51 and 295 times faster than the second-order finite-difference method for 1% and 0.1% accuracy, respectively. The spectral grid method has also been validated by results obtained by the finite-element method, semianalytical (Airy function) method, and the Numerov's method.

Entire-Domain Versus Subdomain Attachment Modes for the Spectral-Domain Method of Moments Analysis of Probe-Fed Microstrip Patch Antennas

Two different attachment modes that are widely used within the spectral-domain method of moments (MoM) analysis of probe-fed microstrip patch antennas are investigated and compared. Either of these attachment modes, the one being an entire-domain mode and the other a subdomain mode, is required for the accurate analysis of probe-to-patch junctions when used together with the MoM. In this paper, more light is shed on the ability of either approach in modeling microstrip patches of various sizes, residing on planar multilayered substrates, ranging from quite thin to relatively thick. Through a comprehensive comparison between numerical and experimental results, it turns out that the subdomain approach is somewhat more versatile than the entire-domain approach.

Characterization and analysis of high temperature superconducting microstrip andcoplanar resonators using a spectral domain method

Microwave characteristics of planar high temperature superconducting microstrip lineresonator (MSR) and coplanar waveguide (CPW) resonators have been estimated using afull wave spectral domain technique in conjunction with the complex resistive boundarycondition. The computer aided design method developed is applied to simulate thecharacteristics of planar resonators. The proposed method has been validated withexperimental results after taking into account the practical operating conditions. A reasonableagreement for the theoretically computed and measured resonant frequency and unloadedQ-value with experimental data of Porch et al (1995 IEEE Microw. Theory Technol. 2306–14) has been observed for the MSR operated at 5 GHz as well as for the CPWresonator at 7.95 GHz.

Scattering of Gaussian Beam From a Hemispherical Boss on a Conducting Plane

A new expression of a Gaussian beam derived by using a spectral domain method is applied to the scattering problem from a hemispherical boss on a conducting plane. On the method of images, the original problem is reduced to that of the scattering of two Gaussian beams by a full sphere. The scattered fields are expressed in simple closed forms which are valid when the diameter of the boss is comparable to or less than the Gaussian beamwidth. The difference between the bistatic radar cross section of a Gaussian beam and that of a plane wave is discussed.

Mutual coupling between spherical‐rectangular microstrip antennas

AbstractThe mutual coupling between rectangular microstrip patches mounted on a spherical structure is studied in this paper. The analysis approach is based on the spectral‐domain method of moments (MoM). An approximate method is developed to calculate coupling between currents located on different patches. A laboratory model is built to test different configurations of patches and to validate the calculated results. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 387–391, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11389

Modelling of GaAs-MMIC microstrip line up to 40 GHz

Modelling of MMIC multidielectric microstrip line on GaAs substrate for its precise characterization has been presented in this article. An accurate design database for the characteristic parameters of the microstrip line, namely, effective dielectric constant, characteristic impedance, and attenuation coefficient, has been generated using the spectral-domain method (SDM). The accuracy of the developed database for the frequency range 1 to 40 GHz has been verified with the experimental results. On-wafer measurements have been carried out to minimize the parasitic losses at the high frequencies and the effect of CPW-pads has been de-embedded from the measured S-parameters to obtained accurate characteristic parameters of the microstrip line. The theoretical and the measured values of the characteristic parameters of microstrip lines show good agreement within 1% to 2%. This work is expected to be useful in GaAs foundries for accurate MMIC-CAD modelling of microstrip lines up to 40 GHz. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14, 475–482, 2004.

Accurate computer‐aided modeling of multilayer GaAs microstrip lines using a spectral‐domain method

AbstractMultilayer microstrip lines are an integral part of MMIC. This paper presents an analysis of multilayer GaAs microstrip lines using a spectral‐domain method (SDM), taking into account the effect of the variation in the thickness of various layers of substrates on the characteristic impedance and the effective dielectric constant of the line. Some of the theoretical results are validated by the measured results on three‐layer GaAs microstrip lines, showing a close agreement within a 1% deviation over a large frequency range up to 20 GHz. The proposed CAD model is expected to provide an economical and fast CAD procedure for GaAs‐MMIC foundries. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 159–162, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11156