Spectral Domain Method Research Articles

Dispersion characteristics of open and shielded microstrip lines under a combined principal axes rotation of electrically and magnetically anisotropic substrates

This work examines the dispersion properties of microstrip transmission lines whose substrate permittivity and permeability tensors are rotated simultaneously. The analysis takes into account both shielded and open structures, including both single and coupled microstrip line geometries. The spectral-domain method is utilized to formulate the dyadic impedance Green's function, and Galerkin's method is applied to find the propagation constants. Numerical studies are performed when the angular difference between the principal axes of ( epsilon ) and ( mu ) tensors is fixed, but both are rotated from 0 to 90 degrees . The dispersion characteristics for all structures are computed over a wide frequency band that ranges from 0.1-100 GHz. The study indicates that propagation properties of microwave integrated circuits (MICs) with dielectrically and magnetically anisotropic substrates (such as composites) can be changed considerably by the misalignment of material and structure coordinates systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design of impedance-transforming microstrip-balanced stripline tapered transitions

An improved approach to the computer-aided modelling of impedance-transforming microstrip-balanced stripline tapers used in microwave doubly balanced mixers is presented. The spectral domain method has been used to determine the parameters of a suspended microstrip with finite ground plane width. Calculations show that dispersion effects in the analysed structure are insignificant. The designed and realised 50–100ω transition on a 1.5mm thick alumina substrate exhibited very good or acceptable performance up to 10 and 15GHz, respectively. A method to suppress undesired modes appearing in the case of shielded transitions has been proposed and experimentally verified.

Regular solution of singular integral equation for finlines

The analysis of unilateral finlines has been completed using a new method, regular solution of singular integral equation (RSSIE). It is demonstrated that the results obtained by this method are more accurate than those computed by the spectral domain method (SDM) by comparing the data measured. In some special cases where the results can be obtained exactly, the new method gives more accurate values than those calculated by the SDM. Dominant and higher-order modes can be calculated effectively and accurately. The computer time required by this method is decreased considerably compared with SDM (about 1/45 of the time required by SDM).

Analysis of single and coupled microstrip lines on anisotropic substrates using differential matrix operators and the spectral-domain method

A differential matrix operator technique is presented to simplify the formulation of boundary-value problems for open millimeter-wave integrated circuits that use anisotropic substrates. The spectral-domain method is applied to analyze the propagation characteristics of single and coupled microstrip lines printed on anisotropic substrates whose properties are described by both ( in ) and ( mu ) tensors. In addition to considering the permittivity and permeability as a uniaxial or biaxial tensor, the effects of coordinate misalignment between the principal axes of ( in ) and those of the structure in the transverse plane are also included. It is shown that the misalignment in ( in ) and the presence of the ( mu ) tensor have a significant effect on the dispersive properties of these two structures. >

Radar cross-section of dielectric-coated conducting cylinder loaded with periodic metallic strips using mixed SDM, CGM and FFT : TE incidence

A mixed technique is presented for calculating the radar cross-section characteristics of a dielectric-coated conducting cylinder with TE-wave incidence loaded with periodic metallic strips. The technique is based on the spectral-domain method (SDM), conjugate gradient method (CGM) and fast Fourier transform (FFT). Since the property of circular Toeplitz matrix has been used, only memory directly proportional to NsNb (Ns is the number of strips and Nb is the number of basis functions for approximating the currents on the strips) is needed, which allows treatment of the cylinder loaded with tens or even hundreds of strips. The RCS of a dielectric-coated conducting cylinder loaded with many periodic metallic strips are first calculated. Numerical results show that the RCS can be effectively controlled by adjusting the period or the spaces between strips.

Full-wave analysis of radiating planar resonators with the method of lines

The method of lines (MoL) is extended to analyze radiating planar resonators by the use of absorbing boundary conditions. For stratified layers, an equivalent network is derived to set up a system equation by simple multiplication of hybrid matrices. As an example, the complex resonant frequency of a microstrip patch is computed and compared to results achieved with the integral equation method in spectral domain. The radiation in the near-field region is depicted by a vector plot of the energy flow, given by the real part of the Poynting vector. >

Dispersion characteristics of the broadside-coupled coplanar waveguide

The dispersive properties for the even- and odd-modes of the broadside-coupled coplanar waveguide (CPW) are determined using the spectral domain method. Various numerical results of the even- and odd-mode effective dielectric constants as a function of frequency are presented and discussed. It is found that the structure has a very weak dispersion. This fact is further confirmed through a comparison between the calculated dynamic and quasi-static results of the even- and odd-mode effective dielectric constants. The low dispersion feature signifies the fact that the quasi-static analysis is adequate for designing practical microwave and millimeter-wave circuits employing broadside-coupled CPW. >

Analysis of bilateral coplanar waveguides printed on anisotropic substrates for use in monolithic MICs

The spectral-domain method is applied to the analysis of bilateral (double-sided) coplanar waveguides that are printed on electric and/or magnetic anisotropic substrates. A nondecoupling approach is used to solve the coupled differential equations for the transverse propagation constants inside the substrate. The dyadic admittance Green's function is derived for both open and shielded bilateral coplanar waveguides, taking into account the anisotropy of the material. Finally, numerical results, describing the propagation characteristics of these structures, are presented for both electric and magnetic wall symmetries.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Resonance in a spherical-circular microstrip structure with an airgap

The resonance problem of the spherical-circular microstrip structure with an airgap between the substrate layer and the ground conducting sphere is studied by using a rigorous Green's function formulation in the spectral domain and Galerkin's moment method calculation. Complex resonant frequencies are obtained in this study, which provide the resonant frequencies and half-power bandwidth of the structure. From the numerical results, it is found that with the increasing of the airgap thickness, the half-power bandwidth of the structure is considerably increased. This improves the low-bandwidth characteristics of microstrip structures. Details of the numerical results are presented and discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new technique for the quasi-TEM analysis of conductor-backed coplanar waveguide structures

Numerically efficient and accurate formulae based on the spectral domain method for the analysis of conductor backed coplanar waveguide structures are presented. Quasi-TEM parameters are obtained for these waveguide structures by using piecewise linear functions to approximate the potential distribution at the air-dielectric interface. Techniques such as nonuniform discretization and bound estimation are described which demonstrate shorter computational times. Results on the characteristic impedance calculation of standard coplanar waveguide are given to demonstrate the numerical accuracy and efficiency of the method presented here. >

Application of the spectral domain method for the study of surface slow waves in nonreciprocal planar structures with a multilayered gyroelectric substrate

The full-wave spectral domain approach together with the equivalent boundary method is used to analyse the nonreciprocal wave propagation in laterally open boundary planar structures with a multilayered gyroelectric substrate. A study of the nonreciprocal surface slow waves appearing in an externally magnetised MIS line is presented. This work also presents the ability of that configuration to support both slow wave and nonreciprocal effects with reasonable losses. Various numerical results are presented that show the dependence of the propagation parameters on the magnitude and orientation of the biasing magnetic field. It is shown that external control of the magnitude of the biasing field permits equalisation of the modal phase velocities in a pair of coupled strips on a magnetised MIS configuration. >

Broadband Microstrip Antennas on Electrically Thick Substrates

Two configurations of broadband microstrip antennas are proposed and analyzed numerically by the full-wave spectral-domain method. One is a square Archimedean spiral microstrip antenna which yields circular polarization; the second configuration is a log-periodic patch microstrip antenna, which radiates linearly. In this paper, the definition of bandwidth of an antenna is redefined and is based on both VSWR and radiation pattern behavior. A 25% bandwidth for a square Archimedean spiral microstrip antenna and a 2:1 bandwidth for a log-periodic patch microstrip antenna are achieved using electrically thick (1/8λ to 1/4λ) substrates.

Effects of substrate anisotropy on coupled bilateral finlines

The spectral-domain method is used to study coupled bilateral fin lines on uniaxial and biaxial substrates. New results describing dispersion characteristics of both the even and odd modes, including the effects of the misalignment between the waveguide coordinate system and that of a substrate, are also provided. © 1992 John Wiley & Sons, Inc.

Closed-form expressions for a number of Fourier-Bessel series encountered in the GSD method (waveguide analysis)

In the application of the generalized spectral-domain (GSD) method to the analysis of waveguides, infinite sums over eigenmodes have to be evaluated. The efficiency of the GSD method is considerably enhanced if these sums can be replaced by closed-form expressions. Up to now, appropriate identities are known for circular and rectangular waveguides only. Expressions associated with sector waveguides are considered. >

Analytical inversion of a class of infinitely dimensioned matrices encountered in some microwave problems

A method is presented for analytically inverting a class of infinitely dimensioned matrices that are usually encountered in the analysis of microwave problems by applying the generalized spectral domain (GSD) method. It is shown that numerically inverting the truncated matrix and truncating the analytically inverted matrix leads to different results, which converge to each other very slowly. CPU time and storage requirements of a number of algorithms based on the GSD method can consequently be improved by making use of the analytical inversion of such matrices.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multiple dielectric structures to eliminate moding problems in conductor-backed coplanar waveguide MIC'

A conventional conductor-backed (grounded) coplanar waveguide (CBCPW) leaks energy from its dominant mode in the form of a parallel plate mode in the substrate region at all frequencies which can generate undesirable coupling effects and produce an ineffective circuit. A multiple dielectric structure with appropriate dimensions is used to suppress the leakage effects and the spectral domain method (SDM) predicts the critical frequency (transition point for leaky and nonleaky modes) for the waveguide. Experimental data verify this procedure and demonstrate the significance of the moding (leakage coupling) problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effects of misalignment on propagation characteristics of transmission lines printed on anisotropic substrates

The spectral-domain method is applied to study the propagation characteristics of grounded transmission lines on biaxial substrates whose axes are misaligned with those of the line. The three structures under investigation are the grounded slotline, microstrip, and the edge coupled line. In the formulation, an expression for the Green's function that is valid for substrates which are simultaneously characterized by their permittivity and permeability tensors is derived. The off-diagonal elements of the permittivity tensor, present due to the misalignment of the axes, are used to examine the dispersion properties of these transmission lines with numerous case-studies presented for different angles of rotation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Microstrip resonators on anisotropic substrates

The spectral domain method is applied to study shielded microstrip resonators printed on anisotropic substrates. A Green's function that takes into account the dielectric anisotropy effects is derived through a fourth-order formulation. Galerkin's method is then applied to form the characteristic equation from which the resonant frequency of the microstrip resonator is numerically obtained. Results for a microstrip situated on an isotropic substrate are used to validate the theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dispersion characteristics of moderately thick microstrip lines by the spectral domain method

The influence of the metallization thickness on the propagation characteristics of the microstrip lines is modeled by utilizing the computationally efficient spectral domain method with an approximate Green's function. The Green's function is based on the current and charge distribution at the top and bottom surfaces of the microstrips. The calculated effective dielectric constants and impedances are plotted for single and coupled microstrip lines as a function of frequency. It is seen that the effective dielectric constants obtained from resonance measurements are in good agreement with the calculated values for moderately thick (t/W<or approximately=0.15) single and coupled lines.<<ETX>>

A multipole analysis of a dielectric loaded coaxial rectangular waveguide

A multipole analysis of a coaxial rectangular waveguide whose inner conductor is circular is made in order to determine the TE and TM modes of the system. The analysis is based on using multipole (dipole, quadrupole etc.) electric and magnetic current sources to generate field solutions in the waveguide. These solutions are used to match the electromagnetic boundary condition in a homogeneous coaxial rectangular waveguide and to determine the TE and TM eigenvalues of the waveguide system. Eigenvalue results are compared with results of the generalized spectral domain method and to eigenvalue results for a ridged waveguide. Propagation in a coaxial rectangular waveguide is also studied when the coaxial rectangular waveguide is loaded with lossy inhomogeneous dielectric material. A variational formula is used to relate the TEM, TE, and TM modes of an empty coaxial rectangular waveguide to the propagation in the loaded inhomogeneous dielectric waveguide.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>