Complex Resonant Frequency Research Articles

Analysis of a cylindrical-rectangular microstrip structure with an airgap

The resonance problem of the cylindrical-rectangular microstrip structure with an airgap between the substrate layer and the ground conducting cylinder is studied by using a rigorous full-wave approach and a moment method calculation. The resonance condition is satisfied by complex resonant frequencies, which provide the information of resonant frequency and half-power bandwidth of the structure. Numerical results indicate that, with the increasing of the airgap thickness, the half-power bandwidth of the structure at the efficient radiating mode of HE/sub 0.1/ is considerably increased, which improves the narrow bandwidth characteristics of microstrip structures. Details of the numerical results, including the results for the planar rectangular microstrip structure with an airgap, are presented and analyzed. >

Resonance in a cylindrical wraparound microstrip structure with superstrate

Analysis of the resonance problem of a cylindrical wraparound microstrip structure with superstrate is presented. In this study the rigorous full-wave formulation and Galerkin's method are used. The numerical convergence for the selected sinusoidal basis functions with edge singularity is also discussed. Numerical results of the superstrate loading effects on the real and imaginary parts of complex resonant frequency of the structure as a radiator at TE/sub 01/ mode and as a resonator at HE/sub 10/ mode are calculated and analyzed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Resonant frequencies and Q-factors of a spherical cavity loaded by an eccentric dielectric sphere

A rigorous analysis for both resonant frequency and the Q-factor of the intrinsic modes in a spherical cavity loaded by an eccentric dielectric sphere is proposed. For generality, the outer shell of the structure is considered to be an arbitrary physical medium, e.g. a conductor of large but finite conductivity or a dielectric of high permittivity. With a rigorous representation for the field of the mode, energy leaking out from the structure or dissipated in the loading dielectric of loss might be taken into account by the final characteristic equation determining complex resonant frequencies. Therefore, each complex resonance obtained from the equation contains the information of the Q-factor, as well as the resonant frequency of the corresponding mode. Higher-order modes in a metallic spherical cavity loaded by an eccentric dielectric sphere are evaluated with the formulae, and numerical results for both resonant frequencies and Q-factors are obtained. >

Analysis of a dielectric resonator antenna in a cylindrical conducting cavity: HEM modes

Numerical modelling has been performed for the hybrid HEM modes of a flush-mounted dielectric resonator antenna in a cylindrical conducting cavity. The antenna is formed by a conducting cavity with a dielectric post and radiates through an annular slot in the upper ground plane. Coupled aperture magnetic current integral equations are used to model the slot and the effect of the post resonator and the cavity are included via Green&apos;s function techniques. The moment method is applied to the coupled integral equations and the complex resonant frequencies for the antenna structure are found by searching for the zeros of the determinant of the impedance matrix in the complex frequency plane. The radiation Q factor, slot field distribution and radiation field are subsequently computed at the resonant frequency. The HEM modes with the lowest resonant frequencies have been investigated for different geometrical configurations.

Resonance in a spherical annular‐ring microstrip structure

AbstractThe resonance problem of a spherical annular‐ring microstrip structure is investigated rigorously by using a Green's function formulation in the spectral domain. Numerical results of the complex resonant frequencies are obtained by using Galerkin's moment method. The convergence of the numerical calculation using different numbers of basis functions is also discussed. Typical numerical results of the resonant frequency and the quality factor, obtained from the real and imaginary parts of complex resonant frequency, for the microstrip structure used as a resonator element at TM11 mode and as an efficient radiator at TM12 mode are presented. Effects of the curvature on the resonant frequency and the quality factor of the structure are also analyzed and discussed.

Natural boundaries for Hamiltonian maps and the genesis of the Siegel disk.

The presence of a natural boundary in the angle complex plane of the function conjugating an area preserving map with a rotation is a signature of nonintegrability. Numerical results suggest that the boundary arises from the condensation of singularities when a real nonresonant frequency is approaohed by a sequence of complex resonant frequencies. For the quadratic map of the complex plane F:z'=λz+z 2 the function conjugating the linear part of F with F has q cuts with end points on a spiral if λ=e 2πip/q-a with a a>0. When p/q tends to a (quadratic) irrational number and a→0 the points coalesce on the boundary of a circle, whose image is the Siegel disk

Resonance in a superstrate-loaded cylindrical-rectangular microstrip structure

The complex resonant frequencies of the cylindrical-rectangular microstrip structure loaded with a dielectric superstrate layer is studied using a rigorous full-wave analysis, and the numerical results are obtained using the Galerkin moment method calculation. The numerical convergence for the selected sinusoidal basis functions with and without the edge singularity condition is also discussed. Numerical results for the dependence of the real and imaginary parts of the complex resonant frequencies on the superstrate permittivity and thickness are calculated and analyzed, and are compared with those obtained for the planar microstrip structure. >

Resonance of a rectangular microstrip patch on a uniaxial substrate

Effects of uniaxial anisotropy in the substrate on the complex resonant frequency of the microstrip patch antenna are investigated in terms of an integral equation formulation. The complex resonant frequency of the microstrip patch antenna is calculated using Galerkin's method to solve the integral equation. The sinusoidal functions that are selected as the basis functions, which show fast numerical convergence. Numerical results indicate that both the resonant frequency and the half-power bandwidth are increased due to positive uniaxial anisotropy and decreased due to negative uniaxial anisotropy. >

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>

Resonant attenuation in electromagnetic wave scattering from conducting elongated objects

The authors study the resonant attenuation as determined by the imaginary parts of the complex eigenfrequencies of perfectly conducting elongated objects: spheroids, cylinders with flat ends, and cylinders with hemispherical endcaps. Complex resonance frequencies are obtained from the principle of phase matching of surface waves. For the case in which these surface waves are generated by plane waves at broadside incidence, the simultaneous presence of cylindrical circumferential-wave resonances and of the resonances of meridionally propagating surface waves is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Resonance in a superstrate-loaded rectangular microstrip structure

The complex resonant frequency of a superstrate-loaded rectangular microstrip structure is investigated. The study is performed by using a full-wave analysis and Galerkin's moment method. The numerical convergence using sinusoidal basis functions, with and without considering the edge singularity to expand the unknown surface current distribution on the rectangular patch, is discussed. Numerical results for the effects of superstrate permittivity and thickness on the complex resonant frequency of the rectangular microstrip structure are also presented. >

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. >

Analysis of microstrip‐microslot applicator for biomedical applications

AbstractWe propose to investigate planar applicators and, more specifically, microstrip‐microslot applicators laid on multtiayered lossy media and covered or not with a dielectric protective layer. Using the two‐dimensional spectral domain approach (SDA), we obtain the complex resonant frequency Fc. Comparison with the experiment shows that this analysis improves the previous one‐dimensional modelization. © 1992 John Wiley &amp; Sons, Inc.

Analysis of a dielectric resonator antenna in a cylindrical conducting cavity: te and tm modes

A new configuration for a flushmounted resonator antenna is presented in which the antenna is formed by a conducting cavity with a dielectric post, and radiates through an annular slot in the upper ground plane. An aperture magnetic current integral equation is used to model the slot, and the effect of the post resonator and cavity are included via Green&apos;s function techniques. The formulation is presented for the azimuthally-independent TE and TM cases. The moment method is applied to the integral equation, and the complex resonant frequencies for the antenna structure are found by searching for the zeroes of the determinant of the impedance matrix in the complex-frequency plane. The radiation Q factor, slot-field distribution, and radiation field are subsequently computed at the resonant frequency. Various TE and TM modes have been investigated for different geometrical configurations.

Analysis of microstrip resonators of arbitrary shape

A space-domain approach based on a mixed-potential integral equation formulation is developed for efficient computation of complex resonant frequencies of laterally open microstrip-pitch resonators of arbitrary shape. The effects of the substrate-which may consist of any number of planar, possibly uniaxially anisotropic, dielectric layers-are rigorously incorporated in the formulation by means of the vector and scalar potential Green's functions. The current distribution on the conducting patch is approximated in terms of vector basis functions defined over triangular elements. Computed resonant frequencies, quality factors, modal currents, and far-field radiation patterns are presented for several microstrip resonators. For patches of simple, regular shapes, the results are in agreement with published data obtained by specialized techniques, which, unlike the method presented here, are not easily extendible to arbitrary shapes. >

Improvements in the analysis of a TH0mp cavity for precise complex permittivity measurements

AbstractAn analysis of the relationship between complex permittivity and complex resonance frequency is proposed for a cylindrical cavity oscillating in a TM0mp mode. Effects of wall conductivity, coupling loops, and holes for the insertion of dielectric samples are fully taken into account. With dielectric samples of small radii, insertion holes produce the most important corrections. Their effect is modelled through a finite difference solution of the field equations in the neighbourhood of the holes. A computer program is described for the analysis, the use of which is illustrated with results of measurements.

Resonance in spherical-circular microstrip structures

The resonance problem of a circular microstrip disk mounted on a spherical surface is studied theoretically. The radiator is replaced by a surface current distribution. The effects of the dielectric substrate as well as the curvature effect are taken into account by the Green's function formulation in the spectral domain. A vector Legendre series is defined. Cavity model current distribution is used as the current basis. Galerkin's procedure is used to solve for the complex resonant frequencies. Numerical results show that the effect of the curved surface on the resonant frequency and quality factor of the microstrip patch may be significant. In general, when the radius of the sphere is decreased, the effective radius of the patch will be reduced and the radiation loss is increased. >

Rigorous analysis of the TM0n modes in a dielectric-post resonator with an annular slot in the upper plate

The problem of a cylindrical dielectricpost resonator with an annular slot in the upper plate is rigorously solved. The analysis is based on an integral equation for the electric field in the slot which in the absence of external excitation has nontrivial solutions only at the complex resonant frequencies of the structure. This integral equation is solved numerically by the method of moments, and the resonant frequencies are determined as the zeros of the associated matrix determinant in the complex frequency plane. Attention is limited to the axisymmetric TM0n modes. Sample numerical results are given, including the complex resonant frequencies, the associated modal fields, and the radiation patterns of the first few resonator modes, and show the dependence of these quantities on the width and location of the annular slot.

State-space analysis of the quantum-well injection transit time diode

A state-space linear model of the quantum-well injection transit time (QWITT) diode is developed. The resulting system of equations is suitable for time- and frequency-domain analysis of the QWITT diode with its external circuit, and since the eigenvalues (complex resonant frequencies) are an integral part of the formulation, the method is extremely useful for the design of oscillator circuits and for the study of stability problems that are associated with supplying bias to the diode. The model includes the effects of velocity overshoot and carrier diffusivity as well as the physical geometry of the devices being studied. It is tested by comparing the predicted small-signal impedance with other well-known models for similar devices. Using state-space analysis, it is predicted that long diodes with a positive injection conductance will not have an input impedance with a negative real part at any frequency.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Complex resonance frequencies in acoustic-wave scattering from impenetrable spheres and elongated objects

The complex resonance frequencies of impenetrable (rigid or soft) elongated objects, namely, spheroids and cylinders with hemispherical end caps, including the spherical limit of the latter are studied. Complex resonance frequencies are obtained from the principle of phase matching of surface waves. For the case where such surface waves are generated by plane acoustic waves at broadside incidence, the simultaneous presence of cylindrical circumferential-wave resonances and of the resonances of meridionally propagating surface waves is discussed.