高速印刷电路板间垂直通孔的建模与分析

通孔是现代高速印刷电路板中最常用的互连结构之一,其在传输信号特别是高速信号时会带来一系列信号完整性问题,因此对其进行准确、快速、有效的电磁建模与仿真将变得极为重要。该文使用一种基于Foldy-Lax方程的全波分析法并结合网络级联理论对其进行电磁建模。在单层垂直通孔结构中,建立柱体通孔间的Foldy-Lax多径散射方程,求得柱体通孔的激励场系数,计算出单层垂直通孔的散射矩阵,再应用多端口网络级联理论便可得到多层垂直通孔的散射矩阵。最后给出了四层垂直通孔散射参数的计算结果,并与已有文献结果进行了比较,两者吻合良好,从而验证了该方法的有效性。     

Analysis of a large number of vias and differential signaling in multilayered structures

A method is presented for full-wave modeling of vertical vias in multilayered circuits. The analysis of the interior problem is based upon the cylindrical wave expansion of the magnetic field Green's function. The multiple interaction among vertical vias is modeled by the Foldy-Lax scattering formula. Multilayered effects are included by using cascaded network of the single-layer components. The exterior problem of the via and the transmission line is analyzed using the method of moments approach. The exterior and interior problems are combined into a system of equations to facilitate the solution of a large number of vias. Using this approach, the scattering matrix of problems of several thousand vias can be calculated with moderate CPU and memory requirement. Numerical results have been obtained for different via configurations and for a large range of frequency. Also illustrated are results for common and differential mode in differential signaling with surrounding idle and shorting vias.     

Electromagnetic scattering from a coaxial dielectric circularcylinder loading a semicircular gap in a ground plane

An exact dual series solution of a plane wave incident on a coaxial dielectric circular cylinder imbedded in a semicircular gap of a ground plane is presented. Both TM and TE cases are considered here. The scattered field is represented in terms of an infinite series of cylindrical waves with unknown coefficients. By applying the boundary conditions and employing the partial orthogonality of the trigonometric functions the scattering coefficients are obtained. The resulting infinite series is then truncated to a finite number of terms to produce numerical results. For the sake of comparison with the published data some special cases are introduced first. The comparisons showed excellent agreement in all cases     

Analysis of the microstrip disk antenna element

The circular microstrip antenna element is formed by a radiating disk closely spaced above a ground plane. It is modeled as a cylindrical cavity with magnetic walls which can be resonant in the transverse magnetic (TM) modes. The far fields and the radiation conductances for different mode structures have been calculated assuming a magnetic line current flowing along the perimeter of the disk. The directivity of a disk antenna excited in the dominant mode is between 4.8 dB and 9.9 dB, depending on the size. Losses, due to imperfect supporting dielectrics and to the finite conductivity of the conductors, have been derived by means of a perturbation technique. Graphs are given for design purposes showing the input impedance, theQfactor, and the radiation efficiency at resonance for different modes and thicknesses. The air-filled microstrip antenna has the highest efficiency and the broadest bandwidth at a given resonant frequency.     

A multicomposite, multilayered cylindrical dielectric resonator forapplication in MMIC's

A method, based on the mode matching technique, to study various resonant modes of a multicomposite, multilayered cylindrical dielectric resonator is presented. Dielectric sphere and cone resonators placed in practical environments are investigated. The calculated resonant frequencies show very good agreement compared with the numerical results of the finite difference method for the spherical resonator and with the measured values for the conical resonator, respectively. Experimental investigations show that the conical resonator can be coupled to a circular microstrip line, which has small size at high frequencies and may be integrated together with an oscillator     

Multiple scattering among vias in lossy planar waveguides using SMCG method

Large-scale full-wave multiple scattering among cylindrical vias in planar waveguides is modeled using the Foldy-Lax equation. The formulation includes the skin effects of the conducting power/ground plane. Numerical solution of the Foldy-Lax equation with large number of unknowns is computed efficiently using the sparse-matrix canonical-grid method. In this method, interactions among vias are decomposed into the strong interactions part and the weak interactions part. The calculation of the weak part is carried out using two-dimensional (2-D)-fast Fourier transform (FFT) by translating the locations of the vias onto the uniform grids. The final solution of the Foldy-Lax equations is calculated by an iterative method. The results show O (N log N) CPU efficiency and O (N) memory efficiency. This makes large scale via problems possible for computer simulation.     

Gaussian beam scattering from a conducting cylinder partially buried in a ground plane

The problem of scattering from an infinitely long conducting cylinder that is partially buried in a perfectly conducting ground plane due to an obliquely incident gaussian beam is solved by an exact procedure based on the method of images by first adopting a simplification originally proposed by Kozaki. The incident and the specularly reflected fields are expressed in terms of cylindrical vector wave functions multiplied by a weighting function which involves the beam parameters like the radial distance of the source and beam width. The scattered fields originating from the cylinder and its image in the ground plane are expressed in terms of cylindrical vector wave functions. The boundary conditions on the surface of the cylinder are then imposed and this procedure leads to a coupled infinite system of equations for the even and odd mode expansion coefficients of the scattered field. These equations are solved numerically for the case of cylinders having electrical radius in the Rayleigh and resonance regions. Both the transverse magnetic and transverse electric polarizations of the incident beam wave are considered and some representative numerical results for the scattered far-field are presented in graphical form. The magnitude of the induced current for the TM polarization is calculated and compared with the corresponding case of plane wave incidence.     

Scattering from lossy dielectric objects buried beneath randomlyrough ground: validating the semi-analytic mode matching algorithm with2-D FDFD

A new semi-analytic mode matching (SAMM) algorithm is verified by two-dimensional (2-D) finite difference frequency domain (FDFD) simulations of scattering resulting from uniform plane waves incident on randomly rough dielectric half-spaces containing buried dielectric targets. The SAMM algorithm uses moderately low-order modal superpositions of cylindrical waves, each of which satisfies the 2-D-Helmholtz equation in its appropriate region (air, ground, or mine) and then matches all nonzero electric and magnetic field components at each interface by inverting a highly overconstrained dense linear matrix equation by singular value decomposition. That is, the set of cylindrical mode coefficients is found which best fits the boundary conditions in a least squares sense. For smooth ground, coordinate scattering centers (CSCs) are chosen at the mine center and at its image above the plane to model scattering. For randomly rough ground, additional CSCs are located within the rough boundary layer. Excellent agreement between 2-D-FDFD and the 2-D version of SAMM is observed, with 2-D-SAMM being at least an order of magnitude faster. 3-D-SAMM is estimated to be four orders of magnitude faster than 3-D-FDFD, with drastically reduced memory requirements     

Coupling Parameters Between a Dielectric Resonator and a Microstripline

The coupling coefficient between a microstripline and the dipolar magnetic (TE/0gamma delta/ ) mode of a cylindrical dielectric resonator is evaluated by using two methods numerical and analytical. Theoretical and experimental extenal quality factors, as well as the scattering matrix parameters which consider the substrate material, the ground plane, and the distance between the line and the resonator, are presented.     

A discussion of rotating wave fields for microwave applications

The concepts of angular momentum, resonant frequencies, and electromagnetic fields in different types of rotating wave modes are studied. A number of interesting and unique properties of rotating waves are discussed, including their constant electric and magnetic field energies. The range of current uses for rotating waves is indicated. An analysis of rotating waves in cylindrical cavity resonators is presented. The TM₁₁₀ rotating mode for a cylindrical resonator is discussed in some detail     

Circularly symmetric distributed feedback laser: coupled modetreatment of TE vector fields

The vector orientation of transverse electric (TE) fields in deriving coupled mode equations for radially outward- and inward-going modes in a circular waveguide diffraction grating is treated. The equations are derived for cylindrical waves in a system that is translationally invariant along the cylinder axis; the derivation is then extended to the waveguide geometry. The coupled mode equations are used to describe the operation of the circularly symmetric distributed feedback (DFB) laser. While predicting a similar dependence of the laser threshold gain on an azimuthal mode order to that found by a simpler, scalar-field treatment, the vector-field treatment predicts a fundamental difference in the location of the cavity resonances. The circular DFB laser is expected to lase in multiple azimuthal modes but maintain a relatively narrow overall spectral width     

Radial mode analysis of electromagnetic wave propagation on slotted cylindrical structures

A systematic method to solve electromagnetic wave propagation problems associated with slotted cylindrical structures is to represent the field by a set of radial modes, the discontinuity by a multimode junction network, and to solve the transverse resonance equations. Derivations of the radial mode representation of the field and the network representation of a slot are provided. The application of this method to a slotted circular waveguide is also given, and its solutions show good agreement with previous findings.     

Dielectric resonator antenna using aperture coupling

A practical antenna configuration for use at microwave and millimetre wave frequencies is investigated. It consists of a circular cylindrical dielectric resonator fed by a microstrip feedline through a coupling aperture in the ground plane between them. Several elements, with different physical parameters, operating between 14 and 16 GHz were constructed and tested. Experimental results confirm the effective and practical performance of the antenna structure.<>     

Effect of air gap on cylindrical dielectric resonator antenna operating in TM/sub 01/ mode

The results of a numerical study on the effect of an air gap on the input impedance and resonance frequency of a cylindrical dielectric resonator (CDR) antenna operating in the TM/sub 01/ mode as a function of dielectric constant are presented. The CDR resides on a conducting ground plane and is excited by a coaxial probe through the bottom of the ground plane. Some of the numerical results are validated experimentally.<>     

A rigorous analysis of a cross waveguide to large circularwaveguide junction and its application in waveguide filter design

A rigorous analysis is obtained for the problem of scattering at the junction of a cross-shaped waveguide and a larger circular waveguide. The general case of an arbitrary offset and orientation of the cross waveguide axes is considered. The fields matching over the cross aperture of the smaller guide is facilitated by using the transformation of the circular cylindrical Bessel-Fourier modal fields of the circular guide into a finite series of exponential plane wave functions. This permits an analytical finite series solution for the elements of the fields mode matching matrix, from which the general scattering matrix of the junction is obtained. The application of the formulation to circular waveguide filter design is emphasized in the numerical examples. Excellent agreements between theoretical and experimental results are obtained in all the numerical examples     

The two-cone open resonator

The resonator is an open structure formed by two concave conical reflectors mounted coaxially, and it supports traveling wave resonances. In a simplified wave picture of the field, the normal modes look like a set of plane wavefronts propagating parallel to the axis in one direction and conical wavefronts propagating in the opposite direction. One of the normal modes has TM01- TM0Ntype symmetry for the two traveling waves, and exhibits lower diffraction losses than a plane Fabry-Perot resonator of similar dimensions. This type of mode field established in a suitable dielectric could presumably couple to an electron stream along the axis through the Cerenkov effect, and would thus provide feedback.     

一种适用于超宽带通信的微带垂直转换结构

该文提出一种适用于超宽带电路的基于过孔的微带垂直转换结构。通过在过孔附近的电源层上蚀刻平面电磁带隙单元来抑制电源分配网络谐振,降低其在过孔处的自阻抗,以改善垂直互连结构传输性能。将互连结构分解为过孔处耦合的微带线结构和电源平面对结构,并使用网络分析方法快速估算系统传输性能。仿真和实验测试表明,在3.1-10.6 GHz的超宽带频段内过孔的插入损耗小于0.4 dB。与在电源分配网络之间添加短路过孔方法相比,该结构在传输性能相当的前提下减少了一个布线层,从而降低了设备成本。     

Excitation of a cylindrical microstrip structure with arbitrarily shaped printed elements by a plane wave

The problem of excitation of a cylindrical microstrip structure by a plane wave is considered. The structure is a printed element on a circular dielectric substrate containing a coaxial metal cylinder. In the scattering regime, the structure under study adequately simulates a cylindrical microstrip antenna operating at resonance frequencies. The printed element is equivalent to the radiator of this antenna. The problem is solved in the spectral domain with the use of the method of moments and piecewise-specified basis functions. The effect of the radiator’s shape on the radar cross section of the structure is investigated. It is shown that a change in the radiator’s topology substantially affects the formation of new oscillation modes whose resonance frequencies noticeably shift to the lower frequency region from their positions in the case of a radiator having a rectangular cylindrical shape.     

Locally resonant cavity cell model for electromagnetic band gap structures

Mushroom-like electromagnetic band gap (EBG) structures exhibit unique electromagnetic properties that have found a wide range of electromagnetic device applications. This paper focuses on the local resonance behaviors of EBG structures, and a simply locally resonant cavity cell (LRCC) model for mushroom-like EBG structures is presented to gain insight to the physical mechanism of the EBG structures and the interaction of electromagnetic waves with EBG structures. The LRCC model proposes two kinds of main resonance modes: One is the mono-polarized mode that accurately predicts the position of the surface wave suppression bandgap, which is equivalent to the LC parallel resonance based on quasistatic assumption in principle, and the other is the cross-coupling polarized mode that exhibits some interesting resonant phenomena, which has not been observed previously. Parametric studies including the radius effect of the metal plated vias are effectively performed by using the LRCC model. Some numerical simulations and experiments of EBG structures, such as square, triangle, and hexagon lattices, are given to illustrate the applications and validation of LRCC model proposed by this paper.     

薄膜体声波谐振器有限元仿真与设计

为了抑制薄膜体声波谐振器的寄生谐振,建立了薄膜体声波谐振器的二、三维有限元模型。通过频率响应仿真,分析了不同电极结构的谐振器在中心频率处的振动位移分布情况和频率响应曲线,评估了不同电极结构对谐振器寄生振动的影响,并完成谐振器电极结构的优化设计,实现了谐振器寄生振动抑制。根据仿真优化结果表明,设计并制作了工作频率在1.873GHz的薄膜体声波谐振器,谐振器插入损耗0.7dB,无明显寄生谐振,对设计进行了验证。