Effect of substrate dielectric anisotropy on the frequency behaviorof microstrip circuits

In this paper, we carry out a full-wave analysis of shielded two-port microstrip circuits, in which the metallizations are embedded in a multilayered substrate that may contain isotropic dielectrics and/or anisotropic dielectrics. The Galerkin's method in the spectral domain is applied for determining the current density on the metallizations of the circuits when their feeding lines are excited by means of delta-gap generators, and the matrix pencil technique is subsequently used for deembedding the scattering parameters from the computed current densities. Results are presented for the scattering parameters of some microstrip discontinuities and filters printed on both isotropic dielectric substrates and anisotropic dielectric substrates. These results show that when substrate dielectric anisotropy is ignored, errors arise when computing the scattering parameters of microstrip discontinuities and when predicting the operating frequency band of microstrip filters     

Spectral-domain analysis of shielded microstrip lines on biaxiallyanisotropic substrates

The spectral-domain technique is extended to the study of shielded microstrip lines on biaxial substrates. The analysis simultaneously includes dielectric and magnetic anisotropy effects. A fourth-order formulation leads to the determination of the appropriate Green's function for the structure. The characteristic equation is formed through the application of the Galerkin method to the equations resulting from the boundary conditions on the strip. Numerical results calculated by this method for isotropic as well as dielectrically anisotropic substrates are compared with the existing data, and in both cases a very good agreement is observed. New data on the propagation constant of the shielded microstrip with different substrate permittivities and permeabilities are presented to illustrate the effects of the material parameters on the characteristics of the microstrip line     

Unified Approach to Solve a Class of Strip and Microstrip-Like Transmission Lines

This paper presents a unified analytical approach to solve a class of shielded strip and shielded microstrip-like transmission lines with multilayer dielectrics under TEM-wave approximation. The analysis makes use of the variational technique in the space domain combined with the "transverse transmission line" method. Expressions are derived for the capacitance of a single line, coupled two-line and coupled four-line structures. The same formulas can be used for a class of such structures by the substitution of a single parameter, namely, the admittance at the charge plane, which can be obtained using the standard transmission line formulas. Numerical results of two special structures, namely, the broadside-coupled suspended microstrip lines, and broadside-coupled inverted microstrip lines, using two suspended, dielectric substrates are included. The technique presented is the simplest compared to any other analytical procedures reported in the literature.     

Complex modes in shielded suspended coupled microstrip lines

The existence of complex modes in electrically shielded suspended coupled microstrip lines has been studied extensively, and the results are presented. A rigorous full-wave spectral-domain approach (SDA) with a newly proposed and tested set of basis functions can efficiently and accurately determine the propagation characteristics of the dominant, higher-order, and complex modes for planar or quasi-planar transmission lines. These basis functions are validated by comparing the convergence study of field solutions with those obtained by various sets of preconditioned bases and by the unconditioned subdomain ones. Excellent agreement is obtained for the propagation constants and the normalized complex longitudinal and transverse current distributions on conducting strips for the strongly coupled microstrip lines. For all the particular case studies discussed, it is shown that the complex modes may exist in all the shielded suspended coupled microstrip lines, even when the substrate dielectric constant is low. Theoretical results for the fundamental, higher-order, evanescent, and complex modes are presented for suspended coupled microstrip lines     

Quasi-static analysis of shielded microstrip transmission lineswith thick electrodes

An extended point-matching method for analyzing the shielded microstrip transmission lines with thick electrodes has been developed based on the method by Marcuse (1989). This method provides a simple and fast approach to the quasi-static analysis of the structures. The calculated fields are used to estimate the characteristic impedance and effective dielectric constant of the structures. The results agree well with available theoretical results obtained using other methods, such as the finite element method and the boundary element method. This method can be further applied to other microstrip lines widely used in monolithic microwave integrated circuits (MMICs) applications     

Pulse dispersion distortion in open and shielded microstrips usingthe spectral-domain method

The spectral-domain method is used to compute the effective dielectric constant [ϵ_r/_eff(f)] of open and shielded microstrip lines to analyze the dispersion distortion of short electrical pulses. Precise expressions for the longitudinal and transverse current distributions allow a high level of accuracy for ϵ_r/_eff(f). It is determined that computation time can be minimized for the open microstrip calculations by using the shielded microstrip formulation provided large dimensions for the conducting walls are assumed     

Full-Wave Analysis of Inside Cylindrical Microstrip Lines by Finite Element Method

In this paper, a full-wave analysis using finite element method is presented to investigate the dispersion characteristics of inside cylindrical microstrip lines, which are essential to the design of some conformal microstrip circuits in millimeter wave bands. Numerical results of frequency-dependent effective dielectric constants are given for different structural dimensions and dielectric constants of substrate. Some useful conclusions are derived for the design of the special conformal microstrip lines.     

The dispersion characteristics of shielded microstrip lines on magnetized ferrite and anisotropic dielectric substrates

The dispersion characteristics of the dominant mode in shielded microstrip lines on magnetized ferrite and anisotropic dielectric substrates have been obtained. The solution is obtained by applying the transverse equivalent transmission line in the spectral domain and Galerkin's method. Numerical results for the frequency-dependent propagation constants are presented which could be used in designing directional couplers and isolators.     

Broadside, Edge-Coupled, Symmetric Strip Transmission Lines

This paper analyzes the propagation parameters of the general, shielded, broadside, edge-coupled, symmetric strip transmission line using the transverse transmission line method combined with the variational technique in the space domain. A simple approximation to the charge distribution on the conducting strip is assumed. Extensive design data on the characteristic impedances, effective dielectric constants are generated for a) broadside, edge-coupled, homogeneous striplines, b) broadside, edge-coupled, microstrip lines, c) broadside, edge-coupled, microstrip lines with inverted dielectric. The effect of the shielding side walls on the characteristic impedances is investigated. The results presented should find application in the design, fabrication of directional couplers, filters having complex electric responses.     

Complex modes in lossless shielded microstrip lines

The possible existence of complex modes in lossless shielded microstrip lines was investigated using the singular integral equation method. The method is used for the analysis of three lossless shielded microstrip line structures with different substrate permittivities. To confirm the validity of the method, results are compared with existing data for propagating modes. Complex modes were found in the moderate and high permittivity structures.<>     

Dissipation Loss Effects in Isolated and Coupled Transmission Lines

This paper describes a computer-aided analysis of dissipation losses in uniform isolated or coupled transmission lines for microwave and millimeter-wave integrated-circuit applications. The analysis employs a quasi-TEM model for isolated transmission lines and for the even- and odd-mode transmission lines associated with coupled-line structures. The conductor and dielectric losses are then related to equivalent charge density distributions, which are evaluated using a method-of-moments solution. The transmission lines treated by this analysis may contain any number of Iossy conductors and inhomogeneous dielectrics, consisting of any number of different homogeneous dielectric regions. A development is provided to explicitly relate the four-port terminal-electrical performance of directional couplers to evaluated even- and odd- mode loss coefficients. Examples of evaluated losses are presented in graphical form for isolated lines of inverted microstrip and trapped inverted microstrip and edge-coupled microstrip with a dielectric overlay. The analysis accuracy has been confirmed using microstrip and coplanar waveguide configurations. A comparison is made of the total loss characteristics for microstrip, coplanar waveguide, inverted microstrip, and trapped inverted microstrip. Calculations are compared with measurements for the coupled-line structure. Accuracy of the solution and suggested refinements are discussed. Five computer programs are documented.     

几种复合传输线特性阻抗的计算

本文就高速光电器件微波封装提出了有希望的几种复合传输线（微带＋共面线，屏蔽微带＋共面线，微带＋不对称共面线），采用边界元法计算了它们的特性阻抗，给出了几组有工程价值的计算曲线，并讨论了实验结果。     

Closed-form expression for the capacitance of the shielded microstrip circular disc capacitor by dividing the capacitance approach

In this paper, a closed-form expression for the static capacitance of the shielded microstrip circular disc capacitor is derived. The approach used is based on dividing the capacitor's total capacitance into the air and dielectric (parallel-plate and edge) capacitances. Numerical results for typical values of the disc's physical dimensions are given.     

毫米波硅基微机械屏蔽膜微带线和滤波器

介绍了一种屏蔽膜微带线,该型传输线为介质薄膜所支撑,周围为空气,并为金属面所屏蔽,具有可忽略不计的衬底损耗及色散效应,以及很小的辐射损耗。运用HFSS三维电磁场仿真软件对毫米波屏蔽膜微带线与滤波器进行了仿真设计,运用MEMS工艺在两层高阻硅衬底上进行了样品的研制。样品取得了良好的测试结果,其中屏蔽膜微带线插入损耗小于0.1dB/mm。     

Frequency-Dependent Characteristics of MicrostripTransmission Lines

A method for determining the frequency-dependent characteristics of both single and coupled lines in shielded microstrip is presented. Numerical results are given for a variety of dielectric configurations and the effects of geometry on the dispersion characteristics are examined in detail. Of particular interest are the characteristics of coupled lines on compensated dielectric structures, i.e., structures that are capable of achieving equal even- and odd-mode phase velocities, and the effects of dispersion on the directivity characteristics of such lines are discussed. In addition, the variation of impedance as a function of frequency, where the impedance is defined as the ratio of the power to the square of the longitudinal current, is presented for representative cases of single and coupled lines.     

Rectangular resonators in inverted microstrip and suspended microstrip

Resonant frequency characteristics of rectangular resonators in a generalized shielded suspended substrate line are analysed using a rigorous spectral domain technique. The computed dominant mode resonant frequency of rectangular resonators in a suspended microstrip with centred dielectric, inverted microstrip and suspended microstrip are presented as a function of various structural parameters. These characteristics are distinct from those obtained for a conventional microstrip rectangular resonator. Experiments are carried out in the frequency range 4-18 GHz to verify the computed resonant frequencies for a suspended microstrip with a centred dielectric using first-order basis functions. The results should find applications in the design of inverted microstrip and suspended microstrip passive microwave and millimetre wave integrated circuits.     

A Comprehensive Technique to Determine the Broadband Physically Consistent Material Characteristics of Microstrip Lines

This paper describes a method to extract the relative complex dielectric permittivity from propagation coefficient measurements on microstrip lines. The material characteristics of microstrip lines fabricated on two different types of substrates commonly used in microwave circuit and printed circuit boards are investigated. The mechanisms that cause the effective permittivity of microstrip lines to be dispersive are explored. The technique includes creating closed-form effective permittivity equations to relate the effective permittivity of the microstrip lines to the real part of the dielectric permittivity of the substrate. Curve-fitting methods are used to create causal dielectric material models that relate the imaginary part of the dielectric permittivity to its real part. The methods developed in this paper can be used to characterize low-loss dielectric materials whose polarization is dominantly dipolar within the microwave frequency range in high-speed packaging applications.      

屏蔽类微带传输线准静态特性的有限元分析方法

本文建立了有限元法分析屏蔽类微带传输线的通用程序。以屏蔽悬置微带线为例,计算了其准静态特性参数,并与用变分法的计算结果进行了比较,两者吻合很好,表明了本文编制的有限元法分析程序的正确性。     

The new method of time-domain analysis of a planar transmission line with discontinuity

In this paper, the new technique of time-domain analysis of discontinuities in a planar transmission line is presented. In the process of time-domain analysis, the analysis model of system and the concept of transfer function are employed and the frequency-domain method of lines and the technique of the fast Fourier transform are used. The results of time-domain data and frequency-domain characteristics for the shielded microstrip with step discontinuity are given and compared with the published results of other authors.     

A new formulation of the boundary condition at infinity for ahybrid radiation mode and its application to the analysis of radiationmodes of microstrip lines

A new formulation of the boundary condition at infinity for a hybrid radiation model is introduced. It is shown that its application leads to an iterative solution of the problem in the spectral domain. The validity of the condition is proved by its application to the analysis of a laterally shielded dielectric slab. Using this condition, an iterative method in the spectral domain is proposed in order to analyze striplike stratified transmission lines. As a result, two solutions, classified as perturbed longitudinal electric (LSE) and longitudinal section magnetic (LSM) modes, are obtained. Numerical results concerning the convergence of the method as well as the field distribution are presented for the case of a microstrip line