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.     

An Analysis of Gap in Microstrip Transmission Lines

Although microstrip transmission lines have been widely used in microwave integrated circuits, the discontinuity structures in the microstrip transmission lines such as a gap, an abruptly ended strip conductor, and so on, have hardly been analyzed. An analytical method and numerical results for a gap capacitance in the microstrip transmission line are described. The equivalent circuit parameters are formulated with three-dimensional Green's functions, based on a variational principle. The numerical results are in good agreement with the published experimental data. The fringing effect of an abruptly ended strip conductor is also investigated.     

A rigorous analysis of a coaxial to shielded microstrip linetransition

The transition from a coaxial to shielded microstrip line is analyzed by applying a rigorous mode-matching technique. The symmetry axes of the two transmission lines are assumed to be parallel, while the relative position of the coaxial line center conductor with respect to the microstrip line is taken to be arbitrary. The fields inside the shielded microstrip line are expanded in terms of the normal hybrid modes, while in describing the fields inside the coaxial line the transverse electric and magnetic modes are utilized. Both propagating and evanescent modes are taken into account in each transmission line. A modified mode-matching procedure is used on the junction plane of the two transmission lines to formulate the corresponding discontinuity problem. The mode-matching equations are solved by applying projection techniques. Numerical stability and computational efficiency are achieved in determining the scattering parameters of the coaxial to microstrip line transitions. Numerical results are computed and presented for several coaxial-to-microstrip-line transition geometries     

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。     

Double-layer microstrip structures—lumped capacitances and open-circuit end correction

The analysis is reported of the lumped capacitance and open-circuit end effects of finite-length strip conductors in double-layer microstrip structures. Two specific configurations, namely double-layer microstrip and microstrip-with-overlay configurations, are considered. The analytical approach uses the variational technique in the Fourier transform domain in conjunction with the transverse transmission line technique. It is identified that the only parameter needed to analyse the lumped capacitances and open-circuit end effects of these microstrip structures is the admittance at the charge plane. This parameter can easily be determined from the two-wire transmission line equivalent circuit. Extensive numerical data are generated for the lumped capacitances and open-circuit end effects of the finite-length strip conductor in double-layer microstrip and microstrip-with-overlay configurations. The data presented should be useful in designing lumped elements and filters in these configurations.     

Analysis of Microstrip-Like Transmission Lines by Nonuniform Discretization of Integral Equations

The nonuniform discretization of the integral equation on the tangential electromagnetic (EM) field on the boundary surface is proposed as a numerically efficient method to analyze the microstrip-like transmission lines. The calculated results of the propagation constant of the microstrip line based on this method are compared with other published analytical results. Various types of planar striplines are treated by the same formulas. The dominant and higher order modes of shielded microstrip line are discussed and compared with the longitudinal-section electric (LSE) and linear synchronous motor (LSM) modes of a two-medium waveguide.     

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     

Micromachined W-band filters

Results are presented for high performance planar W-band filters based on silicon micromachining techniques common in microsensor fabrication. Two types of micromachined planar transmission lines are studied: microshield line and shielded membrane microstrip (SMM) line. In both of these structures, the conducting lines are suspended on thin dielectric membranes. These transmission lines are essentially “floating” in air, possess negligible levels of dielectric loss, and do not suffer from the parasitic effects of radiation and dispersion. A 90 GHz low pass filter and several 95 GHz bandpass filters are tested and display excellent performance which cannot be achieved with traditional substrate supported circuits in CPW or microstrip configurations. A full-wave finite-difference time-domain (FDTD) technique verifies the measured performance of the W-band circuits and provides a basis for comparison between the performances of membrane supported circuits and equivalent substrate supported circuits     

Corner Function Analysis of Microstrip Transmission Lines

A new method of analysis of microstrip transmission lines using corner functions (eigenfunctions) is presented. Assuming the TEM mode propagation for the shielded microstrip line structure, solutions are set up in a series of corner functions, which isolates the singularity at the edge of the strip. The boundary conditions are satisfied by using a method of successive integration of boundary errors. Numerical results are obtained for the charge distribution from which the microstrip line characteristic impedance is determined. Excellent agreement with published theoretical results and experimental data is obtained. The numerical results clearly bring out the power of the method.     

一种贴片电感电容测量新方法的研究

为了得到贴片电感电容在微带电路中的精确值,提出一种基于矢量网络分析仪的电感电容自动测量系统.依据LC谐振电路和微带传输线理论设计制作测量夹具,通过Matlab编写田口优化算法计算得到已知电感电容值,并基于GPIB接口对矢量网络分析仪实现程控,采用VC ＋＋6.0工具开发自动测量系统的用户界面.给出了具体的设计思路和测量方法,实测结果表明,该系统实现了对微带电路中电感电容的快速精准测量,具有很高的实用价值.     

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.<>     

The Reflection Definition of the Characteristic Impedance of Microstrips

The frequency-dependent characteristic impedance shielded microstrips is computed by the scattering matrix of the step of rectangular transmission line to the shielded microstrip including higher order hybrid modes. This method avoids the ambiguities of the hitherto known definitions based on TEM quantities. For the dispersion characteristics a resonant model is used which reduces the number of the characteristic equations required. Numerical results are given including strips of finite thickness placed unsymmetrically in the shielded microstrip.     

Characterization of microstrip lines near a substrate edge anddesign formulas of edge-compensated microstrip lines [MMICs]

The proximity effects of microstrip lines near a substrate's edge present a problem for effectively designing high-packing-density MMICs (monolithic microwave integrated circuits). Proximity effects of this type are analyzed using the rectangular boundary division method. It is assumed that the cross-sectional dimensions of transmission lines in the MMICs are small compared with the wavelengths to allow the use of the quasi-TEM-wave approximation. Then, the concept of edge-compensated microstrip lines to keep the characteristic impedance constant near a substrate edge is introduced to circumvent the proximity effects and to expand the interconnection flexibility of microstrip lines on MMIC substrates. The practical design parameters of edge-compensated 50-Ω microstrip lines are given in the form of numerical data and simple polynomials for CASD (computer-aided design) work with a curve-fitting procedure. Results of capacitance measurements are compared with this theory with errors of about 1% resulting     

Distributed mosfet amplifier using microstrip†

Viewing the input capacitance of a mosfet amplifier stage as an integral part of a microstrip transmission line, leads to a distributed amplifier of simple design. With today's mosfets, a bandwidth in excess of 500 MHz can be achieved ; it will be possible to extend this bandwidth substantially in the future by the use of mosfets with lower input capacitance. In addition, some data are given on transmission lines employing substrates of high dielectric permittivity.     

Analysis of two-layer three-coupled microstrip lines on anisotropicsubstrates

Two-layer three-coupled microstrip lines on anisotropic substrates are analyzed. A variational method used for a single layer is generalized here to two layers by obtaining potential distributions. Extreme values of two variational functionals are found for the estimation of the upper and lower bounds on the line capacitance. The odd and even mode capacitances and characteristic impedances are obtained. The extended spectral domain method is used to show a very accurate propagation constant for the full-wave analysis     

The Even- and Odd-Mode Capacitance Parameters for Coupled Lines in Suspended Substrate

Static capacitance characterizations are derived for coupled thin-film conductors in the suspended substrate geometry, which includes shielded microstrip as a special case. In particular, a satisfactory treatment of closely coupled and narrow lines is obtained where, because of the dominance of the edge singularity, "mesh point" analyses are inadequate. The present work was carried through to meet the need in interactive design procedures for characterization of a general transmission geometry. For these procedures, algorithms are required that take little storage and are suitable for very rapid calculations. Capacitance formulas are derived from variational series based on conformal transformations, and these series are converted to easily evaluated finite forms. Calculation of the even- and odd-mode fringing capacitances for coupled limes is made for finite line widths assuming a periodic array of lines. The applicability of these capacitances to a single pair of lines and to finite filter arrays has been checked experimentally. Routines for lower bound values of fringing capacitances are given. Upper bound formulations validate the accuracy of the lower bound calculations.     

Characteristics of microstrip transmission lines withhigh-dielectric-constant substrates

An efficient numerical code is developed from a full-wave analysis in the Fourier transform domain to determine the characteristics of a single-strip or multistrip coplanar transmission line. Modes of both even and odd symmetries are included. The impedance of the transmission line is calculated using the power-current equivalent model. Coupling constants between the even and the odd modes are also calculated. Results are provided for a shielded two-strip coupled microstrip transmission line on high-dielectric-constant substrate such as lanthanum aluminate with applications to superconducting transmission lines     

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.     

Accurate Approach for Computing Quasi-Static Parameters Off Symmetrical Broadside-Coupled Mlcrostrips in Multilayered Anisotropic Dielectrics

In this paper, we present a method for calculating the propagation parameters of shielded broadside- end broadside edge-coupled microstrip transmission lines. Conductor strips are assumed to be embedded in a multilayered isotropic and/or anisotropic medium. This method provides accurate expressions for computing upper and lower bounds for the true values of mode capacitances, The effects of side wall-shielding and anisotropy of the material are investigated. Some particular multilayered structures are analyzed, which could be applied to the design of directional couplers and filters.     

Monolithic Capacitors as Transmission Lines

The results of network analyzer measurements of high-Q multilayer (monolithic) chip capacitors show that the devices have the characteristics of open-circuited transmission lines. Both standard sizes (MIL-CDR-14 and MIL-CDR-12), ranging in capacitance values from 4.7 to 1000 pF, were tested on microstrip lines. A simple model of a periodically loaded line provides a dispersion relation that accounts for the distribution of resonant frequencies. The orientation of the capacitor with respect to the microstrip affects the occurrence and nature of resonances. This phenomenon is shown to result from a distributed excitation source. The unfolding of the capacitor to produce the periodic line is shdwn to produce anomalies in the dissipation loss when skin depth and electrode thickness are comparable.