Dispersion Characteristics of Microstrip Lines

A coupled-line analysis is used in conjunction with Carlin's model in order to find the frequency dependence of the propagation constant and of the characteristic impedance of dispersive microstrip lines. The characteristic impedance of the coupled lines decreases with frequency.     

Asymptotic Eigenequations and Analytic Formulas for the Dispersion Characteristics of Open Wide Microstrip Lines

Through the matched asymptotic expansions technique, asymptotic eigenequations for the even and odd modes of an open wide microstrip transmission line are derived. The eigenequations, and simplifications thereof which do not involve integration, can he solved easily for the effective permittivity. Even though d/W is assumed to be small, the solutions are good even if d/ W/spl cong/0.8 when compared with the numerical results of Jansen. From these eigenequations, asymptotic formulas for the effective permittivity can be derived which are excellent when d/ W/spl cong/0.2. When the frequency goes to zero, we reproduced the asymptotic formula derived under the quasi-TEM approximation in [8]. The asymptotic analysis provides good physical insight into the problem, otherwise unavailable from numerical analysis.     

微带线在各向异性介质主轴旋转时的色散特性

首次用时域有限差分法（ＦＤＴＤ）研究了在电和磁双各向异性介质中张量［ε］和［μ］的主轴同时旋转时，开式和屏蔽微带线的色散特性。结果表明，其传播特性与［ε］和［μ］的光轴偏差角有明显的关系。     

Pulse Dispersion and Shaping in Microstrip Lines

A method for determining the modal dispersion of gigahertz-bandwidth pulses on microstrip transmission lines is described. We have investigated the evolution of temporal waveforms propagating on microstrips, with very good agreement noted between experimental pulse shapes and numerical simulations. The resulting pulse distortion contributed to a pulse-shaping application where 100-ps rise times were stretched to the nanosecond durations necessary to control the shape of high-energy optical pulses used in fusion research. The tunability of the shape of the rising edge was investigated through variation of the stripline geometry and the substrate material. Additional effects due to high-frequency attenuation in several dipolar liquid dielectrics were substantiated experimentally, and the relevance of the results has been discussed.     

A New Technique for the Analysis of the Dispersion Characteristics of Microstrip Lines

Dispersion characteristics of shielded microstrip lines are investigated using a new technique. The method utilizes the well-known singular integral equation approach for deriving an alternate form of eigenvalue equation with superior convergence properties. It is shown that accurate numerical results may be obtained from this eigenvalue equation using only a 2x2 matrix equation. In comparison, the conventional formulation of the problem requires the use of matrices that are much larger in size. Aside from the numerical efficiency, the simplicity of the method makes it possible to conveniently extract higher order modal solutions for the propagation constants that affect the high-frequency application of microstrip lines. Even though the derivation of the determinantal equation requires some intricate mathematical manipulations, the user may bypass these completely and use the final eigenvalue equation which is programmable on the computer.     

An Appraisal of Methods for Computation of the Dispersion Characteristics of Open Microstrip

A number of methods in the literature for computing the dispersion characteristics of open microstrip are compared in the case when substrate thickness is comparable to strip width. Significant discrepancies between the various results are found, and several suggestions are made to explain them.     

Spectral-Domain Approach for Calculating the Dispersion Characteristics of Microstrip Lines (Short Papers)

The boundary value problem associated with the open microstrip line structure is formulated in terms of a rigorous, hybird-mode representation. The resulting equations are subsequently transformed, via the application of Galerkin's method in the spectral domain, to yield a characteristic equation for the dispersion properties of the open microstrip line. Numerical results are included for several different structural parameters. These are compared with other available data and with some experimental measurements.     

A Technique for Computing Dispersion Characteristics of Shielded Microstrip Lines (Short Papers)

The boundary value problem associated with the shielded microstripline structure is formulated in terms of a rigorous hybrid-mode representation. The resulting equations are subsequently transformed, via the application of Galerkin's method in the spectral domain, to yield a characteristic equation for the dispersion properties of shielded microstrip lines. Among the advantages of the method are its simplicity and rapid convergence. Numerical results are included for several different structural parameters. These are compared with other available data and with some experimental results.     

椭圆微带线色散特性的直线法分析＊

本文用直线法对椭圆微带线的色散特性进行了研究,导出了色散特性方程.在共焦椭圆情况下,当频率较低时,本文结果与准TEM波分析结果趋于一致。同时给出了两种微带结构的色散曲线。     

圆柱形微带,耦合线的色散特性分析

本文利用一种全波分析方法－－柱面坐标中的二维时域有限差分法，数值模拟了圆柱形均匀微带线和耦合线的色散特性。讨论了柱面坐标二维时域有限差分（ＦＤ－ＦＤ）法的基本理论和处理方法，并给出不同带宽的圆柱形微线和不同耦合宽度与耦合间隙的圆柱形合线的色散特性。这些结果对微波与毫米波集成电路过渡区的设计是有价值的。     

Microstrip Dispersion Model

The assumption that the quasi-TEM mode on microstrip is primarily a single longitudinal-section electric (LSE) mode leads to a transmission line model whose dispersion behavior can be analyzed and related to that of microstrip. Appropriate approximations yield simple, closed-form expressions that allow slide-rule prediction of microstrip dispersion.     

Measured Odd- and Even-Mode Dispersion of Coupled Microstrip Lines (Short Papers)

A convenient method is described for the measurement of the odd- and even-mode phase velocities of coupled microstrip lines. Results are presented which show the strong influence on the dispersion characteristics of a closely spaced low-loss shielding cover. The method also enables the loss of the odd and even modes to be determined.     

Dispersion Characteristics of an Open Interdigital-Line Structure

The dispersion characteristics of an open interdigital-line structure were obtained by treating the structure as a radiator. Good agreement between the theoretical solution and the experimental measurements was observed.     

Parameters of Microstrip Transmission Lines and of Coupled Pairs of Microstrip Lines

A theoretical analysis is presented of microwave propagation on microstrip, with particular reference to the case of coupled pairs of microstrip lines. Data on this type of transmission line are needed for the design of directional couplers, filters, and other components in microwave integrated circuits. The inhomogeneous medium, consisting of the dielectric substrate and the vacuum above it, is treated in a rigorous manner through the use of a "dielectric Green's function" which expresses the discontinuity of the fields at the dielectric-vacuum interface. Results are presented in graphical form for substrate dielectric constants of 1, 9, and 16, and a range of values of width and spacing of the strips. Numerical tables for these and other cases are also available. The tables present capacitance, characteristic impedance, and velocity of propagation of the even and odd normal modes. The method lends itself to the treatment of other geometries which are of practical interest, such as "thick" strips, presence of an unsymmetrically located upper ground plane, etc.     

An Approximate Dispersion Formula of Microstrip Lines for Computer-Aided Design of Microwave Integrated Circuits

A simple approximate formula for the computer-aided design of the dispersion property of microstrip lines is reported in this paper which well fits the calculated curves based on a rigorous analysis.     

Losses of Microstrip Lines

This article summarizes state-of-the-art information on losses of single and coupled microstrip lines. Conductor loss, substrate loss (for pure dielectric or magnetic materials), and radiation loss are considered along with the effect of dispersion. Finally, a rough comparison is made between the losses of microstrip and that of several other types of lines used in microwave integrated circuits.     

铁氧体-硅双层基片微带线的谱域导抗法分析

该文提出两种铁氧体-硅双层基片的微带线结构,并通过对麦克斯韦方程的坐标旋转和傅里叶变换导出波导纳,用谱域导抗法进行特性分析。尤其是对微带线的色散特性进行了计算,讨论了微带线各种参数对色散特性的影响,并对它们的特性进行了对比,发现其中一种结构的色散受各因素的影响很小,尤其是介质的工艺尺度,可用于更高集成电路的制造中。     

Characteristic Impedance of Microstrip Lines

It is shown that it is feasible to force the complex power P of microstrip line to be given by the usual circuit definition: P = I* V/2 where I and V are the current and voltage of the equivalent transmission line and * denotes complex conjugation. If this requirement is made, then the three common definitions of characteristic impedance (namely, the voltage-current, power-voltage, and power-current definitions) all become equivalent. The remaining arbitrariness in microstrip characteristic impedance 20 stems not from the choice of definition, as sometimes argued, but from the ability to choose one of the magnitudes |I|, |V|, and |Z/sub 0/| for convenience, and also to choose the phase of either I or V (but not their relative phase). This clarification should make it easier to simplify equivalent circuits for drivers, loads, and discontinuities.     

Microstrip Dispersion Including Anisotropic Substrates

A perturbation-iteration solution based on potential theory is developed for determining the effective dielectric constant, characteristic impedance, and current-charge distribution on a microstrip transmission line with isotropic and anisotropic substrates. The numerical implementation of the theory is described and is suitable for use on a personal computer. Computed data for several common substrate materials are included.     

2-18-GHz Dispersion Measurements on 10-100-Omega Microstrip Lines on Sapphire

Dispersion measurements on microstrip lines with characteristic impedances between 10 and 100 Omega are described, covering the frequency range 2-18 GHz. Single-crystal sapphire cut with a specified crystal orientation was used as the substrate material. Microstrip effective permittivities were calculated from the resonant frequencies of open-ended straight resonators using a technique which eliminated end-effect. The experimental results are compared with some recent dispersion theories. An empirical dispersion formula is independently developed, and is shown to provide well-fitting curves for all the measured dispersion results.