Propagation Parameters of Coupled Microstrip-Like Transmission Lines for Millimeter-Wave Applications

A variational expression is derived for the propagation parameters of coupled microstrip-like transmission lines for millimeter-wave applications using the "transverse transmission line" method. Numerical results are presented for the coupled inverted microstrip lines, and for the coupled suspended microstrip lines. The effects of the top and sidewalls and also of the finite thickness of strip conductors on the even- and odd-mode impedances are studied. The use of a dielectric overlay in equalizing the even- and odd-mode phase velocities is investigated.     

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.     

Variational Method for the Analysis of Microstrip Lines

This paper reports a method for computing the line capacitance of a microstrip line based on the application of Fourier transform and variational techniques. The characteristic impedance, guide wavelength, and the surface potential distribution in the microstrip line are obtained for a range of structure parameters and the dielectric constant. The results calculated from the expressions developed in the paper are compared with the theoretical results presently available in the literature and good agreement is found. Comparison with available experimental results is also made where feasible. Possible applications and limitations of the method are discussed.     

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.     

直线法分析超导微带传输线

本文首次应用直线法结合二流体模型对超导微带传输线进行了分析。针对多层介质结构和普通结构，分别计算了衰减特性、色散特性以及特性阻抗。结果表明超导微带线比普通导体微带线具有更好的性能，如低损耗、低色散和较小的电路尺寸。与已发表的文献相比较验证了本文方法的可行性。     

Least-Weighted-Square Method for Analysis and Synthesis of Transmission Lines

Analysis and synthesis of transmission lines of arbitrary geometry are not easy to realize with currently available methods. The object of this paper is to show that by introducing a new principle to be called the "least-weighted-square invariance deformation," it is possible to solve transmission line problems to desired orders of accuracy. A procedure based on this principle is given for deforming a given transmission line geometry keeping the characteristic impedance an invariant, or for synthesizing a transmission line cross-sectional geometry corresponding to the given constant parameters of the structure. The method is applied to the analysis of transmission lines having a regular polygonal outer conductor and a circular inner conductor. An application to a representative situation in synthesis is also described.     

Correction to "Analysis of Microstrip-Like Transmission Lines by Nonuniform Discretization of Integral Equations" (Letters)

In the above short paper, Ou derived some design equations for interdigital couplers. The purpose of this letter is to point out a limitation which may not be apparent upon reading the above work.     

A Variational Integral for Propagation Constant of Lossy Transmission Lines

By assuming that the current on a lossy transmission line flows in the axial direction, only a variational integral for the propagation constant can be readily obtained. This variational integral shows that the usual power loss method of evaluating the attenuation constant is valid for general transmission lines. This variational integral also shows that the perturbation of the loss-free phase constant is due to the increase in magnetic field energy caused by penetration of the field into the conductors.     

Generalized Analysis of Microstrip-Like Transmission Lines and Coplanar Strips with Anisotropic Substrates for MIC, Electrooptic Modulator, and SAW Application

A unified variational expression is presented for the line capacitance of a general, multilayer anisotropic structure. The propagation characteristics of a variety of striplines, microstriplines, and coplanar strips, in isolated and coupled configurations, with anisotropic substrates having optical axis aligned along the axis of the substrate, are computed. The characteristics of these structures with anisotropic substrates having tilted optical axis are also studied. Using the formulas presented, the study of structures with anisotropic substrates having aligned or tilted optical axis, for various applications including MIC, electrooptic modulator, and SAW IDT, reduces to the determination of a single admittance parameter. This parameter can be obtained from the transmission-line equivalent circuit of the structure almost by inspection.     

传输线时域响应分析中的改进型NILT方法

本文利用拉氏变换的推广定义及初值定理，获得一种传输线时域响应分析的改进型数字拉氏逆变换（ＮＩＬＴ）方法。该方法采取了将分析时间分段并进行传输线初始条件重新设置的步骤，因而比传统的ＮＩＬＴ方法精确、有效。     

多导体传输线时域响应分析的卷积—特征法

本文提出了多导体传输线时域响应分析的卷积-特征法,其最大特点是能分析具有频变损耗和任意负载终端的非均匀传输线.     

Lumped Capacitance, Open-Circuit End Effects, and Edge-Capacitance of Microstrip-Like Transmission Lines for Microwave and Millimeter-Wave Applications

A detailed analysis of lumped capacitance, open-circuit end effects, and edge-capacitance of finite-length strip conductors embedded in multilayer, isotropic dielectrics without sidewalls is presented. The analysis uses the well-known variational technique, in conjunction with the transverse transmission-line technique. The lumped capacitances of square and rectangular conductor patches in sandwiched microstrip, inverted microstrip, and suspended microstrip are computed. Further, extensive data on the open-circuit end effects and edge-capacitances of finite-length strip conductors in these rnicrostrip-like transmission lines are generated. Using the method presented, the analysis of lumped capacitance, open-circuit end effects, and edge-capacitances of finite-length strip conductors in various microstrip-like structures reduces to the determination of a single admittance parameter. This parameter can be simply obtained from the transmissionline equivalent circuit.     

Quasi-TEM Analysis of Microwave Transmission Lines by the Finite-Element Method

This paper describes a finite-element approach to the quasi-TEM analysis of several different types of isolated and coupled microwave transmission lines. Both the first- and higher order ordinary elements, as well as singular and infinite elements, are used to solve for the potential and field distributions in the cross section of the line. Next, the cross-sectional field distribution is inserted in a variational expression to compute the capacitance per unit length of the line, and the effective permittivity and characteristic impedance of the line are obtained from the capacitance value. A perturbational approach is developed for estimating the losses due to conductor and dielectric dissipation and computing the attenuation constant. Both the upper and lower bounds for the capacitance and the characteristic impedance are found by solving the original and the corresponding dual problem. Lines treatable by this method may contain an arbitrary number of arbitrarily shaped conductors, including a system of conductors placed either above a single ground plane or between two parallel ground planes, and inhomogeneous dielectric regions that can be approximated Iocally by a number of homogeneous subregions. The results obtained using the finite-element procedure have been compared for various types of microwave transmission lines and have been found to agree well with available theoretical and measured data.     

基于精细积分法的耦合传输线瞬态分析

在耦合传输线的瞬态分析中提出了一种基于精细积分法的龙格-库塔迭代法。这是一种时域内的数值解法，该方法在对电报方程进行空间离散而获得对时间的一阶微分方程之后，没有采用精细计算法，而是采用了龙格-库塔迭代法。避免了大量的矩阵运算，提高了传输线瞬态响应分析的效率。     

传输线瞬态响应的一种时域分析方法

提出一种传输线瞬态响应的时域分析方法。该方法对电报方程在时域内差分离散,在建立对空间的一阶微分方程组后,采用精细积分法,可获得传输线瞬态响应。这是一种时域内的半解析数值计算方法,具有方法简单、计算精度高等优点,能够有效地分析具有非线性负载的有损耦合传输线瞬态响应问题,也可以用于输电线路的瞬态分析及故障测距。     

A Precise Time-Step Integration Method for Transient Analysis of Lossy Nonuniform Transmission Lines

This paper presents a novel time-domain integration method for transient analysis of nonuniform multiconductor transmission lines (MTLs). It can solve the time response of various kinds of transmission lines with arbitrary coupling status. The spatial discretization in this method is the same as the finite-difference time-domain (FDTD) algorithm. However, in order to eliminate the Courant-Friedrich-Levy condition constraint, a precise time-step integration method is utilized in time-domain calculation. It gives an analytical solution in the time domain for the spatial discretized Telegrapher's equations with linear boundary conditions. Large time steps can be adopted in the integration process to achieve accurate results efficiently. In the analysis of transmission lines with frequency-dependent parameters, a passive equivalent model is introduced, which leads to the similar semidiscrete model as that for the frequency-independent case. In addition, a rigorous proof of the passivity of the model is provided. Numerical examples are presented to demonstrate the accuracy and stability of the proposed method.     

Efficient Eigenmode Analysis for Planar Transmission Lines

A unified analysis for planar transmission fines is performed rising the mode-matching technique. Exploiting the fact that the thickness of the metal coating (fins or strips) is normally very small in comparison to all other dimensions, the characteristic equations are formulated in a way which preserves the physical meaning of their individual terms. Thus, simplifications of far-reaching consequences can be introduced for all eigenmodes showing a cutoff frequency. It is shown in particular that the higher order modes can be derived approximately from the fundamental mode. Moreover, the dispersion relation of fin-lines can be given by a simple expression because the equivalent dielectric constant linearly depends on frequency. Both steps reduce the computer time by about two orders of magnitude in comparison to the spectral-domain method.     

传输线端接复杂电路的电磁耦合时域分析方法

该文基于时域有限差分(FDTD)方法和传输线方程,结合Ngspice软件,提出一种高效的时域混合算法,能够快速模拟空间电磁场作用传输线端接复杂电路的电磁耦合问题.该算法的优势在于实现了空间电磁场辐射与端接复杂电路瞬态响应的协同计算,且避免了对传输线和复杂电路结构的直接建模.首先,将复杂电路通过传输线的特性阻抗进行等效,采用FDTD方法结合传输线方程,求解得到特性阻抗上的入射电流响应.然后,在每个时间步上,将该电流引入复杂电路作为激励源,联合电路模型建立网表文件.最后,使用Ngspice软件读取网表文件,并仿真得到电路各元件上的瞬态响应.通过相应计算实例的数值模拟,与电磁场仿真软件CST的计算结果以及耗用内存和时间进行对比,验证了算法的正确性和高效性.