Wave Propagation on Nonuniform Transmission Lines (Short Papers)

The problem of wave propagation on nonuniform transmission lines is studied. Equations are presented not only for the reflection coefficient but for the transmission and admittance properties as well. They are valid under the assumption that only one mode of propagation exists on the line and that the properties do not change so rapidly that the fundamental transmission line equations are no longer applicable. Since all equations are derived for arbitrary load conditions, an extremely versatile solution of the problem has been obtained.     

An application of FDTD in studying the end effects of slotline andcoplanar waveguide with anisotropic substrates

In this paper, the finite-difference time-domain (FDTD) method is applied in conjunction with the generalized pencil of function (GPOF) technique to evaluate the reflection coefficient from shorted slotlines and coplanar waveguides (CPW) on anisotropic substrates, and to extract the propagation constant along the line from these data. For each frequency, the field solutions at different locations are processed by using the GPOF technique to extract two complex exponents that correspond to the forward and backward traveling waves, which provide all the information about the reflection coefficient and the dispersion characteristic of the transmission line. The advantage of combining the GPOF technique with the FDTD method is that the reflection coefficients can be obtained with a single run. Recognizing that there is a dearth of results for the reflection coefficients of slotline and CPW-line discontinuities with anisotropic substrates, the present problem is also solved by using the spectral-domain method for the purpose of validation, and the two results are found to compare quite well with each other. For further validation, the FDTD and GPOF solutions are derived for isotropic substrates, and are compared with the published theoretical and experimental results     

Shunt stub line impedance matching: a wave reflection analysistutorial

This paper presents a detailed transmission-line wave reflection analysis for the situation where an antenna's feed-point impedance is matched to the transmission-line characteristic impedance through the use of a shunt stub line. In most engineering texts, the steady-state solution to the shunt-stub-line impedance-matching problem is presented in detail. However, the solution in terms of a wave reflection analysis is generally not presented, since the steady-state solution is sufficient for most practical applications. This article is presented as a tutorial review of both the steady-state solution and the solution as determined through a detailed wave reflection analysis. It is conceptually and mathematically demonstrated that the wave reflections created at the antenna and at the stub-line termination do not cancel one another at the stub-line connection point, and they do not stay separate from one another. It is demonstrated that the steady-state impedance match is achieved when the wave reflections created at the antenna and at the stub-line termination combine at the connection point to cancel the initial wave reflections created at the connection point. The analysis and resulting formulas presented are derived for the general problem of a stub line being connected in parallel to a transmission line at any point, and are therefore valid independently of an impedance match being established at the connection point. The analysis and formulas are valid for any combination of transmission-line length, transmission-line properties, antenna impedance, stub line length, and stub line termination impedance     

Chebyshev collocation and Newton-type optimization methods for the inverse problem on nonuniform transmission lines

A frequency-domain inverse problem for the nonuniform LCRG transmission line is considered. The parameters of the nonuniform line are interpolated by Chebyshev polynomials, and the Telegraphers equations are solved by a collocation method using the same polynomials. The interpolation coefficients for the unknown parameters are reconstructed by means of Newton-type optimization methods for which the Jacobian matrix has been calculated explicitly. For the reconstruction of one or two parameters, the algorithm is tested on synthetic data, and the necessity to use regularization is discussed. Finally, the algorithm is tested with measured reflection data to reconstruct shunt capacitances with piecewise constant profiles.     

非均匀传输线特性重构中的噪声影响分析

利用时域反射技术(Time Domain Reflectometry,TDR),由测量得到的时域反射信号,可以重构出非均匀传输线的一些特征参数。当反射信号中混有噪声时,对非均匀传输线特性参数的重构会产生影响。采用Zakharov-Shabat类型逆散射问题的数值反演算法,以指数型非均匀传输线为例,对时域反射信号中混有高斯白噪声情况下的非均匀传输线特性参数重构问题进行了数值实验。数值计算结果表明,在噪声干扰下,算法本身是稳定的,在较宽的信噪比范围内,能有效地重构出非均匀传输线的特征参数。     

Application of the multilevel single-linkage method toone-dimensional electromagnetic inverse scattering problem

An inverse scattering method for the reconstruction of the permittivity and conductivity profiles of a multilayered medium and for that of the impedance profile of a nonuniform transmission line is proposed. The inversion is based on the global minimization of an objective function by the multilevel single-linkage method. The objective function is defined as the mean-square error between the measured data and the data obtained from the solution of the forward problem. An exact formulation for the gradient of the objective function in closed form is derived. The necessary condition for the unique solution of the inverse problem of a nonuniform transmission line is discussed. Reconstruction examples using both experimental and noisy synthetic data are presented     

The Impedance of a Wire Grid Parallel to a Dielectric Interface

Analysis is given for the problem of reflection of a plane wave at oblique incidence on a wire grid which is parallel to a plane interface between two homogeneous dielectrics. It is assumed that the wire grid is a periodic structure and consists of thin cylindrical wires of homogeneous material. The equivalent circuit is derived where it is shown that the space on either side of the interface can by a transmission line, and the grid itself is represented by a pure shunt element across one of the lines.     

Analysis and synthesis of tapered microstrip transmission lines

The input voltage reflection coefficient on a tapered microstrip transmission line is analyzed and a new Fourier transform pair is derived which introduces echo time and frequency as variables. Calculations of the input reflection coefficient take into account the frequency dispersion-characteristics of the effective permittivity. An efficient method is proposed for analysis and synthesis of microstrip tapers and numerical results are presented for microstrip exponential tapers and microstrip Chebyshev tapers     

Periodically Loaded Transmission Lines

In this paper equations for the transmission parameters of a periodically loaded line are derived in closed form with no restriction on the size, type or number of discontinuities. The equations also take into consideration any attenuation that may exist on the line. Several plots of the input reflection coefficient are presented and compared with experimental results. The agreement is very good.     

Image solution for Poisson's equation in wedge geometry

The Poisson's equation for a dielectric wedge is solved by deriving a static image that corresponds to the potential contribution of the wedge. The problem is studied mainly in three dimensions but the solution for the analog two-dimensional problem is also provided. It appears that the use of image sources provides numerically a simple and efficient method to compute the potential inside and outside the wedge. Image sources for the exterior and interior regions consist of a line charge that decays exponentially as a function of complex angle and a set of point charges that can be interpreted as reflection or transmission images of a dielectric plane. All known closed-form solutions in terms of elementary functions are derived for an electrically and magnetically conducting half plane     

A Fabry-Perot acousto-optical cavity for the terahertz band

A periodic structure that is a pair of Bragg gratings produced by a decaying acoustic wave is considered. The problem of light diffraction by such structures is solved. Changes of the cavity transmission function are found with allowance for the attenuation of the propagating acoustic wave. Analytical expressions for the light wave transmission and reflection functions are derived, and it is also shown that narrow reflection (or transmission) lines are formed along with standard transmission windows. In contrast to cavities formed by dielectric mirrors, such a cavity supports a mode with a modulated Q factor. In particular, it is stated that a Fabry-Perot cavity can be applied in the terahertz wavelength band.     

传输/反射法测量复介电常数的若干问题

研究了传输／反射法测量线性材料复介电常数εr的厚度谐振、多值性等问题，得到了解决这些问题的有效方法。通过改进NRW传输／反射法，由散射参数直接得到了归一化特性阻抗与传播常数，从而可以把已有的三个确定复介电常数的方程用到NRW传输／反射法中。联合应用这三个方程解决了上述问题，这使得人们可以用传输／反射法对任意厚度的样品在任意频率上进行复介电常数的稳定测量。用波导取样器与同轴线取样器分别得到的实验结果证明了此方法的有效性与可实现性。     

On geometric sequences of reflection coefficients and Gaussianautocorrelations

The author shows that by interpreting the lattice filter as a discrete transmission line, the problem of determining the reflection coefficients associated with a Gaussian autocorrelation can be solved easily using the Schur algorithm. These reflection coefficients have been shown to be in geometric progression; it is claimed that this has been done in a much simpler and more enlightening manner than in the presentation of G. Jacoriti and G. Scarano (see ibid., vol.75, no.7, p.960-961, 1987). The geometric progression of reflection coefficients leads to a stationarity property of the discrete transmission line, which accounts for the striking simplicity of the expressions for the waves traveling in the line     

Direct coupling from a GaAs laser into a single-mode fibre

Ways of coupling directly to a monomode fibre by neutralising the end reflection from the laser and then using the face of the fibre core as a cavity mirror are proposed. The condition is derived for the optimum transfer of power from the laser resonator to the fibre transmission line.     

Exact image theory for the calculation of fields transmitted through a planar interface of two media

Exact image theory, recently developed for the calculation of fields reflected from a planar interface between two homogenous media, is extended for transmitted field calculation. The image of a point source is found to be a line source located in complex space for proper convergence. Unlike for the reflection image, the transmission image line is seen to be curved in complex space for efficient computation. Expressions are derived for the transmission image of the most general three-dimensional electric and magnetic sources and for media with bothepsilonandmudiscontinuous across the interface. The new theory is verified with several asymptotic tests and properties of the transmission image function are discussed. As an application, radiation from a resonant horizontal loop antenna into the ground is calculated and results are seen to agree with those given in the literature.     

Time-domain reflectometry using arbitrary incident waveforms

A novel time-domain reflectometry technique is developed for detecting the physical structures of transmission lines by using arbitrary waveforms. By discretizing both incident and reflected waves, we formulate the reflection coefficient of a nonuniform transmission line as a polynomial ratio in the Z-transform, wherein the numerator and denominator represent the reflected and incident waves, respectively. A reconstruction scheme is derived to obtain the characteristic impedance profile of a transmission line. Some examples are presented to illustrate the validity of this new technique.     

Propagation of the Quasi-TEM Mode in Ferrite-Filled Coaxial Line

The Suhl and Walker approximation for the propagation constant of the quasi-TEM mode in ferrite-filled parallel plane waveguide has been applied to the ferrite-filled coaxial line. The approximation is compared to exact solutions for a coaxial line filled with a lossless ferrite with close agreement. The propagation constant of the quasi-TEM mode is determined by measuring the complex reflection coefficient of a plane ferrite-air interface. The /spl alpha/ and (/spl beta/ are compared to the Suhl and Walker approximation with losses, and qualitative agreement is found. In order to relate the measured values to the propagation constants, the boundary value problem of the reflection from a plane ferrite-air interface is investigated. Expressions are derived which relate the real and imaginary parts of the propagation constant in the ferrite to an approximation to the complex reflection coefficient of the TEM mode in the empty line.     

高速电路设计中信号完整性的反射分析

针对高速电路设计中信号完整性的问题,文中通过对高速电路中传输线等效电路的分析,从理论及计算角度给出了信号反射现象的形成原因。介绍了两类常用的抑制反射的端接方案, 阐述了6种阻抗端接匹配方法消除反射的原理。通过Cadence公司的SpecctraQuest仿真工具对点对点信号传输网络进行了反射仿真,给出了在不同阻抗匹配方式下的仿真测试结果。结果表明,适当的阻抗匹配方式可以改善信号传输的反射现象。     

传输线的反射干扰

在数字信号处理系统中,时钟信号和数字信号传输因传输始端和终端阻抗不匹配而引起反射干扰,使传输信号的波形出现上冲、下降和振荡。为了抑制这种因阻抗不匹配引起的反射,本文首先从产生这种反射的原因和造成的重大危害分析,提出了反射干扰这一亟待解决的问题;接着从传输线的阻抗特性以及阻抗匹配原理出发,提出了始端和终端阻抗匹配原则,最后给出了几种减小和抑制反射干扰的方法,实践证明使用阻抗匹配这一方法在减小反射干扰是十分有效的。     

Scattering from stacked gratings and dielectrics for various anglesof wave incidence

The theory of scattering matrices and microwave network analysis is used to solve the problem of scattering from cascaded infinite periodic gratings. The total reflection and transmission coefficients are calculated as functions of angle of incidence, wire spacing for each grating separation, wire thickness, and number of gratings that comprise the cascaded structure. The problem of stacking dielectric slabs with periodic gratings is also formulated and solved. In all cases, the secant corrector spectral iteration approach is used as a numerical method for calculating the desired currents and fields. Finally, the calculated values of the reflection and transmission coefficients are presented and compared with reported experimental and theoretical data