Computation of the Characteristics of Coplanar-Type Strip Lines by the Relaxation Method (Short Papers)

The characteristics of new strip lines (i.e., a single strip conductor and a two symmetrical strip-conductor coplanar-type strip line, which consist of single- or two-center strip conductors and ground plates on a dielectric substrate and outer ground conductor) are calculated by the relaxation method. The effect of the outer ground conductor on these lines is analyzed, and the characteristic impedance and velocity ratio are determined. The characteristic impedance is determined experimentally, and the maximum values of the discrepancies compared with the calculated values of each of the lines are 2.0-3.0 percent.     

正方外导体-微带内导体传输线特性阻抗严格解

应用保角变换法,严格推导出正方外导体一单一微带、“十”字微带和耦合微带内导体传输线特性阻抗精确表达式,并给出了不同参数条件下传输线特性阻抗的数值结果。     

An integral equation method for the evaluation of conductor anddielectric losses in high-frequency interconnects

An integral equation method is developed to solve for the complex propagation constant in multilayer planar structures with an arbitrary number of strip conductors on different levels. Both dielectric losses in the substrate layers and conductor losses in the strips and ground plane are considered. The Green's function included in the integral equation is derived by using a generalized impedance boundary formulation. The microstrip ohmic losses are evaluated by using an equivalent frequency-dependent impedance surface which is derived by solving for the fields inside the conductors. This impedance surface replaces the conducting strips and takes into account the thickness and skin effect of the strips at high frequencies. The effects of various parameters such as frequency, thickness of the lines, and substrate surface roughness on the complex propagation constant are investigated. Results are presented for single strips, coupled lines, and two-level interconnects. Good agreement with data available in the literature is shown     

A new micromachined overlay CPW structure with low attenuation overwide impedance ranges and its application to low-pass filters

In this paper, a new micromachined overlay-coplanar-waveguide (OCPW) structure has been developed and its characteristics are studied in detail as a function of the line parameters. In OCPW, the edges of the center conductors are lifted by micromachining techniques and partially overlapped with the ground plane to facilitate low-impedance lines. The elevated center conductors help to reduce the conductor loss by redistributing the current over a broad area. Comparative experiments on low-loss and lossy substrates also confirm the screening effect from the substrate losses by confining the electric field in the air between the overlapped conductor plates. Compared with the coplanar-waveguide (CPW) lines, the OCPW lines show wider impedance range (25-80 Ω) and lower loss (<0.95 dB/cm at 50 GHz). The advantages of OCPW for low-Z₀ lines are utilized to realize a high-performance stepped-impedance low-pass filter at X-band. The OCPW filter shows distinct advantages over the conventional CPW filter in terms of size, loss, skirt, and stopband characteristics     

Approximate Determination of the Characteristic Impedance of the Coaxial System Consisting of an Irregular Outer Conductor and a Circular Inner Conductor

An elementary formula is presented for the determination of the characteristic impedance of a coaxial transmission line consisting of a circular inner conductor and an irregular outer conductor. In this approach, the irregular outer conductor is replaced by an eccentric circular enter conductor which has the same "shield factor" as an irregular one at the extreme of a small wire, and the same formnla is adapted for outer conductors of different shapes by determining values of eccentricity of the equivalent eccentric coaxial lines. The validity of the formula is confirmed by numerical results.     

Characteristic Impedances of Multiconductor Strip Transmission Lines

The design of certain log-periodic microwave circuit elements requires a knowledge of the characteristic impedances of a system of four-coupled strip transmission lines. The system of four strip conductors between parallel ground planes is capable of supporting four different TEM modes which have different characteristic impedances. In this paper, the characteristic impedances of the four modes are determined by a variational method. The variational solution is an upper bound to the exact characteristic impedance of the line. In general, the coplanar strip conductors are located at an arbitrary (but identical) displacement from the parallel ground planes. When the separation between the broadside-coupled strips is precisely one-half the spacing between the parallel ground planes, two of the mode impedances may be determined exactly by means of conformal mapping. The variational solutions are compared to the exact solutions for this special case. Because of the "cell image" principle which holds for the problem, the mode solutions presented here also apply to various single- and two-conductor strip transmission lines with arbitrary displacements. As a result, solutions for the following strip line configurations are available from the analysis: a single strip conductor in a trough, or between parallel ground planes; two coplanar strips between ground planes; two broadside-coupled strips in a trough, or between parallel ground planes. An extensive set of curves are presented which show the characteristic impedances of the four modes as a function of the relative dimensions of the strip transmission line.     

Coupled Strip Transmission Lines with Rectangular Inner Conductors

A method is presented for determining the capacitance of electrostatic fields which have hitherto proved intractable because their solutions required the evaluation of hyperelliptic integrals. The method is illustrated by applying it to the determination of the characteristic impedance of a strip transmission line. The results compare favorably with the results of existing solutions. The method is then used to determine the characteristic impedance of coupled strip transmission lines with inner conductors of rectangular shape. Curves are included which permit the determination of this impedance over a wide range of line proportions.     

Characteristic Impedances of Four-Conductor Transmission Line

A general formula for calculation of the characteristic impedance of four conductor transmission line in a rectangular shield is derived. A number of coupled and single strip transmission lines are considered by simplifying the general formula. Numerical results for a line in a square shield are presented graphically.     

偏心特种截面传输线特性阻抗的分析计算

本文提出了计算偏心特种截面传输线特性阻抗的部分模拟电荷法。由于外导体边界1上的边界条件准确满足,所以这种方法精度较高、且计算量小。文中提出用高斯列主元消去法与最优化方法相结合的技术求解模拟电荷方程组,是提高精度和保证收敛的一种有效算法。文中给出了外导体边界1为圆形、椭圆形、矩形、槽形和平板形五类传输线的Green函数,且对特性阻抗值进行了计算。     

Computation of Impedance and Attenuation of TEM-Lines by Finite Difference Methods

The characteristic impedance and the attenuation of transmission lines supporting TEM modes can be computed by using finite difference methods for solving the Laplace equation for the domain defined by the inner and the outer conductor. The difference equations can be solved by machine computation and the impedance and the attenuation is obtained by integrating the field gradients and the squares of field gradients over both boundaries. The case of a shielded strip transmission line is treated as a numerical example. A computation time of approximately 0.015 hour on the IBM 7094 is required for achieving an accuracy of 0.5 percent for the impedance and 2 percent for the attenuation. The finite difference method is also used for lines which are partially filled with dielectric material and it is concluded that low attenuations are obtained by placing the dielectric material in such a way that high field regions are avoided.     

Exact Theory of Interdigital Band-Pass Filters and Related Coupled Band-Pass Structures

An exact theory of interdigital line networks and related coupled structures is presented. The theory of parallel-coupled line arrays is reviewed briefly, and the derivation of exact equivalent circuits from the impedance matrix using modem network synthesis techniques is discussed. A simplified theory of equivalent coupled structures is introduced in order to avoid the lengthy analysis required when using the impedance matrix approach. Equivalent networks for the interdigital line are obtained by inspection, using a transformed capacitance matrix associated with the two-dimensional geometry of the conductors and ground planes. The techniques presented are simple to apply and allow a given transmission response to be obtained in a variety of line configurations. A practical design example and experimental results are given to illustrate the simplicity of the approach, along with general criteria for the design of practical filter networks with optimum transmission characteristics. The paper is directed toward the design of interdigital band-pass filters; however, the techniques presented can be used to analyze and design a much broader class of microwave networks. The relationship of the exact theory to existing approximate theory is discussed.     

结合保角变换的优化模拟镜象法解多种截面形状同轴线的特性阻抗

介绍一种计算多种截面形状同轴线的新方法结合保角变换的优化模拟镜象法。此法计算量小、精确度高,并能进行误差范围计算。列出对内圆外方、偏心内圆外方和内带形外圆等九种同轴线特性阻抗的计算结果并与其它文献结果进行了比较。     

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.     

Analysis of an Oval Symmetrically Located Inside a Rectangular Boundary by Conformal Mapping

This paper describes the analysis of a transmission line having an oval-shaped center conductor syrnmetrically placed inside an outer conductor in the form of a rectangular waveguide. A conformal transformation is used to calculate the characteristic impedances of oval, elliptic, circular, and planar conductors. The impedance data of these structures are presented in the form of charts for different aspect ratios of the rectangular outer condnctor. The charge distribution on the center conductor is also determined.     

任意镜像阻抗平行耦合线滤波器的设计

任意镜像阻抗平行耦合线滤波器与传统的平行耦合线滤波器相比,通过选择合理的镜像阻抗,可以得到合适的耦合线的宽度与缝隙,因而使滤波器更容易加工。首先从理论上推导了任意镜像阻抗平行耦合线滤波器的设计公式。根据此理论,设计了80Ω的任意镜像阻抗平行耦合线滤波器。通过EM仿真验证了设计公式的正确性与准确性。     

正多边形外导体-圆形内导体同轴传输线特性阻抗的计算

本文提出一种计算正多边形外导体-圆形内导体同轴传输线特性阻抗的方法。由它可以得到正三(四、五、六)边形外导体-圆形内导体同轴传输线特性阻抗的可靠的上限和下限值。当r/R0.5(0.6)时,由它得到的上限和下限值十分接近,有一定的实用价值。     

The Characteristic Impedance of a Family of Rectangular Coaxial Structures with Off-Centered Strip Inner Conductors

A two-parameter family of hyperelliptic integrals is exhibited which maps the upper half-phase into the interior of a rectangle pierced by a reentrant line. Since these integrals can be expressed as the sum of elliptic integrals of the first kind, the odd- and even-mode characteristic impedances of a two-parameter family of coaxial structures whose inner conductors are strips, displaced perpendicularly to their width from the center of the outer rectangular conductor, can be expressed in terms of these well-known functions. Numerical values are given for a range of values of W/B and B/sub 1/ /B. Here W is the width of the strip, B is the height of the outer rectangular conductor, and B/sub 1/ is the distance from the strip to the farthest parallel wall of the outer conductor.     

First-order symmetric modes for a slightly lossy coaxialtransmission line

A complete set of solutions for Maxwell's equations to first order in the normalized surface impedance z_s of the coaxial conductors is found. The derivation of the fields outlined assumes a vacuum dielectric and an infinitely thick outer conductor. It starts from J.P. Stratton's work (1941) with a derivation of the determinantal equation for finding the eigenvalues for both the principal and waveguide modes in a lossy line. The first-order determinantal equation is found, preceded by an equation for calculating the proportionality constant for the fields intermediate between the center and outer conductor. The equations for lossy waveguide modes are new, and the principal mode fields include a term missing from the expressions that are found elsewhere in the literature. The resulting characteristic admittance and distributed line parameters are calculated; the distributed line resistance is significantly different from other calculations found in the literature     

Characteristic Impedance of an Oval Located Symmetrically Between the Ground Planes of Finite Width

A conformal transformation for the analysis of a transmission line with an oval-shaped center conductor symmetrically placed between two finite ground planes is developed. The formulation is used to calculate the characteristic impedances of oval, elliptic, circular, and planar conductors placed midway between the finite ground planes. The results on impedance are presented for various values of ground plane width to spacing ratios.     

Determination of the Characteristic Impedance by a Step Current Density Approximation (Short Papers)

The step current densities are used to determine the characteristic impedance of a transmission line with rectangular shape of the conductors. Numerical results for different rectangular lines with asymmetrical position of the inner conductor are presented. The comparison of the results for the square and rectangular coaxial lines shows quite good agreement with the known data.