Computation of Coplanar-Type Strip-Line Characteristics by Relaxation Method and its Application to Microwave Circuits

The characteristics of new strip lines [i.e., a single strip-conductor coplanar-type strip line (S-CPS), a two symmetrical strip-conductor coplanar-type strip line (T-CPS), and a coupled strip-conductor coplanar-type strip line (C-CPS), which consists of single two-center strip conductors or coupled 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 and side wall on these lines is analyzed and the characteristic impedance and phase-velocity ratio are determined. The characteristic impedance is determined experimentally and the maximum values of the discrepancies compared with the calculated value of each of the lines are 2.0-3.0 percent. Application examples of the coplanar-type strip line to microwave transistor amplifier and parallel-coupled filter are shown. A transistor amplifier of small size, light weight, wide bandwidth, and improved reliability is achieved. A parallel-coupled filter small in size (reduction ratio is more than 50 percent), with good frequency symmetry and featuring easy resonance frequency fine tuning is obtained.     

Wire and strip conductors over a dielectric-coated conducting ordielectric half-space

The complex wavenumber and characteristic impedance are determined for a wire or flat strip over a dielectric-coated half-space that can be a conductor or a dielectric with large permittivity. Elevated microstrip is an example of the configuration. The properties of the wire as an antenna or transmission lines are determined from those of the insulated antenna with a two-layer eccentric insulation. The theory is extended to the strip conductor with the help of a comparison of the tubular and strip conductors over a perfectly conducting half-space     

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.     

Full wave analysis of conductor-backed and multi-layer high-T c superconducting coplanar waveguide

Dispersions, attenuation and characteristic impedance of shielded conductor-backed coplanar waveguide(CBCPW) and shielded three-layer coplanar waveguide (CPW) with finite conductor thickness as well as their superconducting applications are calculated. The method of lines(MoL) is employed to analyze these coplanar waveguides. The analysis is validated by a comparison of the calculated results with those published previously. Effects of finite width of grounded strip for a CPW are considered. Extensive investigation of the numerical convergence for calculation of the characteristic impedance is also described.     

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。     

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。     

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.     

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.     

Characteristic Impedance and Effective Permittivity of Modified Microstrip Line for High Power Transmission

In a quasi-TEM approximation, the calculation of the characteristic impedance and effective permittivity of a modified microstrip line with the upper strip conductor edges turned up from the substrateis presented. Both these theoretically derived quantities are compared with experimental values. To further facilitate the analysis and synthesis of the modified microstrip line, closed-form approximations to the characteristic impedance and effective permittivity have been found containing elementary functions only. The modified microstrip can be used in the construction of lines capable of transmitting high power on substrates having high loss factor and low thermal conductivity, for example, on low-cost plastics.     

On the Cutoff Wavelength of Rectangular-Shaped Microshield Line by Edge Element Method

In this paper, the cutoff characteristic of rectangular-shaped microshield transmission line has been analysed by edge element method. Dependence of cutoff wavelengths on the thickness of metallic signal strip, dielectric constant of dielectric substrate and the width of the rectangular-shaped ground conductor are presented in tabular form. Numerical results in this paper have important values in design of rectangular-shaped microshield lines in microwave and millimeter wave integrated circuits.     

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.     

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.     

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.     

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。     

Tunable Impedance Transformer Using a Transmission Line With Variable Characteristic Impedance

This paper proposes a new structure for a tunable impedance transformer. The proposed transformer consists of a quarter-wavelength transmission line with variable characteristic impedance. The operating principle of the variable characteristic impedance is based on the use of parallel combinations of multiple transmission lines and by controlling the line connection with RF switches. Multiple switches are inserted at the in/out terminals of each transmission line. Since a parallel microstrip transmission line has a unique structure that involves a partially removed ground plane under the conductor line, it is possible to realize a high characteristic impedance line with a wide linewidth.     

Determination of the Capacitance, Inductance, and Characteristic Impedance of Rectangular Lines

This paper determines the capacitance, inductance, and characteristic impedance of rectangular lines by the method of conformal transformation. In practical applications, such lines may be used as transmission links of RF energy, as impedance-transforming sections, or as components in electron tubes. Formulas are given for the calculation of the parameters of rectangular lines having the following characteristics: 1) The inner conductor may have varying thickness compared with the depth of the outer conductor. 2) The axes of the conductors may coincide or may be displaced with respect to each other. 3) The edges of the inner conductor may be rounded to lessen the electrical stress occurring at sharp corners. Excellent agreement has been obtained between the calculated results and those found by use of the relaxation method, by direct measurement of models, and by electrolytic tank measurement.     

Striction and skin effects on the internal impedance value of flatconductors

A frequency domain analysis is used to derive closed formulas giving the internal impedance of a rectangular, flat, nonperfectly conducting solid conductor modeling a ground plane. The approach takes into account the skin effect due to the finite conductivity of the ground plane and the increase of the impedance due to the confinement of the current lines at the contact points, called the striction effect. The computed results show that, in certain situations and within the frequency range of interest for the electromagnetic interference and compatibility community, the internal impedance calculated can no longer be neglected with respect to the external impedance when return conductors are located very near the ground plane     

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     

CHARACTERISTIC IMPEDANCE OF SPECIFIC TRANSMISSION LINES WITH OFFSET INNER CONDUCTORS

The partial charge simulation method is presented to solve the characteristicimpedance of the transmission line of specific cross section with an offset inner conductor.Thismethod has a higher accuracy due to the accurate satisfaction of the boundary condition on theouter conductor.The combined method of the Gauss elimination and optimization is used tosolve the equation of charge simulation,and it is an effective method for increasing the accuracyand assuring the convergence.The Green's functions of five transmission lines(i.e,with circular,elliptic,rectangular,trough and slab conductor)are given.     

An Accurate Approximation of the Impedance of a Circular Cylinder Concentric with an External Square Tube

The problem of determining the characteristic impedance of a concentric coaxial transmission line having a circular inner conductor and a square outer conductor is reexamined. The Green's function for a rectangle is used to determine the geometrical capacitance of a series of structures ranging from 1-46 Omega with an error less than 10 -5. The method of analysis is illustrated in detail for the 1-Omega case. The resitlts are presented in terms of the "outer shield factor" R/sub eff/, which is defined as the ratio of the diameter of an outer circle, having the same capacitance as the outer square, to the side of the outer square, Values of this ratio are tabulated for impedances ranging from 1-46 Omega. These values are also plotted on a curve which can be read with an error of the order of 0.02 Omega for impedances greater than 3 Omega.