Coplanar Waveguide: A Surface Strip Transmission Line Suitable for Nonreciprocal Gyromagnetic Device Applications

A coplanar waveguide consists of a strip of thin metallic film on the surface of a dielectric slab with two ground electrodes running adjacent and parallel to the strip. This novel transmission line readily lends itself to nonreciprocal magnetic device applications because of the built-in circularly polarized magnetic vector at the air-dielectric boundary between the conductors. Practical applications of the coplanar waveguide have been experimentally demonstrated by measurements on resonant isolators and differential phase shifters fabricated on low-loss dielectric substrates with high dielectric constants. Calculations have been made for the characteristic impedance, phase velocity, and ripper bound of attenuation of a transmission line whose electrodes are all on one side of a dielectric substrate. These calculations are in good agreement with preliminary experimental results. The coplanar configuration of the transmission system not only permits easy shunt connection of external elements in hybrid integrated circuits, but also adapts well to the fabrication of monolithic integrated systems. Low-loss dielectric substrates with high dielectric constants may be employed to reduce the longitudinal dimension of the integrated circuits because the characteristic impedance of the coplanar waveguide is relatively independent of the substrate thickness; this may be of vital importance for Iow-frequency integrated microwave systems.     

The Characteristic Impedance of Rectangular Transmission Lines with Thin Center Conductor and Air Dielectric

The characteristic impedance of large-scale rectangular strip transmission line facilities used for such purposes as EMI susceptibtity testing, biological exposures, etc., is discussed. These Iines are characterized by a thin center conductor and an air dielectric. Impedance data obtained by earlier workers, using different analytical and numerical techniques, are reviewed and compared. Exact data are available for the problem involving a center conductor of zero thickness while for the center conductor of finite thickness data are available which are accurate to less than 1.25 percent.     

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.     

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.     

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.     

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 Impedance of the Shielded-Strip Transmission Line

Simple formulas are given for the characteristic impedance of a transmission line consisting of a conducting strip of rectangular cross section centered between parallel conducting plates at ground potential. The formulas agree to within 1.2 per cent with an exact formula for a zero thickness strip. In the case of finite thickness up to a quarter of the plate spacing, the formulas are expected to be at least that accurate. A family of characteristic impedance curves given in this paper should prove useful to the design engineer.     

微带传输线特性的数值分析

本文应用混合模有限元方法分析和计算了微带传输线的各种特性,包括特性阻抗、速度比、色散特性以及带厚的影响,并与有关文献结果作了比较。结果表明,有限元法是对微带传输线进行数值分析的有效方法。     

Characteristics of Inhomogeneous Broadside-Coupled Striplines

A variational method for the analysis of inhomogeneous broadside-coupled striplines is described. The data for even- and odd-mode characteristic impedances, effective dielectric constants, and mode phase velocity ratios are presented. It is found that the phase velocity ratio may be varied over the range 1.14 /spl les/ ( V/sub e/ / V/sub 0/) /spl les/ 3.6 for broadside-coupled suspended microstrip lines (BSML) and 0.36 /spl les/ ( V/sub e/ / V/sub 0/) /spl les/ 0.93 for broadside-coupled inverted microstrip lines (BIML) using materials with dielectric constant less than 16 and S/b /spl ges/ 0.05, W/b /spl les/ 2.0. The effect of nonzero strip thickness is also calculated. It is noticed that the effect of thickness is more pronounced for the odd-mode case than for the even mode. Losses are obtained using the incremental inductance rule of Wheeler. The odd-mode attenuation constant is always higher than the even-mode value.     

Caractéristiques des ondes se propageant dans des structures périodiques a ondes lentes en technologie microélectronique

The charge and the potential at every point in the cross-section of the elementary cell of a microstrip delay line are determined under the quasitem approximation. The authors solve a first order Fredholm type integral equation in the complex plane for a general phase shift of θper cell to get the charge density of the two conductors in the elementary cell. Knowing this, the characteristic impedance, the phase velocity and the effective dielectric constant are determined for the fundamental modes of propagation. From a detailed study of the characteristic parameter variations with the geometry of the line, a general law of coupling is deduced. The dispersion diagram and the iterative impedance of the lines are then determined by considering the boundary conditions of each structure. In addition to the classical meander line, they have studied the interdigital line, these lines having many dielectric layers. They present curves of practical interest in as much as coupling is concerned and an extension of Weiss’ theory, presented in to treat multilayered structures.     

Characteristics of Transmission Lines with a Single Wire for a Multiwire Circuit Board

This paper presents the characteristic impedance Z/sub 0/ and the phase velocity v/sub p/ of transmission lines with a single wire for a multiwire circuit board (MWB) under the quasi-TEM wave approximation. The characteristics are discussed for each of three investigated strictures a: (I)H = h + r, (II)H = h, and (III)H = h - r, where r, h, and H are the radius of the wire, the thickness of the dielectric (adhesive layer), and the distance from the ground plane to the center of the wire, respectively. A charge simulation method is used for the calculation of the parameters. Z/sub 0/ and v/sub p/ are presented in graphical form for adhesive relative dielectric constants epsilon* of 1.0, 2.65, and 5.0 as a function of r/h. An approximate formula of Z/sub 0/ for the structure of case (II) with epsilon* = 5.0 is also presented.     

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 full-wave analysis of microstrip lines by variational conformalmapping technique

Wheeler's mapping, which is useful in the quasi-TEM analysis of microstrip lines, is combined with the full-wave variational formulation to facilitate a finite-element solution. This desirable mapping not only transforms the problem domain into a finite region, but also overcomes the field singularity on the strip edge. Compared with other known techniques, the present method makes fewer assumptions, and is more rigorous as long as the strip thickness is negligible. Numerical results for the frequency dependence of effective dielectric constant, the characteristic impedance, and both longitudinal and transverse current distributions on the strip are also included     

Coupled Strip Transmission Line with Three Center Conductors

An exact analysis is made for the shielded coupled strip transmission line with three center conductors. By means of the immittance matrices presented, the electrical behavior of the coupled strip transmission line of this type may be completely described. Design formulas which enable one to evaluate the cross-section dimensions from the desired values of characteristic immittances are derived for the two kinds of the line configurations. Equivalent circuits of the two-port networks for various port conditions are also presented. In addition, an application is discussed involving the asymmetrical coupled strip transmission line with two center conductors. The appendix gives the derivation of the design formulas by means of conformal mapping techniques.     

Metallization thickness in bilateral and unilateral Finlines

The theory and numerical results are presented to the effective dielectric constant and characteristic impedance of bilateral and unilateral finlines with metallization thickness. The full wave analysis of the transverse transmission line — TTL method is used to determine the electromagnetic fields of the structure in Fourier transform domain — FTD. Applying the suitable boundary conditions and the moment method, a homogeneous matrix system is obtained and the effective dielectric constant is extracted. The characteristic impedance is obtained using the relation between the voltage in slot and the transmitted power. Computational programs are developed to obtain numerical results to the effective dielectric constant and characteristic impedance.     

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.     

An efficient approach to modeling of quasiplanar structures usingthe formulation of power conservation in spectral domain

An enhanced spectral domain approach (SDA) is developed for analysis of complex quasi-planar transmission lines. The method is based on a combination of the spectral domain formulation and power conservation theorem. The relationship between electric and magnetic fields is established inside dielectric layers by using the conventional SDA while the characteristic equation related to interface conditions is derived through the power conservation theorem. Maintaining the inherent advantages of the SDA, this technique is able to easily handle more complex quasi-planar structures. Generalized power formulation is also presented to calculate characteristic impedance. Convergence behavior is discussed considering the nature of power conservation. Various finlines with finite thickness of conductors are analyzed to demonstrate its applications     

An accurate calculation of uniform microstrip transmission lines

An analytical program for calculating the field distribution about a microstrip transmission line bounded by a shielding wall is used to calculate the impedance, velocity, and attenuation parameters. The program input parameters are the dimensions of the strip and shielding wall and the relative dielectric constant of the substrate material. The field distribution about the strip is integrated to find the charge density on the strip and walls with and without the dielectric substrate. From these two calculations, the relative velocity and impedance can be calculated.     

An Accurate Calculation of Uniform Microstrip Transmission Lines

An analytical program for calculating the field distribution about a microstrip transmission line bounded by a shielding wall is used to calculate the impedance, velocity, and attenuation parameters. The program input parameters are the dimensions of the strip and shielding wall and the relative dielectric constant of the substrate material. The field distribution about the strip is integrated to find the charge density on the strip and walls with and without the dielectric substrate. From these two calculations, the relative velocity and impedance can be calculated.