Parameters of Microstrip Transmission Lines and of Coupled Pairs of Microstrip Lines

A theoretical analysis is presented of microwave propagation on microstrip, with particular reference to the case of coupled pairs of microstrip lines. Data on this type of transmission line are needed for the design of directional couplers, filters, and other components in microwave integrated circuits. The inhomogeneous medium, consisting of the dielectric substrate and the vacuum above it, is treated in a rigorous manner through the use of a "dielectric Green's function" which expresses the discontinuity of the fields at the dielectric-vacuum interface. Results are presented in graphical form for substrate dielectric constants of 1, 9, and 16, and a range of values of width and spacing of the strips. Numerical tables for these and other cases are also available. The tables present capacitance, characteristic impedance, and velocity of propagation of the even and odd normal modes. The method lends itself to the treatment of other geometries which are of practical interest, such as "thick" strips, presence of an unsymmetrically located upper ground plane, etc.     

CAD Models for a Boxed Coplanar Waveguide with Multilayered Substrates and Overlays

By the conformal mapping method, CAD-oriented analytical closed-form expressions for the quasi-TEM parameters for a boxed coplanar waveguide (BCPW) with multilayered substrates and overlays are presented. The parameters include the effective dielectric constant, the characteristic impedance, the wavelength of the guided wave, and the capacitance per unit length. All of the formulas obtained in this paper are simple and accurate enough for microwave circuits' designs and are useful for transmission line theory.     

Simple and efficient finite-element analysis of microwave andoptical waveguides

A simple and efficient finite-element method for the analysis of microwave and optical waveguiding problems is formulated using three components of the electric or magnetic field. In order to eliminate spurious solutions, edge elements are introduced. In the edge element approach the nodal parameters are not limited to the magnetic field as in the conventional three-component formulation for the dielectric waveguiding problem. An eigenvalue equation that involves only the edge variables in the transversal plane and can provide a direct solution for the propagation constant is derived. To show the validity and usefulness of this approach, computed results are illustrated for microstrip transmission lines and dielectric waveguides     

Analysis of a new configuration of coplanar stripline

A new configuration of coplanar stripline is presented and analyzed. This configuration is derived by augmenting coplanar stripline (CPS) with electrically wide lateral ground planes on either side of the balanced pair of signal lines. The ground planes should replace line-to-line coupling in complex circuits and eliminate the TE₀ parasitic dielectric slab waveguide mode. Also, the spacing from signal lines to ground planes can be adjusted to change the characteristic impedance. Spectral domain analysis is used to calculate the dispersion characteristics of this transmission line. Analytical expressions for quasi-static values of the line are presented. This configuration of CPS should be useful for balanced high-impedance lines in monolithic microwave integrated circuit (MMIC) and high speed digital circuits     

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.     

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.     

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.     

双层介质基片上的非对称共面线

本文首先用两种不同的模型分析自由空间中非对称共面线,用共形变换技术得到了基本参数的严格解,然后用双曲正切变换分析有限厚度介质基片上非对称共面线,得到了双层介质基片情况下非对称共面线的有效介电常数和特性阻抗的闭合表达式。所得公式简洁准确,便于微波、毫米波和光学集成电路的计算机优化设计。     

Microwave modeling and characterization of thick coplanarwaveguides on oxide-coated lithium niobate substrates for electroopticalapplications

A set of thick coplanar waveguides on lithium niobate substrates with and without a thin SiO₂ buffer layer, has been experimentally characterized through on-wafer measurements. The effective refractive index and attenuation were extracted from raw (uncalibrated) measurements up to 40 GHz through the thru-reflection-line approach. The characteristic impedance was then obtained from the propagation constant, using an accurate estimate of the in-vacuo capacitance from a new conformal mapping approach able to account for large electrode thickness. We observed that the attenuation of lines with or without the oxide buffer layer consistently exhibits a different frequency behavior, thus suggesting that dielectric losses can play a significant role in the upper microwave range. This is confirmed by the results from a full quasi-TEM analytical model, including losses and frequency dispersion. The measured and simulated data show good agreement both for the propagation characteristics (attenuation and effective permittivity) and for the line impedance     

Equivalent Representations of Nonuniform Transmission Lines Based on the Extended Kuroda's Identity

Kuroda's identity may be extended to circuits consisting of lumped reactance elements and nonuniform transmission lines. It is shown that these circuits are equivalent to circuits consisting of cascade connections of nonuniform transmission lines whose characteristic impedance distributions are different from original ones, lumped reactance elements, and ideal transformers. If a characteristic impedance distribution W(x) of an original nonuniform transmission line is given, a characteristic impedance distribution Z(x) of a transformed nonuniform transmission line may be uniquely obtained using W(x). Moreover, by using these equivalent transformations, network functions of these transformed nonuniform transmission lines can he derived exactly.     

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.     

Quasi-static analysis of shielded microstrip transmission lineswith thick electrodes

An extended point-matching method for analyzing the shielded microstrip transmission lines with thick electrodes has been developed based on the method by Marcuse (1989). This method provides a simple and fast approach to the quasi-static analysis of the structures. The calculated fields are used to estimate the characteristic impedance and effective dielectric constant of the structures. The results agree well with available theoretical results obtained using other methods, such as the finite element method and the boundary element method. This method can be further applied to other microstrip lines widely used in monolithic microwave integrated circuits (MMICs) applications     

多层PCB 电源地平面返回路径阻抗的边界元分析

研究了多层印制电路板(PCB)中含有一个信号过孔的电源/地平面返回路径阻抗的频域特性,并分析采用添加短路过孔的方法减小多层PCB的输入阻抗.电源/地平面形成了径向传输线结构,反焊盘处的输入阻抗即为信号电流在电源/地平面间的返回路径阻抗.在电源/地平面外部边界施加PMC(完全导磁体)边界条件,在反焊盘处施加电流激励源,短路过孔轴向电场为零,采用高效的二维边界元法求解.计算了10GHz内电源/地平面返回路径的输入阻抗.结果表明:在两特性相同的平面之间添加短路孔可以降低输入阻抗,同时,电源、地平面的输入阻抗随频率变化交替呈现容性或感性,在反谐振频率处输入阻抗值可达几百欧姆,此外,在频率较低时输入阻抗可用静态电容或静态电感表示.采用基于全波分析的有限元软件验证了计算结果和计算方法的正确性.     

Analysis of a TEM Cell with Septum on a Dielectric Slab

A quasi-TEM approach based on conformal transformation is used for the determination of the characteristic impedance of a rectangular coaxial line (TEM cell) having a symmetrically located inner conductor (septum) supported on a dielectric slab of equal width. The method of determination of the capacitance of the dielectric-filled portion is discussed. The results on characteristic impedance for two values of dielectric constant are presented.     

Multiconductor Transmission Lines In Multilayered Dielectric Media

A method for computing the capacitance matrix and inductance matrix for a multiconductor transmission line in a multilayered dielectric region is presented. The number of conductors and the number of dielectric layers are arbitrary. Some of the conductors may be of finite cross section and others may be infinitesimally thin. The conductors are either above a single ground plane or between two parallel ground planes. The formulation is obtained by rising a free-space Green's function in conjunction with total charge on the conductor-to-dielectric interfaces and polarization charge on the dielectric-to-dielectric interfaces. The solution is effected by the method of moments using pulses for expansion and point matching for testing. Computed results are given for some cases where all conducting lines are of finite cross section and other cases where they are infinitesimally thin.     

Rail track distributed transmission line impedance and admittance:theoretical modeling and experimental results

Frequency-dependent distributed transmission line self and mutual impedances and admittances for a single-track, power-rail electrified railway are obtained by experiment and modeling. Impedance results obtained by numerical calculation from an electromagnetic minimum energy field solution using the finite-element method are compared with analytic impedance models based on the Carson-Pollaczek equations for a stratified, weakly conducting ground and with practical experimental measurements made on a short length of rail track. The running rail self conductances and the power rail to running rail mutual capacitances are also evaluated by the finite-element method and compared with experimental measurements. A physical interpretation of the results is given in terms of conductive and induced ground currents caused by finite ground conductivity and relative permittivity     

Static analysis of V transmission lines

A static analysis of V-shaped transmission lines is performed using a moment method formulation. Measurements were performed on a sample, and the validity of the theoretical results is verified by the experimental data. Characteristic impedance and propagation velocity are found to be strongly dependent on the angle parameter. Comparison with microstrip indicates a lower characteristic impedance and higher effective permittivity for V transmission lines. For multiple lines, the shape of the ground reference leads to lower coupling coefficients and lower mutual inductance and capacitance between adjacent lines     

Measurements of Attenuation and Phase Velocity of Various Laminate Materials at L-Band

Measured data are plotted for the characteristic impedance, velocity of propagation, and attenuation of dielectric sheet supported strip transmission lines for four dielectric materials: teflon bonded glass cloth, epoxy bonded glass cloth, polyester bonded glass mat, and XXXP paper base phenolic. At 1000 megacycles the teflon material is excellent and the epoxy and polyester materials satisfactory for low Q applications, such as microwave transmission lines.     

New multilayer planar transmission lines for microwave andmillimeter-wave integrated circuits

New types of planar transmission lines employing multilayer structures are proposed for possible applications in microwave and millimeter-wave integrated circuits. Detailed investigations are presented through numerical results calculated using the spectral domain technique. The newly proposed transmission lines have many attractive features such as a large impedance range, flexibility and ability to realize complicated, densely packed integrated circuits, as well as miniaturization through the use of thin dielectric layers. Additionally, they possess all of the inherent advantages of the CPW and microstrip line. Their use in microwave circuits is exemplified through a low-pass filter realized using the new slot-coplanar lines with less than 0.5-dB insertion loss and better than 20-dB return loss. The filter's measured and calculated performances also agree well     

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.