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A variational equation is derived for the capacitances of coplanar waveguide (CPW) structures with finite metallization thickness. The equation is expressed in terms of the static potential in the slot region and is solved by applying the hybrid finite-element method (FEM). In case of small metallization thickness, it is reduced to a perturbation formula for the incremental capacitances. Numerical results for the equivalent capacitances of various discontinuities with finite metallization thickness are presented and compared with measured data. The reasonable agreement between the measured data and the theoretical results validates the present approach. Being simple and computationally efficient, the method is suitable to deal with extensive CPW discontinuity problems where the metallization thickness is not negligible. Index Terms - Capacitance, coplanar waveguides, finite-element method (FEM), transmission-line discontinuities.

In this paper we solve the transmission line equations for a Non Uniform Transmission Line (NUTL). The analytical method used is different to the Kuroda's one. First we find the solution in terms of voltage and current waves, then the expression of input impedance that allow us to find the R=const and X=const loci. In particular the solution is found for an exponential NUTL. We find the correspondent representation of the Smith Chart. The NUTL has more advantages with respect to the uniform one. In fact we can use the Generalised Smith Chart to solve easily the problem of a NUTL loaded by a complex impedance. Moreover, we can use the NUTL to match lines with different sections and to model multilayered semiconductor structures. Finally, we show the normalised power behaviour for an exponentially tapered NUTL when the tapering factor is varying.

Leaky dominant mode propagation regimes of a conductor-backed coplanar strip line are rigorously analyzed using the concept of critical or equilibrium points from catastrophe and bifurcation theories, in conjunction with a full-wave integral equation solution. The existence of nondegenerate or Morse critical points (MCP's) and degenerate or fold (turning) critical points (FP's) in coupling and leakage regions are associated with the occurrence of improper real and complex (leaky) solutions. The locations and types of critical points determine the stability and instability of the transmission line system with respect to small changes in geometrical parameters. The dispersion behavior of improper real and complex (leaky) solutions are efficiently reproduced in the local neighborhood of MCP's and FP's using a Taylor series expansion about those points. The qualitative and quantitative dynamic behavior of the transmission line modes can be investigated by examining the evolution of nondegenerate and degenerate points versus some structural parameter, such as strip width. The proposed analysis enables the prediction of bifurcation situations and the existence of improper real and complex solutions and gives a complete description of the system's structural behavior.

A novel technique is developed to reconstruct the physical structures of a nonuniform transmission line from its time-domain or frequency-domain reflection (scattering) coefficient. This technique takes the past history of reflection processes of nonuniform line into considerations, and its accuracy exceeds that of a conventional time-domain reflectometry (TDR) technique. Experimental results are presented to illustrate the validity of this reconstruction technique.

The analytical solution of an ideal linear varied nonuniform transmission line (LNTL) has been obtained and the exact linear two-port ABCD matrix of LNTL has been given correctly for the first time. By using cascaded LNTL sections to approximate an arbitrary characteristic impedance profile, a new technique has been presented in this paper for analyzing an arbitrary nonuniform transmission line (NTL). The technique is far better than the conventional technique in terms of the computational accuracy and intensity since it uses a piecewise-linear characteristic impedance profile in place of the stepped profile used by the conventional technique. Several numerical examples have been given to demonstrate the method.

The eigenmode transformation technique is formulated for the analysis of inhomogeneously filled shielded waveguides containing metal inserts. The permittivity of the filling medium may be an arbitrary function of the transverse coordinates. The method is based on expanding the electromagnetic field in terms of the eigenmodes of the corresponding empty shielding waveguide. The metal inserts have first the effect of linearly transforming the eigenmodes of the empty guide into those of the shielded waveguide containing the metal inserts (including the TEM-modes). Next the inhomogeneity of the filling medium is taken into account which leads to a proper matrix eigenvalue problem. In addition an alternative formulation is derived from a variational approach. Results of both formulations are compared for a shielded circular dielectric waveguide. The eigenmode transformation technique is applied to various types of planar transmission lines, i.e., coupled microstrip lines, finlines, and coplanar lines. The results are compared with those of other methods.

This paper presents a rigorous field theoretical analysis of slow wave mode propagation in coplanar waveguide (CPW) metal-insulator-semiconductor (MIS) transmission lines with a laterally confined doping profile. Two types of transmission line structures are investigated - bulk silicon and semiconductor-on-insulator (SOI). In both cases a Gaussian profile of the doping depth is assumed. It was found that an optimum lateral width of the doping region exists for which both structures exhibit a much better slow wave factor at lower losses than traditional thin-film MIS transmission lines. The abrupt transition between MIS, CPW, and CPW on a normal insulating substrate was investigated as well. It was found that the reflection coefficient increases significantly with frequency and when the lateral width of the doping region is extended over the whole cross section of the CPW. The investigation was carried out using the frequency-domain transmission line modeling (TLM) (FDTLM) method.

The electric screen Jauman absorber [1] is a stratified cascade of dielectric spacers, interlaced with resistive sheets, which is effective in reducing specular reflection from flat or moderately curved conducting surfaces. A literature survey of the period up to 1993 may be found in [2], while the topic has also received more recent attention, e.g., [3]-[9]. Usually, the dielectric constant of the identical spacers is assumed known a priori, and the design problem is to find the sheet surface resistivities that will yield an absorption behavior which meets certain design criteria. This paper presents detail on three efficient and dedicated synthesis algorithms that synthesize absorbers with Butterworth, Equiripple, and Chebyshev absorption properties and should be seen as complementary to the introductory discussion in [2]. To the authors' knowledge, the Chebyshev solutions solve the fundamental problem for the first time.

A method for obtaining analytical solutions of the general transmission line modeling (TLM) dispersion relation for condensed node schemes is described. Exact analytical forms of the dispersion relation for currently available nodes are derived, enabling the efficient study of dispersion solutions without resorting to a numerical solver. Using these analytical relations, the range and behavior of propagation errors is fully explored and visualized, not only for propagation along the axes and diagonals or in a coordinate plane, but for arbitrary angles of propagation in three-dimensional space. Comparisons are presented of the numerical performance of different TLM condensed node schemes.

A general symmetrical condensed node (GSCN) for the transmission line modeling (TLM) method, with six different link line characteristic impedances, six stubs, and six lossy elements is described for the first time. It unifies all the currently available condensed nodes into a single formulation and provides the basis for the derivation of an infinite set of new nodes, including nodes with improved numerical characteristics. The GSCN is derived in two ways: 1) from an equivalent network model and 2) directly from Maxwell's equations using central differencing and averaging. The direct correspondence established between the GSCN TLM and a finite difference scheme for Maxwell's equations provides a rigorous theoretical foundation for all available TLM methods with condensed nodes.

The aim of this paper is to present a practical and easy to analyze coupled pendula system in order to demonstrate, by analogy, the behavior of coupled transmission lines and related devices. The importance of the Coupled Mode Theory is first explained and its derivation is worked out through the use of the spring-coupled pendula, followed by a statement of the theory and its restrictions. The theory is then used for coupled transmission lines in general and a comparison is made between the coupled pendula and coupled transmission lines in order to extract analogous quantities and to recognize the limitations of such an analogy. The coupled pendula are then used to demonstrate the behavior of a forward coupler, tunable filter, optical switch, and parametric amplifier.

In this contribution single and coupled equivalent transmission lines are developed for the propagation of modes in reciprocal and nonreciprocal, anisotropic, bi-isotropic, and bi-anisotropic waveguides. The transmission lines are described by the generalized telegrapher's equations. In order to develop these transmission line models some properties, related to reciprocity, bi-directionality, and mirroring, of general waveguides and generalized transmission lines are investigated. The transmission line models are based on the reciprocity theorem and are valid for arbitrary frequencies.

This paper describes recent results which pertain to the integration and reliability testing of micromachined, membrane-supported transmission line circuits. These circuits employ a 1.4- [[micro]meter]-thick dielectric membrane to support thin-film conducting lines above an air substrate. With regard to integration, the development of a Ka-band solid state power amplifier (SSPA) is presented. The design includes a membrane-supported Wilkinson power divider/combiner with 0.2 dB loss, along with a commercially available monolithic microwave/millimeter wave integrated circuit (MMIC) amplifier stage. Also reported are tests which investigated the survivability of membrane lines under space qualification conditions. No failures occurred as a result of thermal cycling and vibration testing at levels which reached 39.6 grms.

A new method of moment-based formulation for the solution of the telegraphist's equations in nonuniform transmission lines is presented. Entire domain basis functions that build in a frequency variation are used to cover wider frequency and physical dimension ranges. The results obtained using the proposed formulation are validated by comparison to those obtained by a CAD package and to measured data. Different nonuniform lines in microstrip and coplanar technologies on monolithic microwave/millimeter wave integrated circuit (MMIC) and miniaturized hybrid microwave integrated circuit (MHMIC) substrates are investigated with an application to the design a matched taper transition in a MMIC coplanar line.

Microstrip transmission lines residing on bianisotropic material ridges embedded in a multilayered environment are studied using a coupled set of integral equations (IE's). The full-wave IE formulation accounts for general linear media in the ridge region using equivalent polarization currents residing in a multilayered bianisotropic background. Numerical results showing basic propagation characteristics are presented for a variety of single and coupled ferrite ridge structures. It is shown that the use of finite width ferrite ridges as either substrates or superstrates can produce nonreciprocity while confining the ferrite material to a small area in the vicinity of the transmission line.

This paper proposes a circuit model for lossy multiconductor transmission lines (MTL's) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace Transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCB's and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, of which maintains the simplicity and efficiency.

The electromagnetic modeling of wave propagation along a semi-infinite wire with ground return is addressed. External excitation, via plane wave is considered. Both wire and ground plane are assumed to be perfect conductors. Through a spectral approach, a one-port Thevenin model of the structure, valid for any distance between wire and ground, is developed. Such a model allows to evaluate rigorously the limits and the accuracy of the transmission line (TL) equations.

The transient analysis of field-excited networks having complex configurations and nonlinear loads is performed by using a combined frequency- and time-domain procedure. The simulation models of the line-sections are defined in the frequency-domain based on the exact formulation of Maxwell's equations. New expressions of the per-unit-length (p.u.l.) series impedances and shunt admittances are used in order to overcome the limitation of the Carson formulation in case of a poorly conducting ground-plane and in the presence of very fast transients. An efficient procedure is applied for reducing the computation effort of the procedure in case of complex large-dimension networks. Calculations are carried out to predict the overvoltages induced by an EMP-plane wave on a 20 kV-power network above a highly lossy ground and on a signal 18-port-multiconductor network.

The problem of double-sided cylindrical microstrip lines coupled through a rectangular slot in the common cylindrical ground plane is studied using the reciprocity theorem and a moment-method calculation. Theoretical results of the S parameters for the slot-coupled cylindrical microstrip lines are calculated and analyzed. Experiments are also conducted to verify the theoretical results.

The buried microstrip line (BMSL) is a promising transmission line structure for realizing low crosstalk characteristics. The measured crosstalk characteristics of model BMSL's have shown good agreement with the estimated ones based on the rectangular boundary division method and the finite-difference time-domain (FDTD) method, indicating that these calculation methods are appropriate for estimating the performance of BMSL's. These results also confirm our expectation that BMSL's have extremely low crosstalk characteristics such as -100 dB in real circuits at high microwave frequencies. The basic circuit components to construct high-density microwave circuits using BMSL's, couplers, stub matching circuits, and gap-coupled resonance filter circuits, were fabricated and experimentally evaluated.

Cylindrical transmission lines are important for a variety of applications. To calculate their propagation characteristics, the method of lines in cylindrical coordinates has been adopted. By discretizing the angular space direction with radial lines, the two-dimensional (2-D) Helmholtz equation reduces to a set of ordinary one-dimensional (1-D) differential equations, which can be solved analytically in radial direction after an orthogonal transformation. To improve the accuracy of the cylindrical method of lines from second-order to fourth-order, neighboring lines are used to eliminate second-order discretization errors not only in the Helmholtz equation but also in the continuity equation and in the edge condition. The method is suitable for the analysis of asymmetric cylindrical homogeneous and inhomogeneous guided wave structures.

An efficient and simple computer technique based on the quasistatic approximation for the determination of the component values of the equivalent circuits of a broad-class of coplanar waveguide (CPW) discontinuities is introduced. The technique does not depend on the extraction of the component values from the scattering parameters. It uses the spectral domain formulation in conjunction with the method of moments. The concepts behind the method are illustrated using a complex example, the CPW T-junction. A few T-junctions are treated with the technique. Both the measurements and the full-wave electromagnetic simulation support the accuracy of the results.

The finite-difference time-domain (FDTD) method is useful for performing broadband characterization of uniform transmission lines and discontinuities. Modeling a geometry often requires the implementation of an absorbing boundary condition (ABC). When this is the case, numerical reflections from the ABC's will add significant error to the calculated transmission line or scattering (S) parameters. This paper introduces a simple post-processing algorithm for extracting these parameters and correcting for numerical reflection error. Furthermore, this method is shown to have a unique relationship to Prony's method. Practical application and limitations of this technique are also discussed. Finally, the impedance and propagation constant of a miscrostrip line are calculated using this method.

This paper presents finite-difference time-domain (FDTD) analysis of flip-chip interconnects. Transition between coplanar waveguides on the chip and the mother board are investigated over a broad band of frequency by means of Fourier transform of the time-domain results. Objectives of the analysis include the evaluation of bump reflection and insertion loss as well as the reconfiguration of the transition to improve package performance. Novel designs have been developed and presented to reduce the effects of package discontinuities and asymmetry. Staggering the bumps has been found to reduce reflection and insertion loss over a broad band of frequency. A reduction in bump reflection of up to 8 dB per transition can be achieved by staggering the ground and signal connects. The degradation in package performance due to structure asymmetry is also studied. The present designs have been also found to reduce the effects of flip-chip asymmetry on insertion and reflection losses.

The paper presents comparative analysis of the properties of impedance stepped transformers both with monotonous and nonmonotonous step-to-step impedance variation. A miniature stepped transformer of a new structure based on a cascade of an even number of uniform transmission line sections has been synthesized. Section lengths are considerably shorter than a quarter of the central wavelength, and the section impedances alternate. The proposed transformers are the simplest to implement among the available analogs. As an example, the results of the solution of the Chebyshev approximation problem for the four- and six-section transformers of different specifications are given.

This paper presents a boundary element analysis of transmission-line parameters on the basis of the quasi-TEM assumption. Singular boundary elements are employed to adequately express the corner singularities at sharp conductor edges. The boundary integrals consisting of the Green function and singular interpolation functions are regularized by a Taylor expansion technique, and are then evaluated using the standard Gaussian quadrature. The numerical results for test problems show the reliability of the present method.

The actual dielectric loss for transmission lines in thin-film multichip modules is much higher than the calculations from the geometry and bulk material properties. The experiment analyzes signal propagation on transmission lines, fabricated in thin polyimide films on silicon substrates. A through-reflect-line like approach is used to compute the effective dielectric loss. The characterization of microstrip and stripline transmission lines requires accurate modeling of stripline transmission and microstrips.

An accurate and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented. It is shown that the usual A + B [square root of s] representation of these frequency-dependent losses is not valid for some practical geometries. The reason for this is the inaccurate representation of the internal inductance of the conductors at lower frequencies. A computationally efficient method for improving this representation in the finite-difference time-domain (FDTD) solution method is given and is verified using the conventional time-domain to frequency-domain (TDFD) solution technique.

This paper reviews optically controlled wave propagation effects in coplanar transmission lines on semiconducting substrate. Special emphasis is laid upon distributed Schottky photodiodes where a depletion layer is formed below the center conductor. The cross section is that of a InAlAs/InGaAs/InP heterostructure, where the thin InGaAs layer is optimized with respect to optical absorption leading to an optical control of phase velocity, time delay or attenuation. Experimentally, phase shifts as high as 110 deg/mm at 9 GHz using an optical power of merely 50 ??? are obtained for an MBE grown sample with a suitable doping profile and for backside illumination through the tranparent InP-substrate. The theoretical treatment is based upon an equivalent circuit including the optoelectronic properties under different illumination conditions. It is further shown that periodic structures can successfully be used as efficient phase shifters or attenuators with optical control. This leads to interesting applications as optical MMIC's for microwave signal processing.

Analytical solution of lossless field-excited multiconductor transmission lines is presented. The equivalent circuit of a multiconductor transmission line with distributed sources is reduced to a simple lumped parameter circuit with independent voltage sources at both the ends of the transmission line. The transient source waveforms are analytically estimated for exponential time dependence of the external field, as EMP, ESD, and lightning. The method is suitable for a direct implementation in computer-aided circuit analysis codes and enables a very fast analysis for any load condition. Some numerical results are presented for single conductor and multiconductor lines excited by an EMP plane-wave field.

A transmission structure of many parallel conductors is capable of propagating many distinct quasi-TEM modes. A field theory of such modes is developed for a theoretically infinite number of very thin conductors. These possess infinitely many distinct propagation modes, which are the eigenfunctions of a pair of integral operators with Green's function kernels. The modes depend strongly on the structure cross-sectional shape and size, only slightly on the number and placement of individual conductors. The theory is illustrated by a structure comprising many thin parallel wires on a dielectric substrate backed by a ground plane, whose modal functions and velocity distributions are used to solve a simple crosstalk problem.

The effect on the input reflection coefficient of the dimensions of open-ended coaxial lines is investigated. Using a standard FDTD technique, the effects of variations in the flange and conductor dimensions on the reflection coefficient of a 3.6 mm coaxial line immersed in water or methanol are simulated. Simulation results are compared with measurements and previous moment method calculations. It is found that the presence or absence of a flange affects the input reflection coefficient substantially in some cases. The results also show that inversion formulas developed for lines with infinite flanges are not valid for flanges with finite radii.

A Wiener-Hopf-type analysis of the canonical problem of a TEM wave obliquely incident at the edge of the truncated upper conductor of a parallel plate waveguide loaded with a uniaxial anisotropic dielectric is presented. A numerical integration scheme as well as a thin substrate approximation for the reflection coefficient is given. The influence of the dielectric anisotropy and the slab thickness on the reflection coefficient and the edge admittance are investigated. Numerical results show the importance of the dielectric anisotropy and the expected effects in microstrip applications.

Hybrid wave propagation in circularly shielded, single or coupled microslot lines is studied by combining singular integral equation (SIE) with Green's function techniques. Discretization of these SIE's by recently developed algorithms leads to linear algebraic systems whose matrix elements assume exponentially converging, numerically very stable analytical expressions. Dispersion characteristics, modal currents, and cutoff frequencies are presented for several cases. The algorithm converges rapidly requiring a few expansion functions per wavelength.

The quasi-TEM spectral domain approach (SDA) is extended to rigorously and efficiently analyze single and multiple coupled microstrip lines of arbitrary metallization thickness. The charge distributions on both the horizontal and vertical conductor surfaces are modeled by global basis functions. This results in a relatively small matrix for accurate determination of the line parameters of coupled thick microstrips. A convergence study is performed for the results of a pair of coupled lines with crucial structural parameters to explore the conditions for obtaining reliable solutions using the technique. Results for thick microstrips are validated through comparison with those from available measurements and another theoretical technique. The soundness of the technique is further demonstrated by looking into the trend of the results obtained by a simplified model in which the structural parameters are pushed, step by step, to the numerical extremities. Variations of circuit parameters of a four-line coupled microstrip structure due to the change of finite metallization thickness are presented and discussed.

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.

In the present contribution we construct a high-frequency circuit model for the excitation of eigenmodes in general waveguides due to externally impinging electromagnetic waves. The circuit model, consisting of distributed sources in a transmission line model, is based on Lorentz's reciprocity theorem. The classical quasi-TEM solution of this problem is found as a special case from the full-wave model. The theory is illustrated with numerical examples of electric dipoles radiating above thick coupled lossy microstrip lines.

This paper presents a general scheme to compute the four characteristic matrices, [C]. [G], [L] and [R], of a multilayered and multiconductor transmission line with arbitrary cross section conductors under quasi-TEM approach and strong skin effect regime. The conductors are modeled as a set of infinitesimally thin strips following the M-strip model. An spectral domain approach (SDA) has been employed, paying special attention to the efficient computation of the spectral tails. Conductor losses are considered via the incremental inductance rule extended to the multiconductor case.

The surface impedance approach is applied to the quasi-TEM spectral domain analysis of MIC and MMIC lines with lossy metallizations in both the weak skin effect and the strong skin effect regimes. The use of the spectral domain technique makes it possible the analysis of fines with multilayer iso/anisotropic substrates, including semiconductor and/or magnetic layers. PC computer codes have been developed following the proposed technique. Computation times within a few seconds are achieved.

An integral equation technique is used to determine the circuit parameters of the nonreciprocal and nonsymmetrical set of transmission lines that describe a multiconductor line in a layered bi-isotropic background in the quasi-TEM approximation. The integral equation is solved with the method of moments and pointmatching technique. The integrations arising in the problem are handled carefully to allow a fast and accurate implementation. The conductors have an arbitrary cross-section consisting of straight and circularly curved segments. At the edges of the conductors the singular behavior of the surface charge density and surface current density is explicitly taken into account.

The quasi-TEM approximation for multiconductor lines embedded in inhomogeneous bi-isotropic media is developed. It is shown that in the quasi-TEM limit a multiconductor line in bi-isotropic media can be represented by a coupled set of nonreciprocal and nonsymmetric circuit transmission lines. The effect on the circuit parameters of absence of losses, reciprocity and symmetry properties of the geometry and of the equations is investigated. Finally, the generalization to full bianisotropic materials is studied.

This paper describes a novel time-domain node for the TLM method. It has the unique feature of modeling arbitrary inhomogeneous media on a generally graded rectangular TLM mesh without using stubs. Variations in material properties and arbitrary aspect ratios of mesh cells are modeled by allowing different characteristic impedances in a cell, maintaining impulse synchronism throughout the mesh. The complete theory of the new node is given and its implementation on a general TLM mesh is discussed. Numerical results for a canonical resonator loaded with dielectric layers are presented for different grading cases. Substantial savings in computer storage and run-time as well as improved accuracy compared to the uniform mesh are achieved when an appropriate nonuniform grading of the TLM mesh is used.

Multiple discontinuities in microwave transmission lines can cause unusual reflection and transmission loss characteristics as functions of frequency. This article presents a method for developing models that simulate return loss and insertion loss data measured over a broad band of frequencies. The overall cable is modeled as a coaxial transmission line consisting of shunt susceptance discontinuities separated by line lengths. A nonlinear least-squares fit is then performed between theoretical data (from the model) and experimental data. When this method was applied to modeling discontinuities in a slightly damaged S-band antenna cable, excellent agreement between theory and experiment was obtained over a frequency range of 1.70-2.85 GHz.