Full-wave characterization of high-Tcsuperconducting transmission lines

A full-wave numerical analysis is applied to accurately characterize superconducting transmission lines embedded in a layered dielectric medium. A volume integral equation formulation is developed by using a spectral domain dyadic Green's function for stratified media. Galerkin's method with rooftop basis functions for the electric field distribution inside the superconductor is then employed to solve the complex propagation constant. The thickness of the superconducting film is arbitrary in this analysis, and the formulation rigorously accounts for the anisotropy of the superconducting film. The propagation characteristics of a superconducting microstrip transmission line with a thin dielectric buffer layer are investigated. A superconducting stripline configuration with an air gap is also studied     

Complex modes in shielded suspended coupled microstrip lines

The existence of complex modes in electrically shielded suspended coupled microstrip lines has been studied extensively, and the results are presented. A rigorous full-wave spectral-domain approach (SDA) with a newly proposed and tested set of basis functions can efficiently and accurately determine the propagation characteristics of the dominant, higher-order, and complex modes for planar or quasi-planar transmission lines. These basis functions are validated by comparing the convergence study of field solutions with those obtained by various sets of preconditioned bases and by the unconditioned subdomain ones. Excellent agreement is obtained for the propagation constants and the normalized complex longitudinal and transverse current distributions on conducting strips for the strongly coupled microstrip lines. For all the particular case studies discussed, it is shown that the complex modes may exist in all the shielded suspended coupled microstrip lines, even when the substrate dielectric constant is low. Theoretical results for the fundamental, higher-order, evanescent, and complex modes are presented for suspended coupled microstrip lines     

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.     

A microstrip phase-trim device using a dielectric overlay

A design procedure is given for a microstrip phase-trim device using a dielectric overlay on a conventional microstrip line. The physical operation of the device is based on the change in the effective dielectric constant of the microstrip line caused by the presence of the dielectric layer on top of the microstrip line. The amount of phase trim produced by the device can be selected by the appropriate choice of dielectric constant, height, and length of the dielectric overlay. An approximate expression is given for the effective dielectric constant of the microstrip line as a function of the dielectric constant and height of the overlay. Measured results at 10 GHz are compared with predicted performance     

Attenuation and dispersion for high-Tc superconductingmicrostrip lines

The attenuation and dispersion of microstrip lines of the high-T_c superconductor YBa₂Cu₃O₇ (YBCO) on yttria-stabilized zirconia substrates as a function of frequency and temperature are calculated. The effect on pulse propagation of superconducting and model dispersion in addition to the attenuation is demonstrated. At 60 K, microstrip lines of YBCO are significantly less attenuating at frequencies below 500 GHz than microstrip lines of copper at the same temperature. This advantage is particularly significant at the higher attenuations that result as the substrate thickness is made smaller for miniaturization or to improve the microstrip line bandwidth. The application of YBCO for microstrip lines appears to be most useful at frequencies above 100 GHz and dielectric thicknesses less than 100 μm, where the attenuation of cooled copper is prohibitively large. Cooled to temperatures below 20 K, YBCO may make possible a new generation of extremely high bandwidth (~5 THz), small-feature-size (~5 μm) circuits and devices     

MIC Overlay Coupler Design Using Spectral Domain Techniques

A quasi-TEM analysis of dielectric overlay microstrip is described for an overlay extending several conductor Iinewidths beyond the coupled lines. This method permits the analysis of numerous variations of overlay coupler geometries. The relevant spectral domain Green's function is given and used to generate a set of design curves when the overlay is identical in thickness and dielectric constant to the main substrate. A trial 8.34-dB coupler was built. Significant improvement in isolation was noted with the overlay when compared to the equivalently designed uncompensated coupler. The measured values of isolation agree very well with predicted values.     

Computation of Dispersion in Microstrip Line with Anisotropic Substrate and Overlay

This paper presents an analysis of frequency dependent propagation characteristics of microstrip lines with anisotropic substrate and overlay. The method involves setting up of the Green’s functions corresponding to the structure and formulating a dispersion relation in Fourier transform domain. The dispersion relation is constructed in a Galerkin’s procedure. Numerical results are also presented.     

Propagation model for ultrafast signals on superconductingdispersive striplines

The algorithm suitable for the computer-aided design of transmission lines is used to model the propagation of picosecond and subpicosecond electrical signals on superconducting planar transmission lines. Included in the computation of a complex propagation factor are geometry-dependent modal dispersion and the frequency-dependent attenuation and phase velocity which arise as a result of the presence of a superconductor in the structure. The results of calculations are presented along with a comparison to experimental data. The effects of modal dispersion and the complex surface conductivity of the superconductor are demonstrated, with the conclusion that it is necessary to incorporate both phenomena for accurate modeling of transient propagation in strip transmission lines     

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     

Analysis of lossy planar transmission lines by using a vectorfinite element method

The vector finite element method with hybrid edge/nodal triangular elements is extended for the analysis of lossy planar transmission lines. In order to handle lossy conductor transmission lines, the present approach includes the effect of finite conductivity of a lossy area, and the dissipations in metallic conductors and dielectrics are calculated directly by considering a complex permittivity for the lossy region of interest. A propagation constant formulation is used in the FEM, which avoids spurious solutions absolutely and can handle sharp metal edges in inhomogeneous electromagnetic waveguides. Numerical examples are computed for microstrip lines, finlines, and triplate strip lines. The results obtained agree well with the earlier theoretical and experimental results, and thus show the validity of the method. Also, the current distributions on the lossy microstrip lines with finite strip thickness and isotropic substrates are presented     

Simulations of microwave characteristics of high-temperature superconducting microstrip lines by using an empirical two-fluid model

A numerical analysis of the microwave propagation characteristics of a high-temperature superconducting microstrip transmission line is presented. It is based on the transmission line theory and empirical two-fluid model which appropriately incorporates the quasiparticle scattering and residual loss of the superconductor. First, the calculated attenuation constant and phase velocity are compared with those predicted by the conventional two-fluid model for a YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// microstrip line with a linear substrate, lanthanum aluminate, LaAlO/sub 3/. Next, we have specifically investigated the effects of nonlinear substrate such as strontium titanate, SrTiO/sub 3/, on the attenuation constant and phase velocity. The tunable feature of such a microwave device owing to the nonlinear dielectric ferroelectric is illustrated and discussed.     

Identification of propagation regimes on integrated microstriptransmission lines

There has been a resurgence of interest in the propagation characteristics of open integrated microstrip transmission lines. This is due in part to the discovery of diverse propagation regimes for higher-order modes on open lines. In contrast to the dominant EH₀ mode, three distinct propagation regimes exist for higher-order modes on microstrip transmission lines. In this paper, a rigorous spectral-domain integral equation formulation is used to analyze propagation in all three regimes. This formulation provides a clear physical picture of the different propagation regimes based on the mathematical location of poles and branch points in the complex spectral-variable plane. As an illustration, the formulation is applied to the case of an isolated uniform microstrip transmission line. The integral equation is discretized via the method of moments, and entire-domain basis functions incorporating suitable edge behavior are utilized to provide convergence with relatively few terms. The results obtained are compared to the results of other workers, and good agreement is observed     

Dispersion Characteristics of Microstrip Lines

A coupled-line analysis is used in conjunction with Carlin's model in order to find the frequency dependence of the propagation constant and of the characteristic impedance of dispersive microstrip lines. The characteristic impedance of the coupled lines decreases with frequency.     

Stacked superconductor structure for microwave transmission

Propagation characteristics of microwaves along a stacked superconductor microstrip structure are investigated. The suitability of such a structure for practical applications is discussed. A rigorous integral equation formulation has been used for the analysis of such structure. The effect of thickness of superconducting strip on propagation characteristics has been studied. Results presented show that the slow wave propagation and low dispersive coupling are possible in a realistic stacked multi-dielectric and superconducting layers microstrip line package.     

Guided Waves in Limit Cases of Microstrip (Correspondence)

The great difficulty in solving for the propagation constant and effective characteristic impedance for microstrip transmission lines is invariably avoided by assuming quasi-TEM propagation and solving Laplace's equation rather than the wave equation. Deschamps and Wu have qualitatively discussed aspects of the hybrid-mode problem. Zysman and Varon have presented a solution for the related but distinctly different problem of closed microstrip. In this communication we present the basis through which the quasi-TEM analysis may be justified for the limit cases of guided waves on microstrip in which the dielectric constant approaches that of free space or becomes very large. The guided wave problem is formulated exactly in terms of longitudinal electric and magnetic field components satisfying the wave equation and coupled through the boundary conditions at the dielectric interface.     

Analysis of shielded microstrip lines with arbitrary metallizationcross section using a vector finite element method

The finite element method (FEM) with the high-order mixed-interpolation-type triangular element is used to solve the problem of practical microstrip lines with arbitrary metallization cross section. Analyses are carried out to produce the frequency characteristics of propagation constant, characteristic impedance, and attenuation constant of shielded microstrip lines with rectangular, trapezoidal, and semi-trapezoidal strip cross sections. A comparison of the numerical results with those of the existing results shows good agreement and thus verifies the versatility of the FEM. Also, the numerical results show the effects of the metallization cross sections on the transmission properties and thus emphasize the importance of considering the practical microstrip configurations in the design of miniaturized MMICs     

A WH/GSMT-based full-wave analysis for planar transmission linesembedded in multilayered dielectric substrates

A new full-wave analysis method, referred to as the WH/GSMT, is developed to solve multilayered planar transmission line problems. First, the scattering of an obliquely incident parallel plate mode (PPM) by a PEC half plane embedded in a multilayered isotropic dielectric substrate within a PEC parallel plate region is analyzed via the Wiener-Hopf (WH) technique. The solution is then incorporated into the generalized scattering matrix technique (GSMT) to find the (complex) propagation constant and characteristic impedance of the planar transmission lines. The lateral power leakage is taken into account rigorously in the WH/GSMT. Numerical results including the microstrip line, conductor-backed slotline, coupled microstrip lines, and antipodal finlines are presented along with a discussion of the advantages/disadvantages of this method     

Properties of Microstrip Lines on Fused Quartz (Correspondence)

The attenuation constant for microstrip lines on fused quartz and their effective relative dielectric constant were measured and the results are discussed. The propagation losses in these lines proved to be smaller than those mentioned in the literature. The effective relative dielectric constant is found to be independent of frequency up to 12 GHz. The conductors were deposited without an adhesive layer but with sufficient adhesion for pressure bonding semiconductor chips.     

Parallel Line Microstrip Filters in an Inhomogeneous Medium

Parallel coupled microstrip lines in an inhomogeneons medium are studied. The quasi-static capacitance is shown to be linear with regard to the dielectric constant epsilon/sub r/ simplifying the formalism used for analyzing microstrip filters. The electromagnetic advantages of the homogeneous medium carry over to the inhomogeneous medium. This result is obtained by equalizing all the velocities of the propagation modes.     

Frequency-dependent characteristics of thick microstrip lines in lossy multilayered dielectric media

The Spectral Domain Approach (SDA) is used for a rigorous full-wave analysis of thick microstrip lines embedded in lossy multilayered dielectric media. The effects of the conductor thickness on the propagation constant and characteristic impedance are investigated.