The application of the point matching method to the analysis ofmicrostrip lines with finite metallization thickness

The characteristics of a shielded microstrip line with finite metallization thickness are calculated using the point matching method (PMM). The advantage in this case is that the method does not depend on a special geometry of the strip metallization. The approach used is based on satisfying the boundary conditions at discrete boundary points. Numerical results are presented to assert the validity of this approach in cases of large values of strip width-to-thickness ratio. It is found that an increase in the strip thickness is always associated with difficulties in convergence. The examples presented call attention to the necessity of proving the validity of the obtained solutions by other criteria. This is because good convergence behavior of the effective dielectric constant does not always guarantee the correct characteristic impedance or field distribution. In particular, the field distribution is considered as a reliable check for the numerical results     

High precision analysis of finlines on semiconductor substrate

In this study, the effect of the metallization thickness in finlines on semiconcuctor substrate is researched. The propagation parameters are computed to measure the inluence of the metallization. The theory and numerical results are presented to the propagation constant and characteristic impedance of the bilateral and unilateral finlines. 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, the moment method and expanding the fields in a set of suitable bases functions, a homogeneous matrix system is obtained and the propagation constant is computed. The characteristic impedance is obtained using the relation of the voltage in the slot and the transmitted power by the structure. Computational programs are developed to obtain numerical results to the propagation parameters composed by the propagation constant and characteristic impedance.     

Full-wave analysis of coplanar strips considering the finite stripmetallization thickness

An extensive analysis, based on a full-wave mode-matching technique, is described for coplanar strips (CPS) incorporating the strips' finite metallization thickness. Results for the effective dielectric constant and characteristic impedance are presented to show the effect of the metallization thickness. It is found that the characteristic impedance has a strong dependence on the metallization thickness, which signifies the fact that the finite metallization thickness needs to be considered in designing practical microwave circuits employing CPS. Numerical results of CPS with zero metallization thickness obtained using this method are found to be in good agreement with those published previously. Extensive investigation of the numerical convergence of these results is also described     

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.     

Equivalent network representation of boundary conditions involvinggeneralized trial quantities-application to lossy transmission lineswith finite metallization thickness

The derivation of integral equations for solving boundary conditions by mere application of analog Kirchhoff's and Ohm's laws is used. Generalized trial quantities are introduced as virtual adjustable sources in the equivalent network representation of boundary conditions. The lossy conductor domain of a planar transmission line is represented by a particular two-port. Thus, metallic losses can be evaluated for any metallization thickness without restricting the conductor modeling to a simple surface impedance approximation. In this paper, this two-port model is discussed and numerical results relative to a lossy coplanar waveguide (CPW) are presented. These results are in very good agreement with those obtained from the mode-matching technique and with other experimental data available in the literature. The size of matrices involved in the calculation of losses is twice as large as that in the lossless case. Moreover, the authors' formulation can be easily applied to superconducting planar transmission lines     

The influence of metallization thickness on the characteristics ofcascaded junction discontinuities of shielded coplanar type transmissionline

A full-wave analysis based on the mode-matching technique is applied to analyze cascaded junction discontinuities of coplanar-type transmission lines, coplanar waveguide (CPW) and finline. Results for a CPW-finline transition, a shielded CPW gap and a symmetric notch incorporating the finite metallization thickness effect are presented. The influence of metallization thickness on the coupling effect exhibited by cascaded junction discontinuities is also presented and discussed     

Capacitance computation for CPW discontinuities with finitemetallization thickness by hybrid finite-element method

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 the 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 for dealing with extensive CPW discontinuity problems where the metallization thickness is not negligible     

Full-wave analysis of coplanar waveguide discontinuities using thefrequency domain TLM method

This paper presents a full-wave analysis of a variety of coplanar waveguide discontinuities using the frequency domain TLM method. The finite metallization thickness is taken into account as well as metal losses and the interaction of fundamental and higher order modes between cascaded discontinuities. Numerical results are presented for the frequency-dependent s-parameters of transitions between CPW and slotline, CPW and microstrip line and CPW-microstrip overlap transition. The effect of interactions between the CPW discontinuities and the CPW airbridges is also investigated     

Analysis of Finline with Finite Metallization Thickness (Short Papers)

In this paper, we present a method for analyzing finline structures with finite metallization thickness. The method is based on a hybrid mode formulation but it by-passes the lengthy process of formulating the determinantal equation for the unknown propagation constant. Some numerical results are presented to show the effect of the metallization thickness for unilateral and bilateral finlines.     

Accurate quasi-TEM spectral domain analysis of single and multiplecoupled microstrip lines of arbitrary metallization thickness

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     

Analysis of the Characteristics of an Earthed Fin Line

This paper presents a theoretical and experimental investigation of the effective permittivity and the characteristic impedance of the earthed unilateral fin line. Using the Ritz-Galerkin method, the eigenvalue equation for a fin line with finite metallization thickness as well as a longitudinal slit in the metal waveguide mount is derived. The numerical solution converges very rapidly in all the cases investigated. Experimental checks are reported, which verify the results of this method and stress the importance of the effects of the finite metallization thickness and longitudinal slit in the mount at higher frequencies. The theoretical results are compared with results by Hofmann, and they are found to correspond closely.     

Full-wave boundary integral equation method for suspended planartransmission lines with pedestals and finite metallizationthickness

A boundary integral equation method is proposed for the full-wave analysis of suspended planar transmission lines with pedestals and/or finite metallization thickness. Coupled boundary integral equations are formulated on equivalent magnetic currents only on the apertures of subregions using the Green's identity of the second kind. Because it is possible to take a large number of terms in the series expansion of Green's functions in each subregion independently from the order of resulting matrices, this approach can avoid the relative convergence problem. Numerical results for suspended coplanar waveguides are found to have a stable convergence property and to be in excellent agreement with other available theoretical results. Numerical data reveal the effects of conductor thickness and aperture width on the transmission properties of suspended planar transmission lines with pedestals     

Effects of the Thin-Film Metal Ground Embedded in On-Chip Microstrip Lines

This letter studies the influence of embedded thin-film metallization layers, normally designed as ground planes, upon the dispersive characteristics of multilayer microstrip lines. The spectral domain approach is used to analyze the effects of the metallization thickness as a design parameter in two structures: the thin-film microstrip line and metal-insulator-metal-insulator line. Numerical results indicate that the thin metallization layer can excite the slow-wave mode and change significantly the dispersive characteristics. Moreover, at low frequencies a local minimal attenuation can be achieved with certain metallization thickness. Thus, it is necessary to take into account this thin-film metal ground to achieve reliable numerical simulation from dc to millimeter-wave frequencies     

一种分析有限金属厚度和有限电导率的共面波导结构的有效方法

采用分区直线法与渐近拟合阻抗边界条件相结合的方法,对一种具有限金属厚度和有限电导率的共面波导结构的相对介电常数和损耗特性进行了分析,这是一种全波分析方法,并且可以适用于趋肤深度与金属厚度之比为任意数值的情况。计算实例证明了该方法的正确性和有效性。     

Suspended Slot Line Using Double Layer Dielectric

This paper presents a rigorous analysis of a) slot line on a double layer dielectric substrate, and b) slot line sandwiched between two dielectric substrates. The structure is assumed to be suspended inside a conducting enclosure of arbitrary dimensions. The dielectric substrates are assumed to be isotropic and homogeneous and are of arbitrary thickness and relative permittivity. The conducting enclosure and the zero thickness metallization on the substrate, are assumed to have infinite conductivity. The effect of shielding on the dispersion, characteristic impedance, and the effective dielectric constant are illustrated. These results should find application in the design and fabrication of MIC components and subsystems.     

Explicit formulas of propagation characteristics for unilateral finline

In this paper, the unilateral fintine characteristics including finite metallization thickness and depth of mounting grooves are analysed by transverse resonance principle combining moment method. The numerical results are presented, the influence of the finite metallization thickness and depth of grooves on the propagation characteristics are investigated in detail. Finally, a set of explicit formulas for the propagation characteristics of unilateral fintine are developed. To be compared with the rigorous numerical results, the errors are within ±1% for phase constant and ±2% for characteristic impedance respectivelly.     

Optoelectronic measurements of picosecond electrical pulsepropagation in coplanar waveguide transmission lines

Observations are presented concerning the effects of coplanar waveguide transmission lines on the propagation of picosecond electrical pulses using an optoelectronic time-domain measurement technique. Effects of various test structure design factors such as substrate thickness, thickness of transmission line metallization, discontinuity spacing, ground plane width, pulser/sampler line length, and pulser/sampler geometry on picosecond electrical pulse propagation in microwave/millimeter wave coplanar waveguide transmission lines are discussed, and schemes for minimizing the adverse effects of each of the above factors are provided     

Equivalent network representation of boundary conditions involving generalized trial quantities

Virtual adjustable sources are introduced in equivalent network representation of boundary conditions. For this purpose, integral equations are to be solved simple application of analog Kirchoff’s and Ohm’s laws. These adjustable sources represent generalized trial quantities. In order to illustrate this proposed approach, equivalent network representation of lossy planar transmission lines with arbitrary metallization thickness is presented.     

Suspended Broadside-Coupled Slot Line with Overlay

This paper presents a rigorous analysis of symmetric, broad-side-coupled slot line with overlay. The structure is assumed to be suspended inside a conducting enclosure of arbitrary dimensions. The dielectric substrate and the overlay are assumed to be isotropic and homogeneous and are of arbitrary thickness and relative permittivity. The conducting enclosure and the zero thickness metallization on the substrate are assumed to have infinite conductivity. The computed results illustrate a) the dispersion characteristics and characteristic impedance of the coupled slot line structure, b) the variation of the even-mode and also the odd-mode relative wavelength ratio and characteristic impedance with slot width, and c) the effect of shielding on the even-mode and also the odd-mode dispersion and characteristic impedance. This structure should find application in the design and fabrication of MIC components such as magic-T's and directional couplers.     

Dispersion and attenuation characteristics of coplanar waveguideswith finite metallization thickness and conductivity

A new approach of modifying the conventional spectral-domain approach is proposed for an analysis of the coplanar waveguide whose signal strip and ground planes have finite thickness and conductivity. By introducing suitable equivalent sources in the slot and signal strip regions, the problem can be significantly simplified by reducing the two-dimensional numerical integration into the one-dimensional one, thus it can be treated as easily as the conventional spectral-domain approach. By this modified approach, both the phase constant and attenuation constant can be determined simultaneously without using the assumption that the metallization thickness is much larger or smaller than the skin depth. In this work, comparison with published theoretical and experimental results is presented to check the accuracy of the new approach's results. In particular, the effective dielectric constant ϵ_eff and attenuation constant a of a coplanar waveguide with finite metallization thickness and finite conductivity are discussed in detail, together with the current distributions along the signal strip and ground planes