Attenuation Characteristics and Sensitivity Analysis for Coplanar Waveguide

The behaviour of attenuation losses in Coplanar waveguides (CPW) is studied for quasi-planar transmission lines with constant characteristic impedance (Z₀) and resistivity, having different geometry's. This behavior helps in making a suitable choice of the type of structure and its dimensional parameters depending upon the application. Minimization of loss for a chosen substrate thickness, conductivity and impedance is analyzed. Dispersion characteristics of CPW have been plotted for various metallization thicknesses. A sensitivity analysis for effective dielectric constant with respect to various dimensional parameters of CPW is presented.     

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     

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     

The influence of finite conductor thickness and conductivity onfundamental and higher-order modes in miniature hybrid MIC's (MHMIC's)and MMIC's

The effect of finite metallization thickness and finite conductivity on the propagation characteristics of conductor-backed CPW on thin substrate is rigorously analyzed. A self-consistent approach is used together with the method of lines (MoL) to determine the propagation constant, losses and field distribution of the fundamental and first two higher-order modes in coplanar waveguides (CPWs) with finite metallization thickness and lossy backmetallization. The method used is general and can be applied to miniature MHMICs and MMICs including lossy semiconductor substrate. It is shown that the onset of higher-order modes limits the usable frequency range of conductor-backed CPWs. The analysis also includes microstrip transmission lines on thin substrate material. It is demonstrated that a resistive strip embedded into the microstrip ground plane may potentially be useful in the design of integrated planar attenuators     

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     

Finite-Boundary Corrections to the Coplanar Waveguide Analysis (Short Papers)

Conformal mapping calculations of impedance and effective dielectric constant are presented for coplanar waveguide (CPW) lines with finite-substrate thickness. These calculations and experimental data show a departure from the intinite dielectric approximation as the substrate thickness approaches the guide slot width. The quasi-TEM approximation is retained and calculations of static energy density within the substrate are given. This approximation agrees well with field calculations using a finite-element solution to Laplace's equation.     

Low-loss CPW on low-resistivity Si substrates with a micromachinedpolyimide interface layer for RFIC interconnects

The measured and calculated propagation constant of coplanar waveguide (CPW) on low-resistivity silicon (1 Ω·cm) with a micromachined polyimide interface layer is presented in this paper. With this new structure, the attenuation (decibels per centimeter) of narrow CPW lines on low-resistivity silicon is comparable to the attenuation of narrow CPW lines on high-resistivity silicon. To achieve these results, a 20-μm-thick polyimide interface layer is used between the CPW and the Si substrate with the polyimide etched from the CPW slots. Only a single thin-film metal layer is used in this paper, but the technology supports multiple thick metal layers that will further lower the attenuation. These new micromachined CPW lines have a measured effective permittivity of 1.3. Design rules are presented from measured characteristics and finite-element method analysis to estimate the required polyimide thickness for a given CPW geometry     

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     

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。     

共面波导有限金属厚度效应的研究

用保角变换法对共面波导金属厚度效应进行了理论分析，编制了相应的计算机程序，给出了数值解，并对此进行了多元曲线拟合，导出了考虑金属厚度后的形状比k、有效介电常数、特征阻抗、损耗的闭定表达式。用此修正表达式求得特征阻抗及损耗的数值解，并与K．C．格普塔的修正值及实验测量值进行了详细比较，结果表明此修正公式与实验值相符较好。     

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     

Quasi-TEM characteristic impedance of micromachined CMOS coplanarwaveguides

Micromachined coplanar waveguides (CPW's) fabricated in CMOS technology consist of glass-encapsulated metal conductor strips, fully suspended by selective etching of the silicon substrate. The minimum amount of etching necessary for proper operation of the micromachined waveguides is determined by using an isolation criterion. In this paper, the quasi-TEM characteristic impedance of a CPW is derived, including the finite conductor thickness and the thicknesses of surrounding dielectric layers. The employed analytical approach is based on conformal mapping and the partial capacitance technique. The losses both in conductor and dielectric layers are neglected. The analytical results and proposed approximations are verified by integral-equation computation and by measurement of various sample structures     

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.     

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     

A 3-D mode matching technique for the efficient analysis ofcoplanar MMIC discontinuities with finite metallization thickness

A technique is proposed for the efficient analysis of CPW discontinuities including finite metallization thickness. The transverse resonance technique (TRT) is modified by introducing an impressed source that allows a cavity of fixed, instead of variable, dimensions to be analyzed (impressed source technique, IST). At the same time, as with TRT, the field analysis of only homogeneously filled waveguides is required so avoiding the computation of frequency dependent as well as complex modes as with the conventional mode matching technique. On this basis, an extremely efficient code for the analysis of CPW discontinuities, applicable also to interacting discontinuities, is obtained. The same code, which incorporates the modal spectrum of an L-shaped waveguide, can be used to compute a large class of CPW discontinuities including steps, gaps, open ends, etc. Computed results are shown to be in remarkable agreement with the experiments and confirm that the finite metallization thickness may significantly affect the electrical characteristics of CPW circuits     

The method of lines for the analysis of planar waveguides withfinite metallization thickness

The method of lines is extended to calculate waveguide structures with finite metallization thickness. The normally used range of metallization thickness is not a limit for the method. Particularly when calculating small or moderate thicknesses, it is possible to derive the dispersion constant with only one computed result. When using the optimal edge parameter, P_opt, for that computation, the deviation from the exact dispersion constant is less than 0.5%. The advantage of the method of lines is that only small line numbers are necessary. Hence, the computing time is very small     

Analysis of the annular-ring-loaded circular-disk microstripantenna

A rigorous analysis of the natural resonance frequencies and input impedance characteristics of an annular-ring-loaded (ARL) circular-disk microstrip antenna is presented. Using vector Hankel transforms, the problem is formulated in terms of vector dual-integral equations. Galerkin's method is then used to solve the equations to obtain the resonance frequencies and the current distribution on the conductive patches arising from a probe excitation. Due to the singular nature of the current distribution, the singularity subtraction method has been used to accelerate the convergence of basis function expansions. Experiments for determining resonance frequencies and input impedance characteristics of an ARL circular-disk microstrip antenna with various substrate thicknesses have been made. The theoretical results are in good agreement with the experimental data even when the thickness of the substrate is 0.1 substrate wavelength. It is shown that this theory can be used to analyze some microstrip antennas with an electrically thick substrate, including the analysis of mutual coupling between conductive patches or between the path and the feed of a microstrip antenna     

Characterization of shielded coplanar type transmission linejunction discontinuities incorporating the finite metallizationthickness effect

Frequency-dependent characteristics of shielded junction discontinuities between coplanar type transmission lines, specifically coplanar waveguide (CPW) and finline, are analyzed by the mode-matching technique. The effect of finite metallization thickness is also incorporated in the analysis for the first time. Scattering parameters of finline step discontinuity are compared with existing data to confirm the accuracy of the approach. Numerical results for finline step discontinuity, shielded CPW step discontinuity and CPW-finline transition are presented     

Investigations of complex modes in a generalized bilateral finlinewith mounting grooves and finite conductor thickness

A generalized bilateral finline with mounting grooves and finite conductor thickness is analyzed by a full-wave mode-matching method. The final nonstandard eigenvalue equation is derived from the unknown coefficients in the slot regions to reduce the size of the matrix equation. The convergence studies of the mode-matching method is first studied for the fundamental mode of a symmetric bilateral finline. Both the propagation constant and the characteristic impedance as defined by the power-voltage relationship are analyzed and compared to the existing data. Excellent agreement is obtained. The effects of metallization thickness and mounting grooves are discussed. The accurate results obtained for the fundamental mode by the mode-matching method with respect to both relative and absolute convergence were also obtained for the complex modes of the finline. The dispersion characteristics of the fundamental, higher order, evanescent, and complex modes are presented for an asymmetric bilateral finline. The effects of mounting grooves and metallization thickness on the complex mode propagation constants are investigated and discussed