Analysis of a shielded microstrip line with finite metallizationthickness by the boundary element method

A boundary element method is presented for the quasi-static analysis of a shielded microstrip line with finite metallization thickness. The analysis is based on the solution of a system of boundary integral equations which are derived from Green's second identity. Numerical results for the charge distribution along the strip and the effects of metallization thickness on line characteristics are presented. The results show good agreement with data available in the literature     

Application of a Projection Method to a Mode-Matching Solution for Microstrip Lines with Finite Metallization Thickness (Short Paper)

It will be demonstrated that the convergence behavior of the well-knowm mode-matching technique can be improved significantly by a general projection method. The advantage of this approach becomes obvious in the discussion of the electromagnetic field distribution near metal edges. The implementation is rather simple and will be described below. Numerical results and the validity of this method are discussed for shielded microstrip lines with finite metallization thickness.     

A mode projecting method for the quasi-static analysis ofelectrooptic device electrodes considering finite metallizationthickness and anisotropic substrate

The method presented is an extension of the mode matching method (MMM), utilizing the idea of base transformation and vector projection in inner-product space. In contrast to the conventional MMM, this approach decouples the order of the linear equation system from the truncation index of the mode expansion series and is free from the relative convergence phenomenon of the MMM. Coplanar strip electrodes are analyzed, and the effects of the metallization thickness, buffer layer, and conducting enclosure on the effective permittivity, characteristic impedance, and electric field in the substrate are 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     

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     

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     

Transient Analysis of Microstrip Gap in Three-Dimensional Space (Short Paper)

In this paper, we deal with the microstrip gap that should be analyzed in three-dimensional space. The time variations of the electric field at each surface of the stripline having a finite metallization thickness are analyzed. Our method of analysis is based on both an equivalent circuit of Maxwell's equations and Bergeron's method. The former has advantages in the vector analysis by using all electromagnetic components. The latter has advantages in the time-domain analysis of the field. Therefore, our method can analyze field variations in three-dimensional space and time. We present the time variation of the instantaneous electric-field distributions below the strip, at the side of the strip, and at the gap end surface. These results show how the steady-state field distribution grows in the gap.     

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。     

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 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     

Full-wave analysis of coplanar waveguides by variational conformalmapping technique

A new full-wave analysis of coplanar waveguides is presented. The modified mapping technique of C.P. Wen (1969) is used to map the original infinite domain into a finite image domain and also to account for the singularity of fields near the conductor edges. The finite thickness of the dielectric substrate is considered together with the assumptions of lossless guides and negligible metallization thickness. The current distributions on the center signal strip as well as the tangential electric fields over the slot along the air-dielectric interface are examined. Numerical results for the frequency-dependent effective dielectric constants and characteristic impedances of coplanar waveguides are presented. Particular attention is given to the electric field distributions over the air-dielectric interface of slots and the current distributions of the signal strip     

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     

Improved Bidirectional-Mode Expansion Propagation Algorithm Based on Fourier Series

In this paper, an improved version of a 2-D bidirectional eigenmode expansion propagation algorithm based on Fourier series expansion for modeling optical field distribution in waveguide devices is presented. The algorithm is very simple, numerically robust, and inherently reciprocal. It does not require root searching in the complex plane. Proper truncation rules are used to ensure good convergence properties for TM-polarized waves. Perfectly matched layers as absorbing boundary conditions can be implemented in a very simple way using complex coordinate stretching. The approach represents a transition between purely modal and Fourier expansion methods for modeling guided-wave photonic structures.     

A new formulation of the boundary condition at infinity for ahybrid radiation mode and its application to the analysis of radiationmodes of microstrip lines

A new formulation of the boundary condition at infinity for a hybrid radiation model is introduced. It is shown that its application leads to an iterative solution of the problem in the spectral domain. The validity of the condition is proved by its application to the analysis of a laterally shielded dielectric slab. Using this condition, an iterative method in the spectral domain is proposed in order to analyze striplike stratified transmission lines. As a result, two solutions, classified as perturbed longitudinal electric (LSE) and longitudinal section magnetic (LSM) modes, are obtained. Numerical results concerning the convergence of the method as well as the field distribution are presented for the case of a microstrip line     

The current distribution and AC resistance of a microstripstructure

The AC resistance of the strip in a microstrip structure is compared with that of an isolated strip for better understanding of the conductor loss mechanism. An analysis is presented of the AC resistance in a microstrip structure for any metallization thickness by deriving the current distribution over the strip cross section. The analysis uses the separation of variables technique and the Green's function method. It shows that the skin current of the strip is concentrated toward the ground plane in a microstrip structure. In the extreme case, the AC resistance of the strip can be twice as high as the AC resistance of the same isolated strip. The imperfect ground plane also adds to the total conductor loss of a microstrip line. For a wide strip over a lossy ground plane at high frequency, the ground plane surface current distribution is concentrated directly under the strip, and the ground plane AC resistance can be as large as the strip AC resistance. Therefore, the total AC resistance at the microstrip line can be four times as high as that of an isolated strip conductor     

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     

Full-wave analysis of traveling-wave electrodes with finitethickness for electro-optic modulators by the method of lines

In order to optimize broadband electrooptic modulators with traveling-wave electrodes, detailed information about the propagation constant, the field distribution, and the wave impedance of the modulating field is needed. To get accurate results for these characteristic values, the numerically efficient method of lines (MoL) is used. The MoL takes advantage of the planar structure by discretizing the wave equation in the directions parallel to the metallization plane, whereas an analytical formulation is retained for the transverse direction. Thus, not only the hybrid character of the modulating field but also the finite conductor thickness and anisotropy of the substrate are taken into account. Results for asymmetric coplanar stripline electrodes with typical dimensions on SiO₂ buffered LiNbO₃ are presented     

A new approach based on a combination of integral equation and asymptotic techniques for solving electromagnetic scattering problems

We introduce a new approach for combining the integral equation and high frequency asymptotic techniques, e.g., the geometrical theory of diffraction. The method takes advantage of the fact that the Fourier transform of the unknown surface current distribution is proportional to the scattered far-field. A number of asymptotic methods are currently available that provide good approximation to this farfield in a convenient analytic form which is useful for deriving an initial estimate of the Fourier transform of the current distribution. An iterative scheme is developed for systematically improving the initial form of the high frequency asymptotic solution by manipulating the integral equation in the Fourier transform domain. A salient feature of the method is that it provides a convenient validity check of the solution for the surface current distribution by verifying that the scattered field it radiates indeed satisfies the boundary conditions at the surface of the scatterer. Another important feature of the method is that it yields both the induced surface current density and the far-field. Diffraction by a strip (two-dimensional problem) and diffraction by a thin plate (three-dimensional problem) are presented as illustrative examples that demonstrate the usefulness of the approach for handling a variety of electromagnetic scattering problems in the resonance region and above.     

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.