On the quasi-TEM and full-wave approaches applied to coplanarmultistrip on lossy dielectric layered media

The characteristic parameters of coplanar multistrip lines embedded in multilayered lossless/lossy substrates are commonly computed by using either quasi-TEM or full-wave model. Several methods are provided in the literature to deal with this type of structure. A comparative study of quasi-TEM and rigorous solutions is carried out in order to establish criteria for the validity of the quasi-TEM approach. Reliable quasi-TEM and full-wave numerical data have been properly generated by applying an enhanced spectral domain analysis. The authors conclude that the quasi-TEM model yields satisfactory results for many MIC and MMIC practical cases. However, significant errors arise when high conductivity substrates are involved in MMIC applications. A discussion about the computation of the dynamic modal characteristic impedance is also reported, showing how the insertion of the modal orthogonality can save computational effort in a lossy multiport system     

The incremental inductance rule in quasi-TEM coupled transmissionlines

The application of the incremental inductance rule is described for the computation of losses in quasi-TEM coupled transmission lines. It is shown that the well-known formula valid for the single-line case can be extended to the case of normal modes travelling in general coupled structures providing one uses the power-current modal characteristic impedance definition. Numerical results are shown for several coupled lines systems     

A quasi-TEM analysis for curved and straight planar multiconductorsystems

A quasi-TEM (transverse electromagnetic) analysis for straight and weakly curved planar multiconductor transmission lines is presented. This transverse field of a weakly curved planar multiconductor system is described by the static electric and magnetic solutions of the corresponding axially symmetrical structure. The capacitance and inductance matrices of this system of concentric microstrip rings are calculated using the method of lines. A two-port network consisting of circularly curved transmission lines is calculated and the results are compared with measured values. It is concluded that the proposed method of approximation is suited for analysis of microwave components as well as for high-speed digital circuits with interconnections consisting of curved striplines instead of straight lines with discontinuities     

An improved iterative technique for the quasi-TEM analysis ofgeneralized planar lines

The generalized bioconjugate gradient method (GBGM) and fast Fourier transform (FFT) algorithm are used for the quasi-transverse electromagnetic (TEM) analysis of generalized multistrip lines embedded in multilayered lossless/lossy, iso/anisotropic dielectric and/or magnetic media. Important computational improvement is achieved by including asymptotic extraction techniques in the determination of the spatial Green's function matrix. Comparisons with other iterative procedures are presented. Several practical structures are analyzed and numerical results are compared with previously published data     

Frequency-dependent mutual resistance and inductance formulas for coupled IC interconnects on an Si-SiO2 substrate

A highly accurate closed-form approximation of frequency-dependent mutual impedance per unit length of a lossy silicon substrate coplanar-strip IC interconnects is developed. The derivation is based on a quasi-stationary full-wave analysis and Fourier integral transformation. The derivation shows the mathematical approximations which are needed in obtaining the desired expressions. As a result, for the first time, we present a new simple, yet surprisingly accurate closed-form expression which yield accurate estimates of frequency-dependent mutual resistance and inductance per unit length of coupled interconnects for a wide range of geometrical and technological parameters. The developed formulas describe the mutual line impedance behaviour over the whole frequency range ( i.e. also in the transition region between the skin effect, slow wave, and dielectric quasi-TEM modes). The results have been compared with the reported data obtained by the modified quasi-static spectral domain approach and new CAD-oriented equivalent-circuit model procedure.     

Modéles de lignes simples et couplées,idéales et à pertes,pour la CAO des circuits gigabits

This paper describes the principles underlying a library of single and coupled lines, ideal or lossy for the cad of interconnections in gigabit logic circuits. The models are based upon the quasi-TEM approximation, they exploit the method of characteristics and direct simulation in the time domain which give good calculation efficiency. The modeling of lossy coupled lines is original and utilizes modal decomposition in the time domain which may be performed in good approximation for coupled lines of equal widths. The models are integrated in the circuit simulator Macpro to perform the cad of circuit microstrip interconnections. Simulations including the response of the instrumentation are compared with the corresponding measurements on typical configurations of lossy coupled lines deposited on a semi-insulated GaAs substrate.     

Spectral domain analysis of conductor losses in a multiconductorsystem via the incremental inductance rule

Spectral domain analysis is adapted to analyse the conductor losses of a multiconductor system embedded in a multilayered medium using a quasi-TEM approach and assuming a strong skin effect. After adapting the incremental rule to a multiconductor system, the conductor losses are computed in terms of the derivative of the inductance matrix     

基于小波加速的三维导体结构频变电感参数提取

本文首次次多分辨率稀疏化技术引入有耗三维导体结构频变电感参数的提取过程中,通过多分辨率分解对稠密的部分电感矩阵进行稀疏比,有效地加速了对紧耦合部分元等效电路的修正节点分析过程。分别计算了单根导体以及一个矩形螺旋电感的例子。数值结果表明该方法可以显著提高参数提取的效率。     

A moment method solution for TMz and TEzwaves illuminating two-dimensional objects above a lossy half space

A moment method (MM) solution for analyzing the electromagnetic shielding and scattering properties of two-dimensional (2-D) objects over a lossy half space is presented. The materials of the objects can be metal, dielectric, or magnetic. Also, the lossy half space is included to simulate the effects of the earth ground or any flat homogeneous lossy surface. An MM based on a volume formulation and a special Green's function in the spectral domain is developed. Both TM _z and TE_z waves incident upon 2-D metal or lossy material structures are demonstrated for the shielding effects of those bodies in the presence of the lossy ground. Besides, the echo widths of a composite object either in free space or above the lossy half space are determined by using the MM. Some of the results are compared with those by other methods, and good agreements are obtained. The MM solution can be used to study the shielding and scattering problems for cylindrical structures located over a lossy ground     

A Physical Model for On-Chip Spiral Inductors With Accurate Substrate Modeling

A physical-based analytical model for on-chip inductors is developed. A ladder structure is used to model the skin and proximity effects in metal lines. The substrate electric and substrate magnetic losses are accurately modeled by RC and RL ladder structures, respectively. The effective inductance reduction due to the eddy current in the lossy silicon substrate at high frequency is modeled by a negative mutual inductance between the inductor and the substrate. All the model parameters can be calculated from the layout and process parameters. On-chip inductors with different geometries and substrate resistivities were fabricated for the verifications. The measured results are in very good agreement with the proposed model. This generic model can be applied to various substrate resistivities; thus, it is suitable for different technologies. This model can facilitate the design and optimization of on-chip inductors for RF IC applications     

Frequency-domain analysis of coupled nonuniform transmission linesusing Chebyshev pseudo-spatial techniques

The analysis of nonuniform cross-section, lossy, coupled transmission lines for the design and simulation of high-speed microelectronics systems is addressed. A method of performing such simulations under the quasi-TEM assumption is presented. The technique incorporates a Chebyshev expansion in the frequency domain, and is one of the most suitable methods presently in existence for incorporation into computer-aided-design tools     

High-frequency reciprocity-based circuit model for the incidence ofelectromagnetic waves on general waveguide structures

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     

A fast reduced-order model for the full-wave FEM analysis of lossyinhomogeneous anisotropic waveguides

The evaluation of the frequency response of waveguiding structures by means of the full-wave finite-element method requires solving a large generalized eigenvalue problem for each frequency. This paper describes a novel approach, based on the singular-value decomposition, which drastically reduces the order of the eigenvalue problem. By inspection of the singular values, the accuracy level of the procedure may be controlled. The technique is applied to the analysis of open and closed waveguides with arbitrary cross section, lossy conductors, and anisotropic dielectric layers, by means of vector elements of generic order; higher order elements are shown to allow the accurate evaluation of fields inside lossy conductors with fewer unknowns, besides exactly modeling normal field discontinuities at material interfaces. Examples of application of the reduced-order technique are shown concerning both non-TEM and quasi-TEM structures     

Quasi-TEM Analysis of "Slow-Wave" Mode Propagation on Coplanar Microstructure MIS Transmission Lines

We present a simple quasi-TEM analysis of "slow-wave" mode propagation on micron-size coplanar MIS transmission lines on heavily doped semiconductors and compare theoretical results with measurements on four such structures at frequencies from 1.0 to 12.4 GHz. Excellent agreement is found, which shows that the "slow-wave" mode propagating on these transmission lines is, in fact, a quasi-TEM mode. Relatively low-loss propagation along with significant wavelength reduction is observed. Conduction losses of the metal, which have been tacitly ignored in previously published "full-wave" treatments of "slow-wave" mode propagation, are included in the theory and are shown to dominate the attenuation at frequencies below 25 GHz and to still be significant at frequencies up to at least 100 GHz.     

Exact formulas for wave impedance and propagation constants ofhomogeneous, lossy dielectric and/or magnetic materials

Calculations of propagation constants for lossy materials are performed under the approximations of low loss (or high conductivity). To improve the understanding and better predict the analysis of such materials, exact formulation for wave impedance and propagation constants of homogeneous, lossy, dielectric/magnetic materials are proposed. Formulation is based on dielectric and/or magnetic loss tangent of the material     

Quasi-TM MoL/MoM approach for computing the transmission-line parameters of lossy lines

This paper presents a quasi-TM approach for the fundamental mode of transmission lines with semiconductor substrates and nonperfect metallic conductors. The approach has allowed us to develop a transmission-line model by properly defining frequency-dependent parameters in terms of the quasi-static electric potential and the electric current density along the propagation direction in the line. The previous quasi-TM analysis avoids the involved numerical root finding process typical in full-wave analysis, and overcomes the limitations of the conventional quasi-TEM approach to account for the effects of the longitudinal currents present both in the lossy substrates and in the nonperfect conductors. The transmission-line parameters have been computed by a hybrid technique that combines the method of lines with the method of the moments (MoM). The total CPU effort has been considerably reduced thanks to the possibility of finding closed-form expressions for the reaction integrals appearing in the MoM. Comparisons with previous computed and measured results show the validity of the present model.     

A fast spatial-domain method for the suppression ofexcitation-induced spurious modes in SCN TLM

An efficient method for the suppression of excitation-induced spurious modes in the symmetrical condensed node (SCN) transmission-line matrix (TLM) method is presented for the general case of dielectric, anisotropic, or lossy media in planar structures. A special mapping of the field-excitation onto the wave amplitudes of the TLM algorithm completely prevents the emanation of the spurious modes. The application of the mapping in the k-ω space can be done for waveguides with low computational effort. The method is generalized for planar structures with high spatial frequencies of the field at the discontinuities. We use precomputed field templates at the entrance of the three-dimensional (3-D) structures. The mapping is mainly done in the space domain based on the quasi-TEM propagation of the guided waves to keep the computational effort low. Instead of the four-dimensional (4-D) k-ω transformation, only independent one-dimensional (1-D) transformations to the wave coefficient of the conductors direction and ω are necessary. In the case of propagation with low dispersion, the expenditure can be further reduced to 1-D transformations with respect to ω. The efficiency of the present method is demonstrated by investigation of a coplanar waveguide and a triplate waveguide     

Systematic Lumped-Element Modeling of Differential IC Transmission Lines

In this paper, we report a systematic and efficient approach to obtain lumped-element models for differential integrated-circuit interconnect transmission lines covering both the low-frequency R/C as well as the high-frequency quasi-TEM behavior. To accurately model signal delay and loss, and to preserve causality, the frequency dependence of both line resistance as well as the line inductance is included in our model. The impact of ground inductance is also properly covered by the model. The validity of our approach is verified against experimental data collected up to 120 GHz for the even and odd modes on these differential transmission lines. We predict that these lines can transport data over 1-cm distance with rates up to 40 Gb/s, even with some imbalance in differential drive.      

Plane wave coupling to multiple conductor transmission lines abovea lossy earth

The current induced on an infinite multiple conductor transmission line located above a lossy homogeneous medium due to a transient plane wave is discussed. An exact solution is formulated in the frequency domain using a spatial transform technique. The widely utilized quasi-TEM approximation is derived directly from the exact solution with emphasis on the physical consequences of the assumptions made. Both frequency domain and time domain numerical results are presented for typical transmission structures and documented electromagnetic pulse (EMP) excitations. Comparison of the quasi-TEM approximation to the exact solution is made in order to study the validity of its application in EMP coupling problems. The modeling of the EMP source as an incident plane wave is examined by comparing the induced current due to a dipole source with its steepest-descent contribution     

Full vectorial finite element formalism for lossy anisotropicwaveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures containing lossy, anisotropic materials. In this procedure a formulation in terms of the transverse magnetic field component is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus one avoids the unnecessary iterations which arise when using complex frequencies. To demonstrate the strength of the presented method, numerical results are shown for a rectangular waveguide filled with lossy anisotropic dielectric with off-diagonal elements in a permittivity tensor and compared with those obtained by the telegrapher equation method. The results are in excellent agreement both for phase and for attenuation