Multiconductor Interconnects Research Articles

Behavioral Modeling Method of Macromodels for Interconnected Systems With Frequency Characteristics and Nonlinear Termination Networks

This study presents a behavioral macromodeling method for electronic or electrical interconnected systems, when there are frequency-characterized interconnects loaded by nonlinear terminations in systems. Analog behavioral modeling (ABM) was leveraged to capture frequency-dependent characteristics of multiconductor interconnects and properties of nonlinear terminations. Black-box macromodels were developed from the external mathematical behavior of parts, and real systems could be simulated in the SPICE circuit solver. Also, several critical points and constraints concerning ABM models were analyzed and proposed.From the validation results, the relative errors of proposed models are all less than 3%, and the execution time reduces by a factor over 10 concerning the existing interconnect model, which implies the proposed interconnect model can significantly improve the simulation efficiency, and the analysis accuracy can be guaranteed using proposed models of interconnect systems.

GVF: GPU-Based Vector Fitting for Modeling of Multiport Tabulated Data Networks

Modeling of multiport data characterizing high-speed modules, such as packages, vias, and complex multiconductor interconnects is becoming increasingly important in signal and power integrity applications. Vector fitting (VF) algorithm has been widely used by designers for macromodeling and system identification from such multiport tabulated data. Since VF and strategies based on it require many iterations to arrive at an optimal number of converged poles, it is highly desired to reduce the computational cost of each VF iteration. This article advances the applicability of VF to exploit the emerging massively parallel graphical processing units (GPUs) by developing necessary parallelization strategies and investigates their performance while using different GPU libraries. For large problem sizes (an increasing number of poles and ports), numerical results demonstrate that the proposed method while using MAGMA libraries provides significant speedup compared with existing multi-CPU-based parallel VF techniques.

Multiconductor Transmission Line Models for Modal Transmission Schemes

We investigate modal transmission schemes used to reduce echo and internal crosstalk in a multichannel link using an untransposed multiconductor interconnection. The core of such a modal transmission scheme is an appropriate multiconductor transmission line (MTL) model of the interconnection. The standard theory of modal signaling, which emphasizes modal voltages, modal currents, and associated eigenvectors is summarized. Then, we present new results of MTL theory: three theorems on generalized associated eigenvectors and two high-frequency approximations. These results are needed to explain an assumption used in some modal transmission schemes.

Interconnect Modeling Using the Quasi Monte Carlo Integration Technique

A new fast and accurate capacitance determination methodology for interconnect capacitance extraction is presented. The methodology is based on Quasi Monte Carlo integration technique applied to method of moments solution of integral equation. As an example, the interconnects are modeled as parallel plate, cylindrical, and spherical capacitors separated by some distance and multilayered and multiconductor interconnects. The proposed capacitance determination methodology is more efficient and accurate than conventional methods and is also capable of dealing with singularity problem encountered in the kernel of the integrand. It is shown that the computed capacitances have excellent agreement with analytical formula based results within 2% error.

Parameters Variability Effects on Multiconductor Interconnects via Hermite Polynomial Chaos

This paper focuses on the derivation of an enhanced transmission-line model allowing the stochastic analysis of a realistic multiconductor interconnect. The proposed model, which is based on the expansion of the well-known telegraph equations in terms of orthogonal polynomials, includes the variability of geometrical or material properties of the interconnect due to uncertainties like fabrication process or temperature. A real application example involving the frequency-domain analysis of a coupled microstrip and the computation of the parameters variability effects on the transmission-line response concludes this paper.

Identification of Highly Efficient Delay-Rational Macromodels of Long Interconnects From Tabulated Frequency Data

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We introduce a novel formulation of black-box models for long multiconductor interconnects, together with an identification algorithm from tabulated scattering parameters. The fundamental assumption requires a modal decomposition matrix that does not depend on frequency. The model structure includes low-order rational coefficients with suitable delay operators. The latter are included in a feedback loop; therefore, all infinite signal reflections are automatically accounted for. This feature may lead to significant speed up factors during circuit-based transient simulation with respect to other state-of-the-art solutions. The model is cast in a delayed descriptor form, leading to a straightforward conversion to an equivalent SPICE-compatible netlist. Finally, a purely algebraic stability test is presented based on a linear matrix inequality. The very high efficiency of the proposed models is demonstrated through several application examples. </para>

Echo-Free and Crosstalk-Free Transmission in Particular Interconnections

We explore several designs for implementing the special ZXtalk method for completely degenerate interconnections, capable of providing reduced echo and internal crosstalk in multiconductor interconnections. Transmission circuits comprising a MIMO series-series feedback amplifier are adequate to obtain a wide bandwidth. The external crosstalk may also be reduced, using an additional conductor to obtain a pseudo-differential scheme.

Construction and applications of the Dirichlet-to-Neumann operator in transmission line modeling

The Dirichlet-to-Neumann (DtN) operator is a useful tool in the characterization of interconnect structures. In combination with the Method of Moments, it can be used for the calculation of the per-unit length transmission line parameters of multi-conductor interconnections, or to directly determine the internal impedance of conductors. This paper presents a new and fast calculation method for the DtN boundary operator in the important case of rectangular structures, based on the superposition of parallel-plate waveguide modes. Especially for its non-differential form, some numerical issues need to be addressed. It is further explained how the DtN operator can be determined for composite geometries. The theory is illustrated with some numerical examples.

Analytical Frequency-Dependent Model for Transmission Lines on RF-CMOS Lossy Substrates

Transmission lines (T-Lines) are widely used in millimeter wave applications on silicon-based complementary metal-oxide semiconductor (CMOS) technology. Accurate modeling of T-lines to capture the related electrical effects has, therefore, become increasingly important. This paper describes a method to model the capacitance and conductance of T-Lines on CMOS multilayer, lossy substrates based on conformal mapping, and region subdivision. Tests show that the line parameters (per unit length) obtained by the method are frequency dependent and very accurate. The method is also suitable for parallel multiconductor interconnect modeling for high frequency circuits.

MIMO Series–Series Feedback Amplifiers

This brief defines a new type of multiple-input multiple-output (MIMO) amplifier. We present basic structures for this MIMO series-series feedback amplifier (MIMO-SSFA), and the basic design equations. We provide a detailed example showing how this MIMO-SSFA may be used as a transmitting circuit for multiconductor interconnections.

Full‐wave‐based transmission‐line model for lossy‐substrate multiconductor interconnects

AbstractA full‐wave‐based modal analysis is used for simulating a multiconductor coplanar waveguide (CPW) over a selectively etched lossy silicon substrate. Propagating modes, which are similar to the classic ‘common’ and ‘differential’ modes, are extracted, and circuit theory energy relationships are used for the determination of transmission‐line model parameters. A time‐frequency domain technique is employed for implementing the transmission‐line model within a circuit simulator. The model is used to study the effect of etching the dielectric and the substrate for a two‐conductor CPW line. The simulation results show that etching both the dielectric and the lossy substrate improves the loss and dispersion characteristics of the CPW line. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Corrections to &amp;#8220;A New Method for the Reduction of Crosstalk and Echo in Multiconductor Interconnections&amp;#8221;

Corrections to &amp;#8220;A New Method for the Reduction of Crosstalk and Echo in Multiconductor Interconnections&amp;#8221;

A new method for the reduction of crosstalk and echo in multiconductor interconnections

Crosstalk and echo can be reduced in multiconductor interconnections, using (truly) matched terminations and a different modal variable for each transmission channel. We first study a conventional technique for reducing reflections, using grounded linear two-terminal circuit elements. Using the concepts of modal voltages and modal currents, we define a new method for the reduction of crosstalk and echo, which involves specific terminations, specific transmitting circuits to send signals, and specific receiving circuits to receive signals. We establish the design equations and show that the new method is related to a particular choice of eigenvectors, called associated eigenvectors. Simulations of two examples of implementation of this method confirm that it provides reduced crosstalk and echo. We also discuss the implementation of the new method with an interconnection having identical propagation constants for all modes. Finally, we compare the new method with a different concept based on modal variables and unspecified terminations.

Characterisation of high-speed multiconductor interconnections

The paper presents a method for the determination of the capacitance matrix needed in modelling and simulation of signal transmission in multiple coupled interconnecting lines. The method utilises capacitance measurements and thus one of its useful application areas is in the validation of numerous previously published algorithms based on various approximations to field equations, originally developed for the computation of capacitance matrices. The technique described is based on the active separation of the capacitance network, achieved through the use of a unity-gain amplifier. Thanks to the circuit configurations introduced with a unity-gain amplifier it is possible to make direct capacitance measurements in the multiconductor interconnecting structures. Measurement procedures are described and analysis of errors in measured quantities caused by the imperfections of measuring equipment is discussed. A sample of results obtained in measuring manufactured test structures is included for illustration of the method and measuring procedures.

On the two-dimensional capacitance calculation of multiconductor multilayered interconnects

In this paper a method for analysis and modelling of transmission interconnect lines on multilayered dielectric media is presented. The analysis is based on semianalytical layered Green’s function and the electromagnetic concept of free charge density. It allows us to obtain integral equations between electric scalar potential and charge density distributions. These equations are solved by the Galerkin procedure of the Method of Moments. After this, the capacitance matrix of multiconductor interconnect lines in the presence of planar dielectric interfaces is calculated. When there exists no infinite ground plane, we enforce the constraint that the sum of all free charges is zero. The feasibility of the method has been shown by simulations of several transmission-line problems. The results have been compared with reported data obtained by free-space Green’s function method, conformai mapping formulas, generalized method of lines and inverted capacitance coefficient matrix technique. The proposed approach is not inferior to other procedures in terms of generality and memory requirements. At the same time, a reduction of the central processing unit (cpu) time is achieved because the integral equations are solved numerically only on the surface of conductor lines.

An all-purpose dispersive multiconductor interconnect model compatible with PRIMA

This paper describes a new, transmission line-based discrete model for interconnects with per-unit-length, frequency-dependent resistance and inductance. The proposed model is developed in such a manner that the resulting discrete form of Telegrapher's equations constitutes a passive system, and is compatible with passive, reduced-order macromodeling algorithms. The validity of the proposed model is demonstrated through numerical examples.

On the mutual capacitance and inductance of a shielded interconnectfour-line system

In this paper, the capacitance and inductance of afour-line transmission structure is characterized. The procedure used wasdeveloped by Ymeri et al for general analysis ofmultilayer multiconductor interconnects for specific applications inmicroelectronics. The characterization is based on the determination of thequasi-static electric scalar potential in the structure making up thefour-line interconnect. Using the electric potential, the mutualcapacitances and inductances are found. The characterization of thefour-conductor structure is significantly different from the simple conductorpair because the symmetry of the pair is lost. A number of numerical resultsare calculated and presented.

Fast and accurate analysis of the multiconductor interconnects

This paper describes a fast and accurate semi-analytical procedure for determining capacitance and inductance of multilayer structures with multiple conductors in the top layer (with zero and non-zero conductor thickness). The technique uses the quasi-analytic electrostatic Green’s function of multilayer structures, which is integrated to a series expansion valid for uniform charge distributions. Computed results are given for some cases to show the advantages and simplicity of our procedure as compared to the methods available in the literature.

Systematic development of transmission-line models for interconnects with frequency-dependent losses

This paper presents a new method for the extraction of the frequency-dependent, per-unit-length (p.u.l.) resistance, and inductance parameters of multiconductor interconnects. The proposed extraction methodology is based on a new formulation of the magneto-quasi-static problem that allows lossy ground planes of finite thickness to be modeled rigorously. The formulation is such that the p.u.l. impedance matrix for the multiconductor interconnect is extracted directly at a prescribed frequency. Once the matrix has been calculated over the bandwidth of interest, rational function representations of its elements are generated through a robust matrix curve-fitting process. Such a formulation enables subsequent transient analysis of interconnects through a variety of approaches. Direct incorporation of the rational function model into a general-purpose circuit simulator and a standalone multiconductor-transmission-line simulator is demonstrated.

Computation of capacitance matrix for integrated circuit interconnects using semi-analytic Green's function method

In this paper a method for computing the capacitance matrix of a multiconductor interconnect line in a multilayered dielectric region is presented. The number of conductors and dielectric layers are arbitrary. The conductors are infinitesimally thin, and can be placed anywhere in the structure. The formulation is obtained by using a semi-analytic Green's function for multilayer structures, which is integrated to a series expansion, valid for uniform charge distribution on the conductors. In addition, the quasi-analytical evaluation of the entries of the Galerkin matrix leads to a very efficient and accurate computer code. Computed results are given for some cases of the integrated circuit interconnects to show the advantages and simplicity of our procedure as compared to the methods available in the literature.