Parametric macromodeling of lossy and dispersive multiconductor transmission lines

We propose an innovative parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs) that can be used for interconnect modeling. It is based on a recently developed method for the analysis of lossy and dispersive MTLs extended by using the multivariate orthonormal vector fitting (MOVF) technique to build parametric macromodels in a rational form. They take into account design parameters, such as geometrical layout or substrate features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to perform design space exploration, design optimization, and sensitivity analysis efficiently. Numerical examples validate the proposed approach in both frequency and time domain

Partial element equivalent circuit models in the solution of the electric field integral equation

3-D electromagnetic methods are fundamental design tools for complex high-speed systems. Among the integral equation-based techniques, the Partial Element Equivalent Circuit (PEEC) method has received a special attention in interconnect modeling, where mixed electromagnetic/circuit problems need to be solved. Retardation effects and the resulting delays must be taken into account and included in the modeling, when signal waveform rise times decrease and the corresponding frequency content increases or the geometric dimensions become electrically long. In this case, the enforcement of the Kirchhoff laws to PEEC delayed models leads to a set of delayed differential equations in a neutral form. The aim of this contribution is to present an overview of the PEEC method with special focus on the analysis of electrically long structures that require taking delays into account

An enhanced differential surface admittance operator for the signal integrity modeling of interconnects

A new, enhanced formulation of the 3-D differential surface admittance operator is presented in this contribution. By employing closed expressions for the sums of the infinite series that arise from discretizing the operator by means of entire domain basis functions, a more efficient and accurate form is obtained. Convergence analysis demonstrates the performance gain. Additionally, the appositeness of the novel operator is studied by analyzing results for various interconnect structures over a broad frequency range and by comparing with other research and commercial solvers

Entire domain basis function expansion of the differential surface admittance for efficient broadband characterization of lossy interconnects

This article presents a full-wave method to characterize lossy conductors in an interconnect setting. To this end, a novel and accurate differential surface admittance operator for cuboids based on entire domain basis functions is formulated. By combining this new operator with the augmented electric field integral equation, a comprehensive broadband characterization is obtained. Compared with the state of the art in differential surface admittance operator modeling, we prove the accuracy and improved speed of the novel formulation. Additional examples support these conclusions by comparing the results with commerical software tools and with measurements

Carbon Nanotube Interconnect Modeling for Very Large Scale Integrated Circuits

In this research, we have studied and analyzed the physical and electrical properties of carbon nanotubes. Based on the reported models for current transport behavior in non-ballistic CNT-FETs, we have built a dynamic model for non-ballistic CNT-FETs. We have also extended the surface potential model of a non-ballistic CNT-FET to a ballistic CNT-FET and developed a current transport model for ballistic CNT-FETs. We have studied the current transport in metallic carbon nanotubes. By considering the electron-electron interactions, we have modified two-dimensional fluid model for electron transport to build a semi-classical one-dimensional fluid model to describe the electron transport in carbon nanotubes, which is regarded as one-dimensional system. Besides its accuracy compared with two-dimensional fluid model and Lüttinger liquid theory, one-dimensional fluid model is simple in mathematical modeling and easier to extend for electronic transport modeling of multi-walled carbon nanotubes and single-walled carbon nanotube bundles as interconnections. Based on our reported one-dimensional fluid model, we have calculated the parameters of the transmission line model for the interconnection wires made of single-walled carbon nanotube, multi-walled carbon nanotube and single-walled carbon nanotube bundle. The parameters calculated from these models show close agreements with experiments and other proposed models. We have also implemented these models to study carbon nanotube for on-chip wire inductors and it application in design of LC voltage-controlled oscillators. By using these CNT-FET models and CNT interconnects models, we have studied the behavior of CNT based integrated circuits, such as the inverter, ring oscillator, energy recovery logic; and faults in CNT based circuits

M[pi]log, Macromodeling via parametric identification of logic gates

This paper addresses the development of computational models of digital integrated circuit input and output buffers via the identification of nonlinear parametric models. The obtained models run in standard circuit simulation environments, offer improved accuracy and good numerical efficiency, and do not disclose information on the structure of the modeled devices. The paper reviews the basics of the parametric identification approach and illustrates its most recent extensions to handle temperature and supply voltage variations as well as power supply ports and tristate devices

Analysis of crosstalk and field coupling to lossy MTL's in a SPICE environment

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficienc