Natalie Nakhla

DEPACT: delay extraction-based passive compact transmission-line macromodeling algorithm

With the continually increasing operating frequencies, signal integrity and interconnect analysis in high-speed designs is becoming increasingly important. Recently, several algorithms were proposed for macromodeling and transient analysis of distributed transmission line interconnect networks. The techniques such as method-of-characteristics (MoC) yield fast transient results for long delay lines. However, they do not guarantee the passivity of the macromodel. It has been demonstrated that preserving passivity of the macromodel is essential to guarantee a stable global transient simulation. On the other hand, methods such as matrix rational approximation (MRA) provide efficient macromodels for lossy coupled lines, while preserving the passivity. However, for long lossy delay lines this may require higher order approximations, making the macromodel inefficient. To address the above difficulties, this paper presents a new algorithm for passive and compact macromodeling of distributed transmission lines. The proposed method employs delay extraction prior to approximating the exponential stamp to generate compact macromodels, while ensuring the passivity. Validity and efficiency of the proposed algorithm is demonstrated using several benchmark examples

Simulation of coupled interconnects using waveform relaxation and transverse partitioning

The large number of coupled lines in an interconnect structure is a serious limiting factor in simulating high-speed circuits. A new method is presented for efficient simulation of large interconnects based on transverse partitioning and waveform relaxation techniques. The computational cost of the proposed algorithm grows linearly with the number of coupled lines. In addition, the algorithm is highly suitable for parallel implementation leading to further significant reduction in the computational complexity.

Waveform Relaxation Techniques for Simulation of Coupled Interconnects With Frequency-Dependent Parameters

The large number of coupled lines in an interconnect structure is a serious limiting factor in simulating high-speed circuits. Waveform relaxation based on transverse partitioning has been previously presented to address this problem for interconnects with constant per-unit-length parameters. This paper extends the waveform relaxation technique to handle the more difficult and important case of frequency-dependent parameters. The computational cost of the proposed algorithm grows linearly with the number of coupled lines

Fast transient analysis of incident field coupling to multiconductor transmission lines

Due to the rapid surge in operating frequencies and complexity of modern electronic designs, accurate/fast electromagnetic compatibility/interference analysis is becoming mandatory. This paper presents a closed-form SPICE macromodel for fast transient analysis of lossy multiconductor transmission lines in the presence of incident electromagnetic fields. In the proposed algorithm, the equivalent sources due to incident field coupling have been formulated so as to take an advantage of the recently developed delay extraction based passive transmission line macromodels. Also, a method to incorporate frequency-dependent per-unit-length parameters is presented. The time-domain macromodel is in the form of ordinary differential equations and can be easily included in SPICE like simulators for transient analysis. The proposed algorithm while guaranteeing the stability of the simulation by employing passive transmission line macromodel, provides significant speed-up for the incident field coupling analysis of multiconductor transmission line networks, especially with large delay and low losses

Waveform relaxation techniques for simulation of coupled interconnects with frequency-dependent parameters

The large number of coupled lines in an interconnect structure is a serious limiting factor in simulating high-speed circuits. Waveform relaxation based on transverse partitioning has been previously presented to address this problem for interconnects with constant per-unit-length parameters. This paper extends the waveform relaxation technique to handle the more difficult and important case of frequency-dependent parameters. The computational cost of the proposed algorithm grows linearly with the number of coupled lines.

Delay extraction and passive macromodeling of lossy coupled transmission lines

Recently, several algorithms were proposed for time-domain macromodeling of distributed transmission line networks. It has been demonstrated that preserving passivity of the macromodel is essential to guarantee a stable global transient simulation. Techniques such as method-of-characteristics yield fast transient results for long delay lines. However, they do not guarantee the passivity of the macromodel. On the other hand, methods such as matrix rational approximation provide efficient macromodels for lossy coupled lines, while preserving passivity. However, for long lossy delay lines this may require higher order approximations, making the macromodel inefficient. In order to address the above difficulty, this paper presents a new algorithm for efficient macromodeling of lossy coupled lines with long delay. The proposed method employs delay extraction prior to approximating the exponential stamp of the line and guarantees the macromodel passivity. The paper also provides guidelines on the practical applicability of the delay extraction and the matrix rational approximation, based on the knowledge of line parameters.

Parallel and Scalable Transient Simulator for Power Grids via Waveform Relaxation (PTS-PWR)

This paper presents a fast algorithm for transient simulation of power grids in very large scale integration systems using waveform relaxation (WR) techniques. Novel partitioning methods and convergence accelerators are developed for fast convergence of WR iterations when applied to power grid networks. Unlike the direct solvers, the new method is highly parallelizable and scales well with the increasing number of CPUs, leading to significant speed-ups. Numerical examples are presented to demonstrate the validity and efficiency of the proposed method.

Simplified Delay Extraction-Based Passive Transmission Line Macromodeling Algorithm

With higher operating frequencies, signal integrity and interconnect analysis in high-speed designs is becoming increasingly important. Recently, a passive delay extraction-based macromodeling algorithm (DEPACT) has been presented for simulation of long lossy coupled lines. In this paper, a new macromodeling algorithm based on DEPACT is introduced to handle several practical cases of importance, resulting in a simple and compact implementation in SPICE-like circuit simulators. The accuracy and efficiency of the proposed algorithm are validated using several practical examples.

Parallel Simulation of Massively Coupled Interconnect Networks

In a system containing high-speed interconnects, the presence of a large number of coupled lines seriously limits the ability to perform fast simulations. In this paper, a parallel algorithm is presented that allows for simulations of massively coupled interconnects to be performed efficiently. New methods based on physical and time-domain partitioning are developed to create parallelism during transient simulations of large coupled interconnects. In addition, the proposed method exploits the recently developed waveform relaxation techniques to decouple and parallelize the large coupled simulation problem. In this approach, for a simulation of nL lines run on nP processors, the computational complexity is O(nLnP -1). This provides considerable savings as opposed to O(nL ß ), 3 ¿ ß ¿ 4 for full coupled-line simulations.

Simplified Macromodel of MTLs With Incident Fields (SiMMIF)

Electromagnetic compatibility (EMC) analysis of high-speed designs has become imperative due to rapidly increasing radio-frequency interference and emerging technological trends such as higher operating frequencies, denser layouts, and multifunction convergent products. In this paper, a simplified macromodel of multiconductor transmission lines (MTLs) exposed to incident fields is presented. The proposed formulation can also handle frequency dependence of resistance, capacitance, conductance, and inductance (RLGC) line parameters. The method employs the recently developed delay-extraction-based compact and passive MTL macromodel, while developing closed-form expressions for incident field analysis. An error bound for the proposed macromodel is also presented. The macromodel is simulation program with integrated circuit emphasis (SPICE) compatible and overcomes the mixed frequency/time simulation difficulties usually encountered during transient analysis, while guaranteeing the stability of the global transient simulation. The algorithm provides higher accuracy as well as significant speed gains for EMC analysis of transmission line networks as compared to the existing techniques.