Ramachandra Achar

Simulation of high-speed interconnects

With the rapid developments in very large-scale integration (VLSI) technology, design and computer-aided design (CAD) techniques, at both the chip and package level, the operating frequencies are fast reaching the vicinity of gigahertz and switching times are getting to the subnanosecond levels. The ever increasing quest for high-speed applications is placing higher demands on interconnect performance and highlighted the previously negligible effects of interconnects such as ringing, signal delay, distortion, reflections, and crosstalk. In this review paper various high-speed interconnect effects are briefly discussed. In addition, recent advances in transmission line macromodeling techniques are presented. Also, simulation of high-speed interconnects using model-reduction-based algorithms is discussed in detail.

Stability, Causality, and Passivity in Electrical Interconnect Models

Modern packaging design requires extensive signal integrity simulations in order to assess the electrical performance of the system. The feasibility of such simulations is granted only when accurate and efficient models are available for all system parts and components having a significant influence on the signals. Unfortunately, model derivation is still a challenging task, despite the extensive research that has been devoted to this topic. In fact, it is a common experience that modeling or simulation tasks sometimes fail, often without a clear understanding of the main reason. This paper presents the fundamental properties of causality, stability, and passivity that electrical interconnect models must satisfy in order to be physically consistent. All basic definitions are reviewed in time domain, Laplace domain, and frequency domain, and all significant interrelations between these properties are outlined. This background material is used to interpret several common situations where either model derivation or model use in a computer-aided design environment fails dramatically. We show that the root cause for these difficulties can always be traced back to the lack of stability, causality, or passivity in the data providing the structure characterization and/or in the model itself.

A fast algorithm and practical considerations for passive macromodeling of measured/simulated data

Passive macromodeling of high-speed package and interconnect modules characterized by simulated/measured data has generated immense interest during the recent years. This paper presents a fast algorithm for generating passive macro-models for simulated/measured data, based on linear formulation. New constraints are proposed to quickly generate passive macromodels. Examples are presented to demonstrate the validity and efficiency of the proposed algorithm.

Global passivity enforcement algorithm for macromodels of interconnect subnetworks characterized by tabulated data

With the continually increasing operating frequencies, complex high-speed interconnect and package modules require characterization based on measured/simulated data. Several algorithms were recently suggested for macromodeling such types of data to enable unified transient analysis in the presence of external network elements. One of the critical issues involved here is the passivity violations associated with the computed macromodel. To address this issue, a new passivity enforcement algorithm is presented in this paper. The proposed method adopts a global approach for passivity enforcement by ensuring that the passivity correction at a certain region does not introduce new passivity violations at other parts of the frequency spectrum. It also provides an error estimate for the response of the passivity corrected macromodel.

A general class of passive macromodels for lossy multiconductor transmission lines

This paper presents a general class of passive macromodeling algorithm for multiport distributed interconnects. A new theorem is described that specifies sufficient conditions for matrix-rational approximation of exponential functions in order to generate a passive macromodel. A proof is given showing that the currently existing passive matrix-rational approximation of exponential functions is a subclass of the generic approach presented in this paper. In addition, a technique to obtain a compact passive macromodel with predetermined coefficients, based on near-optimal approximation, is presented. The proposed model can be easily incorporated with recently developed passive model-reduction techniques.

Efficient passive circuit models for distributed networks with frequency-dependent parameters

This paper presents an efficient method for the analysis of multiconductor transmission lines with frequency-dependent parameters. The proposed technique generates positive-real representations for the frequency dependency of transmission line parameters as well as closed-form expressions based on exponential Pade approximants. The new model is suitable for inclusion in general purpose circuit simulators and overcomes the difficulty of mixed frequency/time simulation encountered during transient analysis. In addition, the proposed model can be easily incorporated with the recently developed passive model-reduction techniques. Numerical examples are presented to demonstrate the validity and efficiency of the proposed method.

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

Passive interconnect reduction algorithm for distributed/measured networks

This paper presents an efficient algorithm for the transient simulation of multiport distributed interconnect networks in the presence of nonlinear subcircuits. The proposed multilevel multipoint model-reduction algorithm combines the merits of recently proposed Krylov-space techniques and block complex frequency-hopping to generate compact time-domain macromodels. The method overcomes the difficulty of slower transient simulation caused by redundant poles in reduced-order models obtained by Krylov-space methods. Also, it provides an efficient means to translate Krylov-space-based reduced models of distributed/measured networks with frequency-dependent descriptions into time-domain macromodels. In addition, a strategy to preserve the passivity of macromodels during multilevel reduction is presented. An important advantage of the proposed algorithm is that it can directly handle distributed stamps such as transmission lines described by Telegraphers equations, frequency-dependent parameters, full-wave, and measured subnetworks.

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.

Circuit analysis of electromagnetic radiation and field coupling effects for networks with embedded full-wave modules

With continually increasing operating frequencies, the analysis of electromagnetic interference (EMI)-related effects is becoming an important issue for high-speed designs. An algorithm is presented for fast analysis of radiation and incident field coupling effects in high-speed circuits. The proposed technique provides an efficient means for combining the solutions from full-wave field solvers such as the finite-difference time-domain (FDTD) method with circuit level simulators such as SPICE for calculating radiated/coupled fields in arbitrarily shaped interconnect structures. The technique speeds up the whole simulation process by employing a model-reduction-based approach, and also overcomes the numerical stability problems associated with the FDTD, in the presence of nonlinear terminations. In addition, the proposed algorithm provides a direct access to existing vast device libraries of SPICE in EMI analysis.