Wendemagegnehu T. Beyene

Accurate frequency-domain modeling and efficient circuit simulation of high-speed packaging interconnects

The paper describes an efficient frequency-domain modeling and simulation method of a coupled interconnect system using scattering parameters. First, low-order rational approximations of the multiport scattering parameters are derived over a wide frequency range using a robust interpolation technique. The method applies frequency normalization, shift, and Householder QR orthogonalization to improve the stability and the accuracy when solving the resulting systems of equations. For interconnects characterized with frequency-dependent parasitic parameters, the order of the rational of approximation is reduced by using appropriate reference system. Then, the generated multiport pole-residue models are incorporated into a circuit simulator using recursive convolution. Thus, the method avoids explicit convolution, numerical transform, and artificial filtering of a large number of points that are often necessary in conventional approaches. Examples with experimental and simulated results are given to illustrate the method.

Modeling and analysis of power distribution networks for Gigabit applications

As the operating frequency of digital systems increases and voltage swing decreases, it becomes very important to characterize and analyze power distribution networks (PDNs) accurately. This paper presents the modeling, simulation, and characterization of the PDN in a high-speed printed circuit board (PCB) designed for chip-to-chip communication at a data rate of 3.2 Gbps. The test board consists of transmitter and receiver chips wirebonded onto plastic ball grid array (PGBA) packages on a PCB. In this paper, a hybrid method has been applied for analysis, which consists of the transmission matrix method (TMM) in the frequency domain and macromodeling method in the time domain. As an initial step, power/ground planes have been modeled using TMM. Then, the macromodel of the power/ground planes has been generated at the desired ports using macromodeling. Finally, the macromodel of the planes, transmission lines, and nonlinear drivers have been simulated in standard SPICE-based circuit simulators for computing power supply noise. In addition to noise computation, the self and transfer impedances of power/ground planes have been computed and the effect of decoupling capacitors on power supply noise has been analyzed. The methods discussed have been validated using hardware measurements.

Black-box modeling of passive systems by rational function approximation

In this paper, a rational interpolation approach is used to approximate the transfer function of passive systems characterized by sampled data. Orthogonal polynomials are used to improve the numerical stability of the ill-conditioned Vandermonde-like interpolation matrix associated with the ordinary power series. First, the poles of the system are obtained by efficiently and accurately transforming the coefficients of the orthogonal polynomials to the ordinary power series using Clenshaws recurrence algorithm. Then, the residues are solved in real or in complex conjugate pairs to insure a physically realizable system. Finally, the passivity of the system is enforced by applying certain constraints on the poles and residues of the system. The performances of the three most common orthogonal polynomials, Legendre and Chebyshev of the first and second kinds, are also compared to that of the power series.

Advanced Modeling and Accurate Characterization of a 16 Gb/s Memory Interface

As the input/output (I/O) data rate increases to several gigabits per second, determining the performance of high-speed interfaces using conventional simulation and measurement techniques is becoming very challenging. The models of the interconnects have to be broadband and accurate to represent high frequency and second-order effects such as frequency dependence of dielectric losses and surface roughness. The large and small signal behaviors of the transmitter and receiver circuitries have to be correctly represented in link analysis. In addition, the system simulation needs to properly capture the interactions between the circuits and interconnect subsystems to optimize the overall system. However, determining the values of the critical link parameters and their correlations can be complicated. Some of the key parameters are not deterministic and some cannot be observed directly. A combined modeling and measurement approach is indispensable to determine the performance of high-speed links. This paper presents the modeling and characterization techniques employed in the design and verification of a 16 Gb/s bidirectional asymmetrical memory interface. Direct frequency and time-domain methods as well as indirect techniques based on bit-error-rate testing are used to model and determine important link parameters. Complex de-embedding procedures are utilized to extract parameters from externally observed data. On-chip measurements are also used to complement off-chip instrumentation and accurately measure the true performance of the link. The modeling and characterization of prototypes are also discussed and model-to-hardware correlations are presented at component and system levels. Based on both simulation and measurement results, the behavioral model of the complete system is constructed and statistical simulation technique is used to predict the yield and performance at low bit error rate.

Modeling and analysis of power distribution networks for gigabit applications

As the operating frequency of digital systems increases and voltage swing decreases, it becomes increasingly important to accurately characterize and analyze power distribution networks (PDN). This paper presents the modeling, simulation, and measurement of a PDN in a high-speed FR4 printed circuit board (PCB) designed for chip-to-chip communication at a data rate of 3.2 Gbps and above. The test board consists of two transceiver chips placed on wire bond plastic ball grid array (PBGA) packages. The applied analysis method is a hybrid technique that combines the interactions of the power planes, interconnects, and the nonlinear drivers. The power planes and interconnects are modeled using the transmission matrix method (TMM) and rational interpolation, respectively. Then macro modeling is applied to generate reduced-order models to efficiently analyze the whole system including the nonlinear drivers using conventional circuit simulation tools such as SPICE. The transfer characteristics of the power planes are calculated and the effects of the decoupling capacitors and power supply noise are studied. The simulation results are also correlated with measurement data to verify the validity of the method.

Design and verification of differential transmission lines

Differential signaling is a popular choice for multi-gigabit digital applications such as FiberChannel, Infiniband, OIF, RapidIO, and XAUI. This is due to the fact that differential signaling has the ability to reject common mode noise such as cross talk, simultaneous switching noise, power supply and ground bounce noise. To support differential signaling, differential transmission lines are required. There are several ways of designing differential transmission lines on a conventional printed circuit board (PCB). These include microstrip line, edge coupled stripline, and broadside-coupled stripline. This paper describes a methodology for designing and verifying differential transmission lines on PCBs. The electrical performance of these three differential transmission lines is evaluated in both the frequency and time domain. The practical consideration of manufacturing variation is also examined. Finally, accurate HSPICE w-element models are generated for time domain transient simulations.

The design of continuous-time linear equalizers using model order reduction techniques

The peaking gain and the peaking frequency of a continuous-time linear equalizer (CTLE) are considered key design parameters to improve link performance. Many high-speed signaling standards define peaking gain as specification of the transmitter or receiver equalizer to achieve their target data rates. Peaking gain and frequency aside, the zeros play a major role in shaping the frequency response of the CTLE. These zeros closely relate to the poles of the channel to be equalized; thus their locations need to be selected with care when optimizing CTLE parameters. This paper describes a non-iterative method of selecting the equalizer parameters by first matching the frequency response of the CTLE to the inverse loss profile of the channel. The approach uses model order reduction (MOR) techniques to determine the zeros of the CTLE from the channel characteristics.

Application of Artificial Neural Networks to Statistical Analysis and Nonlinear Modeling of High-Speed Interconnect Systems

In designing robust high-speed interconnect systems, the effects of parameter variations on system performance must be studied using statistical analyses. These analyses require repetitive circuit simulations to account for the randomness in parameter values caused by manufacturing and environmental changes. An accurate modeling technique is also essential for capturing the nonlinear relationships between channel parameters and performance. In this paper, the application of artificial neural networks to accurately capture the nonlinear mappings between parameters and performance to speed up the analysis of high-speed interconnect systems is described. An efficient set of data that uses a few simulations or experiments based on orthogonal arrays is proposed to train the neural network. The neural network can then serve to accurately and efficiently generate performance distributions. The usefulness and accuracy of the proposed approach is verified using an extreme data rate memory system that operates at a data rate of 3.2 Gb/s. The histograms and descriptive statistics of the eye height and timing jitter are compared with those obtained from traditional Monte Carlo, regression model, and worst case analyses

An Accurate Transient Analysis of High-Speed Package Interconnects Using Convolution Technique

An accurate transient analysis of a package interconnect requires the modeling and analysis of conductor and dielectric losses, as well as other high-frequency effects of 3D structures. The skin effect and dispersion of interconnects are more accurately modeled in frequency domain. Consequently, an accurate time-domain simulation of such a system is only possible using convolution techniques. Although the convolution method is well understood, the application of windowing for frequency-dependent interconnect analysis is less so. In this paper, we present the practical considerations of window selection and its application to improve the accuracy of convolution simulators. We introduce the Tukey window and study the tradeoff between how smoothly data can be set to zero to avoid aliasing and suppress ripples and how much information tapering will discount at the edge of the window in order to obtain meaningful results. The bandlimiting effects of the Tukey window and other well-known windows are also compared. Finally, to verify the validity and accuracy of the proposed method, a wirebond PBGA package and a PCB-connector system are analyzed using the scattering parameters obtained from simulation and measurement, respectively.

Applications of Multilinear and Waveform Relaxation Methods for Efficient Simulation of Interconnect-Dominated Nonlinear Networks

Applications of multilinear and waveform relaxation methods are presented for efficient transient analysis of interconnect-dominated nonlinear networks. In this paper, two procedures that realize these well-known and fundamental theories in conventional circuit simulation tools are developed by taking advantage of the unique characteristics of interconnect networks. The multilinear theory uses the Volterra functional series to decompose the nonlinear network into multiple linear networks. Then, the solutions of the mildly nonlinear network are obtained from the linear combinations of sequences of responses of the decomposed linear networks. On the other hand, the waveform relaxation technique is used to solve networks with strong nonlinearity. The networks are partitioned into linear and nonlinear subnetworks and each subnetwork is solved iteratively using the waveform relaxation technique. Simplified analysis steps that give good insight into these techniques are also derived analytically. Finally, the accuracy and efficiency of the methods are verified with two examples.