Herng-Jer Lee

Moment computations of nonuniform distributed coupled RLC trees with applications to estimating crosstalk noise

A novel method is proposed to compute moments of nonuniform distributed coupled RLC transmission lines. Recursive formulae of moments of coupled RC trees are extended to those of coupled RLC trees by considering both self inductances and mutual inductances. It can be observed that moment computations of distributed lines outperform those of lumped ones. The inductive crosstalk noise waveform can be accurately and efficiently estimated using the moment computation technique in conjunction with the projection-based order reduction method. Fundamental developments of the proposed approach are described in detail. Experimental results demonstrate the improved accuracy of the proposed method over that of the traditional lumped methods.

Multi-point model reductions of VLSI interconnects using the rational Arnoldi method with adaptive orders (RAMAO)

This work proposes the rational Arnoldi method with adaptive orders for high-speed VLSI interconnect reductions. It is based on an extension of the classical multi-point Pade approximation by using the rational Arnoldi iteration approach. Given a set of expansion points, the transfer function error at each expansion point is derived first. In each iteration of the proposed algorithm, the expansion frequency corresponding to the maximum output moment error is chosen. The corresponding reduced-order model yields the greatest output moment improvement.

Interconnect modeling and sensitivity analysis using adjoint networks reduction technique

An efficient model-order reduction technique for general RLC networks is proposed. The method is extended from the previous projection-base moment matching method by considering both the circuit network and its corresponding adjoint network. By exploring the symmetry properties of the MNA formulation, the proposed method needs only one half of the system moment information compared with previous ones. The passivity of the reduced-order model is still preserved. The relationship between the adjoint network and sensitivity analysis is also discussed. Experimental results demonstrate the accuracy and the efficiency of the method.

Applications of tree/link partitioning for moment computations of general lumped RLC networks with resistor loops

A new moment computation technique for general lumped circuits with resistor loops is proposed. Using the concept of tearing, a lumped network can be portioned into a spanning tree and several resistor links. The contributions of network moments from each tree and the corresponding links can be determined independently. By combining the conventional moment computation algorithms and the reduced ordered binary decision diagram (ROBDD), the proposed method can compute system moments efficiently.

Moment computations for R(L)C interconnects with multiple resistor loops using ROBDD techniques

A new moment computation technique for general lumped R(L)C interconnect circuits with multiple resistor loops is proposed. Using the concept of tearing, a lumped R(L)C network can be partitioned into a spanning tree and several resistor links. The contributions of network moments from each tree and the corresponding links can be determined independently. By combining the conventional moment computation algorithms and the reduced ordered binary decision diagram (ROBDD), the proposed method can compute system moments efficiently

Generalizations of adjoint networks technique for RLC interconnects model-order reductions

The adjoint network reduction technique has been shown to reduce 50% of the computational complexity of constructing the congruence transformation matrix. The method was suitable for analyzing the special multi-port driving-point impedance of RLC interconnect circuits. This paper extends this technique for the general circumstance of RLC interconnects. Comparative studies among the conventional methods and the proposed method are also investigated. Experimental results demonstrate the accuracy and efficiency of the proposal method.

Crosstalk estimation in high-speed VLSI interconnect using coupled RLC-tree models

A comprehensive crosstalk estimation method, using coupled RLC-tree models, in high-speed VLSI interconnects is provided. Based on recursive formulas for the moment computations of RLC-tree models, and a general reduced-order model to approximate the waveform of coupling noise, the waveform can be accurately estimated. The influences of inductance effects on crosstalk can be truly captured by our crosstalk-metric models. Fundamental developments of the proposed method are described in detail. Experimental results show the improved accuracy of the proposed method.

Interconnect model reductions by using the AORA algorithm with considering the adjoint network

This work proposes a hybrid method for interconnect model-order reductions. First, the adaptive-order rational Arnoldi (AORA) method is investigated. An extension of the classical multi-point Pade approximation by using the rational Arnoldi iteration approach are studied. The adaptive-order can be achieved by choosing the expansion frequency corresponding to the maximum output moment error. Secondly, the adjoint network technique is studied. By exploring symmetric properties of the MNA formulation, the computational cost of constructing the congruence transformation matrix can be reduced by 50% compared with the conventional methods.

Moment Computations of Distributed Coupled RLC Interconnects with Applications to Estimating Crosstalk Noise

A method is proposed to compute moments of distributed coupled RLC interconnects. Both uniform line models and non-uniform line models will be developed. Considering both self inductances and mutual inductances in multi-conductors, recursive moment computations formulae of lumped coupled RLC interconnects are extended to those of distributed coupled RLC interconnects. By using the moment computation technique in conjunction with the projection-based order reduction method, the inductive crosstalk noise waveform can be accurately and efficiently estimated. Fundamental developments of the proposed approach will be described. Simulation results demonstrate the improved accuracy of the proposed method over the traditional lumped methods.

Error estimations of projection-based interconnect model-order reduction techniques

Projection-based model reductions become a necessity for efficient interconnect simulations. In order to choose the order of the reduced system that can really reflect the essential dynamics of the original interconnect, the residual error of the transfer function is considered as a stopping criteria. Analytical expressions of this residual error are derived analytically. This approximate transfer function can also be expressed as the original interconnect model with some additive perturbations. These error information provides a guideline for the order selection scheme.