An efficient reciprocity and passivity preserving balanced truncation for RLC networks is presented in this paper. Reciprocity and passivity are fundamental principles of linear passive networks. Hence, reduction with preservation of reciprocity and passivity is necessary to simulate behavior of the circuits including the RLC networks accurately and stably. Moreover, the proposed method is more efficient than the previous balanced truncation methods, because sparsity patterns of the coefficient matrices for the circuit equations of the RLC networks are fully available. In the illustrative examples, we will show that the proposed method is compatible with PRIMA, which is known as a general reduction method of RLC networks, in efficiency and used memory, and is more accurate at high frequencies than PRIMA.

An efficient balanced truncation for RC and RLC networks is presented in this paper. To accelerate the balanced truncation, sparse structures of original networks are considered. As a result, Lyapunov equations, the solutions of which are necessary for making the transformation matrices, are efficiently solved, and the reduced order models are efficiently obtained. It is proven that reciprocity of original networks is preserved while applying the proposed method. Passivity of the reduced RC networks is also guaranteed. In the illustrative examples, we will show that the proposed method is compatible with PRIMA in efficiency and is more accurate than PRIMA.

In this paper, we present a novel analysis approach for large on-chip power grid circuit analysis. The new approach, called ETBR for extended truncated balanced realization, is based on model order reduction techniques to reduce the circuit matrices before the simulation. Different from the (improved) extended Krylov subspace methods EKS/IEKS, ETBR performs fast truncated balanced realization on response Gramian to reduce the original system. ETBR also avoids the adverse explicit moment representation of the input signals. Instead, it uses spectrum representation in frequency domain for input signals by fast Fourier transformation. The proposed method is very amenable for threading-based parallel computing, as the response Gramian is computed in a Monte-Carlo-like sampling style and each sampling can be computed in parallel. This contrasts with all the Krylov subspace based methods like the EKS method, where moments have to be computed in a sequential order. ETBR is also more flexible for different types of input sources and can better capture the high frequency contents than EKS, and this leads to more accurate results especially for fast changing input signals. Experimental results on a number of large networks (up to one million nodes) show that, given the same order of the reduced model, ETBR is indeed more accurate than the EKS method especially for input sources rich in high-frequency components. If parallel computing is explored, ETBR can be an order of magnitude faster than the EKS/IEKS method.

As we scale toward nanometer technologies, the increase in interconnect parameter variations will bring significant performance variability. New design methodologies will emerge to facilitate construction of reliable systems from unreliable nanometer scale components. Such methodologies require new performance models which accurately capture the manufacturing realities. In this paper, we present a Linear Fractional Transform (LFT) based model for interconnect parametric uncertainty. The new model formulates the interconnect parametric uncertainty as a repeated scalar uncertainty structure. With the help of generalized Balanced Truncation Realization (BTR) and Linear Matrix Inequalities (LMI's), the porposed model reduces the order of the original interconnect network while preserves the stability. The LFT based new model even guarantees passivity if the BTR reduction is based on solutions to a pair of Linear Matrix Inequalities (LMI's) generated from Lur'e equations. In case of large number of uncertain parameters, the new model may be applied successively: the uncertain parameters are partitioned into groups, and with regard to each group, LFT based model is applied in turns.

The passive and sparse reduced-order modeling of a RLC network is presented, where eigenvalues and eigenvectors of the original network are used, and thus the obtained macromodel is more accurate than that provided by the Krylov subspace methods or TBR procedures for a class of circuits. Furthermore, the proposed method is applied to low pass filtering of a reduced-order model produced by these methods without breaking the passivity condition. Therefore, the proposed eigenspace method is not only a reduced-order macromodeling method, but also is embedded in other methods enhancing their performances.

This paper describes the matrix order reduction method by the nodal analysis formulation and the application of relaxation-based simulation technique to interconnect and plane networks. First, the characteristics of the power/ground plane networks are considered. Next, the formulation of the plane network by nodal analysis (NA) method is suggested. Furthermore, application and estimation results of the relaxation-based numerical analyses are shown. Finally, it is confirmed that the relaxation-based methods improved by the suggested formulation are much more efficient than the conventional direct-based methods.

We present theoretical foundations about error estimations of the global Krylov subspace techniques for multiple-inputs multiple-outputs (MIMO) Interconnect reductions. Analytical relationships between Lyapunov functions of the original interconnect network and those of the reduced system generated by the global Arnoldi algorithm will be developed. Under this framework, a new moment matching reduced network is proposed. Also, we will show that the reduced system can be expressed as the original network with some additive perturbations.

Two versions of Krylov subspace order reduction techniques for VLSI interconnect reductions, including structure preserving reductions approach and adjoint networks approach, will be comparatively investigated. Also, we will propose a modified structure preserving reduction algorithm to speed up the projection construction in a linear order. The numerical experiment shows the high accuracy and low computational consumption of the modified method. In addition, it will be shown that the projection subspace generated from the structure-preserving approach and those from the adjoint networks approach are equivalent. Therefore, transfer functions of both reduced networks are identical.

This paper presents a methodology based on congruent transformation for distributed interconnects described by state-space time-delays system. The proposed approach is to obtain the passive reduced order of linear time-delays system. The unified formulations are used to satisfy the passive preservation. The details of the mathematical proof and a couple of validation examples are given in this paper.

The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments are still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, two novel model-order reduction techniques called the multiple point global Lanczos (MPGL) method and the adaptive-order global Lanczos (AOGL) method which are both based on the multiple point moment matching are proposed. The frequency responses using the multiple point moment matching method have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on frequency domain will illustrate the feasibility and the efficiency of the proposed methods.

This work proposes a new method for RLCG interconnect model-order reductions in consideration with the adjoint network. Relationships between an original MNA network and its corresponding adjoint MNA network will be explored first. It will be shown that the congruence transformation matrix used in the one-sided projection can be constructed by using the bi-orthogonal bases developed from the Lanczos-type algorithms. In particular, if the multi-port driving-point impedance of RLCG interconnect circuits is the main concern, the transfer functions and system moments of the adjoint network can be directly calculated from those of the original RLCG interconnect network by exploring symmetric properties of the MNA formulation. Therefore, the cost of constructing the congruence transformation matrix can be simplified by up to 50% of the previous methods. Comparative studies among various standard methods and the proposed methods are also investigated. Experimental results on large-scale RLCG interconnect circuits will demonstrate the accuracy and the efficiency of the proposed method.

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.

A new hybrid method for characterizing the irregular power/ground plane pair is developed in this paper by combining the conventional eigen-mode expansion method with the new-presented inverted composition method and a simple model order reduction. By the approach, the eigen-mode expansion method can be extended to the characteristics research of the power/ground plane pair with holes. In this gridless method, ports and decoupling capacitors can be arbitrarily placed on the plane pair. The numerical example demonstrates its good validity.

This paper presents the improvement of the transient response and stability for a two-stage DC-DC converter by removing the output inductor. The conventional two-stage converter consists of a buck converter used as the first stage and a half-bridge converter used as the second stage. The proposed circuit topology removing the output inductor and the conventional topology are compared. Removing the output inductor results in the system-order reduction of the transfer function. As a result, the stability is improved, and the crossover frequency of the open-loop transfer function becomes higher. The effectiveness of the proposed circuit topology was experimentally confirmed.

This paper describes an efficient method for the macromodel generation of hybrid systems which are composed of electromagnetic systems and lumped RLC circuits. In our method, electromagnetic systems are formulated as finite-difference frequency-domain (FDFD) equations, and RLC circuits are formulated as nodal equations. Therefore, unlike the partial-element equivalent-circuit (PEEC) method, the technique presented here does not need any 3-dimensional capacitance and inductance parameter extractions to model interconnects, LSI packages and printed circuit boards. Also the lumped RLC elements can be easily included in the hybrid system of equations, thus it is convenient to model some passive components, such as bypass capacitors. The model order reduction technique is utilized in order to construct macromodels from hybrid system of equations. The accuracy of the proposed method is substantiated with some numerical examples.

A high power dissipation density in today's miniature electronic/mechanical systems makes on-chip thermal management very important. In order to achieve quick to evaluate, yet accurate electro-thermal models, needed for the thermal management of microsystems, a model order reduction is necessary. In this paper, we present an automatic, Krylov-subspace-based order reduction of a electro-thermal model, which we illustrate by a novel type of micropropulsion device. Numerical simulation results of the full finite element model and the reduced order model, that describes the transient electro-thermal behavior, are presented. A comparison between Krylov-subspace-based order reduction, order reduction using control theoretical approaches and commercially available reduced order modeling has been performed. A Single-Input-Single-Output setup for the Arnoldi reduction algorithm was proved to be sufficient to accurately represent the complete time-dependent temperature distribution of the device.

This paper develops a modular synthesis algorithm for timed circuits that is dramatically accelerated by partial order reduction. This algorithm synthesizes each module in a hierarchical design individually. It utilizes partial order reduction to reduce the state space explored for the other modules by considering a single interleaving of concurrently enabled transitions. This approach better manages the state explosion problem resulting in a more than 2 order of magnitude reduction in synthesis time. The improved synthesis time enables the synthesis of a larger class of timed circuits than was previously possible.

The interconnect analysis of on- and off-chips is very important in the design of high-speed signal processing, digital communication, and microwave electronic systems. When the interconnects are characterized by sampled data via electromagnetic analysis, the circuit-level simulation of the network requires rational approximation of the sampled data. Since the frequency band of the sampled data is more than 10 GHz, the rational function must fit into it at many frequency points. The rational function is approximated using the orthogonal least-squares method. With an increase in the number of the fitting data, the least-squares method suffers from a singularity problem. To avoid this, the sampled data are hierarchically approximated in this paper. Moreover, to reduce the computational cost of the circuit-level simulation, the parameter matrix of the interconnects is approximated by a rational matrix with one common denominator polynomial, and the selective orthogonalization procedure is presented.

In order to reduce state explosion problem, techniques such as symbolic state space traversal and partial order reduction have been proposed. Combining these two techniques, however, seems difficult, and only a few research projects related to this topic have been reported. In this paper, we propose handling single place zero reachability problem of Petri nets by using both partial order reduction and symbolic state space traversal based on ZBDDs. We also show experimental results of several examples.

A new numerical technique, termed the method of matrix-order reduction (MMOR), is developed for handling electromagnetic problems in this paper, in which the matrix equation resulted from a method-of-moments analysis is converted either to an eigenvalue equation or to another matrix equation with the matrix order in both cases being much reduced, and also, the accuracy of solution obtained by solving either of above equations is improved by means of a newly proposed generalized Jacobian iteration. As a result, this technique enjoys the advantages of less computational expenses and a relatively good solution accuracy as well. To testify this new technique, a number of wire antennas are examined and the calculated results are compared with those obtained by using the method of moments.