In this article, a numerical inverse Laplace transform (NILT)-based algorithm is used to efficiently approximate key characteristics of coupled high-speed VLSI interconnects, such as 50% delay, overshoot, and peak crosstalk. Through the use of a variable (LC or RC) modal decoupling technique, matrix inversion at each time point and pole of the numerical inverse Laplace formula is computed on a diagonal matrix, allowing for minimal computation times at the cost of a slight reduction in accuracy. The proposed methodology independently solves the modal voltage response at each time point, pole, and line allowing for parallel computation resulting in further speed up. In addition, the order of the NILT approximation can be modified depending on the speed and accuracy needed. Four numerical examples of coupled interconnects are presented to evaluate the accuracy and computational efficiency of the proposed methodology. Overall, the NILT-based algorithm provides useful approximations of the time-domain response, while being significantly faster than SPICE.

Dissipative impedance coupling is introduced in the waveform relaxation algorithm with longitudinal partitioning to address the slow convergence of standard resistive coupling in the analysis of low-loss highly reactive circuits. The pertinence, feasibility, and consistency of the proposed WR algorithm are demonstrated. Its convergence is examined for any passive linear time-invariant (LTI) system. Rational-with-delay impedances are presented to decouple general transmission line circuits. The proposed coupling strategy uses coarse macromodeling of the transmission lines to construct the coupling impedances directly as passive distributed auxiliary circuits. Numerical examples show a superior speed of convergence and further runtime savings.

The convergence of the waveform relaxation (WR) method is demonstrated for a class of circuits: Chains of identical and symmetrical passive subcircuits. The WR algorithm uses resistive coupling to implement the iteration. Every part is modeled as a symmetric and reciprocal linear two-port network. The iteration matrices of the WR operator are constructed for the Gauss-Jacobi and Gauss-Seidel relaxations in the Fourier domain. An upperbound estimate of the spectral radius of the WR operator is presented. It demonstrates the convergence of the method independently of the number of cascaded parts in the chain and the coupling resistance.

While achieving localization using wireless networks, the positioning accuracy of a target device is highly sensitive to the placement of reference nodes. As a result, an in-depth analysis on the optimal placement of reference nodes is extremely useful in order to improve deployment outcome. In this paper, we propose an optimum reference node deployment scheme for Time of Arrival (TOA)-based localization by minimizing the Cramer-Rao Bound (CRB) of localization error. In order to find the global minima of the CRB which is highly nonlinear, a novel method is developed to solve the corresponding optimization problem. The essence of our method is to express the CRB in complex coordinates, and then to minimize the CRB with respect to the angles of reference nodes. The mathematical solution provides an interesting result indicating that the highest localization accuracy is achieved when the reference nodes have uniform angular distribution around the service area where the target is expected. We compare several different reference node deployment schemes through simulations, and the results show our derived optimum deployment provides the best performance.

Received Signal Strength (RSS)-based ranging techniques have recently attracted a lot of attention because of their advantages in terms of low cost and easy implementation. The received signal strength highly depends on the path loss effect of radio wave propagation. When there is obstruction between transmitter and receiver, the signal power can drop significantly on the corresponding obstructed link, which degrades the accuracy of distance estimation. In this paper, we propose a novel RSS-based localization algorithm in obstructed environments with unknown Path Loss Exponent (PLE) based on Maximum Likelihood Estimation (MLE). The proposed algorithm can automatically detect the obstructed links between transmitter and receiver, and reduce the localization error caused by obstruction effect. According to the simulation results, our proposed method shows higher localization accuracy in obstructed environments as compared to other existing schemes.

This paper presents a numerical convolution based approach for transient simulation of distributed networks characterized by band limited frequency domain data when terminated with arbitrary nonlinear circuits. The proposed algorithm uses time-frequency decompositions to extract multiple propagation delays of a distributed network and the associated attenuation losses in a piecewise manner, and implements inverse fast Fourier transform to efficiently convert the frequency response into a sum of delayed time domain responses. Numerical examples illustrate that the proposed algorithm shows significantly more accurate results for networks with multiple long delays when compared to existing numerical convolution techniques.

This paper presents a delay and crosstalk noise model for coupled resistance-inductance-capacitance (RLC) on-chip interconnects. The proposed algorithm, based on a modified Lie formula, is used to convert the solution of the transmission line network into delay algebraic equations to obtain the time domain response. The proposed algorithm is not limited to fixed number of coupled RLC lines or to specific topologies and can be used to model both identical and nonidentical multiconductor lines and loads. For the example presented in this paper, the 50% delay and crosstalk using the proposed method agrees with SPICE results to within 0.75% average error.

This paper describes an efficient approach for time domain sensitivity analysis of lossy high speed interconnects in the presence of nonlinear terminations. The sensitivity information is derived using the recently developed passive method of characteristics. An important feature of the proposed method is that the sensitivities are obtained from the solution of the original network, leading to significant computational advantages. Numerical examples are presented to illustrate the validity of the proposed approach.

In this paper, a closed-form matrix rational-approximation algorithm is proposed to efficiently model the delay and crosstalk noise of coupled RLC on-chip interconnects. A key feature of the proposed algorithm is that, for any rational order, the approximation is obtained analytically in terms of predetermined coefficients and the per-unit-length parameters. As a result, the proposed method is not limited to fixed number of poles and provides a mechanism to increase the accuracy for cases when inductive effects are significant, the length of the line increases, or when the rise time of the signal becomes sharper. An error criterion is provided to select the order of approximation. The algorithm is tested for various single- and coupled-interconnect scenarios. The 50% delay and overshoot results match that of SPICE with less than 2% average error. The crosstalk results also accurately match those of SPICE with less than 4% average error.

This paper presents an automatic, multidimensional Krylov subspace based approach to developing macromodels for nonlinear distributed interconnect networks. The approach avoids the need for extra ports due to nonlinear elements by introducing constraint equations to link the nonlinear and linear portions of the network. Numerical examples have been included to demonstrate the efficiency of the presented algorithm with respect to two metrics: computational cost and the size of the system that will be simulated.

This paper presents an efficient passive macro-modeling algorithm for distributed lossy transmission lines based on method of characteristics (MoC). A new theorem is described that specifies sufficient conditions to guarantee the passivity of the MoC macromodel by construction

In this paper, a novel passive reduced-order macro-modeling algorithm is proposed for structure dynamics in MEMS systems that are described by discrete models through the use of finite element methods (FEM). In the proposed scheme, the system of equations given by the FEM formulation are converted to state-space form such that the state-space equations are compatible with passive Krylov subspace methods based on congruent transformations. As an example, modeling, simulation, and experimental studies are presented for a Butterfly gyro developed at the Imego Institute. Our simulation results for this example are in very good agreement with previous publications using traditional modeling techniques

Time-domain macromodeling of high speed interconnects characterized by distributed transmission lines has generated immense interest during the recent years. It has been demonstrated that, preserving passivity of the macromodel is essential to guarantee a stable global transient simulation. In this paper, a SPICE compatible closed-form passive macromodel for distributed transmission lines is presented. The proposed method enables representation of the distributed stamp in terms of simple delay and resistive elements. The new method while guaranteeing the passivity of the macromodel, provides significant speedup, and enables easy implementation. Necessary formulation and validation examples are given.

Signal integrity analysis has become imperative for high-speed designs. In this paper, we present a new technique to advance Krylov-space based passive model-reduction algorithms to include lossy coupled transmission lines described by Telegrapher's equations. In the proposed scheme, transmission line subnetworks are treated with closed-form stamps obtained using matrix-exponential Padé, where the coefficients describing the model are computed a priori and analytically. In addition, a technique is given to ensure that the contribution of these stamps to the modified nodal analysis (MNA) formulation leads to guaranteed passive macromodel.