Parametric Order Reduction of Nonuniform Interconnect Circuits Using Integrated Congruence Transform

A parameterized model-order reduction algorithm for nonuniform high-speed interconnect with varying design parameters is presented. The constructed reduced-order model (ROM) has a direct time-domain representation, and thus, discretization techniques are not required. The key idea of the new algorithm is to find a common-projection matrix using the integrated-congruence transform (ICT) method that can be used to construct an ROM for any value of the varying parameters. However, the calculated projection matrices using the ICT method are functions of the position along the lines, and thus, finding a common-projection matrix using regular singular-value decomposition (SVD) is not applicable. To address this issue, a Hilbert-space-based SVD is proposed to extract the common-projection matrix

Parallel High-Order Envelope-Following Method for Fast Transient Analysis of Highly Oscillatory Circuits

In this paper, a parallel high-order envelope-following (EF) method is presented. The proposed method exploits the high-order and $A$-stable Obreshkov formula (ObF) to provide superior accuracy and speedup for the EF technique. Utilizing ObF provides accurate and faster analysis while keeping the same accuracy as the conventional low-order integration methods. In addition, a parallel method that is based on multiple-shooting (MS) techniques is used. Using MS allows partitioning and solving the sensitivity equations in parallel. It is also shown that with proper partitioning scheme, high CPU scalability can be achieved

Fast simulation of microwave circuits with nonlinear terminations using high-order stable methods

This paper describes a new method for transient simulation, using high-order stable methods, of microwave structures modeled using a large number of lumped components. The target of the proposed technique is circuit-based simulation of the large linear circuits that arise from full-wave modeling of distributed structures, such as transmission lines and microstrip elements, along with the terminating nonlinear devices. In this case, the cost of the solution of the linear system typically dominates the computational effort. The proposed method takes advantage of the special structure of the block matrices in these applications to reduce the computational cost significantly. The core of the proposed algorithm is based on the idea of 'node tearing' to separate the large linear sub-circuits from the nonlinear devices. This idea faciliates handling the linear sub-circuits using a better matrix factorization technique, resulting in faster simulations compared to classical techniques

Parallel simulation of large linear circuits with nonlinear terminations using high-order stable methods

To meet the growing demand for efficient circuit simulation tools, Obreshkov formula (ObF)-based high-order integration methods were recently proposed. However, one of the challenges in this method is the growing computational cost of the solution at a particular time point with the increasing orders of the ObF. To address this issue and target high-speed circuits with large linear blocks and nonlinear loads, a new parallel framework is proposed in this paper to minimize the CPU time associated with the solution at any time point. For this purpose, recently identified special properties of the resulting circuit matrices and the node-tearing principles are exploited, while developing an efficient parallel simulation framework. Numerical examples are presented to demonstrate the validity and efficiency of the proposed parallel method

High order and a-stable envelope following method for transient simulations of oscillatory circuits

A new enveloped following (EF) method based on high-order Obreshkov integration formula is presented. The new method is suitable for transient analysis of highly oscillatory circuits with widely separated time-scales. In addition, the proposed algorithm is capable of producing high-order numerically stable approximation of the transient response. The use of high-order formulas leads to a significant reduction in the computational time compared to low-order EF methods because it allows taking large steps in time while keeping the same accuracy

Variability Analysis via Parameterized Model Order Reduction and Numerical Inversion of Laplace Transform

A fast algorithm is presented for statistical analysis of large circuits with multiple stochastic parameters. The proposed method combines the merits of the parameterized model order-based techniques and numerical inversion of Laplace transform (NILT). The response of the reduced model at any given time point is expressed as a linear combination of the f