Ram Achar

Passive closed-form transmission-line model for general-purpose circuit simulators

A passive closed-form model for multiconductor lossy transmission line analysis is presented in this paper. The proposed model is suitable for inclusion in general-purpose circuit simulators and overcomes the mixed frequency/time simulation difficulties encountered during the transient analysis. In addition, the model can handle frequency-dependent line parameters. This method offers an efficient means to discretize transmission lines compared to the conventional lumped discretization, while preserving the passivity of the discrete model. Coefficients describing the discrete model are computed a priori and analytically, using closed-form Pade approximants of exponential matrices. Numerical examples are presented to demonstrate the validity of the proposed model and to illustrate its application to a variety of interconnect structures.

Simultaneous time and frequency domain solutions of EM problems using finite element and CFH techniques

This paper describes an efficient method for both time- and frequency-domain solutions of electromagnetic (EM) field problems. In this method EM field problems are formulated using Laplace-domain finite element approach and are solved using complex frequency hopping (CFH) technique. CFH is a moment-matching technique which has been used successfully in the circuit simulation area for solution of large set of ordinary differential equations. Problems consisting of Dirichlet, Neumann and combined boundary conditions can be solved using the proposed algorithm to obtain both time and frequency responses. Several electromagnetic field problems have been studied using the new technique and the speed-up advantage (one to three orders of magnitude) compared to conventional finite element technique is demonstrated. A good agreement between numerical results obtained using the proposed method and the previously published results has been found.

Passive closed-form transmission-model for general purpose circuit simulators

A passive closed-form model for multiconductor lossy transmission line analysis is presented. The proposed model is suitable for inclusion in general purpose circuit simulators and overcomes the mixed frequency/time simulation difficulties encountered during the transient analysis. The method offers an efficient means to discretize the transmission lines compared to the conventional lumped discretization while preserving the passivity of the discrete model. Coefficients describing the discrete model are computed a priori and analytically, using closed-form Pade approximants of exponential matrices.

Passive model reduction of multiport distributed interconnects

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 distributed interconnects described by telegraphers equations. Interconnects can be lossy, coupled, and can include frequency-dependent parameters. In the proposed scheme, transmission-line subnetworks are treated with closed-form stamps obtained using matrix-exponential Pade, where the coefficients describing the model are computed a priori and analytically. In addition, a technique is given to guarantee that the contribution of these stamps to the modified nodal analysis formulation leads to a passive macromodel.

Enforcing passivity for rational function based macromodels of tabulated data

With the continually increasing operating frequencies, complex high-speed package and interconnect modules require characterization based on measured/simulated data. Several efficient algorithms were recently suggested for macromodeling of such data to enable transient analysis in the presence of external circuit elements. One of the difficult issues involved here is the passivity violations associated with the computed macromodel. To address this issue, an efficient algorithm is presented in this paper to enforce passivity for macromodels with passivity violations.

Waveform Relaxation Techniques for Simulation of Coupled Interconnects With Frequency-Dependent Parameters

The large number of coupled lines in an interconnect structure is a serious limiting factor in simulating high-speed circuits. Waveform relaxation based on transverse partitioning has been previously presented to address this problem for interconnects with constant per-unit-length parameters. This paper extends the waveform relaxation technique to handle the more difficult and important case of frequency-dependent parameters. The computational cost of the proposed algorithm grows linearly with the number of coupled lines

Fast transient analysis of incident field coupling to multiconductor transmission lines

Due to the rapid surge in operating frequencies and complexity of modern electronic designs, accurate/fast electromagnetic compatibility/interference analysis is becoming mandatory. This paper presents a closed-form SPICE macromodel for fast transient analysis of lossy multiconductor transmission lines in the presence of incident electromagnetic fields. In the proposed algorithm, the equivalent sources due to incident field coupling have been formulated so as to take an advantage of the recently developed delay extraction based passive transmission line macromodels. Also, a method to incorporate frequency-dependent per-unit-length parameters is presented. The time-domain macromodel is in the form of ordinary differential equations and can be easily included in SPICE like simulators for transient analysis. The proposed algorithm while guaranteeing the stability of the simulation by employing passive transmission line macromodel, provides significant speed-up for the incident field coupling analysis of multiconductor transmission line networks, especially with large delay and low losses

Waveform relaxation techniques for simulation of coupled interconnects with frequency-dependent parameters

The large number of coupled lines in an interconnect structure is a serious limiting factor in simulating high-speed circuits. Waveform relaxation based on transverse partitioning has been previously presented to address this problem for interconnects with constant per-unit-length parameters. This paper extends the waveform relaxation technique to handle the more difficult and important case of frequency-dependent parameters. The computational cost of the proposed algorithm grows linearly with the number of coupled lines.

Delay extraction and passive macromodeling of lossy coupled transmission lines

Recently, several algorithms were proposed for time-domain macromodeling of distributed transmission line networks. It has been demonstrated that preserving passivity of the macromodel is essential to guarantee a stable global transient simulation. Techniques such as method-of-characteristics yield fast transient results for long delay lines. However, they do not guarantee the passivity of the macromodel. On the other hand, methods such as matrix rational approximation provide efficient macromodels for lossy coupled lines, while preserving passivity. However, for long lossy delay lines this may require higher order approximations, making the macromodel inefficient. In order to address the above difficulty, this paper presents a new algorithm for efficient macromodeling of lossy coupled lines with long delay. The proposed method employs delay extraction prior to approximating the exponential stamp of the line and guarantees the macromodel passivity. The paper also provides guidelines on the practical applicability of the delay extraction and the matrix rational approximation, based on the knowledge of line parameters.

Compact Macromodeling of High-Speed Circuits via Delayed Rational Functions

This letter introduces a new method for compact macromodeling of high-speed circuits with long delays, characterized by tabulated time-domain data. The algorithm is based on partitioning the response and subsequently approximating each partition with a low-order sum-of-exponentials, delayed in time-domain. This results in a compact low-order macromodel in the form of delayed-differential equations, which can be efficiently analyzed using SPICE like simulators.