Improved polynomial chaos discretization schemes to integrate interconnects into design environments

Recently, an efficient stochastic modeling method for interconnects with inherent variability in their physical parameters was proposed, based on applying the so-called polynomial chaos (PC) approach in conjunction with a Stochastic Galerkin Method (SGM) onto telegrapher's equations. Although this approach was already very successful from a numerical point of view, the novel technique could not be conveniently integrated into SPICE-like solvers, limiting the applicability of the method. In this letter, the PC-SGM scheme for telegrapher's equations is revisited, pinpointing the origin of this inconvenience and immediately allowing to mitigate the issue. By adapting the traditional discretization of the stochastic telegrapher's equations approach, an augmented, yet deterministic, set of ordinary differential equations is obtained that turns out to be of the same type as the telegrapher's equations, and hence, the physical property of reciprocity is preserved. Consequently, it can be directly and more efficiently handled using SPICE-like solvers, which usually assume matrix symmetries. As an application example, the variability analysis of a state-of-the-art on-chip line for millimeter-wave applications is performed in a SPICE solver

A two-step perturbation technique for nonuniform single and differential lines

A novel two-step perturbation technique to analyze nonuniform single and differential transmission lines in the frequency domain is presented. Here, nonuniformities are considered as perturbations with respect to a nominal uniform line, allowing an interconnect designer to easily see what the effect of (unwanted) perturbations might be. Based on the Telegrapher's equations, the proposed approach yields second-order ordinary distributed differential equations with source terms. Solving these equations in conjunction with the pertinent boundary conditions leads to the sought-for currents and voltages along the lines. The accuracy and efficiency of the perturbation technique is demonstrated for a linearly tapered microstrip line and for a pair of coupled lines with random nonuniformities. Moreover, the necessity of adopting a two-step perturbation in order to get a good accuracy is also illustrated

Variability analysis of interconnect structures including general nonlinear elements in SPICE-type framework

A stochastic modelling method is developed and implemented in a SPICE framework to analyse variability effects on interconnect structures including general nonlinear element

Port controlled Hamiltonian representation of distributed parameter systems

A port controlled Hamiltonian formulation of the dynamics of distributed parameter systems is presented, which incorporates the energy flow through the boundary of the domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. This port controlled Hamiltonian system is defined with respect to a Dirac structure associated with the exterior derivative and based on Stokes' theorem. The definition is illustrated on the examples of the telegrapher's equations, Maxwell's equations and the vibrating string. \u

Ground Transient Resistance of Underground Cables

During transients involving multiconductor lines, the importance of the ground finite conductivity is well known and various techniques and expressions have been presented in literature for the inclusion of its contribution into the per unit length parameters. The direct time domain approach based on the introduction of the transient parameters and on the numerical solution of the telegrapher's equations demonstrated to be accurate and efficient for the analysis of typical transients. In this letter, the expressions for the ground transient resistance for underground cables, based on the closed-form inverse Laplace transform of the classical Pollaczek expressions (valid for the low-frequency-range), are presented and discussed