The impact of a nonideal return path on differential signalintegrity

Printed circuit board transmission lines propagating high-speed digital signals are susceptible to nonideal return paths which may affect signal integrity. In an attempt to clarify this complex issue, this paper presents a study of differential signal integrity issues for the familiar situation in which two coupled microstrip traces are in close proximity to a common reference plane. Differential signaling on coupled microstrip lines and stripline configurations are investigated. Finite-difference time domain simulations are used to demonstrate the impact a nonideal return path can have on differential signal integrity     

Radial basis functions: Developments and applications to planetary scale flows

Radial basis functions (RBFs) can be seen as a major generalization of pseudospectral (PS) methods, abandoning the orthogonality of the basis functions and in return obtaining much improved simplicity and geometric flexibility. Spectral accuracy becomes now easily available also when using completely unstructured node layouts, permitting local node refinements in critical areas. The first major PDE applications for which RBFs have been shown to compete successfully against the best currently available numerical approaches can be found in the geosciences. Examples that are discussed here include translating vortex roll-ups (cyclogenesis), nonlinear flows on the sphere modeled by the shallow water equations, and 3D convection in the earth’s mantle.     

A Comparison of the Currents Induced on an EUT in a TEM Cell to Those Induced in a Free-Space Environment

The finite-difference time-domain method is used to investigate whether the currents induced on equipment under test (EUT) in a transverse electromagnetic (TEM) cell are similar to those induced in a free-space environment. The approach is to simulate an identical EUT in both environments and determine a correlation based on the respective current distributions. The effect of the ratio of EUT to TEM cell sizes on the correlation to free space is also investigated. This paper introduces a metric that quantifies the change in the surface current induced on the EUT in these different environments.     

Stable calculation of Gaussian-based RBF-FD stencils

Traditional finite difference (FD) methods are designed to be exact for low degree polynomials. They can be highly effective on Cartesian-type grids, but may fail for unstructured node layouts. Radial basis function-generated finite difference (RBF-FD) methods overcome this problem and, as a result, provide a much improved geometric flexibility. The calculation of RBF-FD weights involves a shape parameter $\epsilon$. Small values of $\epsilon$ (corresponding to near-flat RBFs) often lead to particularly accurate RBF-FD formulas. However, the most straightforward way to calculate the weights (RBF-Direct) becomes then numerically highly ill-conditioned. In contrast, the present algorithm remains numerically stable all the way into the $\epsilon \to 0$ limit. Like the RBF-QR algorithm, it uses the idea of finding a numerically well-conditioned basis function set in the same function space as is spanned by the ill-conditioned near-flat original Gaussian RBFs. By exploiting some properties of the incomplete gamma function, it transpires that the change of basis can be achieved without dealing with any infinite expansions. Its strengths and weaknesses compared with the Contour-Padé, RBF-RA, and RBF-QR algorithms are discussed.