Abstract: A method for calculating electric field having contributions of an incident electric field from a source and an electric field emitted from another object distinct from the source but in a path of the incident electric field, which is often termed a “scatterer”. This method is formed by a new single-source integral equation which represents the electric field inside the scatterer as a superposition of spherical waves emanating from its boundary. Calculation of electric field using this method is particularly but not exclusively suited for applications such as fault detection in simulations of power systems, remote sensing of stratified structures such as ice, and circuit design concerning chips in electronic packages on circuit boards.

Abstract: A method for calculating electric field having contributions of an incident electric field from a source and an electric field emitted from another object distinct from the source but in a path of the incident electric field, which is often termed a “scatterer”. This method is formed by a new single-source integral equation which represents the electric field inside the scatterer as a superposition of spherical waves emanating from its boundary. Calculation of electric field using this method is particularly but not exclusively suited for applications such as fault detection in simulations of power systems, remote sensing of stratified structures such as ice, and circuit design concerning chips in electronic packages on circuit boards.

Abstract: Methods and systems for use in imaging an imaging domain that spatially separate a scattered field and reconstruct an image based on the spatially separated scattered field (e.g., for use in microwave imaging applications including tumor detection in human tissue, etc.).

Abstract: A new surface impedance model for extraction in lossy two-dimensional (2D) interconnects of rectangular cross-section is presented. The model is derived directly from the volumetric electric field integral equation (EFiE) under the approximation of the unknown volumetric current density as a product of the exponential factor describing the skin-effect and the unknown surface current density on the conductor's periphery. By proper accounting for the coupling between the boundary elements situated on the top and bottom surfaces of conductor with the elements located on the side-walls, the model maintains accuracy from DC to multi-GHz frequencies as well as for conductors with both large and small thickness/width ratios. A generalization of the full-periphery surface impedance model to the three-dimensional electric field integral equation is also described.

Abstract: Systems and methods for modeling a multilayer integrated circuit include three-dimensional interconnect models in multilayered substrates for greater accuracy. Mesh models are used to resolve effects of nearby elements and grid models are used to resolve effects of far-away elements. Sidewall mesh elements of three-dimensional interconnects are projected onto parallel (or substantially parallel) grids between the top and bottom walls of the interconnects so that grid models can be used to resolve three-dimensional effects of interconnects in multilayered substrates.

Abstract: Systems and methods for modeling a multilayer integrated circuit include three-dimensional interconnect models in multilayered substrates for greater accuracy. Mesh models are used to resolve effects of nearby elements and grid models are used to resolve effects of far-away elements. Sidewall mesh elements of three-dimensional interconnects are projected onto parallel (or substantially parallel) grids between the top and bottom walls of the interconnects so that grid models can be used to resolve three-dimensional effects of interconnects in multilayered substrates.

Abstract: Methods and systems for use in imaging an imaging domain that spatially separate a scattered field and reconstruct an image based on the spatially separated scattered field (e.g., for use in microwave imaging applications including tumor detection in human tissue, etc.).

Abstract: A new surface impedance model for extraction in lossy two-dimensional (2D) interconnects of rectangular cross-section is presented. The model is derived directly from the volumetric electric field integral equation (EFiE) under the approximation of the unknown volumetric current density as a product of the exponential factor describing the skin-effect and the unknown surface current density on the conductor's periphery. By proper accounting for the coupling between the boundary elements situated on the top and bottom surfaces of conductor with the elements located on the side-walls, the model maintains accuracy from DC to multi-GHz frequencies as well as for conductors with both large and small thickness/width ratios. A generalization of the full-periphery surface impedance model to the three-dimensional electric field integral equation is also described.

Abstract: To estimate a distribution of voltages or currents in the layers of a multi-layer circuit, an exemplary current flow in each layer is discretized into a number of current vector elements and at least one scalar charge element related to the charge associated with each current vector element. A first distribution of voltages induced in each circuit layer is determined from current vector elements in all of the circuit layers. A second distribution of voltages induced in each circuit layer is determined from the scalar charge elements in all of the circuit layers. For each circuit layer, the first and second distributions of voltages induced therein are combined to determine an actual distribution of voltages in the circuit layer.