Abstract: The invention provides a method to compute the mixed potential contributions to electric and magnetic field in multilayered media, which can be applied in microwave engineering, integrated circuit analysis, and remote sensing. The Spectral Differential Equation Approximation Method (SDEAM) for solving Michalski-Zheng's mixed-potential Green's functions in fully shielded, partially open, and fully open multilayered media are described. The main advantage of SDEAM over other methods is that for a fixed location of the source elevation z?, it does not require fitting from scratch for every z, z?, and ? combination. Because of this advantage, SDEAM can be superior in both performance and accuracy to other existing methods. The well-established boundary value problem numerical solvers also provide SDEAM with robustness for miscellaneous planar multilayered structures.

Abstract: A generalization of the Harrow/Hassidim/Lloyd algorithm is developed by providing an alternative unitary for eigenphase estimation adopted from research in the area of quantum walks, which has the advantage of being well defined for any arbitrary matrix equation. The procedure is most useful for sparse matrix equations, as it allows for the inverse of a matrix to be applied with (Nnz log(N)) complexity, where N is the number of unknowns, and Nnz is the total number of nonzero elements in the system matrix. This efficiency is independent of the matrix structure, and hence the quantum procedure can outperform classical methods for many common system types. We show this using the example of sparse approximate inverse (SPAI) preconditioning, which involves the application of matrix inverses for matrices with Nnz=(N).

Abstract: A method of de-embedding a feed line is shown. The method includes measuring network parameters of a multilayered planar substrate and obtaining network parameters of a feed line using a short-open-calibration (SOC) according to an ABCD-matrix. An “a” block of the ABCD-matrix includes a first matrix multiplied by a transpose of a first short-circuit current. The first matrix is an inverse of a difference of an open-circuit current and a second short-circuit current. A “c” block of the ABCD-matrix includes the open-circuit current multiplied by the “a” block. The method includes de-embedding the network parameters of the feed line from the network parameters of the multilayered planar substrate to obtain microwave circuit network parameters and, responsive to the microwave circuit network parameters being within or not within a specified range, respectively approving or rejecting customer shipment of the microwave circuit.

Abstract: A method of modeling an integrated circuit includes: specifying a layout for the integrated circuit, wherein the layout includes a plurality of devices arranged in a plurality of layers and a plurality of connections between the layers; specifying locations for a source point and an observation point for the integrated circuit; determining a plurality of static images for the source point and the observation point; determining a plurality of discrete complex images for the source point and the observation point; determining a Green's-function value for the source point and the observation point by combining the static images and the discrete complex images; and saving at least some values based on the Green's-function value.

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.