{'fraction_non_alphanumeric': 0.016962843295638127, 'fraction_numerical': 0.0016155088852988692, 'mean_word_length': 5.289340101522843, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Efficient 2-D Finite-Difference Frequency-Domain Method for Switching Noise Analysis in Multilayer Boards

A new numerical algorithm is presented to solve the problem of switching noise in multilayer circuit boards and packages. The algorithm is based on domain decomposition using the finite-difference frequency-domain (FDFD) method. Each layer of the multilayer board or package is modeled using a standard 2-D FDFD scheme and linked to other layers through a multiport network that effectively incorporates the via circuit models between the layers. It is shown that the algorithm is simple to implement and is highly efficient for multilayer boards or packages as the overall FDFD system matrix is highly sparse, thus can be solved very efficiently using advanced sparse matrix solvers. Furthermore, successive solution of the system matrix for different source and victim locations does not call for new fill of the system matrix, thus allowing efficient analysis of different source and victim locations. To validate the new algorithm, we manufacture a three-layer board, measure the scattering parameters between two specific locations, and obtain strong agreement with the solution obtained using the FDFD scheme introduced here.