Optimization of Source Modeling From Phaseless Near-Field Scanning Based on SVD-Defined Eigenmodes

This article proposes a procedure for reconstructing dipole moment models from magnitude-only near-field scanned magnetic fields. Preprocessing uses a finite-impulse response filter to deblur the 2-D divergence of the magnetic fields to locate the dipoles. The procedure defines the modes of the dipole distribution using singular value decomposition. Based on mode decomposition, the modal coefficients are optimized through a pattern search algorithm to obtain the dipole moments. Compared with existing methods, this method reconstructs better phase information in high-noise situations. Using mode decomposition circumvents the problem of a limited number of dipoles that can be solved by existing optimization methods. Real experiments using high-resolution near-field scanned data show that the main emission sources of individual traces inside an integrated circuit (IC) chip can be distinguished through the proposed procedure.

I. Introduction

Sensitivity degradation due to noise sources in integrated circuit (IC) chips is the subject of many studies. To simplify the problem of desensitizing noise sources that generate electromagnetic interference (EMI), an equivalent dipole moment model is solved using a near-field scanning electromagnetic field. The least squares method (LSM) is used to solve the inverse scattering problem, which involves a large matrix, many unknowns, and long calculation time. The large condition number of the matrix also renders the solution susceptible to measurement noise. The calculated distribution of the dipole moment model does not reflect the actual structure. The far-field electromagnetic fields that are calculated using this equivalent model are accurate, but the calculated near-field values vary significantly. Tikhonov regularization and truncated singular value decomposition (SVD) are used to decrease interference due to noise [1], [2], [3]. Besides, some approaches reconstruct current distribution using Fourier transform and eigenmode currents [4]. In order to save near-field scanning time, the sparse source model aims to give solutions by fewer scanning points. These methods utilize L1-norm optimization [5], [6], [7] or matrix decomposition [8] to give sparse solutions.