Fast Fourier transform (FFT)-accelerated, integral-equation-based electromagnetic simulators have gained significant attention due to their ability to compute parasitics of arbitrarily shaped and large-scale voxelized structures on desktop computers. However, FFT-based solvers have limitations as they require voxels of the same size across all Cartesian dimensions. This is a significant limitation, especially for printed circuit boards (PCB)-like geometries of very thin copper layers and much thicker dielectric layers, which leads to an excessive number of voxels, and consequently, a large number of unknowns. In addition, in PCB-like structures, vias represent small details that require finer meshing resolution for proper discretization. This work aims to overcome these limitations by developing a systematic anisotropic strategy for computing matrix-vector products using the FFT-based approach and automatically replacing vias with equivalent R–L lumped elements. Furthermore, a zero-thickness conductor mesh is proposed within the partial element equivalent circuit (PEEC) method framework, which is in turn also suitable for use with other integral-equation-based methods. The accuracy, efficiency, and applicability of the proposed FFT-PEEC solver are demonstrated on three examples.

This work presents a hybrid analytical-numerical procedure that allows the efficient computation of the flux linkage of two misaligned circular coils placed above a stratified ground, which may include non-magnetic as well as magnetic materials. After deriving the Hankel transform describing the flux linkage, the semi-infinite integration interval is continued to the negative real axis. Next, the part of the integrand that exhibits branch point singularities is expressed in pole-residue form. This task is accomplished through the use of a well-established rational function fitting algorithm. Finally, the integration contour is deformed in the complex plane, so as to surround the pole singularities produced by the fitting algorithm. This makes it possible to apply the residue theorem, which leads to converting the integral representation for the flux into the sum of residues at the poles of the integrand. The derived solution has value in practical applications like wireless power transfer systems for battery electric vehicles charging.

The transmission line (TL) model has been used for decades to describe the propagation of signals and power along conducting wires. It is also well-known that it is based on the quasi-transverse electromagnetic (TEM) propagation hypothesis and is only accurate if the distance between the conductors is much smaller simultaneously than their length and the smallest characteristic wavelength of the signals. On the other hand, when these hypotheses are not matched, adopting full-wave methods for studying conductor bundles is not feasible due to the computational complexity of the resulting models. A compromise solution must be sought to represent electromagnetic phenomena more accurately without incurring an intractable computational complexity. Many approaches have been proposed over the years to handle this problem. In this work, we aim to extend to N-conductor TLs a specific method that is elegant and rigorous but currently limited to two-conductor TLs. This allows to model more rigorously 3-D effects such as propagation when the hypotheses of the standard TL theory are no longer matched. At the same time, the resulting model preserves the simplicity of 1-D models and is well suited to be integrated with 3-D models, since it will assume infinity as a reference. As a further outcome, the proximity effect is modeled by resorting to a harmonic expansion of the charge density. The proposed method is validated through three case studies. In particular, it is highlighted that it returns the standard model results when the assumptions underlying the “standard” model of TLs are satisfied. In contrast, it returns different results at high frequencies when the standard model is no longer adequate.

Time-varying (TV) materials have recently gained considerable attention for their ability to manipulate electromagnetic (EM) waves and improve the performance beyond the limits of conventional time-invariant materials. In addition, distributed TV capacitors are becoming more attractive to achieve particular effects. This work presents a systematic approach to modeling TV dielectrics by incorporating TV capacitors in the framework of the partial element equivalent circuit (PEEC) method. Thus, the standard formulation of the PEEC method is modified to include TV dielectrics and lumped elements for general 3D geometries directly in the time domain (TD). It is shown that this is possible through TV capacitances and voltage-controlled current sources. Four numerical examples validate the proposed approach.

Pulsed electromagnetic (EM) field signal transfer from a general EM source distribution to a transmission line (TL) is analyzed with the aid of Lorentz’s reciprocity theorem. In this fashion, the transient voltage induced by the impulsive EM source is expressed through the EM fields as radiated by the TL. These transmitted EM fields are expressed in closed form using an analytical procedure that resembles the Cagniard-DeHoop (CdH) technique. The validity of the proposed reciprocity-based methodology is verified with the aid of an alternative analytical solution describing the EM field signal transfer excited by an impulsive vertical electric dipole (VED). Illustrative numerical examples are presented.

Pulsed electromagnetic (EM) plane-wave interaction with time-varying (TV) highly-contrasting thin sheets are analyzed analytically in the time domain (TD). With the aid of a rigorous analytical procedure, closed-form TD analytical expressions are derived for both E- and H-polarized TD reflection and transmission coefficients. The coefficients are subsequently used to express TD EM fields in the presence of a thin layer with TV conductive and dielectric properties. Illustrative examples concerning selected types of the temporal modulation function are discussed and numerically evaluated.

In computational electromagnetics, numerical methods are generally optimized for triangular or tetrahedral meshes. However, typical objects of general interest in electronics, such as diode packages or antennas, have a Manhattan-type geometry that can be modeled with orthogonal and rectangular meshes. The advantage of orthogonal meshes is that they allow analytic solutions of the integral equations. In this work, we optimize the decoupling of the integrals used in the Surface formulation of the Partial Element Equivalent Circuit (S-PEEC) method for rectangular meshes. We consider a previously proposed decoupling strategy, and we lighten the underlying math by generalizing it. The new method shows improved accuracy and computational time because the number of decoupling integrals is generally reduced. The new S-PEEC method with decoupling integrals is named S-PEEC-DI. The S-PEEC-DI method is tested on a realistic diode package and compared with the volumetric PEEC (V-PEEC) and two well-known commercial solvers.

An analytical approach based on the Cagniard-DeHoop (CdH) technique is applied to derive the time-domain (TD) partial-inductance retarded partial coefficient pertaining to two adjoining brick elements. It is demonstrated that the CdH approach leads to closed-form TD expressions that are easy-to-implement and can be evaluated relatively quickly within any prescribed accuracy. Accordingly, the novel TD formulas introduced in this article can be used to supplement standard (quasi)static partial element equivalent circuit (PEEC) models, thereby improving their stability behavior for high-frequency applications for which the (quasi)static approximation ceases to be valid. Illustrative numerical examples are presented.

In this contribution, physical bounds on the time-domain (TD) response of a linear time-invariant (LTI) system are briefly discussed regarding selected applications in electromagnetic compatibility (EMC). An illustrative example describing a worst-case bound on the plane-wave shielding performance of a planar conductive layer is presented.