This year marks about half a century since the birth of the technique known as the partial element equivalent circuit modeling approach. This method was initially conceived to model the behavior of interconnect-type problems for computer-integrated circuits. An important industrial requirement was the computation of general inductances in integrated circuits and packages. Since then, the advances in methods and applications made it suitable for modeling a large class of electromagnetic problems, especially in the electromagnetic compatibility (EMC)/signal and power integrity (SI/PI) areas. The purpose of this article is to present an overview of all aspects of the method, from its beginning to the present day, with special attention to the developments that have made it suitable for EMC/SI/PI problems.

Reconfigurable intelligent surfaces (RISs) are planar, almost 2-D, structures that can intelligently manipulate electromagnetic waves by low-cost near passive reflecting elements. RISs are considered a potential enabling technology for the sixth-generation (6G) wireless communication systems due to their capability to tune wireless signals, thus smartly controlling propagation environments. This work has a twofold objective: firstly, we present a systematic methodology for characterizing RISs in the time domain, which rigorously includes propagation delays and mutual coupling among RIS elements; secondly, we analyze the RISs through a convolution-based solver that is enriched by a specialized convolution scheme that enables the analysis of systems with complex linear, nonlinear as well terminations. The proposed approach is validated by extensive numerical evaluations against well-established methods based on both frequency- and time-domain analyses, with a varying number of RIS elements, interdistance, and frequency of operation.

Full-wave time-domain computational electromagnetic (CEM) solvers, which are integral equation (IE)-based, may suffer from what is called “late-time instability” problems. This unstable behavior occurs for CEM solvers for very fast rise-time input signals. A multitude of techniques has been devised by researchers over the years to solve the problem. In this article, we pursue an approach for the stable solution of full-wave partial element equivalent circuit (PEEC) models for fast-rising input waveforms. In particular, step and impulse response will be considered that are the most challenging from a stability point of view. For the solver part, a conventional full-wave PEEC code is used that requires one to use retarded partial elements. Unfortunately, a PEEC, as well as impedance Z-(method of moment) solvers using suitable numerical time-stepping methods have stability problems, especially for fast rising impulse or step inputs. An important step forward is achieved in this work by providing a larger class of stable solutions well above the stability achieved for time-stepping methods in the last 50 years. The time-domain stability is achieved by replacing the stepping integration methods with a numerical inversion of Laplace transform (NILT) technique. The NILT transform starts out by applying it to a frequency-domain PEEC solution. The surprising result is that the NILT-based method has a variable time-dependent bandwidth that is advantageous for the full-wave IE solution stability. In this article, we give several examples that show that a PEEC-NILT solution provides accurate and stable results for impulse, step- and piece-wise linear input waveforms.

The computation of self and mutual inductances of coils is a classic problem of electrical engineering. The accurate modeling of coupled coils has received renewed interest with the spread of wireless power transfer systems. This problem has been quite well addressed for coplanar or perfectly coaxial coils but it is known that the misalignment conditions easily lead to a sharp decrease in the efficiency. Hence, it is crucial to take misalignment into account in order to properly design the overall wireless power transfer system. This work presents a study to compute analytically the mutual inductance of non-coaxial pancake coils with parallel axes. The accuracy of the proposed methodology is tested by comparison with the numerical results obtained using the tool Fast-Henry. Then, a wireless power transfer system, comprising a full bridge inverter is considered, showing the impact of the misalignment on the coupling between two pancake coils and, thus, between the source and the load.

Pulsed wave propagation along a transmission line (TL) with time-varying (TV) wavespeed is analyzed using the theory of state variables. The thus obtained propagator solution is validated analytically and discussed with regard to its applications to solving initial-value problems. Illustrative examples are presented.

This work deals with the proposal to derive an explicit analytical expression for the mutual inductance between two coaxial circular coils placed above a conducting medium. The integral representation for the inductance is evaluated starting from expanding the product of the exponential factor and one of the Bessel functions of the integrand into a power series of the integration variable, which coincides with the radial wavenumber. Then, Bessel's differential equation is used to turn the generic power of the integration variable into a linear differential operator with respect to the radius of the source coil. This allows to convert the semiinfinite integral describing the inductance into an infinite sum of simpler integrals whose analytical evaluation is straightforward. Thus, after carrying out term-by-term integration, the mutual inductance is expressed in series form as a combination of spherical Hankel functions and products of cylindrical Bessel functions. The outcomes from the obtained formula for the inductance are compared with the data provided by both numerical integration of the original field integral and the previously published quasi-static solution to the same problem, valid for the special case that the two coils lie at the air–ground interface under the assumption of small receiving coil. The plotted curves reveal that, accuracy being equal, the proposed solution is less time consuming than numerical quadrature schemes, and that it provides accurate results even in the situations where numerical integration fails.