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.

Electromagnetic problems can be solved by using the integral form of Maxwell equations. The Surface Partial Element Equivalent Circuit (S-PEEC) method is an integral equation-based method that is suitable when high-frequency effects, such as skin and proximity effect, are dominant. However, the computation of interaction quadruple integrals is computationally expensive and numerically unstable due to singularities. In previous work, we proved how to decouple one of the quadruple integrals, and showed the gaining in stability and computational time. In this work, we extend the result to the second integral with the curl of the Green's function. Numerical examples prove the acceleration in terms of computational time achieved with the proposed approach. Future work will focus on integration strategy and further optimization of the proposed algorithm.

Computational electromagnetic problems require evaluating the electric and magnetic fields of the physical object under investigation, divided into elementary cells with a mesh. The partial element equivalent circuit (PEEC) method has recently received attention from academic and industry communities because it provides a circuit representation of the electromagnetic problem. The surface formulation, known as S-PEEC, requires computing quadruple integrals for each mesh patch. Several techniques have been developed to simplify the computational complexity of quadruple integrals but limited to triangular meshes as used in well-known methods such as the Method of Moments (MoM). However, in the S-PEEC method, the mesh can be rectangular and orthogonal, and new approaches must be investigated to simplify the quadruple integrals. This work proposes a numerical approach that treats the singularity and reduces the computational complexity of one of the two quadruple integrals used in the S-PEEC method. The accuracy and computational time are tested for representative parallel and orthogonal meshes.

The partial element equivalent circuit (PEEC) method provides an electromagnetic model of interconnections and packaging structures in terms of standard circuit elements. The surface-based PEEC (S-PEEC) formulation can reduce the number of unknowns compared to the standard volume-based PEEC (V-PEEC) method. This reduction is of particular use in the case of high-speed circuits and high-switching power electronics, where the bandwidth extends from low frequencies to the GHz range. In this article, the S-PEEC formulation is revised and cast in a matrix form. The main novelty is that the interaction integrals involving the curl of the magnetic and electric vector potentials are computed through the Taylor series expansion of the full-wave Green’s function, leading to analytical forms that are rigorously derived. Therefore, the numerical integration is avoided, with a consequent reduction of the computation time. The proposed formulas are studied in terms of the frequency, size of the mesh, and distance between the basis function domains. Three examples are presented, confirming the accuracy of the proposed method compared to the V-PEEC method and surface-based numerical methods from literature.

The knowledge of technology directly impacts the subject under study and, ultimately, the student learning. The students’ learning is maximized when technology is tailored to the subject and to the teachers. In this work, we re-designed an engineering course in electromagnetic compatibility to include pedagogical concepts supported by technological tools. We adapted the main ideas from the Technological Pedagogical Content Knowledge framework and designed the web platform based on pedagogical knowledge and technological knowledge. The course in electromagnetic compatibility consists of laboratory activities that cannot be virtualized or digitalized. Moreover, we wanted to keep some of the on-campus classes to increase engagement in the course. Therefore, the final course resulted in a mixed or hybrid education experience. The re-designed course had more positive assessments than previous courses taught with a traditional format.

The distortionless propagation of signals in a medium offers a way to preserve the signal integrity. There exists a condition for distortionless propagation on a transmission line known as the Heaviside condition. This paper proposes the use of the Heaviside condition to characterize and design magnetodielectric materials that provide distortionless propagation in a specified finite frequency band. Plane wave propagation in a magneto-dielectric material is modeled by a transmission line model, thereby assuming TEM mode propagation. Then, the Heaviside condition is employed to derive the frequency-dependent permittivity and permeability functions of the material in rational form, so they satisfy the condition in a specified frequency interval. A procedure to design such materials is described. A numerical example of the design process is provided and an illustration of the effectiveness of modeled material in fulfilling the Heaviside condition in a specified frequency interval both in the time and frequency domains is given, indicating the validity of the approximation. The design procedure areas such a suitable preliminary design guide for deriving a realizable description of a magneto-dielectric, exhibiting the distortionless property in the desired frequency interval, with certain specified requirements put on the loss, or the permeability and permittivity values satisfied. The obtained results may initiate further investigations into the bandwidth restrictions of the approximation, on closed-form design solutions, and the practical realization of such materials.

Power semiconductors, or transistors, constitute the core part of adjustable speed drives, which are commonly used in motor drive applications. Overheat of the semiconductors can compromise their behavior and, eventually, shorten the lifespan of the whole system. Therefore, the thermal management of transistors is crucial both at the design stage and during operation. Commonly performed thermal simulations normally rely on transistor thermal resistance. However, this approach does not account for the thermal behavior in transient regime. Furthermore, it is inappropriate for intermittent applications, such as for drilling machines, where the motor is on and off in repetitive working cycles, and the transistors never reach the equilibrium temperature. The transient thermal behavior is described by the concept of transfer thermal impedance. The transfer junction-to-case thermal impedance is given in the datasheet and assumes a constant ambient temperature; an assumption that is, however, not true in real applications. In this paper, we overcome this main limitation by using a resistive sensor. We consider MOSFETs in a 3-phase inverter, and model their thermal behavior with a well-known algorithm that uses the junction-to-case and junction-to-ambient thermal impedances, along with application dependent parameters. The actual rise of ambient temperature of the circuit board is included in the algorithm by virtue of the resistive sensor. The method has been validated with lab measurements, for two different MOSFETs. The proposed method can be used both at the design stage and during operation of the motor drive. Future works will include refinements of the power loss formulas, of the junction-to-ambient impedance modeling, as well as aging effects of the transistors.

In this paper, we study the delay-rational Green’s-function-based (DeRaG) model for transmission lines. This model is described in terms of impedance representation and it contains a rational and a hyperbolic part. The crucial property of transmission lines models is to be passive. The passivity of the rational part has been studied by the authors in a previous work. Here, we extend the results to the rational part of the DeRaG model. Moreover, we prove the passivity of the hyperbolic part.

The electromagnetic compatibility (EMC) performances of a product can seriously be affected by interconnects. Interconnects can be studied by using the multiconductor transmission lines (MTLs) theory. Mathematical models of MTLs are normally validated with the aid of well-known software, such as MATLAB or PSpice. Simulink is part of the MATLAB suite but is not frequently used, and it is often underestimated both in academia and in the university education. In this paper, we briefly review the mathematical model for MTLs called DeRaG, which is a rational model based on delay extraction. Then, we propose the corresponding Simulink implementation for a 3-conductor transmission line. The Simulink has high readability, is accurate and the simulation time is remarkably faster than the corresponding model obtained in PSpice.

The performance of variable-frequency drives (VFDs) commonly used in energy production plants can be severely affected by electromagnetic (EM) noise in the form of conducted disturbances.

A VFD is composed of an inverter, a motor, and a connecting power cable. The insulated-gate bipolar transistor (IGBT) technology and the pulse-width modulation (PWM) technique, used in the inverter, amplified the role of the power cable, which experiences the so-called “high-frequency” or “transmission line” effects, such as reflections, crosstalk, and distortion. Therefore, a complete EM assessment of a VFD requires an accurate and computationally efficient mathematical model of the cable, which can be studied as a multiconductor transmission line (MTL). Accordingly, we developed the “delay-rational Green’s-function-based” (DeRaG) model that should overcome the main limitations of the existing methods in the literature. In the DeRaG model, the impedance (or admittance) matrix is the sum of a rational series and a so-called hyperbolic part realized by hyperbolic functions. The rational series consists of poles and residues and can be truncated to a suitable size by a delay extraction technique. The hyperbolic part retains the primary information of the high-frequency behaviors, such as attenuation and propagation delays, of a line; thus, the DeRaG model is a wideband model. The DeRaG model is independent of the terminations and sources of the line and enables a delayed state-space representation; it can also account for EM interference. Nevertheless, an EM assessment of a complex system can be performed only using a calculator and proper software. Most of the advanced models for MTLs have been adapted for SPICE-like transient solvers. However, power electronics applications are commonly simulated by using software packages such as Simulink that are optimized for system-level simulations. We thus proposed the implementation of the DeRaG model both in SPICE and in Simulink to embrace a larger group of users and applications. The Simulink implementation was notably proven to be extremely simple and easy to describe. In addition, we focused on the hyperbolic part to qualitatively assess the behavior of an MTL. Our investigation resulted in an outstanding outcome; namely, we provided the distortionless condition for MTLs, whereas the distortionless condition was previously defined only for single-conductor transmission lines as the well-known Heaviside condition. In conclusion, the DeRaG model is a wideband model for the EM analysis of generic transmission lines that is suitable for system-level simulations required in power electronics applications and offers new insights into the physics of the system.