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.

This letter introduces an analytical approach for the evaluation of the complete integral expressions for the time-harmonic electromagnetic (EM) field components generated by an arbitrarily large thin-wire circular loop antenna lying on the surface of a flat and homogeneous half-space. The method consists of casting the integrands of the field integrals into forms in which the square-root terms, originating branch cuts, are replaced with their rational function representations via Newton's method. Explicit expressions for the fields are then derived by applying the residue theorem. The proposed procedure is exact since previous authors have shown that the sequence of rational functions generated by Newton's method converges quadratically to the square root, even if the independent variable is a complex number. Numerical simulations are performed to confirm the validity of the developed formulation.

This paper presents a rigorous derivation of the dc solution of three-dimensional partial element equivalent circuit (PEEC) formulation extended to include simultaneously conductive, dielectric, and magnetic materials. The circuit interpretation of Maxwell’s equations provided by the PEEC method allows to reformulate the dc modeling task in such a way that physical phenomena are fully exploited. Indeed, since the displacements currents are identically zero in dielectrics, Kirchhoff’s current law is enforced in terms of charge conservation internally to dielectrics or at the interface between dielectrics and other materials. A well-posed problem is achieved by adding the charges as new unknowns and identifying the disconnected objects. Two numerical examples are presented demonstrating the accuracy of the proposed method when compared to the dc solution as extracted by the fast Fourier transform of the impulse response and a finite element method simulation.

Plane-geometry single- and multileaf coil antennas fed by radio-frequency (RF) generators are frequently used to produce electric currents and therapeutic ohmic heating in sub- cutaneous fat and muscle tissues by electromagnetic induction. In particular, the butterfly (two-leaf) configuration has been regarded as a high-efficiency geometry for diathermy purposes. The aim of this letter is to prove by numerical simulation that any multileaf coil is significantly less efficient than the round one and that, in general, efficiency worsens with increasing the number of leaves. Simulation results show that for a given power density to be deposited in the tissue, replacing a single leaf with a multileaf structure causes an increase of energy consumption by at least 20%.

Current-carrying multi-leaf planar coils fed by radio-frequency generators are frequently employed to induce eddy currents and therapeutic ohmic heating in biological tissues. Previous studies have shown that adjusting the current direction in the neighboring leaves of a two- or four-leaf structure makes it possible to enhance the focality and selectivity of the diathermic treatment, but the electric field-strength induced in the issue, as well as the associated specific absorption rate (SAR), are far less than those achievable with a simple round coil of the same size. The aim of this paper is to prove that, for a fixed power supply, replacing a round coil with a four times larger four-leaf one makes it possible to significantly increase the deposited peak SAR and, at the same time, assuring a fairly good field localization. What is more, it is found that closing together four round units allows to obtain the same peak SAR provided by each unit considered alone with a reduction of the energy consumption by at least 30%. This demonstrates that the cloverleaf applicator can be successfully employed for heating deep afflicted tissue areas.