Over the last twenty years, the evolution of communications has extended the systems' operating frequency range to the tens of GHz. In this framework, time domain integral equation-based (TDIE) methods for antenna modeling have gained increasing interest. Among them, the Partial Elements Equivalent Circuit (PEEC) method turns out to be attractive for its capability to provide compact circuit models. Similarly to other integral equation-based methods, like the method of moments (MoM) in the time domain (TD), the PEEC method can suffer from late-time instabilities. This work shows that a rigorous computation of the time-dependent partial elements leads to an improved TD formulation of the PEEC method that exhibits better behavior at high frequencies. This is the fundamental premise for having more stable results, preventing the late-time instabilities from appearing in the time domain.

An approximate computational model of an electromagnetic (EM) pulse excited thin-wire antenna is developed. The presented solution methodology is based on the Cagniard-deHoop method of moments (CdH-MoM) and Hallén's approximation of the thin-wire model. It is shown that the proposed time-domain (TD) solution leads to an inversion-free, efficient updating procedure that mitigates the marching-on-in-time accumulation error. An illustrative numerical example demonstrates the validity of the proposed model.

V.A unified description of the time-domain (TD) electromagnetic (EM) field coupling to a transmission line (TL) that is terminated by arbitrary linear time-invariant loads is presented. Closed-form expressions for the electric current induced in the loads are derived with the aid of the EM reciprocity theorem of the time-convolution type. The validity of the solution is demonstrated via illustrative numerical examples.

Pulsed electromagnetic (EM) scattering by short-wire and small-loop antennas loaded by time-varying (TV) loads is analyzed with the aid of time-domain (TD) compensation theorems. TD analytical expressions describing the change of back-scattered EM fields from dipole antennas due to their TV load are given. Illustrative numerical examples are presented.

An analytical approach to the analysis of electromagnetic (EM) reflection and transmission of a plane wave at a time-varying, high-dielectric thin layer is described. Closed-form expressions for the time-domain (TD) reflection and transmission coefficients are derived and successfully validated using an equivalent circuit representation. The cases of the constant-to-linearly increasing and harmonic temporal profiles are analyzed in detail. Illustrative numerical examples demonstrating the pulse shapes of the temporally modulated EM fields are presented.

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.

The pulsed electromagnetic (EM) plane-wave scattering by a thin, high-contrast metasurface with time-varying magneto-dielectric properties is analyzed analytically with the aid of the time-domain (TD) EM reciprocity theorem of the time-convolution type. It is shown that the (1+1)-spacetime scattering problem can be reduced to a system of two uncoupled differential equations that are amenable to analytical solution. The resulting fields induced in the thin layer are subsequently used to express the desired scattered fields. The pertaining zero-reflection condition is discussed. Illustrative numerical examples are presented and validated numerically.

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.