Two techniques for the efficient numerical calculation of the Green's functions for planar shielded circuits and antennas

Abstract

Abstract-In this paper we present new contributions to the computation of the Green's functions arising in the analysis of multilayered shielded printed circuits and antennas. First the quasistatic term of the spectral domain Green's functions is extracted so that the convergence of the reminder dynamic modal series is enhanced. Moreover, it is shown that by extracting a second-order quasi-static term the convergence is further improved. In regard to the quasi-static terms they are computed in the spatial domain by numerically evaluating the associated spatial images series. Then a new and efficient technique is developed for the summation of the slowly convergent modal series. The technique can be viewed as the application of the integration by parts technique to discrete sequences and greatly accelerates the convergence rate of the series involved. It is shown that the new algorithm is numerically very robust and leads to a drastic reduction in the computational effort and time usually required for the numerical evaluation of the shielded Green's functions.

Evaluation of time domain electromagnetic fields radiated by constant velocity moving particles traveling along an arbitrarily shaped cross‐section waveguide using frequency domain Green's functions

“…This effect is shown in Figure 2, where the wake potential in a waveguide example is approached by different number of terms in the summation expression. The convergence of the series is also guaranteed in the limit s approaches zero, as is demonstrated in Álvarez Melcón and Mosig [2000]. This limit represents the waveguide cross‐plane that contains the source charge.…”

A Grounded MoM-Based Spatial Green's Function Technique for the Analysis of Multilayered Circuits in Rectangular Shielded Enclosures

“…In this case, the number of modes required to achieve convergence is very high, and there is not a clear rule to truncate the infinite summations. On the other hand, the use of the spatial domain formulation for this type of analysis is not practical, due to the high computational cost that requires the calculation of multilayered boxed Green's functions [5] [6] [7]. The first filter under consideration is shown in Fig.…”

“…The IE method can be formulated either in the spectral [4], [5], [6], [7], [8] or in the spatial domain [9], [10], [11]. The spectral domain is usually very efficient, but it presents important convergence problems when the dimensions of the cells employed to discretize the printed circuits are very small as compared to the enclosure.…”

Investigations on radio-frequency components and the multipactor phenomenon in high-power space applications

“…5.7, where the wake potential in a waveguide example is approached by different number of terms in the summation expression. The convergence of the series (5.17) is also guaranteed in the limit s approaches to zero, as is demonstrated in [44]. 5.5 Bunches of particles 5.…”

“…The starting point for the study of electromagnetic radiations in an enclosure scenario is the formulation of the electric and magnetic Green's function [39,40,41,42,43,44]. In this sense, an expression for the dyadic Green's function for waveguide regions is derived in Chapter 2.…”