Green’s functions in lossy layered media: integration along the imaginary axis and asymptotic behavior
Research Group
Grupo de Electromagnetismo Aplicado a las Telecomunicaciones (GEAT)Knowledge Area
Teoría de la Señal y las ComunicacionesSponsors
This paper presents an efficient technique for evaluating Green’s functions associated to layered media, when formulated as Sommerfeld integrals in the space domain. The key step in the formulation is that Sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane. It is shown that with this original choice of the integration contour, the numerical effort usually involved in the evaluation of Sommerfeld integrals can be greatly reduced, specially when large source-observer distances are involved. One asset of this technique is that it can be easily incorporated into integral equation based CAD packages for the efficient analysis of complex printed microwave circuit and antennas. In addition, the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media Green’s functions for large source-observer distances.Publication date
2003-12Publisher
IEEE Antennas and Propagation SocietyBibliographic Citation
MOSING, Juan R., ÁLVAREZ MELCÓN, Alejandro. Green’s functions in lossy layered media: integration along the imaginary axis and asymptotic behavior. IEEE Transactions on Antennas and Propagation, 51 (12): 3200-3208, diciembre 2003. ISSN 0018-926XKeywords
Comportamiento asintóticoEcuaciones integrales
Funciones Green
Circuitos impresos
Antenas
Asymptotic behavior
Integral equation (IE)
Circuit board
Antennas
Green's functions
Abstract
This paper presents an efficient technique for evaluating
Green’s functions associated to layered media, when formulated
as Sommerfeld integrals in the space domain. The key
step in the formulation is that Sommerfeld integrals are computed
choosing a suitable integration path which is closed through the
imaginary axis of the complex spectral plane. It is shown that with
this original choice of the integration contour, the numerical effort
usually involved in the evaluation of Sommerfeld integrals can be
greatly reduced, specially when large source-observer distances are
involved. One asset of this technique is that it can be easily incorporated
into integral equation based CAD packages for the efficient
analysis of complex printed microwave circuit and antennas. In addition,
the theoretical developments needed to set up the numerical
algorithm throw a new light on the asymptotic behavior of the layered
media Green’s functions for large source-observer distances.
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