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Closed form solutions to Green's functions in microstrip problems with a thin substrate
Author(s) -
Hoorfar Ahmad,
Chang David C.
Publication year - 1995
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/94rs02927
Subject(s) - planar , microstrip , term (time) , substrate (aquarium) , phase (matter) , range (aeronautics) , mathematical analysis , closed form expression , mathematics , expression (computer science) , integral equation , field (mathematics) , physics , optics , computer science , materials science , pure mathematics , quantum mechanics , oceanography , geology , computer graphics (images) , composite material , programming language
A thin substrate approximation is used to derive closed form solutions for the Green's functions G e and G m appearing in the mixed potential integral equation modeling of planar microstrip structures. The expression for G m is given in terms of the contributions from a source and its image, while that of G e is derived in terms of the so‐called quasi‐dynamic contribution plus a “correction” term. Excellent agreements with the exact numerical integration of the corresponding Sommerfeld integrals for a wide range of parameters are obtained. In particular, it is demonstrated that the addition of the correction term is needed in order to accurately predict the sharp dip and its associated phase reversal that appear in the magnitude of G e in the near field.