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Summary: RESONANCES FOR MICROSTRIP TRANSMISSION LINES
HABIB AMMARI y AND FAOUZI TRIKI y
Abstract. In this paper we rigorously derive asymptotic formulae for resonances associated
with a microstrip transmission line mounted on a planar waveguide with variable electromagnetic
characteristics when the width of the line goes to zero.
Key words. microstrip transmission lines, waveguides, resonances, characteristic numbers,
generalized Rouche's theorem, integral operators, asymptotic expansions
AMS subject classi cations. 78A50, 35J05, 35C15, 35P05
1. Introduction. In this paper we discuss resonance problems inherent in mi-
crostrip transmission lines mounted on planar open waveguides. Microstrip transmis-
sion lines are widely used in printed-circuit technology, microwave integrated circuits,
and antenna industry [7], [15], [6], [11]. Since microstrip transmission lines are highly
resonant structures, an accurate determination of their resonances is of great impor-
tance [4], [7], [15], [6], [11]. Our aim in this work is to rigorously derive asymptotic
formulae for resonances associated with the full Maxwell's equations in a microstrip
transmission line mounted on a planar open waveguide when the width of the mi-
crostrip transmission line goes to zero. The waveguide is half space (y > 0) with the
Dirichlet boundary condition on y = 0. The region 0 < y < h is considered the core
of the ber, while the remainder is considered the cladding. The electric permittivity
of the waveguide is y-dependent in the core, and is constant in the cladding. The
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