e r e r @ p h y s . r d . n .~The design method of complex resonance frequencies of planar (stripline and slotline) resonators having complicated shape has been developed. The method is based on the solution of surface integro-dBerentia1 equations by Galerkin method. The developed method differs from the known ones in using the basis functions defined on the entire surface of complicated domain. The suggested basis fimctions take into into consideration the behavior of electromagnetic field near the metal edges of resonator. Usually integro-differential equations (DE), dual integral equations (DIE), and dual series equations (DSE) are used for the analysis of arbitrary shape printed strip resonators (SR). The first step in solving them is frequently to decompose the whole SR sudace into simple triangular or rectangular sub-domains and to determine the currents induced on these sub-domains. The Galerkin method is normally used for this purpose. If SR has a simple shape (rectangular, elliptic, circular, ringlike), using the entire-domain basis functions is more eficient than the sub-domain ones. Galerkin method with edge-accounting basis hnctions is very useful for SR analysis since it enables one to study the problem by solving the matrix equations consisting usually of a small number of equations. In this work, the basis functions defined on the entire complicated-shape surface are suggested. These fknctions take into account the electromagnetic field behavior at the SR metal edges except of the corner points of SR. In addition, a universal numerical-analytical method of the surface integral calculation that explicitly takes into account the singularity of the kernel has been used to transform the firstkind equations to the second-kind equations.We consider SR havirag the shape of finite strip placed between straight lines )z I = L , curves x = 1 +( z , l from above and x = I -( z , l fiom below. The DIE derived from the boundary conditions can be cast into the following form:where Sthe part of XoZ plane, corresponding to the planar (strip or slot) resonator, z = a x + p z , 7 (a, p)is two-dimensional Fourier transform of the current density hnction at the strip J (x z ) , V = a 7 + p 7is proportional to the Fourier transform 1 1 of the charge density at the strip, f , (P) = / o m (P) -I-k / $ e (P)]/P2
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