The Analysis of Distributed Two-Layers Components in Three-Layer Planar Structure

The algorithms for analyzing of two-layer distributed discontinuities in the form of an inductive section in a microstrip transmission line and an H-shaped slot resonator with a transverse arrangement of “dumbbells“ in its ground plane by the transverse resonance method are improved and developed. This method includes the mutual coupling of components that make up the discontinuity. According to the analysis results, the considered discontinuity is a multifunctional device and has scattering characteristics that contain simultaneously signal transmission and rejection. At this the two-layer discontinuity provides a wideband (up to 40 %) rejection with two-frequency characteristic of resonant reflection, and forms either two narrowband passband filters (about 3 %), or one wideband (up to 10 %) passband.


Introduction
The spectral approach for solution of boundary problems in micro-and millimeter wave range devices design was developed since 80-th years of last century [1]. In [2], the resonance frequencies technique calculation for multilayer planar structure consisted of microstripline resonator at coupled lines and tunable slot resonator in second plane is described. This technique is based on field description of shielded structure in spectral domain in the form of hybrid waves and boundary problem solution by Galerkin's method. The Green's functions formulated for the area being analyzed are universal and applied to various microstripstrip-slot structures. The generalized analysis and design technique for multilayer components based on combination of spectral approach (using immittance matrix) and standard methods of CAD is described in [3][4][5][6]. The interest of researchers in multi-layer planar structures, including DGS-structures (defected ground structure), does not weaken, on their basis, differential bandpass fi-lters, directional coupler and vertical transitions are designed [7][8][9][10][11][12][13][14][15].
In the paper [16], the scattering characteristics of fundamental wave in microstrip line at H-shaped slot resonators with various orientation relative to microstrip line were considered. It was shown, that the such discontinuities provide two-frequency, particularly, wideband attenuation, caused by the discontinues interaction at relatively big distances from each other. The scattering characteristics of multilayer distributed discontinuities included step discontinuity in microstrip line (inductive or capacitive sections) and narrow rectangular slot resonators were considered in works [17,18].
The aim of this work is improving the design technique and investigation of the scattering characteristics singularities at a two-layer distributed discontinuity in three-layer planar structure consisted the inductive microstrip section and H-shaped slot resonator with transversal arrangement of the "dumbbells" in ground plane. The potentially advantages of such structures are extended device functionality and compactness compared with conventional slot resonator [19]. resonator. The procedure of boundary problems solution for resonator with discontinuities in microstrip line and ground plane is described in detail in [17]. The algebraization of boundary problems is carried out using the waveguide basis functions ℎ( ) , , = 1.. , by which the field at aperture of complex shape slot resonator is decomposed, and using vector potentials (electric and magnetic) for the current density in nonhomogenous strip line (ℎ), ( , ) , = 1.. [17].
As in [17], the trigonometric basis is used to describe currents densities in nonuniform strip resonator, on the basis which the two-dimensional eigen functions The intersection points of spectral curves Γ 1 = Γ 2 define resonant interaction frequencies of the fundamental wave in microstrip line with discontinuity, at which the transmission coefficient | 12 | = | 21 | equals to zero.   (parameters of the structure are given in Fig. 6).
The spectra of the eigen frequencies and the characteristics of the two-layer distributed discontinuity with passband (9.6%) and wide stopband are shown in Fig. 8. It is seen that such characteristics can be obtained, if spectral curves obtained by solving the "electric" and the "magnetic" boundary problems have only one intersection point (intersection of two branches of strip modes), and curves of higher waveguide modes obtained by solving the "electric" and "magneto-electric" problems intersect at least in two points (Fig. 8).
In the two-frequency version of discontinuity topology the stop band is placed between two frequencies of resonant passing, Fig. 9a  Note that the developed algorithms allow analyze more complex structures and design wideband junctions and filters, for example, considered in [19]. Unlike [19], the above considered structures perform at least the two functions: passing and stopping in different microwave sub-bands.