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Abstract: In this paper, a folded stepped impedance resonator (SIR), modified by adding an inner quasi-lumped SIR stub, is used as a basis block for a new implementation of dual-band bandpass filters. The main advantage of the proposed filter is to make it possible to independently control the electrical features of the first and second bands. The behavior of the first band basically depends on the geometry of the outer folded SIR. The second band, however, is strongly influenced by the presence of the inner stub. Additional design flexibility is achieved by allowing the inner stub to be located at an arbitrary position along the high impedance line section of the main SIR. The position of the tapped input and output lines can be optimized in order to reach a reasonable matching of the filter at the central frequencies of both passbands. Some designs are reported to illustrate the possibilities of the proposed structure. Experimental verification has been included.
Abstract: This paper proposes an equivalent circuit model that uses lumped elements and transmission lines to explain the transmission of electromagnetic waves through a conducting screen periodically perforated with slits and sandwiched between two different dielectric slabs. The present model relies on the impedance-matching point of view, previously introduced by some of the authors, rather than on the surface plasmon polariton concept. Thus, the model constitutes a simple and insightful framework that easily leads to accurate qualitative and quantitative predictions about the nature of the transmission spectrum of such structures.
Abstract: Extraordinary transmission through periodic distributions of sub-wavelength holes made in opaque screens has been demonstrated and exhaustively studied along the last decade. More recently, extraordinary transmission has also been predicted and experimentally observed through electrically small diaphragms located inside hollow pipe waveguides. This last phenomenon cannot be explained in terms of surface waves excited along the periodic system (the so-called surface plasmon polaritons). Transverse resonances can be invoked, however, as a sound explanation for extraordinary transmission in this kind of systems. In this paper, a simple waveguide system, exhibiting exactly the same behavior previously observed in periodic 2-D arrays of holes, is analyzed in depth. Analogies and differences with the periodic case are discussed. The theoretical and experimental results reported in this paper provide strong evidence in favor of the point of view emphasizing the concept of impedance matching versus surface wave excitation. The role of material losses is discussed as an important practical issue limiting the maximum achievable subwavelength transmission level. Most of our conclusions can be applied to both periodic arrays of holes and diaphragms in closed waveguides.
Abstract: A new type of miniaturized stepped impedance resonator (SIR) for bandpass filter applications is proposed in this paper. The new resonator incorporates a ground plane window with a floating conductor in the backside of the substrate. The ground plane window increase the characteristic impedance of the lines used to implement the inductive region of the quasi-lumped resonator, thus allowing some size reduction. Moreover, the presence of a floating conducting patch printed below the capacitive region of the resonator pushes up the first spurious band of the filter. A meaningful improvement of its out-of-band rejection level is then achieved. The coupling between adjacent resonators is also enhanced thus leading to wider achievable bandwidths. Some filter designs using the new resonator and other standard resonators are included for comparison purposes.
June 2010. Abstract: This paper presents a simple analytical circuit-like model to study the transmission of electromagnetic waves through stacked two-dimensional (2-D) conducting meshes. When possible the application of this methodology is very convenient since it provides a straightforward rationale to understand the physical mechanisms behind measured and computed transmission spectra of complex geometries. Also, the disposal of closed-form expressions for the circuit parameters makes the computation effort required by this approach almost negligible. The model is tested by proper comparison with previously obtained numerical and experimental results. The experimental results are explained in terms of the behavior of a finite number of strongly coupled Fabry-Pérot resonators. The number of transmission peaks within a transmission band is equal to the number of resonators. The approximate resonance frequencies of the first and last transmission peaks are obtained from the analysis of an infinite structure of periodically stacked resonators, along with the analytical expressions for the lower and upper limits of the pass-band based on the circuit model.
Abstract: This paper presents a very simple analytical model for the analysis of the resonant transmission of microwaves or millimeter waves through periodically distributed slits in a thick metal screen. The model is based on equivalent circuits consisting of transmission line elements of known characteristic admittances and propagation constants loaded by capacitors. Closed-form analytical expressions are provided for all the circuit parameters. Alternatively, the circuit parameters can be quickly computed from numerical simulations carried out at a few frequency points. The proposed analytical model accounts for all the details of the observed transmission spectrum, including conventional Fabry-Perot (FP) resonances, which are controlled by the thickness of the screen, as well as extraordinary transmission peaks, which are related to the periodicity. The range of validity of the model as a function of dimensional parameters is discussed. The experimentally observed and numerically predicted redshift of the Fabry-Perot transmission peaks with respect to the ideal Fabry-Pérot resonance condition is accurately accounted for by the capacitors of the model. For narrow slits, the extraordinary transmission peak is linked to the singular behavior of the capacitances at the Rayleigh-Wood anomaly frequency point. Finally, the effect of the lossy nature of the metal screens is included in the model, providing accurate predictions of the transmission losses. Additionally, for lossy screens the model adequately predicts the anomalous behavior of the above mentioned redshift when the slit width becomes comparable to the skin depth in the metal, which is in good agreement with experimental and theoretical data previously reported for a single slit.
Abstract: Two-dimensional periodic arrays of noble metal nanospheres support a variety of optical phenomena, including bound and leaky modes of several types. The scope of this paper is the characterization of the modal dispersion diagrams of planar arrays of silver nanospheres, with the ability to follow individual modal evolutions. The metal spherical nanoparticles are described using the single dipole approximation technique by including all the retarded dynamic field terms. Polarizability of the nanospheres is provided by the Mie theory. Dispersion diagrams for both physical and nonphysical modes are shown for a square lattice of Ag nanospheres for the case of lossless and lossy metal particles, with dipole moments polarized along the x, y, and z directions. Though an array with one set of parameters has been studied, the analysis method and classification are general. The evolution of modes through different Riemann sheets and analysis of guidance and radiation are studied in detail.
Abstract: In this paper, we present a simple circuit model to study the absorption of electromagnetic waves by a multilayer structure with a high impedance surface in the microwave regime. The absorber consists of a stack of two-dimensional arrays of sub-wavelength meshes or patches separated by dielectric slabs and backed by a metallic ground plane, with a single resistive sheet placed on the top layer. We observe the appearance of low-frequency resonances of total absorption, which have been identified as the resonances of Fabry-Perot type associated with the individual reactively loaded dielectric slabs (that are strongly coupled through the subwavelength grids). It is shown that these resonances lie within certain characteristic frequency band defined by the structural parameters of the absorber. The observed resonances are characterized by studying the electromagnetic field behavior using the circuit model and full-wave numerical program. In addition, we show that the patch array absorber provides stable resonances with respect to the angle and the polarization of obliquely incident plane waves.
Abstract: The authors focus on the efficient computation of the slowly convergent infinite series that lead to the off-diagonal elements of the vector potential multilayered periodic dyadic Green’s function. Two different approaches based on Kummer's transformation are applied to the evaluation of these series. The well-known approach that makes use of the generalized pencil of functions (GPoF) and Ewald's method is the fastest approach, but it does not provide accurate results when the distance between the field point and any of the source points is close to zero. To avoid this problem, we present a novel approach based on the GPoF and the spectral Kummer-Poisson's method with higher-order asymptotic extraction. This latter approach is slightly slower than the former one, but it is accurate in the whole range of distances between the field point and the sources.
Abstract: This paper presents a quasi-analytical approach to study the classic topic of transmission/reflection of electromagnetic waves through 1-D periodic arrays of strips/slits in metal screens. The approach is based on standard waveguide discontinuity theory. Starting from field equations, it is inferred a circuit-like reduced-order model with just one parameter to be determined. The value of this parameter can be obtained from the transmission/reflection coefficient provided by any full-wave method at just one single frequency. In this way, the computation effort to obtain very wide-band responses of periodically distributed slits or strips under oblique TE/TM illumination in the presence of loading dielectric slabs is reduced to the full-wave analysis of the structure at a single frequency value. For relatively narrow strip/slit gratings, this procedure gives very accurate results even for very complicated transmission/reflection spectra. An additional advantage of the present approach is that it allows for an easy understanding of the underlying physics of the phenomena involved.
Abstract: This work reports on a modified version of lambda/2 open stubs bandpass filters (lambda/2-OSBPFs) and lambda/4 open stubs bandstop filters (lambda/4-OSBSFs) for wide/narrow bandwidth operation. When wide bandwidths (for lambda/2-OSBPF) or narrow bandwidths (for lambda/4-OSBSF) are required, conventional microstrip implementation of this kind of filters is not possible owing to unattainable high stub characteristic impedance values, which lead to extremely narrow strips. To overcome this drawback, we propose the introduction of slots under the stubs along the grounded backside of the substrate. This provides additional flexibility for the width of the strips printed on the upper side of the substrate, which can be much wider than without the slots. To avoid undesired resonances of the slot mode and radiation problems, printed narrow strip short circuits are distributed along the slotted regions. It is shown that the presence of these strips does not meaningfully affect the filter performance while suppresses the undesired slot mode effects.
Abstract: Here, we report on the transmissivity of electromagnetic waves through a stack of monolayer graphene sheets separated by dielectric slabs at low-terahertz frequencies. It is observed that the multilayer structure possesses band-gap properties and supports a series of bandpass and band-stop regions, similar to the cases of stacked metallic meshes separated by dielectric slabs at microwave/THz frequencies and a metal-dielectric stack at optical frequencies. The transmission resonances in the bandpass region are identified as coupled Fabry-Pérot resonances associated with the individual cavities of dielectric slabs loaded with graphene sheets. It is also noticed that these resonances lie within a certain characteristic frequency band, independent of the number of layers in the graphene-dielectric stack. The study is carried out using a simple analytical transfer-matrix approach or, equivalently, a circuit-theory model, resulting in the exact solution for the multiple dielectric/graphene sheet surface-conductivity model. Also, an independent verification of the observed phenomena is obtained with commercial numerical simulations.
Abstract: In this study the authors present a new surface-impedance model for the accurate computation of the effect of metal losses on the parameters of printed microstrip lines. The novelty of the authors approach lies in the fast and direct calculation of the tangential magnetic fields above and below the strip conductors, which allows us to develop a very efficient quasi-transverse electromagnetic (TEM) solution for the conductor losses of multilayer single or coupled microstrip lines. The overall computational effort of the authors's method is much less than that required by purely numerical approaches. The accuracy of the method has been verified by comparison with other techniques, including a general-purpose full-wave finite elements method. It is also shown that the proposed method provides better results than other previously surface-impedance approaches.
Abstract: In this paper, we study the transmissivity of electromagnetic waves through stacked two-dimensional printed periodic arrays of square conducting patches. An analytical circuit-like model is used for the analysis. The model accounts for the details of the transmission spectrum provided that the period of the unit cell of each patterned layer is well below the wavelength in the dielectric slabs separating the printed surfaces. In particular, we analyze the low-pass band and rejection band behavior of the multilayer structure, and the results are validated by comparison with a computationally intensive finite element commercial electromagnetic solver. The limiting case of an infinite periodic structure is analytically solved and the corresponding band structure is used to explain the passband/stopband behavior of finite structures. In addition, we study in depth the elementary unit cell consisting of a single dielectric slab coated by two metal patch arrays, and its resonance behavior is explained in terms of Fabry-Pérot resonances when the electrical thickness the slab is large enough. In such case, the concept of equivalent thickness of the equivalent ideal Fabry-Pérot resonator is introduced. For electrically thinner slabs it is also shown that the analytical model is still valid, and its corresponding first transmission peak is explained in terms of a lumped-circuit LC resonance.
Abstract: This paper is focused on the application of complementary split-ring resonators (CSRRs) to the suppression of the common (even) mode in microstrip differential transmission lines. By periodically and symmetrically etching CSRRs in the ground plane of microstrip differential lines, the common mode can be efficiently suppressed over a wide band whereas the differential signals are not affected. Throughout the paper, we present and discuss the principle for the selective common-mode suppression, the circuit model of the structure (including the models under even- and odd-mode excitation), the strategies for bandwidth enhancement of the rejected common mode, and a methodology for common-mode filter design. On the basis of the dispersion relation for the common mode, it is shown that the maximum achievable rejection band-width can be estimated. Finally, theory is validated by designing and measuring a differential line and a balanced bandpass filter with common-mode suppression, where double-slit CSRRs (DS-CSRRs) are used in order to enhance the common-mode rejection bandwidth. Due to the presence of DS-CSRRs, the balanced filter exhibits more than 40 dB of common-mode rejection within a 34% bandwidth around the filter pass band.
Abstract: This work presents an equivalent circuit to model the transmission/reflection of a plane wave that impinges obliquely on a periodic arrangement of metallic rectangular dipoles embedded between two dielectric slabs. The equivalent circuit takes advantage of the periodicity of the structure to reformulate the original problem as a certain equivalent waveguide scattering problem. Equivalent transmission lines are used to simulate the wave propagation whereas equivalent lumped circuit elements account for presence of the metallic patches. The obtaining of the circuit parameters is carried out via a systematic procedure, which provides a robust strategy that gives rise to surprisingly accurate results even for rather complex situations. The proposed equivalent circuit model simplifies considerably the original complex electromagnetic problem and provides a valuable physical insight into the parameters that are relevant in the phenomenon as well as an in-depth understanding of the operation principles of the periodic surface. Thus, the reported reduced-order model of the corresponding scattering problem can be a very convenient and helpful tool for the analysis and/or design of many practical devices.
Abstract: An analytical model is presented for the analysis of multilayer wire media loaded with 2-D arrays of thin material terminations, characterized in general by a complex surface conductivity. This includes the cases of resistive, thin metal, or graphene patches and impedance ground planes. The model is based on the nonlocal homogenization of the wire media with additional boundary conditions (ABCs) at the connection of thin (resistive) material. Based on charge conservation, new ABCs are derived for the interface of two uniaxial wire mediums with thin imperfect conductors at the junction. To illustrate the application of the analytical model and to validate the new ABCs, we characterize the reflection properties of multilayer absorbing structures. It is shown that in such configurations the presence of vias results in the enhancement of the absorption bandwidth and an improvement in the absorptivity performance for increasing angles of an obliquely incident TM-polarized plane wave. The results obtained using the analytical model are validated against full-wave numerical simulations.
Abstract: This paper presents a fully analytical model to determine the transmission and reflection properties of planar 1-D distributions of metal strips or slits made in thin metal screens. In contrast with other analytical or quasi-analytical approaches, the formulation incorporates the presence of dielectric slabs and is valid over a wide frequency band, from the long wavelength limit to the grating lobes operation. The model has been adapted to the case where two 1-D planar grids are stacked or a single grid is printed on a grounded substrate. In these cases, the model rigorously takes into account higher order mode interaction between the two stacked arrays of strips/slits or with the ground plane. Oblique incidence and both TE and TM polarizations have been considered. The analytical results show a good agreement with those computed by high-performance numerical methods, accounting for very fine details of extremely complicated transmission/reflection spectra. These results are of straightforward application to a variety of practical situations from microwaves to the terahertz regime. The present methodology can still be useful at higher frequencies provided that adequate models of the planar conductors are incorporated. In general, the model provides physical insight on the nature of the expected spectra and facilitates the design of devices based on planar metallic gratings.
Abstract: An efficient technique is presented for the analysis of finite printed antenna arrays made of identical elements. It is based on a closed-form expression for the spatial-domain Green's function (GF) given as a finite sum of cylindrical waves (obtained through rational function fitting) plus one spherical wave. From there, a multipole expansion can be obtained for planar layered medium GFs. The macro basis function (MBF) technique is applied to the method of moments (MoM) solution of a mixed-potential integral equation, this reduces the size of the MoM impedance matrix and allows for a direct solution. However, the evaluation of the entries of this reduced matrix becomes the dominant contribution to the total computation time. The aforementioned multipole expansion is exploited to provide a fast construction of the reduced MoM matrix, whose elements are the reaction integrals between the MBFs considered to characterize the currents on the array element. The complexity of evaluating the interactions between MBFs is found to be dominated by the calculations related to the spherical wave term. Thus, taking into account the layered medium does not increase the order of the complexity with respect to a multipole-accelerated computation of reaction integrals in a homogeneous medium.
Abstract: In this article, the Method of Moments in the spectral domain (MoM-SD) is applied to the analysis of multilayered periodic structures, containing three coplanar parallel dipoles in the unit cell. It is shown that the use of basis functions with edge singularities in the modeling of the current density on the dipoles leads to important computer memory and CPU times savings in the analysis of the periodic structures. The MoM-SD home-made software is used in the analysis of a shaped beam reflectarray antenna made of cells with three parallel dipoles under the local periodicity assumption. The numerical results obtained for the radiation pattern of the antenna are compared with numerical results provided by the commercial software CSTV and with measurements and good agreement is found.
Abstract: A study of the propagation characteristics and several signal integrity aspects of a conventional coplanar waveguide (CPW) is presented here. The study considers the bound and leaky modes supported by this structure up to high frequencies. The analysis of the dispersion characteristics of the structure is complemented with the study of the voltage excited along the line when fed by a delta-gap source of current. The results thus obtained allow us to discuss on the physical meaning of the modes and the relevance of the residual wave, which is key to link the practical role played by the different modal solutions with the spurious effects that may appear in the structure. The analysis of the eye-diagram performance also reveals that the signal integrity in CPW systems basically relies on the excitation of the parasitic fundamental coupled slotline mode as well as the high-frequency excitation of the continuous spectrum. These aspects have been studied in detail.
Abstract: The method of moments (MoM) is applied to the analysis of the scattering of a multilayered periodic strip grating by a plane wave with oblique incidence and arbitrary polarization. Although this problem has been traditionally solved by means of the MoM in the spectral domain, this is an approach which leads to the computation of slowly convergent infinite summations. In this paper, the problem is solved by means of the mixed potential integral equation (MPIE) formulation of the MoM in the spatial domain. While applying the MoM in the spatial domain, two improvements are introduced which lead to important CPU time savings. First, the multilayered periodic Green's functions are accurately interpolated in terms of Chebyshev polynomials. Second, half the integrals involved in the computation of the MoM matrix entries are obtained in closed form. As a consequence of these two improvements, the spatial domain version of the MoM presented in this paper turns out to be between one and two orders of magnitude faster than the conventional spectral domain version when basis functions that account for edge singularities are used in the modeling of the current density on the metallizations.
Abstract: A broadband reflectarray cell made of three parallel dipoles printed on a dielectric layer is presented. A 33 % bandwidth is achieved for the cell made of dipoles, which is larger than that obtained for a reference cell consisting of three stacked square patches (26%). Using this cell, a 41-cm reflectarray antenna has been designed to produce a collimated beam at 9.5 GHz. The numerical results obtained for the reflectarray antenna made of parallel dipoles show a 1-dB bandwidth of 19 %, a 65 % efficiency, 0.2 dB of losses, and low levels of cross polarization (25 dB below the maximum). These results demonstrate a high performance for the proposed reflectarray antenna made of cells with three printed dipoles.
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