Research in microwave/RF passive devices at UMH-UA
Abstract—The Radiofrequency Systems Group at UMH (Universidad Miguel Hern´andez of Elche), in collaboration with Dr. Stephan Marini from the University of Alicante, has worked in the last years in different research lines. On one hand, we have studied the dispersion properties of periodic structures, in the case of both open and guiding media, through their Brillouin diagram, which provides their allowed and forbidden frequency bands of propagation, and it has been successfully compared to the transmittance of the corresponding periodic lattices of finite dimensions. On the other hand, a very efficient procedure to determine the wideband generalized admittance matrix representation of complex waveguide filters (e.g. in-line direct-coupled-resonator filters with tuning screws, evanescentmode filters with cylindrical conducting posts, as well as folded configurations of real comb-line filters) has been developed, which can also integrate a standard (vertical) or collinear coaxial excitation. In a different field dealing with high-power devices, we have developed a Montecarlo algorithm for studying the multipactor effect in microwave waveguides partially loaded with dielectric layers. In particular, the dependence of the multipactor effect in a parallel-plate dielectric-loaded waveguide on the different geometrical and electrical parameters of the waveguide has been investigated. In addition, we are developing a simulation tool to analyze the multipactor effect in a rectangular waveguide loaded with dielectric layers, including corrugated surfaces.
I. I NTRODUCTION The Radiofrequency Systems Group is formed by Ph. D. En´ rique Bronchalo, Ph. D. Angela Coves, Ph. D. Germ´an Torre´ grosa and Ph. D. Angel A. San Blas from the Departamento de Ingenier´ıa de Comunicaciones of UMH (Universidad Miguel Hern´andez of Elche), This research group, in collaboration with Ph. D. Stephan Marini from the Departamento de F´ısica, Ingenier´ıa de Sistemas y Teor´ıa de la Se˜nal of UA (Universidad de Alicante), has worked in the last years in different research lines which are developed separately in the next sections. II. F ULL -WAVE ANALYSIS OF PERIODIC STRUCTURES A novel full-wave method for the modal characterization of dielectric electromagnetic band-gap structures under oblique plane wave excitation has been developed [1], showing the dielectric lattice periodicity in both the longitudinal and the transverse propagation directions, as shown in Fig. 1. In this method, an eigenvalue problem is obtained in terms of the
Departamento de F´ısica, Ing. Sistemas y Teor´ıa de la Se˜nal Universidad de Alicante 03690 San Vicente del Raspeig, Alicante, Spain
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Departamento de Ingenier´ıa de Comunicaciones Universidad Miguel Hern´andez de Elche Avda. de la Universidad s/n 03202 Elche, Alicante, Spain Email:
[email protected]
Stephan Marini
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´ Enrique Bronchalo, Angela Coves, ´ Germ´an Torregrosa and Angel A. San Blas
Fig. 1. Two-dimensional dielectric electromagnetic band-gap structure under oblique plane wave excitation given by the wave-number vector kinc with an angle of incidence θ. The dashed-line rectangle represents an elemental cell of the lattice with a double periodicity Dy and Dz in the y and z directions, respectively; the material is uniform in the x axis.
generalized ABCD matrix of the periodic cell, whose solution provides not only the propagation constant of the fundamental Floquet mode, but also of the higher order modes of the global periodic structure. In order to check the accuracy and efficiency of the proposed formulation, we have computed and represented in Fig. 2(a) the Brillouin diagram of the first three Floquet modes of an EBG material whose transmittance was studied in [2]. The proposed analysis technique has been successfully validated with HFSS (a commercial software based on the frequency domain finite element method) (see Fig. 2). The transmittance of a finite number of unit cells is also successfully verified in Fig. 2 for 100 periods through comparisons with theoretical results reported in [2]. In addition, we have studied the case of a finite EBG that has a periodic defect in the middle of the structure with two possible configurations, denoted as donor and acceptor defect. We present the case of a finite length 2D EBG made of NL = 25 rod layers with identical characteristics to that described in Fig. 2 in which the defect results from the modification of the depths hp and
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Fig. 3. Transmission coefficient versus ωDz /c for TE polarization (at normal incidence) in a periodic structure with a central defect. The geometrical and physical parameters are: NL = 25, Dy = Dz = 10 mm, l1 = l2 = 5 mm, hp = hh = 5 mm, εr1 = εrh = 1, εr2 = 4. Characteristics of the central periodic cell acting as a donor state: hp = 9 mm, hh = 1 mm (black dash line). Characteristics of the central periodic cell acting as an acceptor state: hp = 1 mm, hh = 9 mm (blue solid line).
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(b) Fig. 2. (a) Brillouin diagram under normal T E plane-wave excitation of an EBG structure with the following parameters: Dy = Dz = 10 mm, l1 = l2 = 5 mm, hp = hh = 5 mm, εr1 = εrh = 1, εr2 = 4. The solid lines correspond to the first mode, the dashed lines represent the second one, whereas the dotted lines represent the third mode. The points show a pair of complex modes, and the circles are the results obtained with HFSS for comparison. (b) Transmittance of 100 periods of this structure.
hh of the central cell of the periodic lattice. Fig. 3 shows in black dash line the transmittance when the central cell has the modified depths of hp = 9 mm and hh = 1 mm, then acting as a donor defect, while in blue solid line it is represented the transmittance of the same periodic material but with an acceptor defect characterized by hp = 1 mm and hh = 9 mm. In this way, this study could be used to tune a narrow bandpass transmission filter. III. CAD OF C OMPLEX PASSIVE D EVICES COMPOSED OF A RBITRARILY S HAPED WAVEGUIDES USING BIRME AND I NTEGRAL E QUATION M ETHODS A hybrid method for the fast and rigorous analysis of complex microwave components composed of cascaded waveguides with arbitrarily shaped cross-section has been developed. For such purposes, an Integral Equation (IE) based modal method originally described in [3] for rectangular geometries has been updated to cope with more complex structures. The objective of this technique is to obtain a multimodal representation of each junction in terms of a Generalized Impedance
Matrix (GIM). The modal method makes use of the modal chart of waveguides with arbitrary cross-section (defined by a combination of straight, circular and/or elliptical segments), which is determined following a revisited version [4] of the classical and well-known BI-RME technique [5]. This rigorous analysis technique has been successfully integrated within a CAD tool of complex microwave passive devices for space applications. Making use of such CAD software package, we can first solve the modal chart of waveguides with arbitrary cross-section, the electromagnetic fields and the complex propagation constants of propagative and also evanescent modes. Next, the new software developed has been used to the analysis and design of modern complex passive waveguide devices like dual-mode filters, evanescent-mode ridge filters and a new twist component for K-band application. A detailed view of the internal pieces of this last device is shown in Fig. 4. The structure presents a compact geometry based on a soft rotation of the E-field through successive square, circular and elliptical waveguides. In Fig. 4 the measurements of a prototype of such device, operating at 26.3 GHz and with a bandwidth of approximately 2 GHz, have been completely recovered by simulated data using a conductivity value of σ = 106 S/m. Finally, the CAD tool developed has been also employed for the full-wave modal analysis of periodic waveguide structures. A new algorithm is used to identify the higher order Floquet modes, as well as to compute the related Brillouin diagrams, of complex closed metallic periodic structures loaded with arbitrarily shaped waveguides [6]. For instance, a rectangular waveguide periodically loaded with centered cross-shaped irises, whose geometry and dimensions can be seen in Fig. 5, has been analyzed. Fig. 6 shows the real and imaginary parts of the normalized propagation constant as a function of k0 p for the first three Floquet modes of such structure. As can be
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Fig. 4. Comparison between simulated and measured scattering parameters for the manufactured 90-twist component. To recover the measurements, a finite conductivity value of σ = 106 S/m has been assumed in the simulation.
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observed, the software tool allows the accurate computation of the dispersion diagram related to the fundamental and higher order Floquet modes. Propagating, evanescent and complex modes of this periodic structures have been properly identified, sorted and computed. IV. CAD FOR THE FULL WAVE ANALYSIS AND DESIGN OF COMPLEX PASSIVE WAVEGUIDE FILTERS INCLUDING COAXIAL EXCITATION
The main objective consists of developing a very efficient CAD tool, that must be able to avoid the repetition of the cumbersome computations performed in the frequency domain, for the analysis and design of complex waveguide devices composed of rectangular cavities loaded with partialheight metallic cylindrical posts, planar waveguide junctions, uniform waveguide sections and boxed resonators including a coaxial excitation (either vertical or collinear). To this aim, the 3D BI-RME (Boundary Integral - Resonant Mode Expansion) method [7] is first applied to derive a wideband Y -matrix used to characterize boxed resonators with inserted metallic posts that can be fed by a generalized coaxial probe. Next, the new
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Fig. 6. Dispersion response for a rectangular waveguide periodically loaded with centered cross-shaped irises shown in Fig. 5. In solid line the first Floquet mode, other higher order Floquet modes in dashed (second) and dashdot (third) lines. The points represent a pair of complex modes.
formulation proposed in [8] is used to characterize the planar waveguide junctions of the structure, thus obtaining a Y matrix with the same form as the one provided by the BI-RME formulation. Finally, the algorithm proposed in [9], which has been extended in order to cope with folded structures including cross-couplings, allows the wideband cascade connection of the previous key building blocks preserving the same form of the pole expansions for the Y -matrices. This CAD tool has been successfully used to design different waveguide filters, all of them including integrated coaxial excitations and partialheight conducting posts. In order to test the accuracy and efficiency of the proposed method, a C-band folded comb-line filter for satellite applications, considering the presence of tuning screws in the center of the resonant cavities, has been successfully designed, manufactured and measured (see Fig. 7). The designed filter is composed of 6 boxed cavities and it includes a collinear discended coaxial excitation. As it can be seen, tuning screws have also been introduced in the coupling windows, for compensating mechanical manufacturing tolerances and fine tuning of the in-band return losses. In Fig. 7, the simulated and measured in-band responses of the comb-line filter are well compared. Apart from compensating the manufacturing tolerances, the tuning screws of the coupling windows have been arranged in order to enhance the in-band electrical response (return losses) of the real structure. The complete simulation of the originally designed comb-line filter (i.e. without considering the presence of the tuning screws in the coupling windows) has requested a CPU effort of 491 s for the full-wave analysis of 601 frequency points. V. M ULTIPACTOR EFFECTS ON WAVEGUIDES LOADED WITH DIELECTRICS
The electron discharge (multipactor) phenomena in parallelplate dielectric-loaded waveguides (see Fig. 8) has been investigated, and its dependence on the different geometrical and electrical parameters of the waveguide under study (different height, dielectric constant, and secondary emission yield
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Fig. 9. Susceptibility chart of a silver parallel-plate dielsilver -loaded waveguide with h/d = 0.5 and εr = 9.5.
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Scattering parameters of the manufactured filter.
VI. C ONCLUSION The different research lines in which the Radiofrequency Systems Group at UMH, in collaboration with Ph. D. Stephan Marini from UA, has worked in the last years have been described, being all of them involved in applications of Electromagnetism to various branches of Electrical Engineering. ACKNOWLEDGMENT This work was financially supported by the Ministerio de Ciencia e Innovaci´on (grant TEC2010-21520-C04), Spain. R EFERENCES
Fig. 8. A parallel-plate waveguide partially filled with a dielectric material of relative permittivity εr . The distance between the two metallic parallel surfaces is d, while the dielectric slab, of height h, is placed on top of one of the metallic plates.
(SEY) responses are considered). The model presented in [10] is used for solving the dynamics of an effective electron, conditioned by the external RF electric field, the dc electric field appearing because of the charging of the dielectric surface, and the repulsion of the charge density existing between the plates. The differences between susceptibility charts in a parallel-plate waveguide with parameters d = 3 mm, h = 1.5 mm and A = 10 cm2 loaded with a fictitious dielectric material, which shares with silver the same SEY properties, have been studied, when varying different geometrical and electrical parameters of the waveguide. As an example, Fig. 9(a) shows a displacement of the multipactor regions to higher f × d and lower V0 values from the empty silver parallel-plate waveguide chart (light gray dots) when a dielectric layer of height h = 0.5d is used to load the structure (black dots). As it is shown in [11] the motion of an electron inside the waveguide is determined by the RF field amplitude, so that if the new axes E0 × (d − h) and f × (d − h) are considered, then as seen in Fig. 9(b), both susceptibility diagrams agree once more. Realistic susceptibility charts have also been computed employing experimental SEY measurements from different metallic and dielectric materials. In addition, we are developing a simulation tool to analyze the multipactor effect in a rectangular waveguide loaded with dielectric layers, including corrugated surfaces.
[1] A. Coves, S. Marini, B. Gimeno, and V.E. Boria, “Full-Wave Analysis of Periodic Dielectric Frequency-Selective Surfaces Under Plane Wave Excitation,” IEEE Transactions on Antennas and Propagat., vol. 60, pp. 2760–2769, Jun. 2012. [2] F. Frezza, L. Pajewski, and G. Schettini, “Characterization and Design of Two-Dimensional Electromagnetic Band-Gap Structures by Use of a FullWave Method for Diffraction Gratings,” IEEE Transactions on Microw. Theory Tech., vol. 51, pp. 941–951, Mar. 2003. [3] G. Gerini, M. Guglielmi, and G. Lastoria, “Efficient integral equation formulations for admittance or impedance representation of planar waveguide junctions,” in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, Jun. 1998, vol. 3, pp. 1747–1750. [4] S. Cogollos, S. Marini, V. E. Boria, P. Soto, A. Vidal, H. Esteban, and J. V. Morro, “Efficient modal analysis of arbitrarily shaped waveguides composed of linear, circular and elliptical arcs using the BI-RME method,” IEEE Trans. Microwave Theory and Tech., vol. 51, no. 12, pp. 2378–2390, Dec. 2003. [5] G. Conciauro, M. Guglielmi, and R. Sorrentino, Advanced Modal Analysis. New York, NY: John Wiley & Sons, 2000. [6] S. Marini, A. Coves, V. E. Boria, and B. Gimeno, “Efficient modal analysis of periodic structures loaded with arbitrarily shaped waveguides,” IEEE Trans. Microwave Theory Tech., vol. 58, no. 3, pp. 529–536, Mar. 2010. [7] P. Arcioni, M. Bozzi, M. Bressan, G. Conciauro, and L. Perregrini, “Frequency/Time-Domain modeling of 3D waveguide structures by a BIRME approach,” Int. J. Numer. Model.-Electron. Netw. Device Fields, vol. 15, no. 1, pp. 3–21, 2002. [8] F. Mira, A. A. San Blas, V. E. Boria, and B. Gimeno, “Efficient pole expansion of the generalized admittance matrix representation of planar waveguide junctions,” Proc. 38th Eur. Microw. Conf., pp. 650–653, 2008. [9] P. Arcioni and G. Conciauro, “Combination of generalized admitance matrices in the form of pole expansions,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 10, pp. 1990–1996, Oct. 1999. [10] A. Coves, G. Torregrosa-Penalva, C. P. Vicente, A. M. P´erez, B. Gimeno, and V. E. Boria, “Multipactor discharges in parallelplate dielectricloaded waveguides including space-charge effects,” IEEE Trans. Electron Devices, vol. 55, no. 9, pp. 2505–2511, Sep. 2008. [11] G. Torregrosa-Penalva, A. Coves, B. Gimeno, I. Montero, C. Vicente, and V. E. Boria, “Multipactor Susceptibility Charts of a Parallel-Plate Dielectric-Loaded Waveguide,” IEEE Trans. Electron Devices, vol. 57, no. 5, pp. 1160–1166, May 2010.
