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Computer-Aided Design of Complex Waveguide Filters for Space Communication Systems J. V. Morro, C. Bachiller, H. Esteban, V. E. Boria Instituto de Telecomunicaciones y Aplicaciones Multimedia (iTEAM) Universidad Politécnica de Valencia Building 8G, access D, Camino de Vera s/n 46022 Valencia (SPAIN) Corresponding author: hesteban@dcom.upv.es Abstract risk of radiofrequency breakdown decreases. Mo- reover, if the dielectric posts are circular the ma- This paper presents a case study of advanced op- nufacturing effort is dramatically reduced com- timization techniques for the automated design pared to square shapes. However, the accurate of complex waveguide filters for space appli- modeling of the circular dielectric resonators is far cation, and a detailed study of the multipactor more complex than for square ones, since circu- effect in different H-plane waveguide filters: all lar and rectangular geometries must be analyzed metallic, loaded with dielectric cylinders and together. Other drawback to the use of dielectric evanescent mode. loading materials in the filters is the increase of loss level due to the dielectric tangent factor. Keywords:multipactor, waveguide filters, dielec- tric cylinders, space communications, computer This paper begins with a case study of advan- aided design, optimization, aggressive space ced optimization techniques for the automated mapping, segmentation, hybridization, genetic design of complex waveguide filters for space algorithms applications. The accurate design of electromag- netic (EM) structures requires a tradeoff between 1. Introduction accuracy and computation time. When designing complex structures, the use of a very accurate si- There are many reasons that lead to develop new mulation tool can be unaffordable. The Aggressive topologies of high frequency filters for space Space Mapping (ASM) methodologies address this applications, i.e: reduction of mass and volume, issue. Aggressive Space mapping [3] can be used increase of thermal stability for high power appli- to reduce the computational burden by using two cations, increase of out-of-band rejection, reduc- different simulation tools of different accuracy tion of manufacturing effort, availability of analy- and efficiency: an efficient but not very accura- sis and design tools for synthesizing a desired te tool (coarse model) in the optimization space response and reduction of risk of radiofrequency (OS), and an accurate but not very efficient tool breakdown (i.e. Multipactor effect [1], [2]). (fine model) in the validation space (VS). These methodologies move the computational burden Rectangular waveguide H-plane filters are one of to the OS, thus reducing the overall computation the most popular technologies for implementing time, while the accuracy is still guaranteed by the satellite communications filters, and many efforts use of the fine model. Although ASM has proved are being devoted to improve their capabilities. The to be very useful for EM design, there is still much development of new topologies in this technology research dedicated to improve the robustness has been historically limited by the availability of and performance of ASM [4]. As an alternative to CAD tools that allow implementing a filter with a those extensions of ASM, we proposed to improve required response and several predefined improve- the ASM approach by using a segmentation and ments in terms of mass, stability or high power ef- hybridization strategy. The speed and robustness fects (i.e. multipactor). An efficient Computer-Aided of the optimization process can be greatly impro- Design (CAD) software package requires a fast and ved by decomposing the structure as proposed in accurate analysis tool for the selected topology [5] and [6]. Moreover, the design process can still and a reliable optimization strategy. be improved by using a suitable combination of several optimization algorithms instead of using The topologies that are analyzed and designed in a single all-purpose technique such as a genetic this work are rectangular waveguide H-plane fil- algorithm. In this paper, the completely automa- ters loaded with cylindrical dielectric posts. When ted CAD tool recently proposed in [7], which does introducing these elements in the filter, the mass not require human intervention, is adapted for the and volume are reduced, the thermal stability and accurate design of several complex waveguide the out-of-band rejection are increased, and the filters: H-plane coupled cavities filters with and 106 ISSN 1889-8297 / Waves · 2009 · year 1 without tuning elements, and novel designs with dielectric resonators. Then, this work presents the results for the multi- pactor effect in the different topologies of filters designed, i.e all metallic ones, filters loaded with circular dielectric posts and evanescent mode fil- Table 4. Types of filters considered in this work. ters loaded with dielectric posts (see Fig. 1). The study has been made on the basis of a multimodal analysis method [8] that enables the computation ŋ near zero. At each iteration j, the next point is of the electromagnetic fields inside the filter and found by a quasi-Newton iteration: the dielectric posts in a very accurate and efficient way. The results for such electromagnetic fields have been successfully compared to results ob- tained with a commercial simulator (Ansoft HFSS 1.2 [9]). Then a comparative study of the multipactor effect that can appear between the two metallic where x(0) = x* and h(j) solves the linear system: em os surfaces of each filter has been performed. In order to achieve a fair comparison, the study was made B(j)•h(j)=-f(j) on several filters with the same frequency respon- 1.3 se. The filters loaded with dielectric posts are sma- ller than all the metallic ones, and some of them B(j) is an approximation to the Jacobian matrix have also a better out-of-band rejection behavior. and is obtained from B(j-1) using the Broyden up- Considering the multipactor discharge, the study date [3]. concludes that the dielectric posts concentrate the electric field inside them, thus producing a smaller level of electromagnetic field outside the dielectric 3. Aggressive Space Mapping with posts than for the all-metallic filters. Following the Segmentation and Hybridization premise that the multipactor discharge can only appear between the metallic surfaces of the filter, Segmentation the dielectric loaded filters can handle more power In [4] and [10], a segmentation strategy was pro- without risk of multipactor breakdown. posed for the design of some filter structures, such as H-plane coupled cavity filters composed of N resonant cavities and N+1 coupling win- 2. Aggressive Space Mapping dows. This segmentation technique transforms Method a slow multidimensional design process into several efficient and robust design steps, whe- The original ASM strategy describes the beha- re a small number of parameters are designed vior of a system by means of two spaces models: at the same time. However, there is the risk that the optimization space (OS), denoted by Xos, and the coupling among all cavities (not just among the validation space (VS), denoted by Xem. We adjacent cavities) is not properly taken into ac- represent the designable model parameters in count. To solve this problem, the segmentation these spaces by the vectors Xos and Xem, respec- strategy proposed in [11] adds new steps to the tively. The objective of the ASM procedure is to original strategy. The resulting new segmenta- find the optimum point Xem in VS that minimizes tion strategy designs the filter through the steps the following non-linear function: summarized in Table I. f(xem )=P(xem )-x*os The Ordinary step designs the parameters rela- ted to cavity i simulating the i first cavities, and 1.3 using for the rest of parameters of the i-1 first cavities the values obtained in former iterations. where X*os is the optimum point in OS and P(xem ) The error function is computed comparing the is the point in OS that satisfies Rf(xem )=Rc(P(xem)), response of the i first cavities with the ideal res- Rf and Rc being the vectors with the responses of ponse. The ideal response of the i first cavities is the fine and coarse models. The ASM procedure obtained using the first i resonators of the proto- finishes when ||f(xem )|| is below some threshold type composed of impedance inverters and half- Table 1. Steps of the proposed segmentation design strategy. Waves · 2009 · year 1 / ISSN 1889-8297 107 wavelength transmission lines. The Coupling the filter, independently of the frequency value. Both the step adjusts, every three cavities, all the design The input threshold power is also a function of parameters of the cavities previously designed, the frequency and can be calculated by using efficiency thus achieving the required small changes in the VMFmax, the characteristic impedance Z0 and robust- the values of the parameters due to couplings and the threshold voltage Vmulti that enables ness can be among cavities. The Central Cavity step designs the multipactor breakdown. This value can be drastically the dimensions of the central cavity simulating obtained by using Multipactor Calculator [14] improved the whole filter structure, and the Final step re- and depends on the type of metallic surface and when a fines the design taking into account all possible the frequency-gap product. suitable interactions among cavities. combination of optimi- Hybrid Optimization zation algo- Both the efficiency and robustness of the opti- 1.4 rithms is used mization process can be drastically improved when a suitable combination of optimization algorithms is used instead of a single algorithm. If only a gradient method is used, it may fail to 1.5 reach the optimum if the starting point is far from it. On the other hand, the use of a robust The minimum of this equation in the whole method such as the simplex method or genetic frequency band provides the maximum power algorithm, largely used in circuit design applica- that the device can handle without multipactor tions, ensures convergence, but at the cost of breakdown. a low efficiency. So, the design procedure has been improved using a suitable combination Distribution of electromagnetic field inside of optimization algorithms in each parameter the filters extraction phase and also in the optimization This section describes the procedure for obtai- needed to obtain x*os. Robust non-gradient meth- ning the distribution of electrical field inside the ods (direct search and simplex) are used at the structures as a function of the frequency. beginning, and, after some iterations, when we are close to the minimum, an efficient gradient All-metal cavities filter algorithms (Broyden-Fletcher-Goldfarb-Shanno The field distribution is obtained from the mul- (BFGS)) is used to refine the solution. This com- timodal scattering matrices (GSMs) of each one bination of algorithms has been proved to per- of the segments that compose the structure of form better than one algorithm alone. The shift the filter. In Fig. 2 the different segments and from one optimization algorithm to another matrices are shown. GSMs of the step (S2, S4, S6, one is controlled by the parameter termination S8…) can be calculated following the well-known tolerance xtol, the termination tolerance of the Mode Matching Method [15], and the GSMs of error function (ftol), and the maximum number of the lines (S1, S3, S5, S7…) are obtained through function evaluations (nFmax) permitted to each analytic expressions. The global GSM is obtained method. ftol is higher for the first algorithm, and using a new efficient recursively connection its value is decreased in each subsequent algo- technique proposed in [16]. rithm. The shift from one algorithm to another, as well as the rest of the whole design process is Fig. 3 shows the regions where the electric field is fully automated, so that no human intervention calculated. For each region the field distribution is needed at all. is obtained by using the following equation [17]: 4. Multipactor breakdown in waveguide filters 1.6 Multipactor effect prediction where The Hatch and Williams [12] model has been Mi is the number of modes in the i segment of used for the study of the multipactor effect insi- the filter. Typically Mi=11. de the filters. In this model, the maximum input power without multipactor breakdown is calcu- xi and zi are the coordinates as defined in Fig. 3. lated by using the electric field distribution insi- de the structure. In the model, the “Voltage Magnification Factor” VMF [13] is defined as the maximum voltage in the structure versus the input voltage (Vin) for all the frequencies. This factor is calculated for all the points inside the filter and the VMFmax is de- fined as the maximum of VMFs. During this work we have found that the maximum of electrical Figure 2. Segments and GSMs matrices of all- field appeared always in the same point inside metal cavities filter. 108 ISSN 1889-8297 / Waves · 2009 · year 1 am(i) y bm(i) are the modal vectors of incident and reflected waves between segments i-1 and i as defined in Fig. 2. is defined in equation. bi is the height and ai the width of each section. Figure 3. Regions for the computation of the electric field. 1.7 Filter loaded with dielectric cylinders Fig. 4 shows the filter with dielectric cylinders and the different segments in which the filter is divided. There are three different types of seg- ments: lines, steps and segment of line loaded with dielectric cylinder. For each one of them a different method is used for the computation of GSMs and the electric field. As in the previous filter, the GSMs of the steps (S2, S4, S8, S10…) are calculated by using the Mode Matching Method [15] and the GSMs of the lines (S1, S3, S5, S7…) are computed analytically. For obtaining the GSMs of the segments loaded with dielectric cylinders Figure 4. Segments and GSMs matrices of the filter loaded with dielectric cylinders. (S6,S12…) the hybrid mode matching method is used [17]. Then all the matrices are connected as described in [16] in order to get the global GSM of the filter. For regions i=1, 3, 5, 6a, 7, 9, 11… (see Fig. 5) the electric field is calculated as described in the previous subsection. The field in regions 6b, 12b... (see Fig. 5) is obtained by using the equation , where Jp and H(2) are the Bessel p and second order Hankel functions, and in and cn are the incident and scattered spectrum coeffi- cients in cylindrical coordinates. Figure 5. Regions for the calculation of electric field of the filter loaded with die- lectric cylinders. 1.8 Finally, in regions 6c, 12c… the field is obtained narrow waveguide, while it is propagating in the by the method described in [8], as follows: input wider waveguide. The procedure followed to calculate the field in- side this filter is similar to the methodology des- cribed in the two previous sections. 1.9 where coefficient sn is: 5. Results High-Order H-plane waveguide filter for spa- ce applications at K-Band The first example under consideration is a con- ventional H-plane waveguide filter with coupled cavities for space applications at the K-band. The ideal transfer function is a standard nine-pole Chebychev response of 96 MHz bandwidth cen- 1.10 tered at 17.3 GHz. and r the radius of the dielectric post. The cavity lengths and coupling aperture widths Evanescent mode filter loaded with dielectric of the filter have been chosen as design parame- cylinders ters (see Fig. 8). The input and output wavegui- In an evanescent mode filter, the fundamental des of the filter, as well as the resonant cavities, mode TE10, is below the cutoff frequency in the are standard WR-62 waveguides (a=15.799 mm, Waves · 2009 · year 1 / ISSN 1889-8297 109 Figure 6. Segments and GSMs matrices of evanes- cent filter with dielectric cylinders Figure 9. Responses of the H-plane waveguide filter. Coarse model response at x* versus the fine os model response at xem. Tunable H-plane waveguide filter for space communication systems In order to test the performance of the design procedure with more complex structures, two tunable H-plane coupled cavity filters have been Figure 7. Regions for calculating the electric field considered. These filters were originally designed of the evanescent filter with dielectric cylinders. and manufactured in [20], where the design was performed manually. The same filters have been b=7.899 mm). The length of all the coupling win- re-designed with the CAD tool proposed in this dows has been chosen to be 2 mm. For the design work. The tuning elements are penetrating posts of this filter, the same modal simulator has been of square cross-section placed at the center of used both as the coarse and the fine model. This each cavity and each coupling window (see Fig. modal simulator characterizes the planar discon- 10). As proposed in [20], the use of these tuning tinuities using the Method of the Moments (MoM) posts allows the use of a common base structure according to the traditional Galerkin procedu- for obtaining filters with responses centered at re [18]. When used as a fine model, the number different frequency bands. The only difference in of accessible modes, number of basis functions the filters at each frequency band is the penetra- in the MoM, and number of kernel terms in the tion of the tuning posts. integral-equation are high enough to obtain very accurate results. On the other hand, when used as The ideal transfer function is a four-pole stan- a coarse model, a small number of modes is con- dard Chebychev band-pass response of 300 sidered in order to obtain a faster simulator at the MHz bandwidth centered at 11 GHz and 13 GHz. expense of a less accuracy. The initial values of The input and output waveguides of the filter, as the design parameters (x(0)) have been calculated os well as the resonant cavities, are standard WR-75 according to the method described in [19]. Fig. waveguides (a=19.050 mm, b=9.525 mm). The 9 shows the comparison between the response length of all the coupling windows has been of the fine model at the final solution in VS (xem) chosen to be 2 mm. The sides of the posts are and the response of the coarse model at x* . It can os fixed to 4 mm in the cavities and 2 mm in the be observed that the desired objective function coupling windows. has been satisfactorily recovered in the VS. This solution has required 185 s of CPU time in a 2.4 The design with ASM using segmentation and GHz Pentium IV PC platform. hybrid optimization required 3 ASM iterations for both filters under severe convergence cri- Figure 10. Manufactured tunable filters with tu- Figure 8. A four cavities H plane rectangular waveguide filter. ning elements. Common base and 11 GHz top. 110 ISSN 1889-8297 / Waves · 2009 · year 1 A different method is used for the analysis of each type of building block Figure 11. Measurements of the manufactured prototypes with tuning elements. terion. The design for the filters centered at 11 and 13 GHz required a total CPU times of 49’50’’ and 33’42’’, respectively, in a PC with Pentium IV processor at 1.7 GHz. Since the fine model is about 250 times slower than the coarse model, the total CPU time required for the direct design of such filters without ASM would be of about Figure 12. H-plane waveguide filter with dielectric 25 hours. This represents an improvement by a resonators. factor of 30, and clearly proves the advantage of using ASM for the design of complex waveguide be observed that the desired objective function devices. The filters have been manufactured in has been satisfactorily recovered in the VS. This two different pieces, an H-plane base structure solution has required about 2 hours of CPU time and a separated top cover including all the tun- in a 3 GHz Pentium IV platform. The total length ing elements. To reduce costs, the same H-plane of the filter (l1+l2+l3+l4+5t) is reduced by al- base has been used for both filters. The common most 50% when compared with the same filter H-plane base and the two different tops includ- without dielectric posts, with the correspondent ing the tuning elements for the filters at 11 and benefit in terms of volume and mass reduction, 13 GHz were manufactured (see Fig. 10) and so critic in satellite communication systems. measured (see Fig. 11). Comparative study of multipactor breakdown H-plane waveguide filter with dielectric reso- The last part of this work evaluates the risk of nators multipactor breakdown in a set of filters. In or- The last structure under consideration is an H- der to have a fair comparison the filters should plane coupled cavities filter with circular dielec- provide the same frequency response, so we tric posts placed in the middle of each cavity (see designed three different filters: all metal cavities, Fig. 12(a)). The ideal transfer function is a standard cavities loaded with dielectric cylinders and eva- four-pole Chebychev response of 300 MHz band- nescent mode loaded with dielectric cylinders width centered at 11 GHz. The input and output filters, which present the same frequency res- waveguides of the filter, as well as the resonant ponse shown in Fig. 13. cavities, are standard WR-75 waveguides (a=19.05 mm, b=9.525 mm). The relative permittivity of the It is important to notice that during the work dielectric posts is chosen to be 24, and the length we have considered that the multipactor break- of all the coupling windows have been chosen to down can only appear between two electric be 2 mm. The remaining dimensions of the struc- plates containing a normal field, so for the cal- ture (cavity lengths, coupling aperture widths culation of the power that a particular filter can and radii of the dielectric posts) have been cho- handle we have used the field inside that filter sen as design parameters. The design procedure but outside the dielectric cylinders. All the die- described in section III can not be directly applied lectric cylinders used in the filters have a dielec- to the design of this kind of filters. It is necessary tric permittivity Ɛr=24. to use a genetic algorithm, since a good start- ing point can not be easily obtained, as well as All-metal cavities filter to suppress the segmentation strategy, since the During the study the authors found that the coupling among cavities is much stronger that in maximum of the electric field was always loca- all-metallic filters. Again the same simulation tool ted on the central longitudinal axis of the filter, is used as the coarse and fine model. This simu- and in the middle of the second cavity indepen- lation tool is described in [21]. It uses a suitable dently of the frequency value. Fig. 14 shows the combination of an analytical method and a hybrid maximum input and output power without mul- technique which copes with the different parts of tipactor breakdown as a function of the frequen- the filter structure. Fig. 12(b) shows the compari- cy. It is interesting that inside the pass band the son between the response of the fine model at amount of input and output power that the filter xem and the ideal response of the filter. It can can handle is the same, around 2500 W, and that Waves · 2009 · year 1 / ISSN 1889-8297 111 A higher losses dielectric reduces the power handling capability Figure 13. Scattering parameters S11 and S21 of the H-plane filters under study. Figure 15. Maximum output power without mul- tipactor breakdown for the cavities filter loaded with dielectric cylinders, loss tangents tgδ=0, tgδ=10-3, tgδ=10-4 Figure 14. Maximum input and output power that the all-metal cavities filter can handle without multi- pactor breakdown as a function of frequency. Figure 16. Maximum output power without mul- outside this band the power is not limited by the tipactor breakdown for the evanescent mode filter multipactor risk but by the electromagnetic res- loaded with dielectric cylinders, loss tangents ponse of the filter. tgδ=0, tgδ=10-3, tgδ=10-4 Filter loaded with dielectric cylinders ller than the all-metal one, which makes that the In this filter the electric field was concentrated electric field is more concentrated in the filter inside the dielectric cylinders, specifically there and that the risk of multipactor breakdown in- was a maximum of field inside the second cylin- creases. Nevertheless, when loading this filter der, being the maximum of field outside the die- with dielectric cylinders, the output power wi- lectric cylinders considerably lower than in the thout multipactor breakdown (see Fig. 16) can be case of the all-metal filter. Nevertheless, loading higher than in the all-metal filter, since the field the filters with a dielectric material can introdu- trends to concentrate inside the dielectric cylin- ce losses in the filter response that can affect the ders. The figure also shows the output power for output power that the filter can handle. Fig. 15 different dielectric materials, with different loss shows the output power that the filter can han- tangent factors, concluding that a good quality dle without the risk of multipactor breakdown factor dielectric (tgδ=10-4) can provide a power for dielectric materials with different loss factors. response similar to the ideal one, while a worse Even with a loss tangent of 10-3 this filter can dielectric reduces this power handling but main- handle the double of power than the all-metal tains it above the all-metal one. one. Moreover, with a rather high quality factor (tgδ=10-4) the behavior of the filter does not di- Comparison of results vert from the ideal (lossless) case. It is interesting to show a comparative study of the three filters considering three relevant items: size, Evanescent mode filter loaded with dielectric maximum field inside the filters and maximum cylinders output power without multipactor risk. Table II The evanescent mode filter is substantially sma- lists the total length of the three filters. The eva- nescent filter presents a reduction in size of about 50% comparing to the all-metal case, and the cavi- ties filter with dielectric cylinders is about 60% of Table 2. Lenghts of the three filters. the original size. The following table presents the maximum value of the electric field inside the fil- ters, for both cases: inside the dielectric cylinders and outside them. When having filters loaded with dielectric materials, the maximum of field is always located inside the dielectric cylinders. This pheno- menon enables the increase of power without risk Table 3. Maximum field (tgδ =1e-4) of multipactor as shown in Fig. 17. Fig. 17 presents 112 ISSN 1889-8297 / Waves · 2009 · year 1 IEEE Trans. Microwave Theory Tech., vol. 43, no. 12, pp. 2874-2881, Dec. 1995. [4] J. W. Bandler, S. Cheng, Q. S.and Dakroury, A. S. Mohamed, K. Bakr, M. H. Madsen, and J. Sön- dergaard, “Space mapping: The state of the art,” IEEE Trans. Microwave Theory Tech., vol. 52, no. 1, pp. 337-361, Jan. 2004. [5] M. Guglielmi, “Simple CAD procedure for mi- crowave filters and multiplexers,” IEEE Trans. Microwave Theory Tech., vol. 42, no. 7, pp. 1347-1352, July 1994. Figure 17. Comparative chart of the output pow- [6] J. T. Alos and M. Guglielmi, “Simple and effec- er for all the filters (dielectric loss factor: tgδ =1e-4). tive EM-based optimization procedure for mi- crowave filters,” IEEE Trans. Microwave Theory a comparative of the maximum output power wi- Tech., vol. 45, no. 5, pp. 856-858, May 1997. thout multipactor risk for the three filters under [7] J. V. Morro, P. Soto, H. Esteban, V. Boria, C. Bachi- analysis considering that the filters loaded with ller, M. Taroncher, S. Cogollos, and B. Gimeno, dielectric cylinders present low losses (tgδ=10-4). It “Fast automated design of waveguide filters can be observed that the cavity filter loaded with using aggressive space mapping with a new dielectric cylinders can handle more than double segmentation strategy and a hybrid optimiza- the power of an all-metal filter. tion algorithm,” IEEE Trans. Microwave Thoery Tech., vol. 53, no. 4, pp. 1130-1142, April 2005. [8] H. Esteban, S. Cogollos, V. E. Boria, A. A. San Blas, Conclusions M. Ferrando “A New Hybrid Mode-Matching/ Numerical Method for the Analysis of Arbi- A case study of advanced optimization techniques trarily Shaped Inductive Obstacles and Dis- for the automated design of complex waveguide continuities in Rectangular Waveguides” IEEE . filters for space applications has been presented in Trans. Microwave Theory Tech., vol. 50, no. 4, this paper. A complete automated design tool has pp. 1219–1224, April, 2002. been developed based on ASM enhanced with [9] Ansoft Corporation. [Online] http://www.an- segmentation and hybridization schemes. This soft.com/products/hf/hfss/. HFSS: 3D Electro- tool has been successfully applied to the practical magnetic Simulation. 2008. design of H-plane coupled cavities filters with and [10] M. Guglielmi, “Simple CAD procedure for mi- without tuning elements, and for the design of H- crowave filters and multiplexers,” IEEE Trans. plane filters with dielectric posts. The multipactor Microwave Theory Tech., vol. 42, no. 7, pp. effect in the filters designed with our CAD tool has 1347-1352, July 1994. been analyzed following a novel analysis techni- [11] J. V. Morro, H. Esteban, P. Soto, V. E. Boria, C. Ba- que that enables also the computation of the elec- chiller, S. Cogollos, and B. Gimeno,“Automated tromagnetic field inside the structure. design of waveguide filters using aggressive space mapping with a segmentation strategy and hybrid optimization techniques,” in Proc. Acknowledgment of the IEEE Int. Microwave Symp., Philadelphia, June 2003, pp. 1215-1218. The authors would like to thank Dr. M. Gugliel- [12] A.J.Hatch, H.B.Williams, “The secondary elec- mi, European Space Research and Technology tron resonance mechanism of low-pressure Center (ESTEC)-European Space Agency (ESA), . high-frequency gas breakdown” Journal of Noordwijk, The Netherlands, for providing proto- Applied Physics, vol. 25, pp. 417-423. April 1954. types and measurements of real filters conside- [13] A. V. M. Ludovico, G. Vercellino and L. Acca- red in this paper. tino, “Multipaction análisis in high power an- tenna diplexers for satellite applications” Pro- ceedings of the Workshop on Multipactor, RF References and DC Corona and Passive Intermodulation in Space RF Hardware, pp. 109. ESTEC, Noord- [1] R. Udiljak, “Multipactor in Low Pressure Gas”. wijk, The Netherlands September, 2000. Master Thesis. Department of Electromagne- [14] ESA/ESTEC. Multipactor Calculator. [Online] tics, School of Electrical Engineering, Chal- http://multipactor.esa.int/index.html. April 2007 mers University of Technology, Göteborg, [15] J.M.Reiter, F.Arndt “Rigorous analysis of arbi- Sweden 2004. trarily shaped H- and E-plane discontinuities [2] R. Udiljak, “Multipactor in Low Pressure Gas in rectangular waveguides by a full-wave . and in Nonuniform RF Field Structures” PhD boundare contour mode-matching method” . Thesis Department of Radio and Space Scien- IEEE Trans. on Microwave Theory and Tech, ce, Chalmers University of Technology, Göte- vol. 43, no. 4, pp. 796-801. April 1995. borg, Sweden 2007. [16] C.Bachiller, H.Esteban, V.E.Boria, A.Belenguer, [3] J. Bandler, R. Biernacki, S. Chen, R. Hemmers, J.V.Morro.“Efficient Technique for the Cascade and K. Madsen, ”Electromagnetic optimiza- Connection of Multiple Two Port Scattering tion exploiting aggressive space mapping,” . Matrices” IEEE Transactions on Microwave Waves · 2009 · year 1 / ISSN 1889-8297 113 Theory and Techniques, vol. 55, no. 9, pp 1880- Valencia as an assistant lecturer. She is secretary of 1886, September 2007 the iTEAM Institute of Multimedia Technology and [17] H. Esteban,“Análisis de Problemas Arbitrarios Communications of the Polytechnic University of de Dispersión Electromagnética Mediante Valencia. She is teaching signal and systems theory Métodos Híbridos” PhD Thesis, Departamento , and microwaves. She has participated in several de Comunicaciones, Universidad Politécnica teaching innovation projects as the development de Valencia, Spain 2002. of GUIs for teaching electromagnetic phenomena. [18] G. Gerini, M. Guglielmi, and G. Lastoria, She is now working in her Ph.D. Thesis on electro- “Efficient integral equation formulations for magnetism and radiofrequency circuits. admittance or impedance representation of planar waveguide junctions,” IEEE MTT-Symp. Dig., vol. III, pp. 1747-1750, 1998. Héctor Esteban González [19] P. Soto, J. Gómez, A. Bergner, V. E. Boria, and R. received the degree in Te- Chismol, “Automated design of waveguide fil- lecommunications Engi- ters using space mapping optimization,” in Proc. neering from the Polytech- of 3rd Eu. Conf. on Numerical Meth. in Electro- nic University of Valencia magnetism, Poitiers, March 2000, pp. 228-229. (UPV), Spain, in 1996, and [20] V. E. Boria, M. Guglielmi, and P. Arcioni, “Com- the Ph.D. degree in 2002. puter-aided design of inductively coupled He collaborated with the rectangular waveguide filters including tu- Joint Research Centre, Eu- ning elements,” Int. J. of RF and Microwaves ropean Commission, Ispra, Italy. In 1997, he was Computer-Aided Engineering, vol. 8, no. 3, pp. with the European Topic Centre on Soil (Euro- 226-236, May 1998. pean Environment Agency). He rejoined the UPV [21] C. Bachiller, H. Esteban, V. E. Boria, J. Morro, L. in 1998. His research interests include methods Rogla, M. Taroncher, and A. Belenguer,“Efficient for the full- wave analysis of open-space and gui- CAD tool fo direct-coupled-cavities filters with ded multiple scattering problems, CAD design of dielectric resonators,” in 2005 IEEE AP-S Int. microwave devices, electromagnetic characte- Symp. Dig., Washington D.C., June 2005. rization of dielectric and magnetic bodies, and the acceleration of electromagnetic analysis me- thods using the wavelets and the FMM. Biographies Vicente E. Boria Esbert José Vicente Morro received the Ingeniero de received the Telecom- Telecomunicación and the munications Engineering Doctor Ingeniero de Te- degree from the Universi- lecomunicación degrees dad Politécnica de Valen- from the Universidad Po- cia (UPV), Valencia, Spain, litécnica de Valencia, Va- in 2001, and is currently lencia, Spain, in 1993 and pursuing his Ph.D. degree 1997, respectively. In 1993 at UPV. In 2001, he beca- he joined the Departamento de Comunicacio- me a Research Fellow with the Departamento nes, Universidad Politécnica de Valencia, where de Comunicaciones, UPV. In 2003 he joined the he is Full Professor (since 2003). In 1995 and 1996 Signal Theory and Communications Division, he was held a Spanish Trainee position with the Universidad Miguel Hernández, where he was a European Space research and Technology Centre Lecturer. In 2005, he rejoined the Departamento (ESTEC)-European Space Agency (ESA), Noordwi- de Comunicaciones, UPV, as an Lecturer. His cu- jk, the Netherlands. Since 2003, he has served on rrent interests include CAD design of microwave the Editorial Boards of the IEEE Transactions on devices and EM optimization methods. Microwave Theory and Techniques. He is also member of the Technical Committees of the IEEE-MTT International Microwave Symposium Carmen Bachiller and of the European Microwave Conference. His received her degree in current research interests include numerical me- Communication Enginee- thods for the analysis of waveguide and scatte- ring from the Polytechnic ring structures, automated design of waveguide University of Valencia in components, radiating systems, measurement 1996. She worked from techniques, and power effects in passive wave- 1997 to 2001 in the com- guide systems. pany ETRA I+D, S.A as a Project Engineer in re- search and development on automatic traffic control, public transport management and public information systems using telecommunication technology. In 2001 she joined the Communica- tion Department of the Polytechnic University of 114 ISSN 1889-8297 / Waves · 2009 · year 1

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