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Abstraction in Assumption-based Argumentation

Apostolakis, Iosif

A Semantical Approach to Abstraction in Answer Set Programming and Assumption-based Argumentation

Popescu, Andrei

Advancing Algorithmic Approaches to Probabilistic Argumentation under the Constellation Approach

Lehtonen, Tuomo

Complexity Results and Algorithms for Preferential Argumentative Reasoning in ASPIC+

Robins, Luke

Bartlett, Chad

Arsanjani, Arash

Teschl, Reinhard

Bösch, Wolfgang

Höft, Michael

IEEE MICROWAVE AND WIRELESS TECHNOLOGY LETTERS, VOL. 33, NO. 11, NOVEMBER 2023 1517A 3-D-Printed Dielectric Resonator forTriple-Mode ApplicationsLuke Robins , Member, IEEE, Chad Bartlett , Member, IEEE, Arash Arsanjani , Member, IEEE,Reinhard Teschl, Member, IEEE, Wolfgang Bösch , Fellow, IEEE, and Michael Höft , Senior Member, IEEEAbstract— This work presents a novel 3-D-printed triple-modedielectric resonator for microwave filter applications. The designdemonstrates the use of an odd number of periodic rings placedalong a dielectric combline resonator to create a miniaturizedfilter structure capable of creating a quasielliptic triple-modefilter response. A new approach suitable for 3-D-printing of theperiodic rings is presented using support structures that takethe form of struts. The resonator is fabricated using aluminawith lithography-based ceramic manufacturing and housed ina compact single-cavity structure. The filter is designed foroperation with a center frequency of 10.78 GHz, fractionalbandwidth (FBW) of 2.13%, and a measured quality factor ofapproximately 1700.Index Terms— Additive manufacturing (AM), alumina, band-pass filter, dielectric resonator, stereolithography, triplet.I. INTRODUCTIONMICROWAVE filters are a critical part of moderntelecommunications systems. In some circumstances,the technology chosen to implement the structure can resultin bulky, heavy products or in formats that are difficult tointegrate. Therefore, it is important to investigate miniatur-ization methods for these types of filters while working tomaintain high-quality factors and dynamic filtering responses.Many approaches to miniaturization exist, such as the use ofdielectric resonators, which reduce the structural size by com-pressing the electromagnetic fields [1], metamaterials [2], andmultimode monoblock filters [3]. In a recent work on utilizingceramic additive manufacturing (AM) for dielectric comblineresonators [4], the quality factor performance of higher modeswas increased and dual-mode operation was achieved throughchanges in the geometry. In this work, the concept of periodicchanges in the geometry is expanded to triple-mode operations.A filter that utilizes the combination of the TM010 and the twoorthogonal TE111 modes and operates at 10.78 GHz with afractional bandwidth (FBW) of 2.13% is designed. It featuresManuscript received 21 April 2023; revised 21 June 2023 and 15 August2023; accepted 24 August 2023. Date of publication 19 September 2023;date of current version 8 November 2023. This work was supported bythe European Union’s Horizon 2020 Research and Innovation Programunder the Marie Skłodowska-Curie Grant 811232-H2020-MSCA-ITN-2018.(Corresponding author: Luke Robins.)Luke Robins, Arash Arsanjani, Reinhard Teschl, and Wolfgang Bösch arewith the Institute of Microwave and Photonic Engineering, Graz Universityof Technology, 8010 Graz, Austria (e-mail: lrobins.p@gmail.com).Chad Bartlett and Michael Höft are with the Department of Electrical andInformation Engineering, Kiel University, 24143 Kiel, Germany.Color versions of one or more figures in this letter are available athttps://doi.org/10.1109/LMWT.2023.3311812.Digital Object Identifier 10.1109/LMWT.2023.3311812Fig. 1. Alumina (εr = 9.5 and tanδ = 8·10−5 [6]) resonator comparison:(a) post, (b) solid-ring, and (c) five-ring.Fig. 2. Solid-ring E-field distributions middle cut. (a) TM010. (b) TE111.(c) TE111⊥. (d) Side on view.increased distance to the next spurious mode while decreasingthe material and weight at the same time, highlighting theflexibility in resonator design possibilities enabled through theuse of ceramic stereolithography-based 3-D-printing.II. TRIPLE-MODE RESONATOR DESIGNTo demonstrate the build-up of the 3-D-printable resonatorstructure, a progression of the resonators is presented in Fig. 1.The most basic resonator configuration, consisting of a dielec-tric post placed in a cylindrical cavity, is shown in Fig. 1(a).The first four modes in this configuration are: TM010, TM011,TE111, and TE112. It is important to mention that these modesare not purely TM or TE due to the asymmetric placementof the resonator. However, the respective longitudinal fieldcomponents are small. The addition of a solid ring (SR)on the post, as demonstrated in Fig. 1(b), can influence thepositions of these modes relative to each other. The simulatedfield concentrations of the first two modes are illustrated inFig. 2. From these, it can be observed that the TM mode hasmore field concentrated at the center of the cavity along thecentral post, while the TE mode is most concentrated nearthe outside edge of the introduced ring. These areas of fieldconcentration can be exploited to, somewhat independently,shift the resonant frequency of the TM010 and TE111 modes,allowing the modes to be close enough together to be usefulin a dual-mode configuration. Additionally, the TE111 has an© 2023 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License.For more information, see https://creativecommons.org/licenses/by/4.0/1518 IEEE MICROWAVE AND WIRELESS TECHNOLOGY LETTERS, VOL. 33, NO. 11, NOVEMBER 2023Fig. 3. Resonant frequency study for the SR and FR resonators, demonstrating the (a) triple-mode operation ratio while keeping a fixed height(Hsr1 = 4.25 mm), (b) mode separation improvement with a fixed ratio (Dsr1/Hsr1) = 1, and (c) further mode separation using the FR resonator andsweeping the central post diameter with (Dsr1 = Dr1 = 5.6 mm).identical orthogonal mode at the same resonant frequency [seeFig. 2(b) and (c)], and, therefore, a triple-mode implementationis possible. The effect of the ratio of ring height (Hsr1) to theoutside diameter (Dsr1) is shown in Fig. 3(a). Interestingly,for the desired triple-mode operation point, the optimal ratiowas found to be approximately 1. Parameter sweeps withthis ratio fixed are shown in Fig. 3(b). Keeping the outsidediameter of the SR fixed while sweeping the diameter ofthe central post (Dsr) is demonstrated in Fig. 3(c). Theseresults demonstrated that the resonator can be optimized forboth triple-mode operations and situated at a point where thedistance to the next mode is a maximum, ultimately movingthe TE111 away from the spurious TM011 and TE112 modes.Similar results can be achieved using a five-ring (FR) structureas shown in Fig. 1(c). A comparison of the respective shiftsin resonant frequency, between SR and FR, can be seen inFig. 3(c) and it highlights that the TE112 mode is shiftedto higher frequencies when using the FR profile and givesapproximately 60% (1 GHz) of additional separation to thedesired modes.III. FABRICATION CONSIDERATIONSFabrication of the FR configuration would require approxi-mately 22% less material and result in an 18% lighter resonatorwhen compared to the SR resonator. Due to these advantagesand the fact that the FR resonator has a higher degree ofcomplexity, lithography-based 3-D-printing was chosen forfabrication. Using the principles outlined previously, a triple-mode resonator specified for 10.8-GHz operation was designedfor fabrication. The model of the FR resonator is depicted inFig. 1(c), where the dimensions are given as: Hr0 = 5.62,Hr1 = 1.5, Hr = 18.6, Dr = 1.6, Dr1 = 5.6, and Hs =0.5 (mm).The resonators were fabricated using a Lithoz CeraFab7500 printer, with an XY resolution of 40 µm and aprinting-layer height of 50 µm. Multiple fabrication roundswere required to enable successful printing. The large differ-ence between the central post and outside ring radius createdoverhangs too large to be easily printed without support.The transition areas from the post to the ring were prone tobreakages during printing due to sheer stress.To overcome this, supporting struts were introduced inbetween the rings as shown in Fig. 4. However, it should beFig. 4. Modified triple-mode resonator for printing. (a) Side view. (b) Per-spective view. (c) Fabricated resonator.Fig. 5. Input coupling: (a) TM010, (b) TE111, and (c) simulated results.noted that the addition of material can cause the TM modesto shift to lower frequencies, and therefore, keeping the strutsas thin as possible was critical for the design to succeed. Thefinal strut-adapted resonator design is shown in Fig. 4 withthe following dimensions: Hr0 = 9, Hr1 = 1, Hr = 18.51,Dp = 1.6, Dr = 6.05, Hs = 0.5, R = 1, St = 0.12 (mm), andθ = 30◦. The resonators have a simulated Qu of approximately11 000 in a copper cavity and 6000 in brass.IV. TM010 AND TE111 TRIPLE-MODE FILTERA third-order filter centered at 10.78 GHz with a returnloss of 20 dB and an FBW of 2.13% was designed to verifythe resonator concept and show an application of dynamicalumina-based 3-D-printing. The triplet uses a cylindricalcavity with a radius of 7.5 mm and a height of 21.8 mm andencompasses the 3-D-printed resonator specified in Section III.SMA probes were chosen as a simple approach to feeding,where the input coupling can be controlled by the lengthof the probe into the cavity. Horizontal placement of theprobes was used as more space was available on each wallto accommodate both feeds for the triplet case. The probefeeding provides a challenge, as in this case, the TM010 andTE111 electric fields are almost entirely orthogonal to eachother. The field configurations are shown in Fig. 5(a) and (b),highlighting a small area toward the top of the resonator wheresome of the electric field components are oriented horizontallyROBINS et al.: 3-D-PRINTED DIELECTRIC RESONATOR FOR TRIPLE-MODE APPLICATIONS 1519Fig. 6. Designed triple-mode filter: (a) side view, (b) top view, (c) simulated and measured performance, and (d) alternate zero configuration.for both modes. Placing the feeds at this position enablesthe simultaneous excitation of both modes. Fig. 5(c) showsthe feasible input coupling achieved by varying the probedepth. The coupling can be further increased by a deliberatemisalignment of the resonator with respect to the center of thecavity, as further demonstrated in Fig. 5(c), allowing for widerbandwidths and more gradual changes in regard to the inputcoupling.To achieve triple-mode operation, the ports were placedat 90◦ relative to one another. A metallic screw was placedat 45◦ between the ports to excite both orthogonal TE111modes and a metallic screw controlling TM010 was placednext to the resonator on the floor of the cavity. The screws arepositioned close to the maximum electric field of the respectivemode for the most impact. Two additional screws for eachTE111 mode were included to allow for the tuning of each.The final filter responses and layout are provided in Fig. 6.Extraction of the exact coupling parameters in this triple-modeconfiguration is difficult due to innate parasitic and loadingeffects. Therefore, a simplified analogous transversal couplingmatrix, which excludes the cross-coupling, is included to aidthe initial filter design: MS1 = 0.59, M1L = 0.54, MS2 =0.59, M2L = 0.54, MS3 = −0.81, M3L = 0.83, M11 =−1.6, M22 = 1.54, M33 = −0.135, and MSL = −0.039.The dimensions are given as: PL = 3.7, S1 = 1.1, S2 = 0.8,S3 = 1.83, S4 = 3.35, L1 = 4.5, Hp = 11.4, and Hs = 9 (mm).The transmission zero (TZ) appearing below the passbandis generated by the relationships between the input couplingto each mode with the source to TE111⊥ having the oppositephase. In this case, the TZ position can be moved by keepingcoupling into mode TE111⊥ fixed and adjusting the couplingof TM010 and TE111. As the coupling into TM010 is decreasedand into TE111 is increased, the TZ moves downward awayfrom the passband. The selected probe-feeding setup limitsthe flexibility in positioning the TZs, as changes in inputcoupling influence at least two of the modes at a time. Thereis, however, a way to keep the TZ below the passband andcreate an additional TZ above the passband; this is done byreducing the source-to-load coupling. This can be achieved byrotating one of the inputs by 25◦ clockwise from the positionin Fig. 6(b), thus reducing the coupling between the ports.While the input coupling of the TM mode is independent ofthe rotation of the feeds, the coupling for the two TE modeschanges based on the rotation of the feeding. This allowsthe response illustrated in Fig. 6(d), whereby the second TZabove the passband is caused by the higher-order TE112 modeinteracting with the TE111 which bypasses the resonator. TheTABLE ICOMPARISON TO RECENT WORKS ON THE DIELECTRIC RESONATOR ANDCERAMIC 3-D-PRINTED FILTERSsimplified analogous transversal coupling matrix: MS1 = 0.52,M1L = 0.41, MS2 = 0.51, M2L = 0.52, MS3 = −0.87,M3L = 0.83, M11 = −1.5, M22 = 1.43, M33 = −0.17, andMSL = −0.017.V. FABRICATION AND MEASUREMENTThe designed resonator and filter cavity were fabricatedusing Lithalox 350 and brass, respectively, with a resonatorshown in Fig. 4(c). The resonator was glued to the bottomlid by hand using superglue and, as such, makes achieving anexact alignment difficult, leading to slight shifting in frequencyand quality factor degradation. However, this simple processis accurate enough for a proof-of-concept filter and allowsfor the verification of the performance of the 3-D-printedresonator. The measured filter performance is compared to thesimulated S-parameter in Fig. 6(c) and largely matches thatof the simulation, aside from a 40-MHz shift. The extractedquality factor is approximately 1700, while the simulated valueis in the range of approximately 3600. These deviations areattributed to the manual assembly process and additional lossesintroduced by the superglue and the tuning screws. Table Iprovides a comparison of this work to recent 3-D-printedfilters and demonstrates the overall compactness while stillmaintaining quality factor performance.VI. CONCLUSIONThis work introduces a novel 3-D-printed triple-modedielectric resonator that enables the use of the TM010 andthe two orthogonal TE111 modes together in a triplet imple-mentation. Additionally, the work presents a thin strut-likesupport geometry to enable the printing of alternating ring-type structures. The resonator was fabricated and demonstratedfor a triplet filter implementation operating at 10.78 GHz,highlighting potential applications of 3-D-printed ceramic res-onator structures.1520 IEEE MICROWAVE AND WIRELESS TECHNOLOGY LETTERS, VOL. 33, NO. 11, NOVEMBER 2023REFERENCES[1] V. Nocella, L. Pelliccia, C. Tomassoni, and R. Sorrentino, “Miniaturizeddual-band waveguide filter using TM dielectric-loaded dual-mode cavi-ties,” IEEE Microw. Wireless Compon. Lett., vol. 26, no. 5, pp. 310–312,May 2016, doi: 10.1109/LMWC.2016.2549181.[2] A. Arsanjani, C. Bartlett, L. Robins, R. Teschl, W. Bösch, andM. Höft, “Metasurfaces for filter miniaturization and out-of-band rejec-tion improvement,” IEEE Microw. Wireless Technol. Lett., vol. 33, no. 3,pp. 271–274, Mar. 2023, doi: 10.1109/LMWT.2022.3221467.[3] D. Miek et al., “Ceramic additive manufactured monolithic X-shapedTM dual-mode filter,” IEEE J. Microw., vol. 2, no. 3, pp. 496–506,Jul. 2022, doi: 10.1109/JMW.2022.3167250.[4] L. Robins et al., “3D-printed dielectric resonators for quasi-TE112mode singlets, doublets and dual-mode filters,” IEEE Access, vol. 10,pp. 130326–130338, 2022, doi: 10.1109/ACCESS.2022.3228764.[5] X. X. Yuan, L.-H. Zhou, and J.-X. Chen, “Triple-mode bandpass filterbased on silver-loaded ring-shaped dielectric resonator,” IEEE Microw.Wireless Compon. Lett., vol. 28, no. 9, pp. 789–791, Sep. 2018, doi:10.1109/LMWC.2018.2853568.[6] Lithoz. Materialübersicht LCM-Technologie. Accessed: Jul. 25, 2022.[Online]. Available: https://lithoz.com/wp-content/uploads/2022/04/LITHOZMaterialfolder DE web.pdf[7] C. Carceller, F. Gentili, D. Reichartzeder, W. Bösch, andM. Schwentenwein, “Development of monoblock TM dielectricresonator filters with additive manufacturing,” IET Microw., AntennasPropag., vol. 11, no. 14, pp. 1992–1996, Nov. 2017, doi: 10.1049/iet-map.2016.1051.[8] A. Perigaud, O. Tantot, N. Delhote, S. Verdeyme, S. Bila, andD. Baillargeat, “Bandpass filter based on skeleton-like monoblocdielectric pucks made by additive manufacturing,” in Proc.48th Eur. Microw. Conf. (EuMC), Sep. 2018, pp. 296–299, doi:10.23919/EuMC.2018.8541710.[9] A. Widaa, F. Cacciamani, L. Pelliccia, C. Tomassoni,V. T. di Crestvolant, and M. Höft, “Compact ultra-wideband bandpassfilter using additively manufactured TM-mode dielectric resonators,” inProc. 52nd Eur. Microw. Conf. (EuMC), Sep. 2022, pp. 115–118, doi:10.23919/EuMC54642.2022.9924504.[10] E. López-Oliver, C. Tomassoni, F. Cacciamani, L. Pelliccia, andV. T. D. Crestvolant, “Bandpass filter based on 3-D-printed ceramicresonators,” in Proc. 24th Int. Microw. Radar Conf. (MIKON), Sep. 2022,pp. 1–5, doi: 10.23919/MIKON54314.2022.9924680.[11] A. Widaa, C. Bartlett, and M. Höft, “Design of compact quasi-elliptic bandpass filters based on coaxial inset resonators,” IEEEAccess, vol. 11, pp. 18739–18749, 2023, doi: 10.1109/ACCESS.2023.3247137.

English

A 3-D-Printed Dielectric Resonator for Triple-Mode Applications

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