3D-Printed Dielectric Resonators for Quasi-TE112 Mode Singlets, Doublets and Dual-Mode Filters

This paper demonstrates the use of a ceramic stereolithography-based additive manufacturing process to fabricate higher-order mode dielectric resonators. In this work, dielectric resonators with concentric rings around a combline rod structure are 3D-printed using alumina. The integration of the concentric rings for the use of the TE112 mode allows for a more compact cavity structure and a higher unloaded quality factor when compared to a simple dielectric combline resonator with a similar S-parameter response. The achievable improvements in quality factor for the TE112-mode resonators utilising concentric rings are compared through simulations and experimental results. The measured results demonstrate an increased average in the unloaded quality factor of $\text{Q}_{u}\approx ~2172$ which is approximately 44%. Additionally, the application of the 3D-printed resonators is further demonstrated in a TE112 singlet, doublet, and dual-mode filter configuration.


I. INTRODUCTION
Radio frequency (RF) filters are critical building blocks of modern telecommunication systems for terrestrial and satellite applications. In a typical RF receiver, for example, the placement of a filter directly after the receiving antenna means that the filter's performance significantly contributes to the overall system loss, noise, and power handling performance. The higher the insertion loss of the filter, the higher its contribution to the noise figure, with higher thermal expansion/heat, and lower overall achievable throughput [1], [2].
Specifically for space applications, more losses in the system mean more resources or costs need to be provisioned for thermal management systems or means of heat dissipation.
The associate editor coordinating the review of this manuscript and approving it for publication was Wenjie Feng.
In the case of coaxial combline resonators, periodic rings have been used to achieve a virtual enlargement of the resonator, i.e. increasing the inductance [6]. The work presented in [7] demonstrates a reduction of the ohmic losses with minimal added manufacturing complexity by rounding the corners in the cavity and bottom of the coaxial resonator. Nevertheless, the achievable quality factor of such metallic coaxial structures still does not meet the stringent requirements for several high-performance applications.
A standard approach to achieving increased quality factor performance in cavities is using dielectric resonators to concentrate the fields away from the walls of the housing cavity, thus reducing the losses and increasing quality factor [8], [9]. As an alternative to the TE 01δ mode traditionally utilised in the literature, reference [10] demonstrates three-layered TE 102 mode Bragg-reflection dielectric resonators, which achieve quality factors one order of magnitude higher than conventional resonators. Another design in [11] makes use of a dielectric post that has been shaped in such a way to make mounting in the middle of a cavity possible, thus moving the fields away from the floor and roof of the resonator and reducing losses when compared to a similar TM or combline dielectric resonator configuration.
Besides low-loss (and associated high quality factor), the need for simplified assembly and size reduction is usually also a requirement that drives innovation, most notably in weight and power sensitive application areas like satellite communications. The combination of additive manufacturing with dielectric materials provides the opportunity to tackle these requirements simultaneously. In [12], the authors demonstrate how the use of a novel additively-manufactured alumina resonator can be used to enable this in filter applications. Another example is the approach of manufacturing ceramic monoblock filters, which has received a lot of interest as it requires in the ideal case only metallisation and minimal assembly. Examples of various TM single and dual-mode printed filters are provided in [13], [14], and [15]. Metallisation and manufacturing tolerances proved challenging in [13] and [14]. In reference [15], more success was achieved by including a metal mask/backplate on which the tuning elements could be attached so that the manufacturing defects could be more easily compensated. In [16], the ability to print variable dielectric constants inside waveguide structures to achieve bandpass filtering was proposed.
The work in this paper demonstrates how the flexibility of additive manufacturing (AM) can be used to increase quality factor performance through changes in the geometry of a dielectric resonator. To this end, the concept of periodic perturbations in the form of concentric rings around a dielectric resonator rod is explored to improve the quality factor performance of filters and resonators. The remainder of the paper is split into five sections; first, the effect of geometric variations in the form of concentric rings on a post resonator is demonstrated to improve the obtainable quality factor. The proposed resonator is then implemented into a singlet configuration in a metallic cavity where examples of transmission-zero control are highlighted. Subsequently, the performance of the novel singlet configuration is compared to an equivalent singlet with a standard ceramic-rod resonator. The configuration is later expanded into a doublet configuration, which was fabricated and measured, to demonstrate the potential applications of the proposed structure. Lastly, a dual-mode four-pole filter is demonstrated and discussed with the results then briefly concluded.

II. CONCENTRIC-RING RESONATOR DESIGN
The effect of adding concentric rings on a metallic combline resonator to increase the quality factor was demonstrated in [6], through the use of a metallic combline/ring structure. Simulation of the quality factor showed an improvement in the order of Q l ≈ 200 for the addition of three concentric rings, and Q l ≈ 400 for six concentric rings. In this work, a similar approach is studied using sets of concentric rings on dielectric combline resonators to provide compactness and improve quality factor performance.

A. CAVITY MODES
To study the effects of concentric rings placed around dielectric posts, first, the resonate modes of the simple post were simulated and identified for reference. An alumina (ε r = 9.5) post with a length of 18.6 mm and a diameter of 4.61 mm, positioned inside a cylindrical cavity (height of 21.95 mm, diameter of 12 mm) with one end grounded, illustrated in Fig. 1.(a), has a quasi TM 010 electromagnetic field as the fundamental mode at approximately 8.9 GHz.  The fields due to the resonator being positioned on the floor of the cavity, are not identical to a pure TM 010 mode VOLUME 10, 2022 as they have components in the propagation direction, and the maxima of the fields are shifted in position. The contribution of the field in the Z-direction is significantly smaller. Thus, considering the pure mode provides insight into the behaviour of the resonator and enables design or excitation choices. This quasi-mode behaviour applies to the rest of the modes discussed as well. The resonator was simulated with a weak excitation, the response of which is shown in Fig. 2. These modes were identified to be the (1) TM 010 , (2) TM 011 , (3 & 4) TE 111 , (5 & 6) TE 112 and (7) TE 011 , with simplified field representations shown in Fig. 3. Note that the TE 111 and TE 112 modes have identical orthogonal modes at their resonant frequencies, which can be used in dual-mode configurations.

B. APPLICATION OF CONCENTRIC RINGS
Adding rings to the simple post resonator in symmetrical pairs increasing in number as illustrated in Fig. 1 was investigated. The number of rings, as well as their size and spacing affect the structure's quality factor performance. Additionally, the changes will shift the resonator's centre frequency, so this needs to be compensated for to ensure performance at the desired frequency. Applying symmetrical pairs of rings onto the post was found to have an increase in quality factor for the TE 112 mode, with the quality factor of lower modes remaining largely the same as that of the simple post.
In order to obtain an optimal quality factor, the fields should be moved upwards, away from the floor of the cavity. When positioned correctly, the rings provide a similar effect to the solution proposed in [11], which reduces the losses due to the currents in the bottom wall of the cavity which in turn raises the quality factor. The unloaded quality factor is proportional to the energy stored by the resonator over the energy dissipated as described in Equation (1). The elements contributing to the loss in these configurations are dominated by the conductor losses and the dielectric losses as shown in Equation (2). As the alumina used has a very low loss of tanδ = 8·10 −5 [17], reducing the conductor losses will have the greatest impact on the quality factor. This can be achieved by raising the conductivity of the sidewall material or moving the field away from the walls. Fig. 4 and Fig. 5 show the effect of using zero, two and six concentric rings on the electric and magnetic fields, which are gradually being moved to the centre of the cavity. Table 1 and Fig. 6 demonstrate a comparison of the quality factor of the resonator with varying symmetrical concentric-ring configurations inside brass and copper cavities. At 14 GHz, an increase of around 2700 was achieved for the TE 112 mode using six rings when compared to that of the post.

III. 3D-PRINTING METHODOLOGY AND CONSIDERATIONS
The printing process, technology, and materials used in ceramic-based additive manufacturing lead to considerations  that must be factored in at the design stage. The technology used for the printing of the alumina resonators is known as lithography-based ceramic manufacturing (LCM) [18]. The 3D-print process flow is shown in Fig. 7, which starts with the preparation of a CAD model (1). The material, in this case Lithalox HP350, is a printable slurry consisting of powdered ceramic particles that are suspended in a photosensitive organic binder (2). The slurry is hardened layer by layer onto a build platform using ultraviolet light (3). Next, the printed parts need to be cleaned using airbrushes and a solvent, as they are covered in uncured slurry resulting from the printing, which needs to be removed (4). Once complete, the parts must undergo a debinding step to remove the organic binder (5), followed by a sintering step (6) to form dense ceramic parts. The debinding and sintering steps are done at high temperatures up to 1650 • C and shrinkage of the parts occurs, which needs to be compensated for at the print step. The values of shrinkage compensation used for the HP350 were taken as 1.233 in XY-and 1.273 in Z-direction [15]. Depending on the geometry, these values may need to be adjusted slightly for more accuracy, once the final part dimensions are measured. The CeraFab 7500 printer was used, with an XY resolution of 40 µm and printing-layer height of 50 µm.
A centre frequency of 14 GHz was chosen to be within a printable range of sizes with the given dielectric constant. The large diameter difference between the rings and the central post creates shear stress failure points, which can delaminate during the printing process. Large unsupported overhangs are also prone to sagging under their own weight. To avoid these issues, a chamfer was added to the bottom edge of each of the rings in order to provide a more gradual transition. The modification caused a reduction of around 550 in the quality factor, as the rings had to be made thicker and could not be positioned as closely together. The printed resonator dimensions are given in Fig. 8 with the printed resonators shown in Fig. 9 during the cleaning procedure.

IV. DESIGN AND SIMULATION
In this section, the design parameters and simulated performances of the singlet, doublet, single-mode and dual-mode filters are discussed. VOLUME 10, 2022 A. TE 112 MODE SINGLET A single resonator with input and output ports can be set up to achieve a pole and transmission zero combination by exciting one of the TE 112 modes with a TE 111 source-to-load bypass coupling. This type of structure can be described by a singlet configuration which has been extensively detailed in work such as [19], and [20]. The positioning of the transmission zero can be influenced by moving the position of the probe feeds along the height of the resonator. The phase relationship between the TE 112 and the TE 111 at the two ports can be exploited to shift the position of the transmission zero below or above the passband. Fig. 10 demonstrates the possible port configurations (inline or offset). If the fields of both modes at the ports are in phase with each other, the transmission zero will be positioned below the passband, and if the modes at the ports are out of phase at either port, the transmission zero will appear above the passband, as demonstrated in detail in [21] and [22]. Fig. 11 and Fig. 12 demonstrate possible transmission zero configurations for below and above the passband, respectively. The transmission zeros can be positioned freely all the way to the lower and upper spurious bands. The depth  and height of the probe feed influence the input coupling as shown in Fig. 13. If finer control and stronger input coupling are required, the probe can be replaced with a T-shaped feed structure, shown in Fig. 14, by soldering a piece of wire to the end of the probe. A comparison of the achievable input coupling of the probe compared to the T feed for the same heights is shown in Fig. 14. This comes at the cost of increased assembly complexity and modification difficulty. The width of the wire attached to the pin also influences coupling strength, resonant frequency and achievable transmission zero positions, all of which need to be considered when using this type of feeding. A cylindrical cavity was chosen for this implementation to provide the ability to rotate the feeds and the coupling screws around the cavity in the upcoming dual-mode configuration. A singlet was designed for the standard post case as well as for the concentric-ring resonator. The pole/zero locations were optimised for both cases to have a similar response. The coupling matrix of the singlets is given in Equation (3).

B. TE 112 DUAL-MODE DOUBLET
Using both orthogonal TE 112 modes, a doublet [23], [24] can be implemented in a single cavity. The dual-mode operation is achieved using a screw at 45 • to excite both modes within the cavity. Two additional screws are used to control the centre frequency of each of the poles in much the same way as the method described for the TE 111 mode in [25] and [26]. Fig. 16 shows the strength of coupling of the two modes based on the depth of the screw. The deeper the screw, the stronger the coupling into the second TE 112 mode. It is also important to note that the position of the screw along the resonator influences the maximum achievable coupling strength. The screws should be placed at the maximum of the fields for the strongest effect. The position can be changed depending on the desired coupling to optimise for the manufacturing process, however, they also have an effect on the transmission zero positioning, which needs to be compensated. The second feed was rotated around the axis of the resonator by θ = 52 • to shift the second transmission zero above the passband as shown in the inset of Fig. 17. The coupling matrix of the doublet is given in Equation (4). Fig. 17 shows

C. CASCADED SINGLETS
Two singlets were positioned back to back, with a coupling iris, to achieve a two-pole filter for demonstration purposes. A T-shaped feed was chosen to enable stronger input coupling as demonstrated in Fig. 14. The transmission zeros of the filter are achieved in the same way as for the individual singlet, where the position of the feeds along the height of the resonator determines their location. The transmission zeros were positioned close to the passband to achieve a steep cutoff, with the filter centred at 14 GHz and a fractional bandwidth of 0.3%. The coupling matrix is given in Equation (5), and the simulated performance of the filter is given in Fig. 18. The doublet can also be extended into a back-to-back configuration to create a four-pole, two-zero, dual-mode filter. The coupling between the two resonators is achieved through a split iris, separated by a solid block in the centre. This block allows the TE 112 mode to couple while rejecting most of the TM 011 mode and pushing the TE 112 mode to lower frequencies, thus increasing the spurious free range below the passband by approximately 1.5 GHz. A comparison between this design and a standard iris can be seen in the inset of Fig. 19, where a demonstration of the improved spurious performance is depicted. The coupling matrix of the dual-mode filter is given in Equation (6)

V. MEASUREMENT DISCUSSION
In this section, the measurement results of the fabricated singlets, doublet and dual-mode filters are discussed. After fabrication, the dielectric resonators were found to be slightly larger than specified due to over-polymerisation of approximately 60 µm on each side in the XY-direction. As Fig. 21 illustrates, changes in the outside diameter of the resonator lead to a shifting of the resonant frequency. The over-polymerisation caused a 2.16% increase in the dimensions of the resonators and led to a downward shift in frequency of approximately 173 MHz in a simplified eigenmode simulation. Secondly, glueing the resonators to the floor of the cavities, thereby removing direct contact with the metal by inserting a lower dielectric material layer between the two, also shifts the resonant frequency downwards. Misalignment and tilting of the resonators during the manual assembly can lead to additional frequency shifts, especially of the transmission-zero positions. These effects will be demonstrated in the doublet and dual-mode filter cases by inclusion into a modified simulation model to validate.

A. QUALITY FACTOR
Two sets of cavities were milled for the printed resonators, one of each made from CW614N brass and CW008A copper alloys with electrical conductivities of 14.6 MS/m and 58 MS/m as per the data-sheet [29] and [30], respectively. The resonators were then glued to the base of the lid in each cavity as shown in Fig. 22. In this case, the assembly was done by hand which limits the achievable positioning accuracy. For commercial applications, more sophisticated methods of alignment and assembly should be used to ensure performance and repeatability. To improve the repeatability of the process and aid with the alignment, holders for each resonator were 3D-printed, shown in Fig. 23, for the glueing process. The quality factors of the post and the concentric-ring sample resonators were measured using the weak coupling method described in [27] and [28]. The measurements are sensitive to the alignment of the resonator with respect to the centre of the cavity, with a slight misalignment influencing the quality factor. A second consideration is that with a misalignment, a perturbation is caused in the field and the second orthogonal mode is coupled into as well, this will also affect the achieved quality factor of the measured resonance. The glue used to fix the resonators was standard off-the-shelf superglue and so introduces loss. The measured results of the Q-factor analysis are given in Fig. 24. Ten samples of each resonator were measured. An average value for the post was found to be approximately Q u = 4955 and Q u = 7125 for the concentricring resonator. This difference on average is approximately 2171 which is around 44%. The maximum achieved quality factor for each was Q u = 5366 and Q u = 7274, respectively, with a difference of 1907. The measurements were then repeated for the concentric-ring resonator in the copper cavity with an average Q u = 11841. These results represent the best values achieved throughout the measurements and assembly process. The measured results are consistently close to the simulated values with the concentric-ring resonator. The rings have the effect of reducing the current along the base of the resonator and thus the losses from the mounting method with glue have less of an influence on the measured values. This is not the case for the regular post which, along with slight misalignment, helps explain the lower than predicted quality factor values. In the case of the post-type resonator, more sophisticated methods of mounting and lower loss/conductive adhesives could be attempted to improve the performance, this however would still be lower than that of the proposed concentric-ring type resonator. For both resonators, future print iterations could be scaled using a new compensation ratio to provide a more accurate result and shift the frequency back closer to that of the simulated value.

B. TE 112 MODE SINGLET MEASUREMENT
The measured performance of the post and concentric-ring resonator brass singlets is shown in Fig. 25. The frequency shift of the resonators can be attributed primarily to the above mentioned enlargement of around 120 µm and slight tilting of the resonator due to the manual assembly. The concentric ring resonator has a measured insertion loss of 0.42 dB with an estimated Q u ≈ 5900 compared to the simulated Q u ≈ 6900. The measured resonant frequency shifted downwards by 1.93%, and the zero shifted downwards by 1.47%.  The uneven shifting of the pole and zero can be explained by slight tilting of the resonator during assembly, which changes the height of the probe feed slightly along the resonator compared to the design. Aside from the frequency shift, the results show good agreement with the simulated values.

C. TE 112 DUAL-MODE DOUBLET MEASUREMENT
The fabricated CW614N brass doublet is shown in Fig. 26, along with the measured performance in Fig. 27. The response has shifted downward in frequency by 1.43%, which is primarily attributed to the increase in resonator size and the use of glue. This hypothesis was confirmed by increasing the resonator size and adding a thin layer (70 µm) of glue (ε r = 3.3) between the base of the resonator and the cavity in the simulations. The modified simulation results are also shown in Fig. 27 and align well with the measurements. The tuning screws of the fabricated filter allowed for most of the response to be recovered, however, a shift in the transmission zero shift below the passband and the degraded quality factor performance remain. The quality factor of the filter was calculated to be approximately 1800 compared to a simulated 3700, with an insertion loss of less than 0.39 dB and a return loss that averages 20 dB throughout the passband.

D. TE 112 DUAL-MODE FOURTH-ORDER FILTER
The assembled CW614N brass dual-mode filter is shown in Fig. 28, which was measured for two different zero positions. Comparison of 3D-printed dielectric filters in literature (where f 0 is center frequency, TZ is transmission zero, 0 is wavelength at the centre frequency and Q u is the unloaded quality factor).  The measured performance with the dual-mode coupling screws at the height of 17.7 mm is shown in Fig. 29 and the second in the same filter with the coupling screws mirrored around the centre to the floor at 5.2 mm in Fig. 30. This demonstrates zero configurations on either side or both below the passband within the same design. It was not possible to fully recover the response due to the asymmetry and misalignment of the resonators. Each resonator position is also not identical to the other, with shift or angular misalignment being different in each. The tilting strongly affects the input coupling between the modes and differs at the two ports due to the manual assembly. The performance is thus degraded without additional means of recovery. Similar to the doublet case, modified simulations were performed for each filter to confirm the cause of the frequency shift. Again the resonator size was increased to match the fabricated dimensions, and a 70 µm layer of glue was added to the simulation. For the first configuration, it was also necessary to include a resonator tilt of 2 • to model the shift in transmission zeros more closely. In both cases, an effective conductivity of 0.6 MS/m was simulated to approximate the increased losses of the prototypes. These modified simulations are also included in Fig. 29 and Fig. 30, respectively. The filters achieved an insertion loss of less than 2.08 dB and a return loss that averages 14 dB throughout the passband, and quality factors of 1100, compared to a simulated 5600. The filter response was shifted downwards by 2.66% for the first zeros configuration and 1.3% for the second.
The quality factor for all the prototypes fabricated, especially in the dual mode cases, experienced degradation compared to the simulated values. These prototypes were designed and manufactured for verification of the core concept of this work. They were all assembled by hand, in a simple manner, by the author. The most significant contributing factor to the reduction in quality factor is the accurate alignment and placement of each of the resonators inside the cavities, which is the case for dielectric resonators generally. The tuning screws present in the design could not wholly compensate for these assembly defects, thus making complete recovery of the filter response and associated quality factors impossible. Additionally, the tuning screws are made of brass, which contributes to a further reduction in the achievable quality factor. For future work, more sophisticated assembly methods would significantly improve the measured performance of the prototypes. Table 2 provides a comparison of this work with other recent works on 3D-printed dielectric filters.

VI. CONCLUSION
A novel 3D-printed resonator structure with concentric rings around a dielectric post resonator has been proposed to increase the quality factor performance. The rings enable an improved performance by moving the TE 112 mode fields inside the cavity upwards and away from the cavity VOLUME 10, 2022 floor and thereby reducing conductive losses. The novel concentric-ring resonator was measured and compared to a standard post at the same resonant frequency. The ten samples measured showed an average increase in the unloaded quality factor of 2171, or approximately 44%, successfully validating the design. The resonator was demonstrated in a singlet configuration with easily controllable zero positioning. Additionally, a doublet configuration was presented, successfully fabricated and measured. The doublet was extended into successfully demonstrating a dual-mode fourth-order filter with two transmission zeros in two configurations. The causes for frequency shift and performance degradation in the prototypes were also identified and validated through simulations. This work proves the design concept and highlights the potential of 3D-printed resonators to greatly improve the loss performance.  His institute has more than 45 researchers, on average 60 publications per year and a research project turnover of e1.7 million per year. Previously, he was the Chief Technology Officer (CTO) of the Advanced Digital Institute, Shipley, U.K., a not-for-profit organization to promote research activities. Earlier, he worked as the Director of the Business and Technology Integration for RFMD, Reading, U.K., and for almost ten years, he has been with Filtronic plc, Yeadon, U.K., as a CTO of Filtronic Integrated Products and the Director of the Global Technology Group, New York, NY, USA. Before joining Filtronic, he held positions with the European Space Agency (ESA), Paris, France, working on amplifier linearization techniques, with MPR-Teltech, Burnaby, BC, Canada, working on MMIC technology projects, and with the Corporate Research and Development Group of M/A-COM, Boston, MA, USA, where he worked on advanced topologies for high-efficiency power amplifiers. For four years, he was with DaimlerChrysler Aerospace (now Airbus), Munich, Germany, working on T/R modules for airborne radar. He is currently the Dean of the Faculty of Electrical and Information Engineering, Graz University of Technology, which also incorporates 13 institutes and 18 full professors. He has published more than 150 articles and holds four patents. He is a fellow of the IET.