Additively Manufactured and Monolithically-Integrated Triple-Mode Post-Loaded Cavity-Resonator-Based Bandpass Filters

This manuscript reports on a new class of triple-mode post-loaded cavity-resonator based bandpass filters (BPFs) alongside their design methodology and a monolithic integration scheme using stereolithography apparatus (SLA) 3D printing. The proposed BPF concept exhibits the following unique features: i) miniaturized size accomplished by combining three modes within the volume of a single post-loaded cavity resonator, ii) bespoke coupling element configurations that facilitate the realization of transmission zeros (TZs) in the out-of-band response and iii) monolithic SLA integration that further reduces the size and weight of the entire filter as opposed to conventional split-block manufacturing schemes. For proof-of-concept validation purposes, two three-pole/two-TZ BPFs and a six-pole/four-TZ BPF operating at 2.9 GHz, 3.2 GHz and 3.2 GHz with a fractional bandwidth (FBW) of 16.3%, 15.2%, 14.2% respectively, were designed, manufactured, and tested. They exhibited passbands with in-band insertion loss < 0.37 dB, that corresponds to an effective quality factor (Qeffs) > 780.


I. INTRODUCTION
Emerging wireless applications such 5G communications, internet-of-space (IoS) and drone-based surveillance are increasingly calling for RF transceivers able to support multiple communication standards while having a small footprint.To facilitate their development, bandpass filters (BPFs) with low loss and high selectivity need to be integrated in their RF front-ends to support their operation in complex electromagnetic (EM) environments [1].Low-cost, size compactness and light-weight are other critical metrics for these filters particularly for the ones serving ground or space-based communication platforms.In these systems, fully-metallic rectangular cavity resonator-based filters are typically being employed due to their high quality factor (Q), their high-power handling capacity, and mechanical robustness [2].However, these types of filters are bulky and are manufactured by expensive CNC machining processes that require post-fabrication tuning due to being based on split-blocks.
Examples of MMR-based single-band coaxial-resonators are shown in [31], [32].Particularly, a triple-mode coaxial cavity-based BPF with a center frequency of 2.5 GHz was demonstrated in [31].However, it requires a suspended external coupling structure that is sensitive to mechanical vibrations.In [32], a 2.55 GHz quad-mode BPF with modified coaxial resonators is reported.Nevertheless, it is based on a cumbersome CNC-based split-block assembly process.
Additive manufacturing (AM) or 3D printing has been increasingly explored as an alternative method for manufacturing 3D RF components.Metal-based AM processes such as selective laser sintering (SLS) [33], directive metal layer sintering (DMLS) [34] offer high mechanical robustness and are potentially suitable for monolithic integration.Albeit efforts to reduce their sensitivity to fabrication imperfections [35], they exhibit high surface roughness [36], [37], [38] and have high manufacturing cost.Resin-or plastic-based processes such as fused deposition modeling (FDM) [39] or stereolithography apparatus (SLA) [40], [41], [42], [43], [44], [45], [46] exhibit lower cost and SLA-based processes exhibit better surface roughness.Nevertheless, due to the need for surface metallization, devices with complex internal structures, e.g., coaxial cavities, are still manufactured as split-blocks that require post-assembly with screws [40], [41].In addition, high radiation loss is present in these assemblies due to the surface current being disrupted by the split-block design.
In this article, a new class of triple-mode post-loaded cavity resonator-based BPFs are proposed alongside a unique monolithic manufacturing concept using SLA 3D printing.The proposed filter concept exhibits the following unique characteristics: i) miniatured size enabled by combining three modes within the volume of a single resonator, ii) novel coupling electromagnetic elements that facilitate the realization of TZs alongside their independent tuning and iii) monolithic SLA  integration that further reduces the size and weight of the entire filter as opposed to conventional split-block manufacturing schemes.
The article is structured as follows: Section II presents the theoretical foundations and operating principles of the proposed post-loaded cavity-based BPF concept alongside its EM design methodology.In Section III, the manufacturing details and experimental validation of the concept are discussed.Finally, the major contributions of this work are outlined in Section IV.

II. THEORETICAL FOUNDATIONS
The 3D model of the proposed triple-mode post-loaded cavity-resonator concept is illustrated in Fig. 1.It consists of an air-filled cylindrical cavity that is capacitively-loaded with three closely-spaced posts.The posts are evenly distributed around its center and give rise to three closely-spaced resonant modes.Using Ansys HFSS eigen-mode simulation, the H-field distribution of the first three resonant modes are illustrated in Fig. 2(a)-(c), namely Mode 1, the fundamental quasi-TM 010 mode in Fig. 2(a) and Mode 2, 3, i.e., a pair of degenerate quasi-TM 11 mode, namely TM 11 + and TM 11 -in Fig. 2(b) and (c).As it can be seen, the H-field of Mode 1 is circulating around the center of the cavity, behaving as if there is a single post in the cavity center.Mode 2 is mainly concentrated around the two bottom posts while Mode 3 is stronger around the top post as shown in Fig. 2(c).By appropriately sizing the cavity and the post, the first three modes can be brought at closely-spaced frequencies and exploited for the realization of a BPF whose passband is shaped by three-poles.The geometry of an example BPF using the triple-post-loaded resonator is detailed in Fig. 3.As shown, two SMA connectors are tapped at two of the three posts to couple the RF signal in and out of the cavity.A top wing is added at the top side of each post as shown in pink in Fig. 3 and is extended towards the center of the cavity to independently control the resonant frequencies of each mode.Furthermore, it increases the capacitive loading.As shown in the green part in Fig. 3, a wing is added at the bottom of each post extending it towards the other two posts to facilitate tuning of the degenerate mode.
To demonstrate the operating principles of the proposed three-post loaded cavity concept, the resonant characteristics of each mode are examined using Ansys HFSS eigen-mode simulation as a function of different geometrical parameters and are as shown in Fig. 4. Specifically, Fig. 4(a) demonstrates that increasing the distance from the edge of the top wing to the cavity center d h augments the frequency of all three modes, however it has a more pronounced effect on the resonant frequency of Mode 2 due to reducing the capacitive loading of the post.Furthermore, larger d hm (i.e., distance from the intermediate top wing to the cavity center), results in higher resonant frequency for Mode 3 while the other two modes remain the same as demonstrated in Fig. 4(b).As depicted in Fig. 4(c) and (d), altering the size of the capacitive gaps g and g m (g is the gap size of the posts connecting to the RF output, g m is the gap size of the intermediate post) affect the resonant frequency of the modes in a similar fashion as in the case of d h or d hm , since they also affect the capacitive loading of the posts.In particular, increasing g or g m moves Mode 2 or Mode 3 to higher frequencies, while the resonant frequency of the remaining two other modes is almost constant.The distance between the bottom wings, i.e., d l and d lm , can be used to fine tune the frequency of the degenerate modes.In particular, increasing d l lowers the resonant frequency of Mode 2 as shown in Fig. 4(e), and a lager d lm lowers the resonant frequency of Mode 3 frequency as shown in Fig. 4(f).
Based on the aforementioned mode analysis of the triplemode post-loaded cavity-based resonator, three BPFs, namely two three-pole/two-TZ BPFs (Filter A, Filter B) and a higher order six-pole/ four-TZ Filter C are designed for proof of concept validation purposes and the design process is detailed in the next section.

A. COUPLING ROUTING DIAGRAM-BASED ANALYSIS OF THE TRIPLE-MODE POST-LOADED CAVITY-RESONATOR-BASED BPF
Using as a basis the triple-mode post-loaded cavity resonator in Fig. 3 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Depending on the relative frequency of node 1 in relation to the one of node 2, 3, the TZs can be located either below or above the passband.As shown in Fig. 6(b), when the resonant frequency of node 1 is larger than the ones of node 2, 3, all TZs are located below the passband.Fig. 6(c) and (d) demonstrates the TZ movement for different resonant frequencies of node 3 and 2. In particular, increasing the frequency of node 3 or decreasing the frequency of node 2 will make TZ 1 move away from the passband while TZ 2 comes closer to the passband.Fig. 6(e) demonstrates the synthesized response for different values of m 13 .As it can be seen, reducing m 13 also moves TZ 2 closer to the passband while TZ 1 remains almost constant.Therefore, by properly selecting the coupling values and the resonating frequency of the modes, the TZs can be designed as desired.It should be noticed that only negative coupling can be realized for m 13 in the practical filter design.
Overall, to practically realize the proposed filter concept only the resonant frequency of the resonators and the external coupling (Q ext ), i.e., m s1, m s2 , m s3 in Fig. 6 need to be specified.Whereas the resonant frequency of the modes can be determined by the eigenmode-based parametric analysis in Fig. 4, Q ext can be calculated via full-wave simulations in  ANSYS HFSS.Specifically, Q ext is realized by tapping two SMA connectors to two of the posts.The strength of Q ext can be controlled by altering the tapping location h e as shown in Fig. 7. Specifically, increasing h e lowers Q ext for all of the three modes.

B. THREE-POLE TWO-TZ BPF WITH TZS ABOVE THE PASSBAND: FILTER A
Using the CRD in Fig. 6(a), the resonator configuration in Fig. 3, and the abovementioned design method, a threepole/two-TZ BPF with center frequency of 3.3 GHz and fractional bandwidth (FBW) of 15% is designed as a proofof-concept validation.The EM-simulated power transmission response (|S 21 |) is shown in Fig. 8(a) and (b) for alternative geometrical parameters to demonstrate how the TZs can be controlled.The rest of the geometrical dimensions of Filter A are listed in Table 1.The coupling matrix for Filter A is given in (1).The final EM-simulated response is compared with the coupling matrix synthesized response as depicted in Fig. 5.

TABLE 1. Geometrical Parameters for Filter A (Units: mm)
As it can be seen, the EM simulated S-parameter show an excellent agreement with the theoretically synthesized response, successfully validating the proposed CRD.
To better illustrate the suitability of the CRD for the triple-mode post-loaded cavity resonator BPF, the following comparisons can be considered: From the CRD synthesized result in Fig. 6(d), increasing the frequency of node 2 (-m 22 ) results in f TZ1 closer to the passband and moves f TZ2 to higher frequencies.This pattern is consistent with the full-wave EM simulation result shown in Fig. 8(a), where increasing d h results in the same TZ variation.As noted in the eigenmode simulation result in Fig. 4(a), a larger d h moves Mode 2 to a higher frequency.Therefore, the variation of CRD can be accurately mapped to the physical resonator structure, further validating the suitability of the proposed CRD model.As another example, increasing d hm moves Mode 3 to a higher frequency from the eigenmode result in Fig. 3(b).Using the CRD synthesized results in Fig. 5(c), a larger node 3 (representing mode 3) frequency moves f TZ1 away from the passband and f TZ2 closer to the passband, which is consistent with the EM-simulated result shown in Fig. 8(b).Overall, by modifying the size of the coupling wing on the top of the posts, the frequency of both TZs can be independently controlled, allowing alternative types of quasi-elliptic transfer functions to be realized.It should be noted that although transfer-functions with TZs located on both side of the passband could be theoretically realized using the CRD in Fig. 6(a), they cannot be practically realized using the proposed cavity structure due to the limitation of the realizable coupling coefficients.

C. THREE-POLE TWO-TZ BPF WITH TZS BELOW THE PASSBAND: FILTER B
In this section, a filter design (Filter B) with TZs placed below the passband is considered.As shown in Fig. 6(b), in order to move both TZ to the lower side of the passband, the frequency of the Mode 1 needs to be higher than the degenerate modes.This is hard to achieve using the three-post cavity resonator in Fig. 1.However, by reducing the distance of the top wings d h and d hm , the frequency of the degenerate modes is reduced so that it is lower than that of Mode 1 as shown in Fig. 4  The geometrical parameters of Filter B are listed in Table 2 for a center frequency of 2.9 GHz and an FBW of 16%.Fig. 9 depicts the EM full-wave S-parameters and compares them to ones obtained via the CRD synthesis which appear to be in a good agreement.The coupling matrix is provided in (2).EM parametric simulations were also conducted to determine the location of the TZs.As shown in Fig. 10(a

D. SIX-POLE FOUR-TZ BPF: FILTER C
To explore the scalability of the proposed MMR concept to higher order transfer-functions, a six-pole/four-TZ BPF (Filter C) is designed for a center frequency of 2.8 GHz and an FBW of 13.5% by cascading Filter A and B through a 90°a ir-filled coaxial line with 50 characteristic impedance, corresponding to m 45 = 1 in The impedance of the line is obtained by optimization.It should be noticed that there is a stepped segment in the middle of the coax line to facilitate connecting two cavities that have different heights.The CRD and 3D model of the resulting filter are shown in Fig. 11   It should be noted that after cascading the two single-cavity filters, two spurious resonances at both side of the passband are generated [50] due to the distributed nature (around 90°a t f c ) of the coax line.They can be suppressed by setting the TZ right at the frequencies of the spurious modes.As demonstrated in Fig. 12(a) and (b), both spurs can be easily suppressed thanks to the independent tuning of the TZs that is

III. EXPERIMENTAL VALIDATION
To experimentally validate the triple-mode post-loaded cavity-resonator-based BPF concept, Filters A, B, and C were designed, manufactured, and measured for passbands having a center frequency of 3.2 GHz, 2.9 GHz, 2.8 GHz and FBWs of 15%, 16%, 13.5% respectively.A 3D monolithic integration approach enabled by SLA 3D printing was investigated for all the filtering components.Metallization was performed through a commercially available Cu-plating process that facilitates a copper thickness of 50 μm (>20× skin depth at the design frequency).Considering the closed-form geometry of the cavity resonators, non-radiating slots need to be added on the cavity walls to facilitate flow of the liquid-based metallization process inside the cavity volume.The size and the location of the slots are carefully chosen so that they do not affect the filter EM performance of the BPFs [42].As shown in Fig. 13, the H-filed distribution on the resonators' s upper wall remains un-changed after adding the non-radiating slots, which indicates that the filters' performance is not affected.Fig. 14 demonstrates the CAD model for SLA printing and the manufactured prototype of Filter A and B before and after Cu-plating.To facilitate monolithic SLA-based 3D printing, support structures need to be added to ensure the success of the printing process.As shown in Fig. 14(a), external support structures are added beneath the filter volume and can be easily removed after printing.Furthermore, the filter is oriented with an angle of 30°to avoid the generation of internal support structures and deformation of the upper cavity wall.A similar approach was followed for the manufacturing of the rest of the filters.It should be noted that a small hole with 1 mm depth was added to the post to fit the SMA probe.
An Agilent N5224A PNA was used to characterize the S-parameters of all of Filter A, B, C. The RF measured performance of Filter A and B are illustrated in Fig. 15 and are compared with their corresponding EM simulated one.The measured RF performance of the filters can be summarized as follows.Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.are shown in Fig. 16(a) and (b).It should be highlighted that a small internal support structure was added to facilitate printability of the air-filled coax line as shown in Fig. 16(a).The internal support structure was manually removed through the non-radiating hole prior to the Cu-plating process.Permanent bars are also added between the multimode resonators to enhance mechanical robustness.Its RF measured performance is provided in Fig. 17 together with its corresponding EM-simulated one.The measured RF performance can be summarized as follows: f c = 3.42 GHz, FBW = 13.3%, f TZ1 = 2.89 GHz (130 MHz higher than simulation), f TZ2 = 3.07 GHz, f TZ3 = 3.72 GHz, f TZ4 = 4.69 GHz, minimum in-band IL = 0.37 dB, which corresponds to a Q eff = 790.A frequency shift of TZ 1 is observed and it can be attributed to the manufacturing tolerance of the 3D printer, in particular at the bottom wing distance d lm.Fig. 18 demonstrates the wide-band simulation and measurement response of filter A, B, and C. As shown, a spurious resonance appears at around 10 GHz (3f c ) for filter A, 8 GHz for filter B(2.7f c ) and C (2.4f c ) and exhibit good agreement with the simulations.Overall, a decent agreement between RF measured and EM-simulated results can be observed, successfully validating the proposed triple-mode post-loaded cavity-resonator-based BPF concept using monolithic SLA integration.The measured weights of filter A, B, and C are 15 g, 15 g, and 27 g, respectively, which is significantly lighter compared to their all-metal CNC-machined counterparts.
Table 3 provides a comparison between state-of -the-art MMR-based BPFs and the proposed triple-mode post-loaded cavity-resonator-based BPF.As it can be seen, the proposed concept is the only post-loaded MMR that is furthermore implemented in a monolithic fashion.By using the compact capacitively-loaded resonators, and by combining multiple modes within the volume of a single cavity resonator, the filters reported in this work exhibit significantly smaller size compared to rectangular cavity-based filter, e.g., in [15], [16], [17].Compared to the cylindrical cavity filter with perturbation posts in [21], [23], the proposed post-loaded triple-mode filter is significantly smaller due to the stronger capacitive loading.In addition, by using the proposed transversal-type CRD and the novel tuning elements (top and bottom wings), the proposed filter in this work exhibits two independently controlled TZs.As comparison, the coaxial MMR-based filter in [31] did not present a TZ control method and the filter in [32] was only able to tune one of the TZs using coupling screws.Besides, compared to the filter in [32], the proposed filter utilized different TM-type modes to realize the transfer-function, and a different transversal type-CRD is proposed that better reflects the physical mode distribution inside the MMR cavity as opposed to the serial-type CRD that is based on intra-post couplings in [32].Furthermore, the SLA 3D printed resonator concept exhibits comparable Q eff to CNC machined fully-metallic coaxial resonator-based BPFs as in [31].It should be noticed that the MMR-based BPFs in Table 3 are all based on traditional CNC machined split-block manufacturing process.Therefore, their practical filter footprint is significantly larger than their listed internal sizes due to the need for assembly screws, whereas the sizes of the filters in this work are listed as overall sizes, demonstrating the potential of the proposed 3D printing integration approach for compact and low-loss RF filtering.

IV. CONCLUSION
This article presented the design, manufacturing, and experimental testing of a novel monolithic BPF configuration using post-loaded triple-mode resonators.SLA 3D printing is used as an enabling manufacturing technology to facilitate monolithic integration, size compactness and low weight.The proposed BPF architecture exhibits the following unique features: i) miniatured size facilitated by the combination of three resonating modes within a single low-profile postloaded MMR cavity, 2) bespoke coupling structures (top and bottom wing) that facilitate the generation and independent tuning of TZs in the out-of-band response of the BPF and iii) monolithic SLA integration that further reduces the size and weight of the entire filter when compared to traditional CNC-machined cavities with multiple blocks.Detailed design procedures are discussed using as a basis CRD synthesis and full-wave EM simulations.For proof of concept validation purposes, two three-pole/ two-TZ BPFs and a six-pole/ four-TZ BPF operating at C-band were designed, manufactured, and tested.Measurement results demonstrated transfer functions with passband IL < 0.37 dB, which corresponds to a Q eff > 780.A promising agreement between measurement and EM-simulations was observed, successfully validating the proposed post-loaded MMR cavity-based BPF concept using monolithic SLA integration.

FIGURE 1 .
FIGURE 1. 3D model of the triple-mode post-loaded cavity resonator where the air-filled metallic cavity is loaded with three cylindrical metallic posts.

FIGURE 3 .
FIGURE 3. 3D and EM simulation model of the triple-mode post-loaded cavity resonator-based BPF.(a) Bird-eye view.(b) Top-view.(c) Side-view.(d) Detailed top-view showing top wings.(e) Detailed bottom-view showing bottom wings.

FIGURE 4 .
FIGURE 4. Resonant frequency of each mode as a function of different geometrical parameters obtained through eigenmode simulations.(a) d h .(b) d hm .(c) g.(d) g m .(e) d l .(f) d lm.
, a three-pole BPF can be materialized.Due to the VOLUME 3, NO. 4, OCTOBER 2023 1239

FIGURE 5 .
FIGURE 5. Full-wave EM simulation and coupling matrix synthesized response of the three-pole/ two-TZ BPF of filter A.

FIGURE 7 .FIGURE 8 .
FIGURE 7. External coupling Q ext as a function of the SMA taping location h e .

TABLE 2 .FIGURE 9 .
FIGURE 9. Full-wave EM simulation and coupling matrix synthesized response of the three-pole/ two-TZ BPF of filter B.
), changes in the size of the bottom wing of the post d l mainly affect f TZ2 while f TZ1 remains almost constant due to varying the frequency of Mode 2. In particular, increasing d l moves TZ 2 closer to the passband due to the mode 2 frequencies being.Fig. 10(b) exhibits the EM-simulated |S 21 | for different d lm values.As discussed in the eigen-mode simulation results in Fig. 4(f), larger d lm values result in lower Mode 3 frequencies, which move f TZ1 closer to the passband as also demonstrated in the EM simulated results in Fig. 10(b).
(a) and (b) respectively.Note that node 4 and 5 in the CRD

FIGURE 10 .
FIGURE 10.EM-simulated |S 21 | of the proposed three-pole/two-TZ BPF (Filter B) for different geometrical parameters showing TZ tuning (a) d l variation.(b) d lm variation.

FIGURE 11 .
FIGURE 11.(a) CRD for the cascaded six-pole/four-TZ BPF (Filter C).(b) 3D geometry and EM simulation model of filter C.

FIGURE 12 .
FIGURE 12. EM simulated |S 21 | of the six-pole/four-TZ BPF (Filter C) in Fig. 9 for different geometrical parameters showing spurious suppression.(a) d h variation (b) d lm variation.

FIGURE 13 .FIGURE 14 .
FIGURE 13.Surface distribution of the H-field for filter A at 3.3 GHz.(a) Without slots.(b) With non-radiating slots.

FIGURE 16 .
FIGURE 16.(a) CAD model for SLA-based manufacturing.The details of the inter-connect coaxial TL are also shown alongside a temporary internal support element which is mechanically removed after manufacturing.External permanent bars have been also added between the two resonators to enhance printability and mechanical stability.(b) Manufactured prototype before and after Cu-plating (with SMA connector) for filter C.

FIGURE 17 .
FIGURE 17. RF-measured and EM simulated S-parameters for filter C.

FIGURE 18 .
FIGURE 18. Wide-band RF-measured and EM simulated S-parameters showing spurious performance (a) filter A. (b) Filter B. (c) Filter C.