Monolithic Multiband Coaxial Resonator-Based Bandpass Filter Using Stereolithography Apparatus (SLA) Manufacturing

This article reports on a new class of additive manufacturing (AM) and monolithically integrated multiband coaxial bandpass filters (BPFs). They are based on <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> in-series cascaded multiresonant sections that each of them consists of <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> resonators and <inline-formula> <tex-math notation="LaTeX">$K - 1$ </tex-math></inline-formula> admittance inverters. In this manner, a transfer function containing <inline-formula> <tex-math notation="LaTeX">$K N$ </tex-math></inline-formula>th-order passbands in between <inline-formula> <tex-math notation="LaTeX">$K - 1$ </tex-math></inline-formula> stopbands can be realized. A monolithic stereolithography apparatus (SLA)-based integration concept is proposed for these BPFs for the first time. For proof-of-concept validation purposes, multiple multiband BPF prototypes at the <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>- and <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula>-bands were designed, manufactured, and tested. They include: 1) a dual-band second-order BPF with passbands centered at 3.7 and 4.2 GHz, fractional bandwidths (FBWs) of 8.1% and 4.2%, and effective quality factors (<inline-formula> <tex-math notation="LaTeX">$Q_{\mathrm{ eff}}$ </tex-math></inline-formula>) above 1000 for both of its passbands; 2) a dual-band third-order BPF with passbands centered at 3.7 and 4.0 GHz, FBWs of 4.9% and 3.3%, and <inline-formula> <tex-math notation="LaTeX">$Q_{\mathrm{ eff}}$ </tex-math></inline-formula> above 1300; and 3) a triband second-order BPF with passbands centered at 3.5, 3.7, and 4.2 GHz, FBWs of 4.6%, 2.7%, and 5.5%, and <inline-formula> <tex-math notation="LaTeX">$Q_{\mathrm{ eff}}$ </tex-math></inline-formula> above 1100, successfully validating the proposed monolithic multiband coaxial BPF concept.

The majority of the multiband BPF configurations to date are based on planar PCB-based topologies [2]- [6]. The 3-D CNC-machined waveguides [7]- [10], helical resonator-based BPFs [11], dielectric resonator-based BPFs [12]- [14], and substrate integrated waveguides (SIWs) [15], [16] have also been presented. Among them, coaxial cavity resonator-based configurations are the most preferred filtering solutions for base stations and satellite communication systems due to their high quality factor (Q), compact size, and wide spurious-free range [17], [18]. However, the majority of these concepts are focused on single-band bandpass-type transfer functions and are manufactured with fully metallic CNC-machined parts that make them heavy, costly, and limit the complexity of the realizable transfer function.
Multiband coaxial cavity filters are typically implemented with multimode or stepped-impedance resonators [19]- [26]. For example, in [19] and [20], a second-order dual-band BPF is designed using a dual-capacitively loaded cavity. However, this concept is limited to the realization of two passbands. In [21], and [22], stepped-impedance resonators are used to create two passbands. Nevertheless, the complexity of their geometry hinders their practical development for higher frequencies or number of bands. Furthermore, they exhibit moderate insertion loss (IL = 1.9 dB [21] and 2.8 dB [22]). Dual-mode coaxial cavity resonators using double ground plane [23], intermediate conductor [24], [25], and stub-loaded resonators [26] have also been proposed. In yet another approach, multiband functionality is obtained by creating transmission zeros (TZs) in a single passband [27], [28]. Nevertheless, all the aforementioned designs are limited to dual-band and low-frequency operability due to their manufacturing complexity.
Digital additive manufacturing (AM) or 3-D printing is increasingly explored as a key enabling technology for the realization of complex 3-D geometries with low weight and fast turnaround design-to-prototype time [29], [30]. Based on the type of the additively manufactured material, AM processes are categorized into two types, i.e., metal-and plastic/resin-based. Although metal-based AM, such as direct metal laser sintering (DMLS) [31], selective laser sintering (SLM) [32]- [36], binder jetting [37], and electron beam melting (EBM) [38], exhibits high mechanical robustness and is potentially suitable for monolithic integration, they suffer from high surface roughness, which results in high IL for high-frequency RF components [39], [40]. Plastic/resin-based This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ AM process, such as stereolithography apparatus (SLA), provides lower surface roughness. However, due to the need for internal metallization, the manufactured RF components using SLA printing can only be materialized as split blocks and assembled via screws that increase their weight, loss, and complexity of the filter [41]- [44].
SLA monolithically integrated components have been demonstrated in [45]- [49], however for open-ended structures such as rectangular waveguide filters and couplers. Coaxial cavity filtering architectures are still being implemented as split blocks due to their enclosed geometry [50]- [52]. For example, an SLA-based S-band verticalintegrated multipart coaxial cavity filter was demonstrated in [50]. However, it exhibited a high IL of about 1.3 dB (effective quality factor (Q eff ) of 100). In [51], a 1.9-GHz SLAbased coaxial cavity BPF with mixed electromagnetic (EM) coupling was reported. Although it exhibited a fairly high Q eff (600), its assembly required multiple screws that increased its overall size and weight. Zhao and Psychogio [53]- [55] demonstrated the potential to realize a fully enclosed coaxial resonator monolithically and applied this concept to singleband in-line and vertically integrated BPFs with significantly reduced size and weight.
Building upon the monolithic coaxial resonator concept in [53]- [55], this article investigates for the first time a new architecture for highly miniaturized multiband BPFs as well as an SLA-based monolithic integration concept that facilitate the realization of multiple bands within a compact volume. This article is organized as follows. In Section II, the theoretical foundations of the multiband BPF concept are demonstrated through various synthesized examples and coupling routing diagrams (CRDs). Section III introduces the monolithic integration concept through various EM design examples and filter prototypes implemented at the C-band. Finally, Section IV summarizes the major contributions of this work.

A. Multiband BPF Concept
The details of the proposed Nth-order, K -band BPF are shown in Fig. 1 through its CRD and conceptual power transmission response. It is based on N in-series cascaded multiresonant sections that each of them consists of K resonators and K − 1 admittance inverters and creates a transfer function that contains K Nth-order passbands in-between K − 1 stopbands. It should be noticed that each stopband contains N TZs. The TZs in each stopband can be either merged or split depending on the frequencies of the shunt resonators in the multiresonant section. To demonstrate the operating principles of the concept, various theoretically synthesized examples are considered and are discussed in Sections II-B-II-D.

B. Second-Order Dual-Band BPF
The CRD and the theoretically synthesized power transmission and reflection response for the example case of a second-order dual-band BPF are shown in Fig. 2. The filter is comprised of two in-series cascaded multiresonant sections (N = 2) and each section is shaped by two resonators (K = 2). If all the resonators are set to resonate at = 0 (M xx = 0, M xx is the self-coupling coefficient for x = 2, 3, 4, and 5), two passbands with equal bandwidth (BW) will be created and they will be located at the center frequencies p1,2 where M 1 is the inter-resonator coupling coefficient between resonators 2 and 3 and resonators 4 and 5. Furthermore, one stopband will be created in-between the two passbands at S = 0, as shown in Fig. 2(b) [56]. To facilitate passbands with dissimilar BWs, the shunt resonators (3,5) need to resonate at different frequencies M xx (i.e., M 3,3 = M 5,5 = M xx = 0). In this case, the stopband will be located at It should be noted that when altering the resonant frequency of the shunt resonators, not only the frequency of the stopband but also the location of the passbands is altered. To counteract this effect, the frequency of the inline resonators (2, 4) needs to be set equal to −M xx . This is shown in the synthesized examples in Fig. 2(c). Namely, by properly altering the frequency of the in-line and the shunt resonators, the location of the stopband and the BW of each passband can be independently controlled while maintaining the same center frequency. In particular, when the stopband is closer to the lower band, its BW will be narrower, while the BW of the higher band will be wider.

C. Third-Order Dual-Band BPF
To investigate the potential of the multiband concept to higher order transfer functions, the example case of a third order (N = 3) dual-band (K = 2) BPF is considered in Fig. 3. Similar to the previous example, the center frequency of each band is controlled by M 1 when all of the in-line and the shunt resonators resonate at = 0. Larger values of M 1 move the passbands away from the stopband and the center frequency of each passband can be calculated using (1). If dissimilar BWs are preferred, the shunt resonators (resonators 3, 5, and 7) need to resonate at a different frequency than the inline resonators, as shown in Fig. 3(c). The location of the stopbands in this case is given by (2), where x = 3, 5, 7.

D. Second-Order Triple-Band BPF
A second-order (N = 2) triple-band (K = 3) BPF example is considered in Fig. 4 to explore the scalability of the multiband concept to a higher number of bands (i.e., three in this case). When all of its resonators resonate at = 0, the center frequencies of each passband are given by the following equation: where M 1 and M 2 are the inter-resonator coupling coefficients of the multiresonant sections in Fig. 4(a). For illustrative purposes, Fig. 4(b) shows how the center frequencies of the passbands are altered when varying M 1 with M 2 fixed. As expected, the first and third passband are separated further away as M 1 increases. Note that when increasing M 1 , the BW of the second passband will also decrease. In this case, the center frequencies of the stopbands are given by S1,2 = ±|M 2 |.
As shown in Fig. 4(c), by altering the frequency of the stopbands by means of M 2 , the BW of each passband can also be altered and can be used to counteract the BW change when altering M 1 .

III. EXPERIMENTAL VALIDATION USING MONOLITHICALLY INTEGRATED COAXIAL FILTERS
To practically implement the multiband BPF concept using monolithically integrated coaxial resonators, the design and integration concept for fully enclosed capacitively loaded coaxial resonators is first explained. Afterward, its applicability to various multiband BPFs is discussed and validated experimentally.

A. Monolithically Integrated Coaxial Resonators
Fig. 5(a) and (b) shows the 3-D geometry for the example case of a capacitively loaded coaxial cavity resonator that is designed to resonate at 4.2 GHz and to be manufacturable as a single piece using SLA [53]- [55]. In particular, the RF signal is launched through the SMA probe that is connected onto the resonator post. The connection point determines the strength of the external coupling that can be altered by changing the height h e , where larger external coupling values can be obtained for larger values of h e . To ensure that the SMA and the post are well connected, a small hole with depth of l p = 1 mm is added in the post. To facilitate metallization of the internal surfaces of resonator structure, nonradiating slots are added on the cavity walls to allow for the Cu-plating chemicals to flow inside the resonator. The size and location of the slots need to be appropriately designed so that they do not affect the resonators' unloaded quality factor (Q u ). To achieve this, the surface currents of the resonator are first analyzed using eigenmode simulations. As it can be seen in   Fig. 5(e), the current distribution of the perforated cavity is similar to the fully enclosed cavity in Fig. 5(d), indicating their minimal impact on the resonator's performance. This is also verified by full-wave EM simulations in ANSYS HFSS where Q u is calculated for a different number of slots and sizes and is summarized in Fig. 6. Three types of perforation schemes are considered in Fig. 6(a), i.e., 4, 8, and 12 slots with a width of w s and their effect is shown in Fig. 6(b). As it can be seen, in most cases, Q u above 2500 is maintained, which is acceptable when compared to the fully enclosed case having Q u of 3073. To maintain a high Q u while ensuring successful metallization, an eight-slot perforation scheme with w s of 2 mm is selected for the BPFs of this work. To facilitate monolithic SLA 3-D printing while avoiding the need for internal support structures, the SLA manufacturing model of the resonator needs to be tilted by an angle of 30 • with respect to the printer building platform, as shown in Fig. 6(c).

B. Inter-Resonator Coupling and External Coupling
To practically implement the proposed multiband BPF concept, eigenmode simulations need to be conducted to calculate the physical dimensions of the inter-resonator coupling element (an iris in this case) and map the simulated value of k i, j to the coupling coefficient of the desired transfer function in Section II, where the relationship between k and the normalized coupling coefficient m is given by where FBW is the fractional bandwidth of the filter. Fig. 7(a) shows an eigenmode simulation model containing two 4.2-GHz coaxial cavity resonators at a distance d 0 that is coupled with an iris and is simulated using Ansys HFSS.
As it can be seen in Fig. 7(b), k 1,2 will decrease as the distance between the resonators increases. k 1,2 may also be altered by modifying the dimensions of the iris. The relationship between the external coupling coefficient Q ext and the normalized source-to-resonator coupling coefficient m 0,1 is given as follows: To extract the relationship between Q ext and the tapping location of the SMA connector to the post, the simulation model in Fig. 7(c) is used. As shown in Fig. 7(d), Q ext is mainly dictated by the height of the SMA probe h e and decreases for larger values of h e .

C. Second-Order Dual-Band Coaxial BPF
Using as a basis the CRD in Fig. 2, the monolithic coaxial cavity resonator configuration in Fig. 5, and the Q ext and k 1,2 design guidelines in Fig. 7, a second-order dual-band BPF prototype is designed with a low-frequency passband centered at f 1 = 3.7 GHz and having an FBW = 8% and a highfrequency passband centered at f 2 = 4.2 GHz and having an FBW = 4%. The EM model of the dual-band BPF is shown in Fig. 8. The external coupling M A0 is materialized by the connection of the SMA probe and is controlled by its height h e . The inter-resonator coupling (M A1 and M 1 ) is controlled by the distance of the resonators. In particular, M A1 is determined by d 0 and M 1 by d 1 . The radius of the post a = 5 mm and the outer wall b = 15 mm is the same for all coaxial resonators. Thus, the frequency of each resonator is only dependent on the capacitive gap, i.e., g in Fig. 5, which is set as g 0 for the inline resonators and g 1 for the shunt resonators in Fig. 8(b). Fig. 9 shows the EM-simulated response of the 3-D coaxial filter in Fig. 8. As it can be seen in Fig. 9(a), the distance of the two passbands can be controlled by d 1 , which alters the inter-resonator coupling M 1 . As d 1 increases from 22.5 to 27.5 mm, the center frequency of the two passbands is altered from f 1 = 4.0 GHz and f 2 = 4.3 GHz to f 1 = 3.8 GHz and f 2 = 4.5 GHz. Fig. 9(b) shows that the location of the TZ can be controlled by changing the capacitive gap of the shunt resonators g 1 , which in turn alters their center frequency. As g 1 increases from 0.8 to 1.2 mm, the frequency of TZ is altered from f TZ = 4.4 GHz to f TZ = 3.8 GHz.
To facilitate SLA monolithic manufacturing of the 3-D multiband BPF, it is necessary to optimize the printing setup. Figs. 10 and 11 show two possible ways that the filter could be oriented during the printing process, i.e., the inline resonators are placed in parallel to the x-axis of the printer shown in Fig. 10 or parallel to the y-axis, as shown in Fig. 11. Since the RF signal needs to flow undisturbed within the filter volume, internal support structures should be avoided. Therefore, it is important that the device is self-supported during manufacturing. If the filter is oriented as in Fig. 10   (inline resonators are laid on the x-axis of the printer and tilted by about 30 • around the y-axis), an unsupported area will be generated around the slots above the coupling iris  between the shunt resonators, as highlighted in Fig. 10(c). Due to the horizontally oriented hollow slot in between the hanging resonators, subsequent layers cannot be built, and the manufacturing will fail. However, when the filter is oriented as in Fig. 11 (inline resonators are laid on the y-axis), the slots in-between the hanging resonators will be vertically oriented and this area will be supported by the existing layers, i.e., the structure is self-supported. Therefore, the printing orientation in Fig. 11(c) was adopted for the manufacturing of the dualband second-order BPF.
The SLA 3-D printed dual-band second-order BPF prototype is shown in Fig. 12(a) and (b) before and after Cu-platting. A commercially available Cu-plating process with 50-μm copper thickness (>15× skin depth in the operating frequency) is employed. The RF performance is characterized with a Keysight N5224A PNA and the RF-measured and EM-simulated S-parameters are shown in Fig. 12(d).
The measured performance is summarized as follows-lowfrequency band: center frequency f 1 = 3.69 GHz, FBW = 8.1%, and minimum in-band IL = 0.26 dB that corresponds to Q eff = 800; and high-frequency band: center frequency f 2 = 4.24 GHz, FBW = 4.25%, and minimum in-band IL = 0.30 dB that corresponds to Q eff = 1000. The measured IL is attributed to the surface roughness of the copper layer and the finite Q u of the resonators. The TZ split observed in the RF measured response is due to the two shunt resonators not operating at the exact same frequency. This is attributed to the manufacturing tolerances. Overall, the RF measurement response is in fair agreement with the EM simulated one successfully validating the proposed monolithically integrated multiband BPF concept.

D. Third-Order Dual-Band Coaxial BPF
A third-order dual-band BPF prototype was designed using as a basis the CRD in Fig. 3, the monolithic coaxial cavity resonator configuration in Fig. 5, and the k 1,2 design guidelines in Fig. 7. Its 3-D EM model and relevant dimensions are shown in Fig. 13. The monolithic SLA-printed filter before and after Cu-plating is shown in Fig. 14(a) and (b) alongside its printing setup in Fig. 14(c). The measured RF performance is summarized as follows and is shown in Fig. 14(d) alongside its EM simulated response-low-frequency band: center frequency f 1 = 3.67 GHz, FBW = 4.9%, minimum in-band IL = 0.32 dB, and Q eff = 1020; and high-frequency band: center frequency f 2 = 3.96 GHz, FBW = 3.28%, minimum in-band IL = 0.34 dB, and Q eff = 1300. The measured response exhibits a small difference in the FBW of the passbands, and however, it is only 1.5%. This is attributed to the fabrication tolerances that shift the frequency of the shunt resonator. As discussed in Sections II-B and II-C, the FBW of both bands can be altered by changing the shunt resonator frequency. Overall, the measurement response is in fair agreement with the EM simulated one successfully validating the proposed monolithic multiband BPF concept.

E. Second-Order Triple-Band Coaxial BPF
To explore the scalability of the monolithic coaxial multiband concept to transfer functions with a large number of bands, a second-order triband BPF was designed, manufactured, and tested. Its EM CAD model alongside its dimensions is shown in Fig. 15. The monolithic SLA-printed part before and after Cu-plating is shown in Fig. 16(a) and (b) alongside the printing setup in Fig. 16(c). The measured RF performance is shown in Fig. 16(d) alongside its EM simulated response and is summarized as follows-first passband: center frequency f 1 = 3.48 GHz, FBW = 4.6%, minimum in-band IL = 0.44 dB, and Q eff = 780; second passband: center frequency f 2 = 3.72 GHz, FBW = 2.69%, minimum in-band    Table I provides a comparison of the proposed monolithic multiband coaxial BPF concept with state-of-the-art coaxial cavity-based multiband BPFs and other AM coaxial filters. As shown, this is the first practical demonstration of a monolithic multiband coaxial BPF configuration. Furthermore, it has a higher number of passbands than all the rest of the CNC-based multiband concepts and significantly higher Q eff . Conventional split-block-based CNC-machined filters are limited to dual-band transfer functions [21]- [27] and their Q eff is lower, e.g., Q eff = 100 in [50] and Q eff = 600 in [51].

IV. CONCLUSION
This article has presented the design, manufacturing, and experimental validation of monolithic SLA-manufactured coaxial cavity resonator-based multiband BPFs. The proposed multiband concept is realized by N in-series cascaded multiresonant sections, where each section is shaped by K resonators and K − 1 impedance inverters. In this manner, a K -band transfer function shaped by the Nth-order passbands can be created. To practically realize the BPF concept, a monolithic integration approach using SLA 3-D printing of coaxial cavity resonators is proposed. To validate the multiband coaxial resonator BPF concept, multiple filter prototypes have been developed and tested, including a second-order dual-band BPF, a third-order dual-band BPF, and a second-order triple-band BPF. Excellent agreement between the simulated responses and the RF-measured ones has been observed. To the best of the authors' knowledge, this is the first time that a monolithic multiband coaxial cavity BPF concept is presented. Furthermore, this is the first practical demonstration of multiband coaxial cavity BPFs with more than two passbands.