Vertically Integrated Coaxial Resonator-Based Multiband Bandpass Filters Using SLA 3-D Printing

This letter reports on a novel multiband RF filtering concept and a compact low-loss integration scheme for coaxial resonator-based multiband bandpass filters (BPFs). Size compactness is achieved by: 1) vertically stacking its constituent resonators, so that the available 3-D volume is optimally occupied; 2) the use of subwavelength capacitively loaded coaxial resonators; and 3) monolithic integration enabled by stereolithography apparatus (SLA) additive manufacturing (AM). A unique coupling routing diagram (CRD) is proposed and implemented with capacitively loaded coaxial resonators that allow to independently control the passband and stopband frequencies and facilitate both symmetric and asymmetric responses. A dual-band and triple-band BPFs operating at sub-6 GHz were designed, manufactured, and tested demonstrating highly miniaturized form factors and passbands with in-band insertion loss (IL) < 0.2–0.3 dB, i.e., $Q_{\mathrm {eff}}$ : 640–1030.


I. INTRODUCTION
T HE unprecedented growth of wireless communications is calling for RF systems able to support multiple applications and high data rates. In these systems, bandpass filters (BPFs) with high quality factor (Q), high selectivity, and multiband functionality are in need. For space-or terrestrial-based stations, lightweight and size compactness are other important metrics. The majority of multiband BPFs to date have been implemented using planar microstrip [1] or substrate-integrated waveguide architectures [2] that exhibit high insertion loss (IL) (2-4 dB) and limited power handling capabilities. Waveguide-based fully metallic filters [3] have lower IL and can handle higher power. However, they are based on multipart integration solutions that are bulky and expensive.
Coaxial cavity resonator-based filters are preferred for satellite or base-station applications due to their small size, lowloss, and wide spurious-free range [4]. Most of the existing coaxial multiband BPFs are based on multimode or steppedimpedance resonators [5], [6], [7], [8] that are hard to be extended to more than two bands. Multiband configurations where a narrow set of frequencies are notched out from a wide passband have been shown in [9] and [10]. Although they exhibit a greater number of passbands (>2), they require large number of resonators that result in increased volume and high manufacturing cost.
Additive manufacturing (AM) techniques are increasingly used for RF filters due to their low cost, fast turnaround time, and ability to manufacture complex geometries. Among them, stereolithography apparatus (SLA) has gained popularity due being easily accessible and leading to parts with low surface roughness, yet it has mostly been used as a replacement of conventional multipart computer numerical control (CNC) machining. Although it is fairly straightforward to manufacture monolithic waveguides [11], [12], most of the 3-D coaxial filters have been materialized as split blocks due to their geometrical complexity [13], [14]. A monolithic integration approach using SLA was demonstrated in [10] for in-line multiband BPFs. In [15], vertically integrated coaxial BPFs were presented with significantly reduced size; however, they were only shown for single-band topologies.
Expanding upon [10] and [15], this letter explores the potential to realize highly miniaturized vertically integrated multiband filters using coaxial-resonator-based configurations alongside a novel compact monolithic integration scheme for single SLA printing. The proposed multiband concept exhibits the following unique characteristics: 1) compact size and minimized (8× improvement) axial ratio (AR) enabled by vertical integration of subwavelength coaxial resonators; 2) combined use of inline and vertical couplings within the 3-D volume of the filter; 3) transfer functions with independently controlled passbands and stopbands; and 4) monolithic integration facilitated by SLA manufacturing.

A. Dual-Band Filter Concept and Vertical Integration Scheme
A conceptual illustration and the 3-D electromagnetic (EM) model of the proposed vertically integrated dual-band secondorder BPF is shown in Fig. 1  loaded coaxial resonators, namely, two in-line resonators (res. 1 and 3) and two shunt resonators (res. 2 and 4) that are vertically stacked with the in-line ones. The dual-band BPF has two second-order bands and functionalizes the coupling routing diagram (CRD) in Fig. 2. For each resonator, the center frequency is determined by the size of the capacitive gap g and the radius ratio of the cavity wall b and the center post a. The RF signal is inserted in the cavity by tapping the SMA connector to the post of the first resonator. This also acts as the external coupling (m a0 in Fig. 2), whose magnitude is controlled by the height of the SMA h e . The interresonator coupling between the in-line resonators 1 and 3 (m a1 in Fig. 2) is provided by the coupling iris [10]. For each pair of vertically stacked resonators (e.g., 1 and 2), the interresonator coupling m 1 is materialized by partially removing their shared ground plane and its magnitude is controlled by the size of the coupling window d i [15]. A septum is added between resonators 2 and 4 to prevent coupling between them.
The theoretical synthesized response is depicted in Fig. 2(b) for different m 1 values. To obtain a dual-band transfer function, all resonators need to be synchronously tuned at = 0, and the center frequency of the two passband is determined using the following equation: Using as a basis this CRD, a dual-band BPF was designed for m a0 = 1.1, m a1 = 1, and m 1 = 1 and two bands centered at f c1 = 3.70 and f c2 = 4.15 GHz with fractional bandwidths (FBWs) FBW 1 = 10.3% and FBW 1 = 8.0%, respectively. The performance of the filter is analyzed by EM simulations in ANSYS HFSS. Its dimensions are listed in Fig. 1. To characterize the effective usage of volume of a 3-D object, the metric of AR in the following equation is used: Note that for a given cubic space, the optimal AR is (2) 1/2 . Based on this definition, the AR of the vertically integrated dual-band BPF has been calculated equal to 3.5. If compared with a conventional dual-band BPF integration of the CRD in Fig. 2, where all resonators placed on the same horizontal plane, the AR would be 10.9. Therefore, a 3× AR improvement can be obtained by using the proposed vertical integration concept.

B. Triple-Band Filter Concept
To explore the scalability of the vertically stacked multiband concept, a second-order triple-band prototype was designed in     Fig. 4. A similar CRD has been shown in [16], however, for multibandstop microstrip filters. Compared to the dual-band case, an additional shunt resonator is added at the other side of each in-line resonator to create an additional stopband. The frequencies of the stopbands S1,2 are determined by the resonance of the shunt resonators using the following equation: S1 = −m 2,2 = −m 5,5 and S2 = −m 3,3 = −m 6,6 . (3) As shown in Fig. 4(b), the stopbands can be tuned independently and by only altering the resonant frequencies of their shunt resonators (i.e., 2 and 5 for S1 and 3 and 6 for S2 ). The bandwidth (BW) of each passband may be altered when tuning the shunt resonators. However, the BW change can be counteracted by tuning the frequency of the in-line resonators or m 1 and m 2 , as shown in the synthesized example cases in Fig. 4. Fig. 4(c) exhibits the transfer function dependence on m 1 and m 2 . By altering m 1 and m 2 , the separation between the passbands can be controlled, where increasing their magnitude leads to lager separation. Compared to a multiband CRD topology where all shunt resonators are placed on the same side of the in-line resonators [9], [10], the proposed CRD allows for independent tuning of the passbands and stopbands and facilitates asymmetrical transfer functions with different BWs.
To further demonstrate the merits of the vertically stacked multiband BPF approach, a triple-band BPF with two   second-order bands was designed. Its three bands are centered at f c1 = 3.6, f c2 = 4.0, and f c3 = 4.4 GHz with FBW 1 = 10.3%, FBW 2 = 6.0%, and FBW 3 = 7.6%, respectively. Its dimensions are listed in Fig. 3 (its EM simulated response is provided in Fig. 8) and correspond to an AR of 2.47. It should be noted that if the same CRD were to be implemented with all of the resonators placed on the same plane, then an AR of 13.2 would be obtained demonstrating a significant 5× AR improvement.

III. MANUFACTURING AND MEASUREMENT
For the proof-of-concept validation purposes, the proposed vertically stacked dual-band and triple-band BPFs were manufactured using SLA. To facilitate metallization, nonradiating slots are added on the cavity walls to allow for the Cu chemicals to flow inside the BPF volume. The orientation of the slots must be parallel to the surface currents to prevent radiation, as shown in Fig. 5, for the case of a dual-band BPF with and without the nonradiating slots.
To enable monolithic SLA printing, the filter orientation, the number, and location of the support structures need to be appropriately selected to achieve printability while using a minimal number of internal support structures. As shown in Fig. 6(a), external support structures are placed beneath the filter and can be readily removed after the printing. To avoid deformation of the inner structure, a few internal supports are added to support the post of resonators, as shown in Fig. 6(b). They are mechanically removed after the printing through the nonradiating slots. A commercially available Cu-plating process with a uniform 50-µm copper thickness (>20× skin depth at operating frequency) is applied to all filter parts.
The SLA printed prototype of the dual-band and triple-band BPFs before and after Cu-plating is shown in Fig. 7(a) and (b). The measured S-parameters are shown in Fig. 8(a) and (b), and their respective performance is listed in Table I. In particular, for the dual-band BPF, the effective quality factor (Q eff ) is  670 and 750, while for the triple-band case, Q eff = 640, 1030, and 900. The minor frequency shift for the passbands of the triple-band BPF is due to manufacturing tolerances. Overall, a decent agreement has been achieved between measurements and simulations, successfully validating the vertically integrated multiband coaxial BPF concept.
A comparison with the state-of-the-art multiband coaxial BPFs is provided in Table I. As it can be seen, the proposed multiband BPF is able to realize transfer functions with higher number of passbands (>2), which is otherwise challenging for conventional stepped impedance resonator-based filters, see [5], [6], [7], [8]. Furthermore, the use of monolithic SLA printing has resulted in smaller size and weight and similar Q eff when compared to traditional CNC-machined filters as for example the ones in [5], [7], and [8]. Compared to the work in [10], an 8× AR improvement is achieved for the case of the triple-band BPF. Furthermore, it is based on a distinct CRD, facilitating the realization of asymmetrical passbands. Finally, the proposed concept allows for more complicated multiband configurations to be realized when compared to the single-band BPF in [15].

IV. CONCLUSION
This letter reported on a new class of compact coaxial cavity resonator-based multiband BPFs. Size compactness is achieved by using vertically stacked coaxial resonators and monolithic 3-D printing. A unique CRD is proposed for multiband BPFs that facilitate independent control of each passband and stopband and asymmetrical responses. A dualband and a triple-band BPFs were demonstrated for concept validation.