Monolithic integration concept

The configuration of the capacitively-loaded coaxial cavity resonator is shown in Fig. 1. It has been designed using the design method in [Reference Anand and Liu52]. Non-radiating perforations are added on the top, bottom, and side walls of the cavity resonator so that the Cu-plating solution can flow inside the SLA-manufactured part during the metallization process. RF signal is injected into the cavity by connecting the inner conductor of the SMA connector to the capacitive post. To ensure stable connection, a small hole with depth l_p [Fig. 1(b)] is added in the center post. To minimize the radiation loss, the location, size, and orientation of the slots were selected so that they do not interrupt the surface current flow. This is shown in [Reference Zhao and Psychogiou51] where the current flow on the resonator walls is compared before and after adding the slots. The current flow is similar to the case of the fully enclosed cavity due to the slots being added in parallel to the current, resulting in small radiation loss at the design frequency and an unloaded quality factor Q of 3379 as opposed to 3399 in the fully enclosed case.

Fig. 1. Monolithically-integrated coaxial cavity resonator with non-radiating slots. (a) Bird eye view of the EM model. (b) Side view of the EM model. (c) Bird eye view of the CAD printing model (blue area: filter body; grey area: support structure). The slots are for the purpose of facilitating the metallization process. The resonator dimensions are: a = 3, b = 10, g = 1, h = 7, h _e = 3.5; all units are in mm.

Single-band two-pole BPF

Using as a basis of the monolithic integrated coaxial cavity resonator in section “Monolithic integration concept”, a two-pole BPF was designed. Its coupling routing diagram (CRD), synthesized response, 3D EM, and CAD model for 3D printing are shown in Fig. 2. For a desired fractional bandwidth (FBW), e.g. 15%, the external coupling Q_e is first calculated using (1) where k _0,1 is the normalized coupling coefficient (equal to 1 in this case).

(1)$$Q_e = \displaystyle{1 \over {k_{0, 1}^2 \times {\rm FBW}}}.$$

Fig. 2. Two-pole coaxial cavity-resonator based BPF with perforated walls to enable the Cu-platting process. (a) CRD and synthesized response (white circle: source and load; black circle: resonating node. k _0,1 = 1, k _1,2 = 0.8). (b) Bird eye view. (c) Side view. (d) 3D CAD model for 3D printing. The BPF dimensions are: a = 3, b = 10, g = 1, h = 7, h _e = 3.5, d = 14, all units are in mm.

In the physical structure, Q_e is materialized by connecting the inner conductor of the SMA to the capacitively-loaded post. Its magnitude is controlled by the height of the connecting position h_e. As shown in Fig. 3(a), as h_e increases, k _0,1 increases; this is primarily a result of the electric field being stronger between the post and the upper resonator wall due to the capacitively loading effect. The control of inter-resonator coupling, k _1,2, is determined by the distance d between the two posts. As shown in Fig. 3(b), the k _1,2 will increase as the distance between the two posts decrease. Using as a basis of these parametric plots, the distance of the resonators and the location of the connecting location of SMA connector are selected for the desired FBW as shown in Figs 3(b) and 3(c). Slots are also present in this case to facilitate the Cu-platting solution to flow within the filter volume. The EM-simulated response of the designed BPF for a center frequency (f_cen) of 5.3 GHz and FBW of 15% is shown in Fig. 4.

Fig. 3. (a) Q_e and k _0,1 as a function of h_e and (b) k _1,2 as a function of d for the single-band BPF in Fig. 3.

Fig. 4. RF-measured and EM-simulated response of the single-band coaxial-resonator based BPF in Fig. 3.

To validate the practical viability of the monolithic concept, a prototype was manufactured using as a basis the 3D CAD model in Fig. 2(d) and a desktop SLA-based 3D printer with 25 μm layer resolution. For its metallization, a Cu-platting commercial process (from RepliForm, Inc., Baltimore, Maryland, USA) with 50 μm metal layer thickness (>20x skin depth at design frequency) was employed. To compensate for the copper layer thickness, a 50 μm is employed in all geometrical dimensions in the final CAD model for SLA 3D printing. The manufactured prototype (before and after Cu-plating) of the two-pole filter is shown in Fig. 5. Its RF-measured response was characterized with a Keysight N5224A PNA and is shown in Fig. 4. It exhibits the following RF characteristics: f_cen = 5.25 GHz, minimal in-band IL = 0.25 dB, and 3 dB FBW = 13%, which corresponds to an effective quality factor of Q_eff = 500. Overall, the RF-measured performance is in good agreement with the EM-simulated one, successfully validating the proposed monolithic integration concept.

Fig. 5. Manufactured prototype of the single-band filter using as a basis the BPF model in Fig. 3. (a) Before Cu-plating. (b) After Cu-plating.

Single-band diplexer

To explore the applicability of the monolithic coaxial-resonator concept to the design of more complex frequency-selective RF components, an RF diplexer configuration consisting of two two-pole BPFs was designed and is shown in Fig. 6. The design uses a coaxial transmission line-based T-junction for size compactness which is shown in this implementation for the first time. To better illustrate the design methodology for the diplexer, the circuit is divided into two sections: (i) the single channel BPF and (ii) the T-junction. Although the single channel filter design mainly follows the approach described in section “Single-band two-pole BPF”, when the BPF is integrated into the RF diplexer, one of its external couplings (e.g. RF port 2 in Fig. 2) needs to be materialized as an air-filled coaxial transmission line as opposed to the Teflon-filled case in the conventional single channel, so that the overall RF diplexer can be manufactured monolithically as shown in Fig. 6. As a result, the difference in the external coupling needs to be compensated by adjusting the connection point height of the inner conductor of the air-filled coax (h_{l 2} and h_{h 2}) as shown in Fig. 6(b).

Fig. 6. Single-band RF diplexer. (a) Bird eye view of the 3D EM model. (b) Side view of the 3D EM model. (c) 3D CAD printing model. The dimensions of the diplexer are as follows: a = 5, b = 15, g _l1 = g _l2 = 0.8, g _h1 = 1.1, g _h2 = 1.12, l ₁ = 3, l ₂ = 4.6, h = 6, h _l1 = h _h1 = 2.5, h _l2 = h _h2 = 2, d _l = 26.9, d _h = 26.7, all units are in mm.

The details of the T-junction design are shown in Fig. 7. Similar to the coaxial cavity resonator, non-radiating holes were added to the outer conductor to facilitate the Cu-platting process. In order for both bands to be matched and to maximize the isolation of the different channels, the T-junction must be designed so that the input impedance of the low-band channel (Z_l) presents an RF open at the higher frequency band (f_h) and the input impedance of the high-band channel (Z_h) presents an RF open at the lower frequency band (f_l) [Reference Basavarajappa and Mansour54]. To satisfy this condition, the phase of the T-junction needs to be properly designed. As shown in Fig. 7(c), Z_l presents an RF open at f_h = 4.2 GHz when l ₁ = 3 mm. Similarly, l ₂ is selected to be equal to 4.6 mm for Z _h to present an RF open at f _l = 3.3 GHz.

Fig. 7. (a) Design principle of the T-junction. (b) EM model of the proposed T-junction. (c) Simulated reflection coefficient of the lower frequency channel S_l of the T-junction.

To validate the RF diplexer concept, a prototype was designed with the following RF characteristics (Fig. 8). Low channel: center frequency f _l = 3.3 GHz, FBW = 7.5%; high channel: center frequency f_h = 4.2 GHz, FBW = 7.5%. The RF-measured S-parameters and manufactured prototype are respectively shown in Figs 9 and 10. The RF-measured characteristics are summarized as follows: low channel: f_l = 3.35 GHz, minimal in-band IL = 0.34 dB, and 3 dB FBW = 7.16%, corresponding to an effective quality factor of Q_eff = 580; high channel: f_h = 4.12 GHz, minimal in-band IL = 0.62 dB, and 3 dB FBW = 7.52%, which corresponds to an effective quality factor of Q_eff = 330. The lower Q_eff in the high-frequency channel is attributed to the surface roughness of Cu-plating. Nevertheless, the measured RF performance is in a fair agreement with the EM-simulated S-parameter response, successfully validating the RF diplexer concept.

Fig. 8. RF-measured and EM-simulated S-parameters of the single-band coaxial-resonator-based diplexer in Fig. 7.

Fig. 9. Manufactured prototype of the single-band coaxial-resonator-based RF diplexer, based on the EM model in Fig. 7. (a) Before Cu-plating. (b) After Cu-plating.

Fig. 10. Dual-band coaxial-resonator-based BPF. (a) CRD and synthesized response (k _0,1 = 1, k _0,2 = −1, k _1,3 = k _2,4 = 1, k _1,1 = k _3,3 = −k _2,2 = −k _4,4 = 5). (b) Bird eye view. (c) Side view. (d) 3D CAD model used for SLA 3D printing. The indicated dimensions are as follows: a _l = 3, a _h = 2, d _l = 24.2, d _h = 13.6, m = 5.3, g _l = g _h = 1, h _l = 2, h _h = 7, h = 5. All units are in mm.

Dual-band BPF

The dual-band coaxial BPF concept is based on the CRD and its corresponding synthesized response in Fig. 10(a). Its practical development, as shown in Figs 10(b)–10(d), uses as a basis a dual-resonant coaxial resonator [Reference Liu, Katehi and Peroulis53] that is materialized by two capacitively-loaded posts (a_l and a_h) that control the resonant frequency of each of the BPF passbands (f_l and f_h). In order for the bandwidth of the two passbands to be independently controlled, both the external coupling factor (Q_el and Q_eh) and the inter-resonator coupling factor (k _1,3 and k _2,4) of each band need to be altered individually. In particular, for the external coupling, a two-section network allowing for the SMA connector to connect to two different locations of the two posts (h_l, h_h) has been developed and is illustrated in Fig. 10(b). As shown in Fig. 11, h_h majorly affects Q_eh whereas h_l majorly affects Q_el. The inter-resonator coupling (k _1,3 and k _2,4) can be controlled by altering the separation of the posts. In particular, the coupling at the higher passband k _1,3 is majorly affected by the distance (d_h) and the coupling k _2,4 by the distance d_l as shown in Fig. 12.

Fig. 11. External coupling factor for the low-frequency band (Q_el) and for the high-frequency band (Q_eh). (a). Dependence on h_h. (b) Dependence h_l.

Fig. 12. Inter-resonator coupling for the high-frequency band k _1,3 and for the high-frequency band k _2,4. (a) Dependence on d_{h .} (b) Dependence on d_l.

Using as a basis these design guidelines, a dual-band BPF was designed for the following RF characteristic: low-frequency passband: f_l = 3.5 GHz, FBW = 13%, high-frequency passband: f_h = 5.2 GHz, FBW = 4%. Its EM-simulated response is provided in Fig. 13.

Fig. 13. RF-measured and EM-simulated S-parameters of the dual-band coaxial-resonator-based BPF in Fig. 11.

To validate the dual-band BPF concept, a prototype was manufactured using a desktop SLA 3D printer and is shown in Fig. 14. Its performance was characterized by means of S-parameters and is shown in Fig. 13 alongside its corresponded EM-simulated response. Its RF-measured performance can be summarized as follows: low-frequency passband: center frequency f_l = 3.34 GHz, minimal in-band IL = 0.32 dB, 3 dB FBW = 11.1%, corresponding to Q_eff = 420; high-frequency passband: center frequency f_h = 5.04 GHz, minimal in-band IL = 0.84 dB, and 3 dB FBW = 2.6%, corresponding to Q_eff = 670. The observed frequency shift can be attributed to the fabrication tolerance especially in the capacitive gap (g_l and g_h). Overall, the simulation and measurement exhibit fair agreement with measured return loss >13 dB in both bands.

Fig. 14. Manufactured prototype of the dual-band coaxial-resonator-based dual-band BPF based on the CAD model in Fig. 8. (a) Before Cu-platting. (b) After Cu-platting.

Dual-band RF diplexer

Using as a basis the dual-band BPF concept in section “Dual-band BPF”, an RF diplexer with two second-order dual-band channels has been designed and is shown in Fig. 15. It is comprised of three parts, i.e. two dual-band second-order BPFs and a coaxial transmission line T-junction. Similar to the channel design of the single-band diplexer, each of them needs to be re-designed so that one of its RF ports is air-filled prior to be incorporated into the RF diplexer. The redesign is achieved by tuning the height of the coupling network, namely h_{p 0}, h_{p 1}, and h_{p 2}. After designing the two channels, the T-junction of the diplexer is designed in a similar way as the one described in Fig. 7(a). The EM-simulated response is provided in Fig. 16.

Fig. 15. (a) Bird eye view and (b) side view of the proposed dual-band coaxial cavity resonator-based diplexer. The indicated dimensions are as follows: a _l = 3, a _h = 2, d ₁ = 21.5, d _l2 = 26.4, d _h1 = 11.5, d _h2 = 16.4, g _l11 = g _h11 = 1.2, g _h12 = 1.75, g _l12 = 0.9, g _l21 = g _l22 = g _h22 = 0.5, g _g21 = 0.47, h _l1 = h _l2 = 2, h _h1 = h _h2 = 8, h _p0 = h _p1 = h _p2 = 5. All units are in mm.

Fig. 16. RF-measured and EM-simulated S-parameters of the dual-band RF diplexer in Fig. 16.

A photograph of its manufactured prototype is provided in Fig. 17 and its RF-measured performance is plotted in Fig. 16. It is summarized as follows: channel 1: low-frequency band: center frequency f_{l 1} = 2.96 GHz, minimal in-band IL = 0.24 dB, 3 dB FBW = 14.9% (Q_eff = 520); high-frequency band: center frequency f_{h 1} = 4.48 GHz, minimal in-band IL = 0.18 dB, 3 dB FBW = 4.2% (Q_eff = 800); channel 2: low-frequency band: center frequency f_{l 2} = 3.46 GHz, minimal in-band IL = 0.18 dB, 3 dB FBW = 18.9% (Q_eff = 600); high-frequency band: center frequency f_{h 2} = 5.34 GHz, minimal in-band IL = 0.38 dB, 3 dB FBW = 3.56% (Q_eff = 650). Although a fair agreement is obtained between the EM simulations and the RF measurements, a frequency shift can be anticipated. It is attributed to the added fabrication tolerances due to the increased complexity of the inner structure and the need for a few internal support structures for the external coupling network. These need to be removed manually prior to Cu plating, which affects the quality of the capacitive posts.

Fig. 17. Manufactured prototype of the dual-band coaxial-resonator-based RF diplexer, using as basis the CAD model in Fig. 12. (a) Before Cu-plating. (b) After Cu-plating.

Comparison with state-of-the-art 3D printed coaxial filters

A comparison of the proposed monolithic coaxial-resonator-based BPF/diplexer concept with state-of-the-art (SOA) 3D printed coaxial BPFs is shown in Table 1. As shown, the proposed concept is the only one that allows for monolithic integration, resulting in smaller size and weight if compared to its split block counter parts, e.g. the ones in [Reference Venanzoni, Dionigi, Tomassoni and Sorrentino47]. Furthermore, it exhibits a significantly higher Q_eff when compared to the split-block approach in [Reference López-Oliver, Tomassoni, Silvestri, Bozzi, Perregrini, Marconi, Alaimo and Auricchio44] and at a higher frequency due to its monolithic implementation. Furthermore, the proposed monolithic concept has been demonstrated for significantly more complex architectures than the SOA including a dual-band BPF and a single- and dual-band diplexer that are shown in this work for the first time. It should be noticed that the material for the SLA printing used in this work has a heat deflection temperature of 73.1 °C at 66 psi. For applications where high-temperature performance is required, e.g. satellite communication system, the material could be replaced with heat-resistant resin for stable operation of the device.

Table 1. Comparison with the state-of-the-art 3D printed coaxial cavity-based BPFs

Ref, reference; Func., functionality; Mono., monolithic; #Band, number of bands; T.W., this work; N/A, not reported; * = estimated value, all the referred filters are manufactured using SLA 3D printing technique.