Light and small radio frequency (RF) components are usually preferred for use in low Earth orbit (LEO) satellite systems, since they help launch multiple satellites using a single platform, thus reducing launch costs [1–4]. In general, RF filters can be designed using transmission lines, coaxial cables, and waveguide technologies. Among these, waveguide filters are the most suitable for satellite communication systems due to their low energy loss and high power-handling capabilities [5]. A typical waveguide filter design couples the fields in the E- or H-planes using irises, stubs, or posts [5–8] to achieve the desired frequency response. However, despite their superior performance, the use of waveguide filters is limited by their larger volume and heavier weight compared to other filter designs. Nonetheless, numerous efforts have been made to improve both their performance and size-related issues. In [8], a hybrid filter technique for controlling the width and height of a physical waveguide was proposed, achieving an out-of-band (OOB) rejection of −30 dB, although the use of an array of resonators led to a relatively long waveguide length of 3.69λ. In [9], a waveguide bandpass filter (BPF) with a spherical resonator operating in the X-band was designed to achieve OOB rejections of −35 dB and −20 dB in the lower and upper passbands, respectively. This study utilized 3D printing along with copper plating to fabricate a prototype that weighed only 280 g.

With the advent of the era of metamaterials, several designs for metamaterial-based filters have been actively studied [10–15]. In [10, 11], microstrip line-based filters were designed using split-ring resonators (SRRs). The design proposed in [10] operated at a center frequency of 2.4 GHz, attaining a passband bandwidth of 300 MHz at the 0.7 dB insertion loss criterion. In [11], a 2 × 3 SRR array was designed, achieving a maximum in-band transmission coefficient of 0.92 at around 180 GHz. In [12, 13], the concept of a zeroth-order resonator was employed to design the filter, which attained wide- and dual-band frequency responses. Notably, metamaterials have also been employed in waveguide filters. For instance, in [14], the coupling between metamaterial unit cells in a waveguide was adjusted by controlling the separation between the cells, demonstrating an OOB rejection of −30 dB at a filter length of 3.38λ. Recently, the authors of [15] proposed a locally resonant metamaterial (LRM)-based waveguide BPF design to reduce the length of the filter section. By designing the LRM inside the filter section, both the lower polariton (LP) and upper polariton (UP) were generated through electromagnetic coupling, with the hybridization bandgap (HBG) located near the LRM’s resonance frequency. The bandwidth between the LP and the HBG formed the passband of the BPF, which was designed using pin-shaped unit cells and demonstrated an OOB rejection of −20 dB. The OOB rejection was further improved by tuning the width of the waveguide, although it came at the cost of a narrower passband bandwidth, which reduced to about 5% at an OOB rejection of about −40 dB.

In this letter, we present a cross-shaped LRM unit cell design for use in waveguide BPFs operating at a center frequency of 7.5 GHz with a bandwidth of 500 MHz, especially targeting LEO satellite applications. The proposed BPF was constructed to meet certain performance criteria, including the target frequency and bandwidth, an insertion loss of less than 1 dB, a reflection coefficient of more than −10 dB, and OOB rejection of more than −40 dB. The simulated results obtained using the proposed design showed an improved OOB rejection performance of more than −50 dB, along with a passband bandwidth of 8.3%. Compared to the pin-shaped design in [15], the proposed design increased the quality factor (Q) of the passive filter by increasing the total capacitance in the filter section. Furthermore, for experimental verification, a prototype was built using a Stratasys Fortus 450mc fused deposition modeling (FDM) 3D printer and electroless copper plating techniques, with the size and weight of the fabricated filter being 0.79λ × 0.40λ × 2.49λ and 42 g, respectively. The proposed waveguide BPF filter passed signals ranging from 7.25 GHz to 7.75 GHz while also achieving an insertion loss of less than −1 dB, as indicated by the measured results. Furthermore, it exhibited an OOB rejection of over −40 dB, which is sufficient for satellite communication system applications. Notably, the full-wave electromagnetic (EM) simulations in this work were conducted using the CST Studio Suite.

Fig. 1(a) depicts the configuration of the LRMs inserted into the proposed waveguide BPF, which comprises a filter section and a matching section. The LRMs are placed in the filter section, while the matching section contains certain components, termed meta-ports, for impedance matching. The matching section is connected to a WR-112 flange (not shown in Fig. 1) with aperture dimensions of 28.5 mm × 12.62 mm. The shape and dimensions of the designed cross-shaped LRM unit cell are presented in Fig. 1(b). Notably, the reduced width of the waveguide filter section is expected to result in impedance mismatch in the evanescent mode filter [16]. Therefore, the meta-ports, as illustrated in Fig. 1(c), are coupled to the metamaterial unit cells located adjacent to the filter section to enhance wave transition for impedance matching [15]. As shown in Fig. 1(a), the proposed filter is composed of 9th-order LRMs positioned symmetrical to the center of the filter section, whose width is 9.6 mm. However, the spacing between the LRM unit cells is not the same—varying from 6.4 mm to 8.2 mm—with the meta-port separated from the first unit cell by 3.85 mm. We designed the filter to operate in the C-band.

The transmitter of a LEO satellite requires its filters to have a 500-MHz passband bandwidth along with a 1 dB insertion loss criterion and OOB rejection lower than −40 dB. As depicted in the inset in Fig. 2, full-wave EM simulations conducted for the proposed filter achieved a 600-MHz bandwidth within 7.06–7.67 GHz and 7.05–7.68 GHz at |S₁₁| < −15 dB and |S₂₁| < −1 dB, respectively. Although the desired operating frequency was 7.25–7.75 GHz, the filter was intentionally designed to induce a downward frequency shift so as to account for the 1.8% fabrication error resulting from thermal expansion of the 3D printing material. Meanwhile, OOB rejection was −51 dB at 6.81 GHz and −56 dB at 7.92 GHz.

To measure the skirt characteristics of the proposed filter, we defined the shape factor (SF) as BW_40dB/BW_1dB [17, 18], where BW_40dB and BW_1dB refer to the absolute bandwidths of |S₂₁| at −40 dB and −1 dB, respectively. Notably, the lower the value of this ratio, the higher the skirt characteristics. The simulation results showed the SF of the proposed filter to be 1.53—a lower value than that of existing filters in the literature—as discussed in detail later in this paper.

Fig. 3 depicts the reactance characteristics of the proposed filter and a pin-shaped LRM filter [15] with regard to the reference filter. The black dashed boxes in Fig. 3(a) indicate increased stored electric energy density (w_e) between the wall of the waveguide filter and the bar of the cross-shaped LRM along the x-axis, likely due to the increased capacitance resulting from the proposed cross-shaped unit cell compared to the pin-shaped one in Fig. 3(b). This resulted in an increase in Q, thereby leading to sharper OOB rejection. Fig. 3(c) shows the input reactance of the proposed and reference designs, with the stopband shaded in gray. It is evident that compared to the reactance of the reference pin unit cell design within the stopband, the reactance of the proposed design declines with increased capacitance. Overall, the simulation results in Fig. 3 show that the cross design is more capacitive than the reference design, enabling improved OOB rejection.

The final design in Fig. 1(a) shows that the spacing between each cross-shaped unit cell is different after optimization, as opposed to the initial design with equal spacing. To examine this, we generated a dispersion diagram considering equal spacing between the cross-shaped unit cells in the LRM, since it is primarily responsible for the formation of the filter’s passband at frequencies between the LP and HBG. Fig. 4(a) depicts the boundary conditions considered for extracting the dispersion diagram, with D representing the metamaterial unit-cell spacing. Notably, the xy-plane was set based on the periodic boundary condition, while the yz- and xz-planes were set based on a perfect electric conductor to mimic the filter section of the waveguide, whose height and width were set to 12.62 mm and 9.6 mm, respectively. The simulated results obtained for D are presented in Fig. 4(b), where the HBG, shaded blue, is located at around 8 GHz, while the UP and LP, both shaded gray, occur at frequencies above and below the lower frequency band, respectively [15]. Moreover, Fig. 4(b) reveals that the bandwidth of the passband is dependent on D. In the initial filter design, the D between every unit cell was set to 7.6 mm. Although the dispersion diagram in Fig. 4(b) indicates that the desired bandwidth can be achieved using this setup, the insertion loss fluctuated around −6.5 dB in the passband, while the input impedance could be matched only from 7.06 GHz to 7.31 GHz, considering the −10 dB criterion. Nonetheless, the OOB rejection was quite good at −62 dB. Effectively, spacing optimization was carried out to compensate for the insertion loss and impedance matching to finally arrive at the design illustrated in Fig. 1(a).

Fig. 5 presents the parametric study results obtained using the proposed cross-shaped unit cell for total dimensions x_total and y_total, with all other parameters held constant at the values specified in Fig. 1(a). Fig. 5(a) and 5(b) clearly show that a reduction in x_total and y_total leads to an upward shift in the passband. Although the overall bandwidth remains nearly constant, a slight dependence on these design parameters is observed, with x_total exhibiting a more significant influence than y_total. This can be attributed to the dominant role of x_total in determining the capacitive loading of the filter section, which directly affects the unit cell’s resonance condition. Additionally, although y_total has a relatively smaller effect on bandwidth, its variation can still alter the coupling strength between adjacent unit cells and, in turn, influence both insertion loss and return loss. Thus, precise dimensional control in the fabrication process is crucial for maintaining the intended filter characteristics. Overall, these findings highlight the importance of optimizing both x_total and y_total to achieve a stable frequency response and high filter efficiency in practical applications.

Furthermore, we evaluated the frequency response characteristics of the proposed design based on the order of the included unit cells. Fig. 6(a) illustrates an 11th-order cross-shaped LRM waveguide filter with two additional LRM unit cells, highlighted in yellow, positioned symmetrically at a distance of 8.3 mm from the center. This modification extended the total length of the filter section to 79.5 mm—16.6 mm longer than the 9thorder LRM waveguide filter depicted in Fig. 1(a). Apart from this extension, all other design parameters were kept unchanged to ensure a direct comparison.

In Fig. 6, the simulation results of the 11th-order filter are presented along with the results of the 9th-order filter from Fig. 2, replotted for comparison. Since the width of the filter section and the unit cell dimensions were kept constant, the passband bandwidth exhibited minimal variation. However, the inclusion of the two additional LRM unit cells, as depicted in Fig. 6(c), significantly enhanced OOB rejection, which improved by approximately 20 dB at 7.92 GHz. This improvement suggests that increasing the order of the filter can further suppress unwanted signals outside the passband, thereby enhancing overall filtering performance.

However, practical considerations, such as fabrication complexity, increased structural weight, and space constraints, must also be taken into account when determining the optimal filter order. In this study, given the stringent size and weight limitations pertaining to RF system integration, the 9th-order design was ultimately selected for the final prototype. This design choice ensured a balance between filtering performance and implementation feasibility, making it well suited for application in compact and lightweight communication systems.

The plastic structure of the proposed 9th-order BPF was built using an FDM 3D printer and then coated with 5 μm copper through electroless plating [19]. We chose not to use metallic 3D printing due to possible weight concerns for the final prototype. Photos of the fabricated prototype are presented in Fig. 7. Notably, in the first measurement, the frequency responses of the prototype shifted upward by 0.2 GHz compared to the desired design specification of 7.25–7.75 GHz. This can be attributed to a slight expansion in dimensions during the 3D printing process, despite the use of polycarbonate material with a low thermal coefficient of 70.2 μm/m°C [20]. This is also why the frequency of the simulated design shifted downward by 0.19 GHz, as shown in Fig. 2.

For comparison, the simulation results meeting the 7.25–7.75 GHz band, which were obtained by tuning the size of the unit cell and meta-ports in the x-axis and by adjusting the distance between the meta-port and the first unit cell of the filter section, are plotted in green in Fig. 7(b) and 7(c), while the results obtained using the final prototype based on the design values in Fig. 1 are plotted using blue lines. The simulated and measured results show a 1 dB ripple within 7.25–7.75 GHz, but matching trajectories from 7.25 to 7.82 GHz for S₁₁ < −10 dB. Furthermore, OOB rejection at 7.0 GHz and 8.0 GHz was found to be −49 dB and −43 dB, respectively—slightly worse than the simulated values of −51 dB and −56 dB—owing to the lower conductivity of copper plating compared to bulk copper [21, 22]. Moreover, as shown in Fig. 7(a), the prototype weighed 42 g, which is sufficiently lightweight for use in satellite communication systems—for instance, it is more than 25 times lighter than the aluminum computer numerical control (CNC)-milled prototype reported in [14].

Table 1 compares the bandwidth, SF, length, and weight of the proposed BPF with those of other 3D-printed waveguide BPFs reported in the literature. The proposed BPF shows the lowest SF value, although it is heavier than the BPF in [15]. This heaviness can be attributed to our design being longer by about 70 mm at the lower operating frequency. However, with approximately the same OOB rejection as [15], our work achieved twice the bandwidth. Overall, the proposed BPF, given its small length and light weight, exhibits characteristics that make it suitable for use in satellite communication RF systems.

This letter proposes a lightweight 3D-printed LRM filter for improved OOB rejection. A cross-shaped LRM was designed to attain additional capacitance in the waveguide filter section, resulting in strong coupling between the unit cells and the waveguide wall. SF was employed to evaluate the OOB of the proposed design and compare it with those of the other 3D-printed filters reported in the literature, with the former exhibiting the best performance. The design procedure for the filter is also explained in detail. Moreover, the results obtained using the prototype, constructed by carefully accounting for thermal expansion, successfully verified the simulations. However, it must be noted that although the proposed filter is lightweight and exhibits favorable SF features, its thermal characteristics when loaded into satellite systems need to be studied in more detail in future research.