# Effective Size Reduction of the Metallic Waveguide Bandpass Filter with Metamaterial Resonators and Its 3D-Printed Version

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## Abstract

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^{−2}mm but rather 10

^{-1}mm, which is good for manufacturers but challenging for component designers. The measurement of the manufactured metal waveguide filters reveals that the passband has about ≤1 dB and ≤−15 dB as the insertion loss and the reflection coefficient, respectively, and the stopband has an attenuation of ≤−40 dB, which are in good agreement with the results of the circuit and the simulation. The proposed filter has a length of 14 cm as the eighth-order BPF, but the conventional waveguide is 20 cm as the seventh-order BPF for the same area of the cross section.

## 1. Introduction

^{−1}mm to avoid the problems of fabrication tolerance, whose lower precision makes this design much tougher than others, using 10

^{-2}mm, with more expensive facilities. Second, the ZOR as a building block for the equivalent network of the eighth-order BPF is substituted for conventional cavities. Third, the resonators are cascaded through short waveguide sections as coupling elements to generate the passband. Additionally, the stopbands have high attenuation. Fourth, the WG BPF of ZORs and coupling elements is physically prototyped by the CNC-milling technique. Fifth, the metallic WG filter is transformed into a 3D-printed version to lower the weight of the structure, potentially proper for fast and mass production. According to [10,11,12], this is the first 3D-printed metamaterial waveguide bandpass filter that has been made by the PC PEKK-based additive process. Sixth, its performance is tested. The suggested method is evaluated by circuit modeling, full-wave EM simulation and measurement. Good agreement between the theoretical results and the experimental results is unveiled from the procedural steps. As noted in the required specifications on the WG BPF, the passband has about ≤1 dB and ≤−15 dB as the insertion loss and the reflection coefficient, respectively; the stopband has 40 dB of noise suppression, whereas its 3D-printed version has a little degraded insertion loss and return loss owing to material loss and surface roughness. Regarding size reduction, the proposed PBFs of metallic and 3D-printed waveguides are 14 cm for the eighth-order filtering, while the conventional waveguide filter of the seventh order is of 20 cm in length. This effect will be obvious for much-higher-order filters and multiplexers.

## 2. Circuit Modeling of the BPF and the WG ZOR, and Its Geometry

#### 2.1. Required Specifications of the BPF for Satellite Wireless Communication

_{order}= 8 is quite close to the specifications in Table 1 for the amplitude of the bandpass filter, as in [13]. It is expressed with the circuit network.

_{11}as the reflection coefficient and S

_{21}as the transmission coefficient of the device. This ideal circuit results in the satisfactory frequency response. The circuit calculation is operated on the basis of the following mathematical procedures.

_{in}to P

_{out}. S

_{11}and S

_{21}are functions of the elements of the finalized ABCD matrix.

#### 2.2. Devising the Metamaterial Resonators in the Waveguide

_{1}as series C from Wall_left to Wall_right and L

_{2}as shunt L from Wall_left to Wall_right are slots and short-circuited with the metal walls, spread in the transvers directions. In the vertical electric field of the TE

_{10}mode, a metal plate gets in the way to capture the E-field and is divided into the upper and lower patches modeled as L

_{R}C

_{R}subresonators connected through a strip equivalent to L

_{1}. Combining the electrical attributes of the elements, for the purpose of the metamaterial resonance at the center frequency, the circuit values are obtained as follows:

_{21}and S

_{11}in the plot of Figure 3b show the resonance as planned.

_{1}, L

_{2}, L

_{R}C

_{R}and L

_{1}to obtain the same frequency response as Figure 3b. As a result, S

_{21}and S

_{11}of the flat WG metamaterial resonator of the physical dimensions written in Table 4 can be obtained when Figure 3e agrees with Figure 3b. Using the frequency response and electromagnetic simulation, the ZOR is verifiable as the metamaterial characteristics.

#### 2.3. Formation of the Passband by Cascading the ZORs with Coupling Elements

_{i}for the eighth order of filtering. Prior to the high-order filter, the second-order BPF is built to see the basic characteristics of the coupling element suggested together with the ZORs.

_{21}in Figure 5b reveals that the slope of the skirt has been hastened compared to the one-pole case in Figure 3b. The gap length of the coupling element between the resonators is obtained by finding the value that generates the desirable S

_{11}and S

_{21}performances because it is varied, as in Figure 5b. The gap length of 15 mm is proper for the second-order case because the impedance matching S

_{11}becomes worse; the bandwidth increases for a gap length of 13 mm, and the bandwidth decreases for gap length 17 mm. Now the attenuation level in the stopband is around 10 dB. To have higher attenuation at the stopband, the structure is extended to the eighth-order filter.

_{ij}. Figure 6a is an open structure before assembly, and Figure 6b is the complete shape. Giving the values to the variables as in Table 6, the full-wave EM simulation provides the designer with the frequency response of Figure 6c. Excellent impedance matching is peeked through an S

_{11}of −20 dB and the insertion loss of an S

_{21}of −0.9 dB in the passband. Among other things, the attenuation has been improved by a large margin with the steeper skirt. It is 40 dB.

## 3. Fabrication of the WG ZOR BPF and Testing the Prototype

^{-1}mm as a coarse approach to ease the mechanical tolerance, the round corners are inevitable. The secondary procedure of design is performed to keep the function of the WG BPF satisfactory, as in Figure 6. This leads to the modified values for the geometrical parameters.

^{−2}mm and no courser in order to achieve the required frequency response. Setting up the structure in the electromagnetic analysis software with the values for the geometrical parameters, the transmission and reflection coefficients are obtained as in Figure 7d, which meets the design requirement. This is very different from cavity filters presented by [15,16,17] in terms of shape and length, and it is physically realized as follows:

_{11}and S

_{21}as in Figure 8e. The insertion loss and the reflection coefficients are about −0.9 dB and −19 dB in the passband, respectively. The roll-off that this manufactured metamaterial filter makes is satisfactory with an attenuation of almost −40 dB. There occurs a discrepancy between the simulated and measured results such that the frequency is shifted downward a bit. It is inferred that connected pieces in the longitudinal direction do not tightly contact each other, making a tiny gap between metal rims with rotational misalignment. This proposed geometry goes through another novel approach for technical improvement. The remarkable size reduction enabled by the introduction to the waveguide metamaterial resonators meets the 3D-printing technique on the basis of fused deposition modeling (FDM), turning into extra weight reduction.

_{11}conv and S

_{21}conv are satisfactory and are almost the same as the s-parameters of the proposed filter from the comparison. For the same cross section, the proposed filter is shorter than the conventional waveguide filter, as clearly seen in Figure 10.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Modified equivalent circuit and its frequency response: (

**a**) circuit (

**b**) S

_{11}and S

_{21}.

**Figure 3.**Circuit model of the CRLH resonator and moved into the waveguide. (

**a**) E-CRLH circuit of the resonator applied to the waveguide cross section; (

**b**) S

_{11}and S

_{21}of the resonator circuit; (

**c**) physical shape of the thin resonator; (

**d**) the resonator is longitudinally flat; (

**e**) S

_{11}and S

_{21}of the resonator structure.

**Figure 4.**Observing the ZOR of the resonator: (

**a**) E-field resonant and confined in a thin plane (

**b**) dispersion diagram.

**Figure 5.**Combining two ZORs through the gap for coupling: (

**a**) structure (

**b**) S

_{11}and S

_{21}vs. gap.

**Figure 6.**Combining eight ZORs through the gaps for coupling (

**a**) open structure, (

**b**) complete structure and (

**c**) S

_{11}and S

_{21}.

**Figure 7.**Realistic geometry of the eighth-order WG ZOR BPF: (

**a**) front view of the thin resonator with the round corners, (

**b**,

**c**) 3D structure and (

**d**) S

_{11}and S

_{21}.

**Figure 8.**Prototyped eighth-order WG ZOR BPF via the CNC-milling process: (

**a**) bird’s-eye view of the thin resonator with the round corners embedded in the flange body, (

**b**) front view of the manufactured filter, (

**c**) top view of the manufactured filter, (

**d**) the device under test where the adaptors match with the flanges and (

**e**) S

_{11}and S

_{21}.

**Figure 9.**Prototyped eighth-order WG ZOR BPF via 3D-printing process: (

**a**) basic idea of FDM [18], (

**b**) the 3D printer employed here and its working mechanism [19], (

**c**) front view of the inside garnished by the flange body, (

**d**) top view of the 3D-printed filter, (

**e**) our 3D-printed WG filter under test and (

**f**) S

_{11}and S

_{21}.

**Figure 10.**Comparing the proposed filter and nonmetamaterial filter with respect to geometries and frequency responses.

Item | Value |
---|---|

Insertion Loss | ≤1 dB |

Center Frequency | 7.5 GHz |

Bandwidth | 500 MHz |

Reflection coefficient | ≤−15 dB |

Out of Band Rejection (or Skirt) | ≤−40 dB (fc $\pm $ 500 MHz) |

Variable | Value | Variable | Value |
---|---|---|---|

${L}_{P1}$ | 0.998 nH | ${L}_{P2}$ | 0.516 nH |

${L}_{P3}$ | 0.417 nH | ${L}_{P4}$ | 0.408 nH |

${C}_{P1}$ | 0.442 pF | ${C}_{P2}$ | 0.859 pF |

${C}_{P3}$ | 1.064 pF | ${C}_{P4}$ | 1.088 pF |

length1 | 20 mm | length2 | 15.6 mm |

length3 | 16.6 mm | length4 | 16.5 mm |

length5 | 16.6 mm |

Variable | Value | Variable | Value |
---|---|---|---|

L_{R} | 1.6 nH | C_{R} | 2.27 pF |

L1 | 0.586 nH | C1 | 0.626 pF |

L2 | 1.51 nH |

Variable | Value [mm] | Variable | Value [mm] |
---|---|---|---|

L1 | 8.8 | W1 | 1 |

L2 | 4.7 | W2 | 1 |

L3 | 3.4 | W3 | 1 |

Variable | Value [mm] | Variable | Value [mm] |
---|---|---|---|

L1 | 8 | W2 | 1 |

L2 | 5.7 | W3 | 1 |

L3 | 2.9 | gap | 15 |

W1 | 1 |

Resonator#1 | |||

Variable | Value [mm] | Variable | Value [mm] |

L1 | 12.2 | W1 | 1 |

L2 | 4.7 | W2 | 1 |

L3 | 1.5 | W3 | 1 |

Resonator#2 | |||

Variable | Value [mm] | Variable | Value [mm] |

L1 | 9.1 | W1 | 1 |

L2 | 4.7 | W2 | 1 |

L3 | 3.1 | W3 | 1 |

Resonator#3 | |||

Variable | Value [mm] | Variable | Value [mm] |

L1 | 8.8 | W1 | 1 |

L2 | 4.8 | W2 | 1 |

L3 | 3.3 | W3 | 1 |

Resonator#4 | |||

Variable | Value [mm] | Variable | Value [mm] |

L1 | 8.8 | W1 | 1 |

L2 | 4.7 | W2 | 1 |

L3 | 3.4 | W3 | 1 |

Gap | |||

Variable | Value [mm] | Variable | Value [mm] |

gap1 | 15.8 | gap3 | 15.2 |

gap2 | 15.5 | gap4 | 15.6 |

**Table 7.**The values of the physical dimensions of the eighth-order filter, factoring in fabrication.

Resonator#1 | |||

Variable | Value [mm] | Variable | Value [mm] |

L1 | 12.77 | W1 | 1 |

L2 | 4.7 | W2 | 1 |

L3 | 1.74 | W3 | 1 |

Resonator#2 | |||

Variable | Value [mm] | Variable | Value [mm] |

L1 | 9.8 | W1 | 1 |

L2 | 4.7 | W2 | 1 |

L3 | 3.48 | W3 | 1 |

Resonator#3 | |||

Variable | Value [mm] | Variable | Value [mm] |

L1 | 9.15 | W1 | 1 |

L2 | 4.7 | W2 | 1 |

L3 | 3.84 | W3 | 1 |

Resonator#4 | |||

Variable | Value [mm] | Variable | Value [mm] |

L1 | 9.1 | W1 | 1 |

L2 | 4.7 | W2 | 1 |

L3 | 3.86 | W3 | 1 |

Gap | |||

Variable | Value [mm] | Variable | Value [mm] |

gap1 | 15.4 | gap3 | 15.3 |

gap2 | 16.8 | gap4 | 14.9 |

${\mathit{f}}_{0}$ (GHz) | Insertion Loss (dB) | Attenuation (dB) | WG Flange | $\mathbf{Resonator}\text{}\mathbf{length}\text{}\left({\mathit{\lambda}}_{\mathit{g}}\right)$ | Meta-Material | |
---|---|---|---|---|---|---|

[5] | 11 | < 1 | 55 | WR-90 | 0.68 | X |

[7] | 11 | < 1 | 50 | WR-90 | 0.51 | X |

[15] | 30 | 2 | 4.6 | WR-28 | 0.57 | X |

[16] | 9.45 | 0.08 | >20 | WR-90 | 0.51 | X |

[17] | 8.175 | 0.35 | 7.9 | WR-112 | 0.41 | X |

This work | 7.5 | 0.9 | 40 | WR-112 | 0.05 | O |

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## Share and Cite

**MDPI and ACS Style**

Cho, J.; Seo, Y.; Cho, J.; Park, K.Y.; Park, J.; Lee, H.; Kahng, S.
Effective Size Reduction of the Metallic Waveguide Bandpass Filter with Metamaterial Resonators and Its 3D-Printed Version. *Sensors* **2023**, *23*, 1173.
https://doi.org/10.3390/s23031173

**AMA Style**

Cho J, Seo Y, Cho J, Park KY, Park J, Lee H, Kahng S.
Effective Size Reduction of the Metallic Waveguide Bandpass Filter with Metamaterial Resonators and Its 3D-Printed Version. *Sensors*. 2023; 23(3):1173.
https://doi.org/10.3390/s23031173

**Chicago/Turabian Style**

Cho, Junghyun, Yejune Seo, Jihaeng Cho, Kyoung Youl Park, Joongki Park, Hosub Lee, and Sungtek Kahng.
2023. "Effective Size Reduction of the Metallic Waveguide Bandpass Filter with Metamaterial Resonators and Its 3D-Printed Version" *Sensors* 23, no. 3: 1173.
https://doi.org/10.3390/s23031173