Design of the proposed waveguide structure and meta-resonators

The design in this study is realized for C-band (4.90-7.05 GHz) applications and a WR-159 rectangular WG is used in the WG structure shown in Fig. 1. The design parameters given in Table 1 are calculated for the dominant TE₁₀ mode. In addition to dimensions such as a, b, and l, some parameters can be listed as f_c (cut off frequency), λ_g (guided wavelength), λ_c (wavelength at cut off frequency), λ₀ (wavelength at operating frequency), β (phase constant) and Z₀ (wave impedance). The internal dimensions of the WG are 20.193 mm x 40.386 mm and the cut-off frequency can be calculated by Equation 1. The operating frequency for the WR-159 WG can take values in the range of $1.25\,{f_c} \lt f \lt 1.89\,{f_c}$ and the values of λ_g, β and Z₀ are given in Equations 2-4, respectively [Reference Genç, Başyigit, Göksu and Helhel33–Reference Genç, Başyigit, Göksu and Helhel36].

(1)\begin{equation}{\left( {{f_c}} \right)_{mn}} = \frac{h}{{2\pi \sqrt {\mu \varepsilon } }} = \frac{1}{{2\sqrt {\mu \varepsilon } }}{\sqrt {{{\left( {\frac{m}{a}} \right)}^2} + {\left( {\frac{n}{b}} \right)}^2}}\end{equation}

Table 1.

Dimensions of the designed waveguide filter

(2)\begin{equation}_g= \frac{{_o}}{\sqrt {1 - {\left( {_o/_c} \right)}^2}}\end{equation}

(3)\begin{equation}\beta = \sqrt {{\omega ^2}\mu \varepsilon - {{\left( {\frac{m}{a}} \right)}^2} + {{\left( {\frac{n}{b}} \right)}^2}\,} \end{equation}

(4)\begin{equation}{Z_o} = \frac{{k\eta }}{\beta } = \frac{{\omega \sqrt {\mu \varepsilon } \,\eta }}{\beta }\end{equation}

where m and n are the modes of the EM wave, ε is the electrical permittivity of the air, μ is the magnetic permeability of the air inside the WG, λ_o is the wavelength in free space, λ_c is the cut-off wavelength, ω is the angular frequency for the operating frequency, η is the intrinsic impedance of the medium. Using the given equations, the values of relevant electrical properties are calculated with Matlab^® and are tabulated in Table 1.

The proposed WG structure consists of two CTR-159 G-type flanges and four modular unit elements and the number of sub-units can be increased if desired. Due to this modular property, the proposed structure can be used for all substrates up to t_sub < 5 mm thickness. To prove this experimentally, Arlon AD 255C and RT/Duroid 5880 are chosen as the thin and thick substrates, respectively. The dimensions of the CSRR-type meta-resonator shown in Fig. 1b for these two different designs are given in Table 2. In addition, the external and internal views of the WGF after the meta-resonator is placed inside the WG structure are shown in Fig. 1c and 1d, respectively. Accordingly, the filter order can be adjusted from 1 to 5 by changing the number of meta-resonators in Fig. 1d. In case no meta-resonator is used in the proposed structure, this can also be used as WG instead of WGF. By changing the number of unit elements, the electrical length can be easily adjusted according to the desired length in the application.

Table 2.

Dimensions of the designed meta-resonators using thin and thick substrates

The equivalent circuit model of a single CSRR given in Fig. 1b can be modelled as a parallel LC circuit [Reference Bage, Das and Murmu4]. In these circuit models, R is neglected since it is very small. The resonant frequency ${\left( {2\pi \sqrt {LC} } \right)^{ - 1}}$ of LC circuits depends on properly determining their geometrical dimensions. Also, high-frequency microwave resonant circuits behave like RLC elements at low frequencies, which can be excited by an external magnetic source. Analytically, using the return loss, insertion loss and bandwidth in the certain band, the lumped element values of a single meta-resonator can be obtained using Equations 5-7 [Reference Bage, Das and Murmu4, Reference Bage29].

(5)\begin{equation}{R} = {Z_0}\frac{{\left| {{S_{21}}\left( {j{\omega _0}} \right)} \right|}}{{2\left( {1 - \left| {{S_{21}}\left( {j{\omega _0}} \right)} \right|} \right)}}\end{equation}

(6)\begin{equation}{L} = 10\,{B_{3dB}}\,{Z_0}\frac{{| {{S_{21}}( {j{\omega _{0}}} )} |}}{{2\omega _{0}^{2}}}\end{equation}

(7)\begin{equation}{C} = \frac{2} {10\,{B_{3dB\,}}{Z_{0}}\,| {{S_{21}}( {j{\omega _{0}}} )} |} \end{equation}

Here, ${\omega _0}$ is the angular frequency (rad/sec), ${f_0}$ is the central frequency of the WGF ( ${\omega _0} = 2{f_0}$), and B_3dB is the bandwidth at the resonant frequency. Z₀ is the port impedance. The values presented in Table 2 are primarily obtained from Eq. 5-7. Since the equivalent circuit of the CSRR meta-resonators with ring geometry is a series LC circuit, the dimensions of the CSRR are determined to provide the desired inductance and capacitance values. The dimensions of CSRRs are accurately optimized with the help of an “optimizer” in the simulation program with a center frequency of 6 GHz, as given in Table 2.

Fabrication of waveguide filters (WFGS) using CNC milling and SLA 3D printing methods

CNC milling method is mostly preferred in the production phase of passive microwave components (antenna, WG, T-junction, WGF, directional coupler, etc.). However, this method has several disadvantages compared to additive manufacturing methods, such as high production cost, physically heavier, difficult production in some geometries, and some materials that cannot be processed with this method. Recently, some 3D printing methods such as fused deposition modeling (FDM), selective laser melting (SLM), and stereolithography (SLA) emerge as alternatives to conventional methods such as CNC milling. The SLA method is a 3D printing method in which high-resolution and detailed 3D objects are fabricated by hardening layer by layer with a laser beam focused on a liquid photopolymer resin. In this 3D printing method, after the part is printed, curing is done using UV rays, and the part can be made more durable. To summarize the pros and cons of these two methods, the comparison of CNC Milling and SLA 3D Printing fabrication methods is given in Table 3.

Table 3.

Comparison of CNC Milling and SLA 3D Printing fabrication methods

All the fabrication steps of the part fabricated using the Elegoo Saturn 3 Ultra 12 K model SLA printer is given in Fig. 2. Figure 2a depicts the interface of the Chitu Box program for printing settings, and Fig. 2b shows the supported view of the part after printing. After printing, the part is kept in a washing container containing isopropyl alcohol (IPA), and then the part is kept in the curing device in Fig. 2c for 15 minutes. This curing process increases the hardening and durability of the printed part. Figure 2d shows the final version of the fabricated part. Standard photopolymer resin is used as the printing material; each layer height is set to 0.05 mm, and the bottom exposure time is set to 35 seconds.

Figure 2.

All the fabrication steps of the part with SLA 3D printing, (a) the print settings using the Chitu Box program (b) the view of the part with supports after printing, (c) the curing process, and (d) the final view of the printed part.

The CNC milling method is easily accessible and widely used. The manufacturing tolerance is expected to be less than 25 µm for high-accuracy manufacturing. In this study, firstly, the CAD model of the designed WGF is obtained, and the created file with .stp extension is utilized in the fabrication phase. For the fabrication, aluminum 6065 material is used, and the WGF in Fig. 3a is fabricated with the help of the First MCV-800 CNC milling machine. The table dimensions of the machine are 400 × 800 mm², and the process is performed at a high value of 6500 min/cycle. A 1.5 mm carbide (diamond) milling cutter is used to process the metal.

Figure 3.

(a) Photo of the sanded part fabricated with the SLA 3D printing, (b) the step of metal coating, (c) the part with 2 K acrylic varnish applied over the entire surface after metal coating to prevent oxidation or corrosion on the surface of the part, and (d) the designed WG structure fabricated with CNC milling.

The part fabricated by the SLA 3D printing method must have metal coating applied to all of its surfaces in order to be used as a WGF, and the metal coating process is shown in Fig. 3. Firstly, the surface of the part is sanded precisely to reduce the surface roughness of the part (Fig. 3b). Using the spraying method, the entire surface of the WGF is homogeneously metal-coated (Fig. 3c). After the varnishing of the part, the metal coating is done in a process consisting of cleaning the surface particles, using a palladium activator, a combination of metal and plastic particles, and an alcohol solvent. Then, 2 K acrylic varnish is applied to the entire surface of the part to prevent oxidation or corrosion on the surface of the part after metal coating, and finally, the part is ready for use (Fig. 3d). Furthermore, the metal coating thickness should be several times the skin depth calculated for the operating frequency [Reference Genç, Başyigit, Göksu and Helhel33–Reference Genç, Başyigit, Göksu and Helhel36]. The most common challenges encountered in the metal coating process are the need for a varnishing process before the metal coating can be applied to the manufactured part, the drying time of the varnishing process must be waited for, and the necessity of repeating these processes to achieve a sufficient level. When these steps are not done very carefully, they present difficulties in terms of both surface roughness and production time. In this study, the surfaces of the WG structure fabricated by the SLA 3D printing method are metal coated to be several times the skin thickness, and the skin depth is calculated according to Equation 8.

(8)\begin{equation}\delta = \frac{1}{{\sqrt {\pi f\mu {\sigma _c}} \,}}\,\end{equation}

where f is the operating frequency and ${\sigma _c}$ is the intrinsic conductivity of the metal. For the center frequency of 6 GHz, the skin depth can be calculated as 0.0694 μm. Moreover, while the CNC milling method is superior to the other production method in terms of temperature stability, the SLA method is superior in terms of cost and low weight. Standard SLA resin has a temperature resistance of up to 70 °C. Also, the CNC milling method is superior in terms of power handling capability, but since substrate material is used in both methods, the determining factor in terms of power handling capability is the substrate material. In applications requiring high power handling, ceramic material should be selected as the substrate instead of polymer-based material.

Simulation set-up and measurement campaign

All simulations in this study are performed via CST Studio Suite^®, a 3D full-wave EM simulation program. Boundary conditions are set as E_t = 0 in the ± x and ± y directions and “open add (space)” in the ± z direction shown in Fig. 4b. Excitation is applied to both terminals of the WG at 4-8 GHz using a waveguide port. The simulations are performed via a Xeon 4214 processor workstation. Frequency solver and tetrahedral mesh type are preferred in the simulation program, and the number of mesh cells varies between 1 000 000–1 500 000.

Figure 4.

(a) Measurement setup for the performance of WGFs using different number and thickness of meta-resonators, (b) simulation setup, (c) S-parameters measurement via VNA of WGFs fabricated with CNC milling, and (d) SLA 3D printing technologies and (e) the designed meta-resonators etched by LKPF device.

The proposed WGFs are fabricated and measured to verify the simulation results with the 6 GHz center frequency. For the measurement of the WGFs, the test setup is given in Fig. 4a, and scattering parameter (S-parameter) measurements are performed with a vector network analyzer (VNA) (Fig. 4c and 4d). These measurements are performed separately for different filter orders and different thickness substrates and compared with simulation results. In all measurements, an HP Hewlett Packard model 8720C VNA operating in the 50 MHz-20 GHz range is used. Also, two waveguide-coaxial adapters and RF cables are used in the measurements. The adapters are SMA/female-type CentricRF brand CWR159SB models with a max. VSWR value of 1.20. The RF cable used is the CentricRF brand model C581-141-XXB of SMA/Male-SMA/Male type. In addition, the SOLT (Short-Open-Load-Through) calibration method, which is widely used and gives accurate results, is used to eliminate systematic errors in the measurement setup. The measurements are performed at the Industrial and Medical Applications Microwave Research and Application Center (EMUMAM) of Akdeniz University.

In this study, meta-resonators having two different substrates are etched with the Proto Laser U4 model LKPF device (Fig. 4e). The dimensions and properties of the substrates are given in Table 2. It is well known that if the dimensions are not adhered to in the milling process of meta-resonators, the inductive and capacitive values in the equivalent circuit of the meta-resonators can drastically shift, and as a result, the filter performance can change significantly. For this reason, the LPKF device with very high technical specifications is chosen for this study. Specifically, the maximum material size (x × y × z) is 229 × 305 × 10 mm³, and the minimum line and cavity size during engraving are 50 μm and 20 μm, respectively. The laser wavelength used is 355 nm with a manufacturing tolerance of ± 1.98 μm and a cutting speed of 200 mm/s.

The surface roughness of WGFS fabricated by CNC milling and SLA 3D printing methods

The surface roughness values (R _a and R _z) of the WGF fabricated with two different manufacturing technologies are measured using the HOMMEL Tester T 500 device at the Innovative Technologies Application and Research Center (YETEM), Süleyman Demirel University, according to the ISO 4287 standard. The sensitivity class of the instrument is Class 1 according to DIN 4772, and the lowest roughness imaging value is 0.01 µm. R _a is the roughness profile’s arithmetic mean of all absolute distances. R _z is the mean maximum peak-to-valley of five successive sampling lengths within the measurement length. This indicates that the extreme values significantly impact the final value of R _z more than R _a. Also, in the measurements, the surface roughness of 3 different surfaces is measured: the aluminum surface fabricated by CNC, the resin surface fabricated by SLA 3D printing, and the surface obtained after metal coating. Each measurement is performed on the inner surface of the WGF. To reduce measurement errors, five measurements are made from different regions, and the average value is obtained. According to the measurement results as given in Table 4, the surface roughness values of the CNC surface, SLA resin surface, and metal-coated surface are 0.3836 µm, 0.168 µm, and 0.058 µm, respectively. As expected, the roughness of the SLA surface is lower than that of the CNC surfaces. The surface roughness of the SLA part is very low, and the roughness decreases further after the metal coating process. The EM performance of passive microwave components increases as the surface roughness decreases.

Table 4.

The values of average surface roughness (R_a) measured for three different surfaces

In addition to surface roughness, another significant parameter is the conductivity of the metal on the surface. As the surface conductivity increases, the EM performance of the component increases accordingly. The aluminum 6065 material used for the CNC milling has a conductivity value of 33.3 × 10⁶ S/m. For metal coating, a mixture of metals is used instead of a single metal. In particular, a mixture of antimony and silver is added to the nickel material to increase the conductivity. As it is well-known, as the metal conductivity increases in WGs, the surface resistivity decreases, and consequently the attenuation of the EM wave inside the WG decreases. Namely, the attenuation ${\alpha _c}$ due to conductor losses in the rectangular WG can be formulated in Equation 9. This parameter is related to Rs, which is the surface resistance of the metal surface of the WG [Reference Chan, Ramer and Sorrentino37].

(9a)\begin{equation}{\alpha _c} = \frac{{{R_s}\left( {2b{\pi ^2} + {a^3}{k^2}} \right)}}{{{a^3}b\beta k}}\end{equation}

(9b)\begin{equation}{R_s} = \frac{{\sqrt {\omega {\mu _0}} }}{{2\sigma }}\end{equation}

where a, and b are the internal dimensions of the WG, k is the wave number, β is the phase constant, σ is the conductivity of the metal in the WG and η is the wave impedance. Also, as the surface roughness increases, it causes microscopic changes in the wave impedance on the inner surface of the waveguide. These local mismatches increase reflections and worsen the S11 value. In addition, increasing roughness lengthens the path of the surface currents. This causes the surface resistance to increase and the attenuation (S21) to be negatively affected. Therefore, as the surface roughness increases, it affects the S parameters, the filter response.

Scanning electron microscope (SEM) is a type of electron microscope that produces images by scanning a focused electron beam across the surface of a sample and provides detailed information about the surface topography and composition of the sample. In this work, the FEI Quanta FEG 250 is used to obtain SEM images of the surfaces. The 500 × and 3000 × SEM images of the surfaces of the WGFs fabricated by CNC milling and SLA 3D printing technology, as well as the surface of the WGF after metal coating, are given in Fig. 5. Accordingly, on the surface of the WGF fabricated with CNC milling technology, knife marks and micro-notches formed by regular and repetitive CNC machining can be seen on the surface. At 3000 × magnification, the characterization of the crystal structure of the material can be observed (Fig. 5a). On the surface of the WGF fabricated with SLA 3D printing technology, a certain irregularity and roughness can be observed, partially due to the layered structure (Fig. 5b). At higher magnification, pores and voids in the bonding regions between the layers are seen as small spherical particles and are a natural result of the layering process. Also, the roughness is less on the surface of the metal-coated SLA part since the metal coating gives the surface a more uniform and homogeneous appearance (Fig. 5c).

Figure 5.

SEM image of different surfaces taken at 500 × and 3000 × magnification, (a) surface of WGFs fabricated with CNC milling, (b) surface of WGFs fabricated with SLA 3D printing before metal coating, and (c) after metal coating.

Frequency responses of the WGFS with the meta-resonators of different thicknesses

The scattering parameters of the designed and fabricated WGF are measured using VNA and compared with simulation results. The simulation and measurement results for the frequency responses of bandpass WGFs from 1^st order to 5^th, fabricated with CNC milling and SLA 3D printing technologies using the CSRR type meta-resonator at the center frequency of 6 GHz, are depicted in Fig. 6. Accordingly, Fig. 6a-6c shows the 1^st, 3^rd, and 5^th order frequency responses for the thin substrate (Arlon AD 255C), while Fig. 6d-6f shows the 1^st, 3^rd, and 5^th order frequency responses for the thick substrate (RT/Duroid 5880). When similar studies in the literature [Reference Bage, Das and Murmu4, Reference Aparicio, Hinojosa, Pereira and Melcón23, Reference Ortiz, Baena, Beruete and Sorolla27] are examined, it is reported that the measured results in this study are quite compatible with the simulated results. In general, the simulated results are slightly better than the measured results as expected. There are some possible reasons for this discrepancy between the results.

Figure 6.

Simulated and measured frequency responses of WGFs using meta-resonators made of thin substrate (Arlon AD 255C): (a) 1^st order filter, (b) 3^rd order filter and, (c) 5^th order filter, simulated and measured frequency responses of WGFs using meta-resonators made of thin substrate (RT/Duroid 5880): (d) 1^st order filter, (e) 3^rd order filter and, (f) 5^th order filter.

These are errors due to impedance mismatch, errors due to the manufacturing tolerance of the WG and meta-resonator, calibration errors, losses between the coaxial-WG adapter and the filter, losses in the RF cable, losses due to the assembly of the parts, and losses due to the surface roughness of the WG structure due to the nature of the material. According to the measured results, the main losses occur at 1 and 2 between the WGF and the coaxial-WG adapter. In addition, during the formation of meta-resonators with the LKPF device, the dimensions of the geometric shapes change micro-scale due to the etching. Due to this, the inductive and capacitive loads of the meta-resonator changes, and the resonance points in the filter response are partially shifted (Fig. 6). With the ring geometry meta-resonators in this paper, the designed filters by nature have medium bandwidth. The filter order increases with each result in Fig. 6 and as the filter order increases, the selectivity (sharpness) of the filter increases, and the number of reflection zeros (RZs) also increases with the filter order.

A performance comparison of the proposed bandpass WGFs for different filter orders and two fabrication methods is given in Table 5. Accordingly, when the return loss (RL) and transmission loss (IL) of the designed WGFs are analyzed, the simulated and measured results are generally compatible with each other. Both fractional bandwidth (FBW), and quality factor (Q) are calculated using frequency points where the transmission loss is − 3 dB. In the WGFs fabricated with CNC milling, RL ranges between 27.95-40.37 dB and 27.10-30.95 dB for thick and thin substrates, respectively, in all filter orders, while in the WGFs fabricated with SLA 3D printing, RL ranges between 29.29-39.44 dB and 32.43-41.7 dB for thick and thin substrates, respectively. Similarly, for WGFs fabricated by CNC milling, IL varies between 0.06-0.34 dB and 0.34-0.97 dB for thick and thin substrates for all filter orders, respectively, and for the WGFs fabricated by SLA 3D printing, IL varies between 0.78-1.65 dB and 0.91-1.93 dB for thick and thin substrates, respectively. The obtained values are sufficient for the proposed filter to be used in many applications.

Table 5.

Performance comparison of the proposed bandpass WGFs for different filter orders and fabrication methods

In the WGFs by CNC milling and SLA 3D printing, FBW in all filter orders varies between 5.67-11.17% and 5.67-9.50% for thick and thin substrates, respectively. Moreover, Q for all filter orders varies between 8.96-17.65 and 10.53-17.65 for thick and thin substrates, respectively. It should be noted that there is an inverse relationship between FBW and Q. As the filter order increases using more meta-resonators, the sharpness of the filter increases, and the unwanted losses in the filter also increase.

The current densities for a single meta-resonator with ring geometry for the thick and thin substrates are depicted in Fig. 7a and 7b, respectively. The highest current density in the resonator is between the two rings, with a maximum current density of 33.3 dB(A/m2) and 36.2 dB(A/m2) for the thick, and thin substrates, respectively. The current directions are opposite on the two rings depending on the phase value. Also, while the E-field distributions for the empty WG is given in Fig. 7c, E-field distribution for the 1^st order, 3^rd order WGF, and the 5^th order WGF are given in Fig. 7d, 7e, and 7f, respectively. As seen in Fig. 7d-f, the E-field value is higher, especially in the region where the meta-resonator is located. The E-field is more intense in the space between the meta-resonators. Furthermore, the main features of the proposed WGF are summarized and quantitatively compared with the recent studies in the literature (Table 6).

Figure 7.

The current densities for a single meta-resonator with ring geometry (a) for the thick substrate, (b) for the thin substrate, (c) E-field distribution in the empty WR-159 WG, (d) E-field distribution for the 1^st order WGF (RT/Duroid 5880 substrate), (e) E-field distribution for the 3^rd order WGF, and (f) E-field distribution for the 5^th order WGF.

Table 6.

The comparison table for the performances of the wave guide filters

* In this work, the filter performance obtained from the SLA fabrication method is relatively lower than that obtained from the CNC milling method. Therefore, these values are given for the SLA fabrication method in Table 5.