Design of 5G-Advanced and Beyond Millimeter-Wave Filters Based on Hybrid SIW-SSPP and Metastructures

Abstract

This article investigates how to exploit the high-frequency mmWave for 5G-advanced and beyond, which requires new filters for the wide bandpass and its multi-sub-band. Based on the substrate-integrated waveguide (SIW), spoof surface plasmon polariton (SSPP), and metastructures, like complementary split-ring resonators (CSRRs), the development of a wide bandpass filter and a multi-sub-band filter is proposed, along with an experimental realization to verify the model. The upper and lower cutoff frequencies of the wide bandpass are controlled through an SIW-SSPP structure, whereas the corresponding wide bandpass and its multi-sub-band filters are designed through incorporating new metastructures. The frequency range of 24.25–29.5 GHz, which covers the n257, n258, and n261 bands for 5G applications, was selected for verification. The basic SIW-SSPP wide bandpass structure of 24.25–29.5 GHz was designed first. Then, by incorporating an Archimedean spiral configuration, the insertion loss within the passband was reduced from 1 dB to 0.5 dB, while the insertion loss in the high-frequency stopband was enhanced from 40 dB to 70 dB. Finally, CSRRs were integrated to effectively suppress undesired frequency components within the bandpass, thereby achieving multi-sub-band filters with low insertion losses with a triple-sub-band filter of 0.5 dB, 0.7 dB, and 0.8 dB in turn. The experimental results showed strong agreement with the design scheme, thereby confirming the rationality of the design.

1. Introduction

As critical components in wireless communication systems, filters face technical challenges in 5G applications, including high-frequency operations, broadband requirements, and multi-sub-band (such as n257 (26.5 GHz–29.5 GHz), n258 (24.25 GHz–27.5 GHz), and n261 (27.5 GHz–28.35 GHz) frequency bands) coordination [1]. To address these constraints, novel design frameworks are being developed to enhance spectral efficiency, improve multi-sub-band interference rejection, and facilitate device integration. SIWs and SSPPs demonstrate exceptional electromagnetic field manipulation capabilities, offering promising pathways for developing advanced filtering solutions.

The advantages of SIWs include low loss, effective out-of-band suppression, fabrication simplicity, and compatibility with planar microwave circuits [2]. In microwave integrated system design, SIW-based filters are widely employed in components and systems such as power dividers [3,4], couplers [5], amplifiers [6,7], phase shifters [8,9], oscillators [10], and antennas [11,12]. In summary, the inherent high-pass characteristics of SIW structures make them particularly suitable for microwave frequency filtering applications.

As a periodic artificial structure, SSPPs emulate surface plasmon polaritons (SPPs) by etching a periodic structure array on the top conducting layer, enabling low-pass characteristics at sub-optical frequencies [13]. Benefiting from strong field confinement and low crosstalk, SSPPs find applications in microwave/RF systems, including antennas [14,15], couplers [16], sensors [17], and power dividers [18]. Particularly, their inherent high-frequency suppression capability facilitates low-pass implementation in bandpass filter designs through upper cutoff frequency control, making SSPPs promising for advanced filtering applications [19].

The exploitation of the high-frequency microwave spectrum enables substantial bandwidth enhancement. By merging the high-pass filter characteristics of SIWs and the low-pass filter characteristics of SSPPs, the resultant SIW-SSPP wide bandpass characteristics must be dealt with to obtain the expected filtering responses of the filters, establishing a new paradigm for high-efficiency microwave filters. To address multi-sub-bands’ filtering requirements in broadband applications, many innovative design methodologies have been proposed and demonstrated using the new artificial structure of narrow bandpass with new combinations of elements such as hybrid resonators [20], stepped-impedance resonators [21], and meta-surface loading techniques, like CSRR. The integration of these approaches with SIW and SSPP technologies has been particularly effective for developing high-frequency broadband multi-bandpass filters, including SIW-based designs [22,23], SSPP-configured filters [24,25], and up-and-coming hybrid SIW-SSPP filters [26,27]. Furthermore, metastructure loading techniques, like CSRR, have been successfully employed to implement multiband operations through electromagnetic coupling control [28,29,30]. However, current research on SIW-SSPP multi-band filters remains insufficient, with unresolved technical challenges in achieving low insertion loss while maintaining a miniaturized multiband design [31], such as the complex dispersion phenomenon caused by the modes of SIWs and SSPPs within the wide bandpass.

In this article, these complex problems are studied, and the corresponding designs and fabrication methods are developed. A novel SSPP structural unit is introduced to ensure a wide band, and the unit achieves the flexible tuning of cutoff frequencies in bandpass filters through integration with conventional SIW technology. The incorporation of Archimedean spiral configurations significantly enhances stopband rejection while maintaining excellent bandpass filter characteristics. To enable frequency selectivity for wireless communication systems, CSRR-loaded structures are implemented to realize multi-bandpass filters with low return loss, low insertion loss, and compact dimensions. The bands chosen are the mmWave bands n257, n258, and n261 for 5G-advanced and beyond.

The structure of this article is as follows: Section 2 provides a detailed analysis of the dispersion characteristics of the SIW and SSPP unit structures and their design methods. Section 3 presents the filters’ operational principles, design procedure, and architecture: comb-shaped tapered SSPPs enable a wideband SIW-SSPP structure; Archimedean spirals enhance the single wideband filter’s performance; dual-symmetry CSRRs achieve the multi-sub-band filter’s multiband response. This section systematically examines the structural design and performance characteristics of the filters. Section 4 presents the experimental validation of the proposed filter prototypes and discusses the measurement results, as well as their comparison with reported works. Section 5 concludes with the methodological framework for SIW-SSPP multiband filter design and a comparative performance evaluation.

2. Principle and Design Analysis of Novel SSPP and SIW with Wide Passband Characteristics

2.1. The SIW

Operating in the fast-wave region, the SIW exhibits a lower cutoff frequency, which inherently generates high-pass filtering behavior with cutoff frequency of TE₁₀ mode. Figure 1a illustrates the schematic unit structure of SIW. $d$ denotes the via diameter, $s$ denotes the via hole spacing, and $W_{siw}$ denotes the center-to-center distance between two rows of vias. The cutoff frequency decreases as the via-hole spacing increases. The analytical relationships governing the cutoff frequency of SIW and structural parameters are derived as follows [32]:

$$f_1={\displaystyle \frac{c}{2\sqrt{{\epsilon }_r}{W}_r}}$$

(1)

$$W_r=W_{siw}-s\left(0.766e^{{\displaystyle \frac{0.4482d}{s}}}-1.17e^{-{\displaystyle \frac{1.214d}{s}}}\right)$$

(2)

in which $f_1$ denotes the cutoff frequency of the SIW, $c$ denotes the speed of light in vacuum, ${\epsilon }_r$ denotes the relative permittivity of the substrate material, and $W_r$ denotes the effective width between the two rows of metallic vias. To mitigate bandgap effects, the structural parameters must satisfy the condition $d<s<2d$. The SIW structure was designed based on the aforementioned equations and optimized using CST simulation software S2 2021, successfully achieving the low-frequency characteristics for the n257 band. This design employed Rogers 5880 as the substrate material, which has copper layer with thickness of 0.035 mm and conductivity of 5.8 × 10⁷ S/m, and the thickness of dielectric substrate was 0.508 mm, the dielectric constant was (${\epsilon }_r$) 2.2, and loss tangent was 0.0009. Figure 1b illustrates the dispersion characteristics of the SIW unit for different $W_{siw}$, in which $d$ = 0.4 and $s$ = 0.38. To obtain the cutoff frequency 24.25 GHz of n257, the value of $W_{siw}$ was chosen as 4.5 mm.

2.2. The Novel SSPP

SSPP operates in the slow-wave region, exhibiting low-pass filter characteristics, and features a higher cutoff frequency when used in bandpass filters. Its dispersion characteristics are influenced by the structure. Here a novel SSPP structure is proposed utilizing elliptical grooves. Figure 2a illustrates the periodic SSPP unit cell configuration (front-side architecture) obtained. The yellow regions represent metallic layers and cyan coloration denotes the substrate. SSPP formed by substrate-exposed grooves patterns are shown in the dielectric substrate color. It has a unit periodicity of $p$, and $a_1$ denotes the SSPP comb spacing, $b_1$ denotes the longitudinal length of SSPP, and $g_1$ denotes the SSPP units groove clearance width. The dispersion properties of SSPPs are typically determined by the parameters of the periodic grooves as follows [33]:

$$\beta =\sqrt{{\epsilon }_{eff}{k}_0^2+{\left({\displaystyle \frac{g_1}{p-4a_1}}\right)}^2{\epsilon }_{eff}{k}_0^2{\tan }^2(k_0\sqrt{{\epsilon }_{eff}}2b_1)}$$

(3)

The lengths of these elliptical grooves can be expressed with Ramanujan formulas as:

$$C_n=\mathsf{\pi }\left(n{a}_1+b_1\right)\left(1+{\displaystyle \frac{3{\left(\frac{b_1-n{a}_1}{b_1+n{a}_1}\right)}^2}{10+\sqrt{4-3{\left(\frac{b_1-n{a}_1}{b_1+n{a}_1}\right)}^2}}}\right)$$

(4)

in which n is the number counted from 0 and 0, and in the middle of an ellipse, a segment of the line is $C_0=2b_1$. The elliptical grooves with semi-axes are ($n{a}_1$, $b_1$).

The corresponding cut-off frequency of SSPP is given as follows [34]:

$$f_2={\displaystyle \frac{c}{4\left(2b_1+{\displaystyle \sum _{i=1}^n{C}_i}\right)\sqrt{{\epsilon }_{eff}}}}$$

(5)

where $f_2$ denotes the SSPP cutoff frequency, and ${\epsilon }_{eff}$ is the effective dielectric constant of the metallic groove structure [35]:

$${\epsilon }_{eff}={\displaystyle \frac{{\epsilon }_r+1}{2}}+{\displaystyle \frac{{\epsilon }_r-1}{2}}{\left(1+12{\displaystyle \frac{h}{g_1}}\right)}^{-{\displaystyle \frac{1}{2}}}$$

(6)

where the groove depth ($h$) of SSPP is 0.035 mm; the groove width ($g_1$) of SSPP is 0.1 mm; and the relative permittivity (${\epsilon }_r$) of the bottom dielectric is 2.2.

The dispersion characteristics or low-pass effects of the SSPP structure are obtained with the calculation based on (3)–(6) and optimized with CST. Figure 2b–d illustrate the dispersion characteristics of the SSPP unit of different structure size parameters, which are obtained to meet the cutoff frequency control requirement of n261 when the optimum of $p$ = 2.88. It shows that the SSPPs operate in the slow-wave region and exhibit a high cutoff frequency, thereby generating low-pass filtering behavior. The cutoff frequency of SSPP decreases with $a_1$ and $b_1$, while demonstrating an increasing relationship with g₁. Figure 2b illustrates how the dispersion relation evolves as parameter $a_1$ increases from 0.45 mm to 0.55 mm, while all other parameters remain at their initial values. Figure 2c,d illustrate similar results for parameter $b_1$ and $g_1$ in turn. Figure 2b shows the results when $b_1$ = 1 and $g_1$ = 0.1. It shows that $a_1$ = 0.5 at the lowest cutoff frequency 29.5 GHz. Figure 2c shows the results when $a_1$ = 0.5 and $g_1$ = 0.1. It shows that $b_1$ = 1 at the lowest cutoff frequency 29.5 GHz. Figure 2d shows the results when $a_1$ = 0.5 and $b_1$ = 1. It shows that $g_1$ = 0.1 at the lowest cutoff frequency 29.5 GHz. So, the optimum sizes are $a_1$ = 0.5, $b_1$ = 1, and $g_1$ = 0.1 for the lowest cutoff frequency 29.5 GHz.

2.3. The Hybrid SIW-SSPP

With the slot structure fixed and the period set to 2.88 mm, the cutoff frequency of the SSPP is 29.5 GHz. Under these conditions, the combination of SIW and SSPP structures enables convenient implementation of a bandpass filter. The SSPP integrates with the SIW to obtain a wide bandpass structure. Figure 3 demonstrates the hybrid SIW-SSPP unit’s structure and dispersion properties. Figure 3a shows the schematic unit structure of SIW-SSPP units. Figure 3b shows the dispersion properties of SIW-SSPP units under the optimal geometric conditions, where $W_{siw}$ = 4.5 mm, $a_1$ = 0.5 mm, $b_1$ = 1 mm, and $g_1$ = 0.1 mm, obtained from the SIW-SSPP dispersion calculation results given in Figure 1 and Figure 2; thus, this structure exhibits both an upper cutoff frequency and a lower cutoff frequency, forming a bandpass response ranging from 24.25 GHz to 29.5 GHz, which complies with the requirements of n257, n258, and n261.

3. Design of the Wide Passband SIW-SSPP Filters with Multi-Sub-Bands

To achieve a multi-band filter operating in the 5G n257, n258, and n261 frequency bands, this section first describes the proposed wide bandpass filter structure covering 24–30 GHz, which is based on the hybrid SIW-SSPP structure in Section 2. Then the wideband filter structure is improved by loading an Archimedean spiral to obtain a single wide bandpass SIW-SSPP filter of optimized performance with improved S-parameters in the passband and enhanced roll-off rate at high frequencies, which significantly upgrades the overall filter performance. Finally, the multi-sub-band filter design and the final filter structure are given.

3.1. The Wide Passband SIW-SSPP Filter

3.1.1. Single Wide Bandpass SIW-SSPP Filter Structure

To achieve bandpass characteristics within the target frequency range, a novel bandpass filter integrating the SIW with comb-shaped SSPPs is proposed, as illustrated in Figure 4a. The structure is made up of SIW formed by two rows of metallic vias connecting the top and bottom metal layers and seven SSPP unit cells embedded in the center. To enhance the roll-off rate in the high-frequency band, the parameters of the SSPP units are gradually tapered from the three central cells toward both ends. Owing to its cutoff characteristics, the effective impedance of the SIW increases sharply near the cutoff frequency. The spacings between adjacent comb-shaped SSPP transition structures are denoted as $a_2$ = 0.4 mm and $a_3$ = 0.2 mm, while the lengths of the comb-shaped SSPP transition structures are represented by $b_2$ = 0.8 mm and $b_3$ = 0.6 mm. The values are optimized.

To improve impedance matching and form a filter structure, the microstrip-to-SIW transition is designed. Based on transmission line theory, the MSL (microstrip lines)-to-SIW-SSPP structure transition segments achieve a smooth impedance transition through the gradual change in the line width in the tapered section of the MSL, thereby optimizing the impedance matching effect and reducing reflection loss. In addition, its gradual structure enables the progressive adjustment of electromagnetic field distribution, suppresses the generation of higher-order modes, reduces related losses, and ensures efficient energy transmission. The width ($W_{ms}$) of the microstrip line is 1.63 mm; the length ($L_{ms}$) of the microstrip line is 3.65 mm; the length ($L_t$) of the transition section is 2.4 mm; the width ($W_t$) of the microstrip-to-SIW coupling junction is 1 mm; the length ($L_{t2}$) of the microstrip-to-SIW coupling junction is 1.2 mm; and the length ($L_{siw}$) of the SIW structure is 20.5 mm. The detailed parameters of the filter structure are summarized in

Table 1. Design parameters of the designed single wide bandpass filter structure (unit: mm).

Parameter	Value	Parameter	Value	Parameter	Value
$L_{siw}$	20.5	$W_{siw}$	4.5	$L_{ms}$	3.65
$W_{ms}$	1.63	$L_t$	2.4	$W_t$	1
$L_{t2}$	1.2	$W_{sub}$	6	$d$	0.4
$s$	0.38	$a_1$	0.5	$a_2$	0.4
$a_3$	0.2	$b_1$	1	$b_2$	0.8
$b_3$	0.6	$p$	2.88	$g_1$	0.1

.

The simulated performance of the designed single wide bandpass filter structure is shown in Figure 4b. Within the −3 dB passband of 24.25–29.5 GHz, the insertion loss is 1 dB with S₁₁ < −7 dB. To further validate the filtering mechanism, surface current at different frequency points were analyzed, as illustrated in Figure 4b. At 23 GHz, the current flow is interrupted by the SIW structure’s cutoff properties, while at 31 GHz, the SSPP structure effectively suppresses current propagation. In contrast, within the passband (24.25–29.5 GHz), the current successfully propagates across the entire structure from Port 1 to Port 2. These observations conclusively demonstrate the single wide bandpass filtering effect. It exhibits a manifest improvement with the concept structure in Figure 3, and Figure 4c shows the corresponding S-parameters, demonstrating the discrepancy.

3.1.2. The Single Wide Bandpass Filter Loaded with Archimedean Spiral Structure

The single-bandpass filter structure designed in the previous subsection exhibited limitations in both stopband attenuation and in-band performance. To address these issues, a new groove structure with Archimedean spirals on both the top and bottom surfaces of the dielectric substrate is introduced, as illustrated in Figure 5a. The Archimedean spiral structure, due to its equidistant rotational symmetry, is suitable for the construction of periodic metamaterials. The resonant frequencies of rings with different radii within a unit cover a wide frequency band, and the coupling of multiple rings enables the smooth phase superposition and the gentle dispersion of the equivalent refractive index. These two mechanisms work together to significantly improve the flatness of the phase response of the metasurface unit within a wide frequency band. The resonant characteristics of the Archimedean spiral are determined by its geometric parameters: the lowest resonant frequency is predominantly governed by the outer radius, while the highest resonant frequency is primarily determined by the inner radius. Between these two extremes, the spiral structure exhibits multiple intermediate resonances, whose frequencies are critically dependent on the inter-turn spacing [36]. This multi-resonant behavior demonstrates remarkable electromagnetic synergy with the SSPP unit described in the preceding section. This synergistic integration enhances the high-frequency cutoff characteristics. The location and sizes of the grooves are optimized out as follows: $mov{e}_{x1}$ = 8.5 mm and $mov{e}_{y1}$ = 1.4 mm are distance from spiral center to starting point, $r_{Arc1}$ = 0.63 mm and $r_{Arc2}$ = 0.21 mm outer and inner radii of the spiral structures, and $g_{Arc}$ = 0.1 mm is the groove clearance width.

Figure 5c presents the S-parameters results. Within the 3 dB of 24–30 GHz passband, S₁₁ remains below −12 dB, while the insertion loss is 0.5 dB. Compared to the unloaded Archimedean spiral structure, the passband exhibits improved flatness. Moreover, S₂₁ drops sharply to −70 dB with a high roll-off rate, indicating significant performance enhancement. To further visualize the effects of loading the Archimedean spiral, the surface current at different frequency points is subsequently analyzed. As observed from the surface current in Figure 5c, at 23 GHz, the current is interrupted by the SIW effect. At 31 GHz, the current is blocked by the combined action of the comb-shaped SSPP structure and the Archimedean spiral. Compared with the surface current at 31 GHz in Figure 3b, the current received at Port 2 is significantly reduced. Within the passband (24–30 GHz), the current propagates through the entire region from Port 1 to Port 2. In summary, after loading the Archimedean spiral, the SIW-SSPP-based wide bandpass filter exhibits improved performance in both the passband and high-frequency cutoff characteristics.

3.2. The Wide Bandpass Filter with Multi-Sub-Bandpass

After loading the Archimedean spiral, the single wide bandpass filter demonstrated significant performance improvement. However, in wireless applications, unwanted signals often require suppression. Therefore, based on the single-band design, this section achieves band segmentation by loading CSRRs, enabling effective rejection of undesirable signals.

3.2.1. Dual-Sub-Bandpass Filter Loaded with CSRRs

As shown in Figure 6a, four identical CSRRs are symmetrically loaded on the ground plane: $mov{e}_{x2}$ = 16 mm and $mov{e}_{y2}$ = 1.45 mm represent the distances from the CSRRs to the central point, $r_1$ = 0.65 mm and $r_2$ = 0.45 mm denote the outer and inner radii of the CSRRs, $g_2$ = 0.1 mm indicates the opening width, and $d_1$ = 0.1 mm corresponds to the ring spacing. When operating near its resonant frequency, a CSRR can be equivalently modeled as an electric dipole. It exhibits negative permittivity around the resonant frequency, resulting in a band-stop effect and generating a resonant absorption peak.

Figure 6b shows the equivalent circuit of the CSRR, which is a resonant loop. $L_{CSRR}$ represents the equivalent inductance and $C_{CSRR}$ represents capacitance of the CSRR, respectively. In the equivalent circuit of an ideal lossless transmission line composed of series inductors and shunt capacitors, the loop is connected in series with the shunt capacitor, forming the equivalent circuit of the CSRR and its MSL. Based on the duality principle, the values of $L_{CSRR}$ and $C_{CSRR}$ for the CSRR can be derived from the equivalent capacitance $C_{SRR}$ and inductance $L_{SRR}$ of its complementary structure SRR. The specific values of $C_{SRR}$ can be calculated using Equation (7) [37].

$$C_{SRR}={\displaystyle \frac{\pi \left(r_1+r_2\right)C_{pul}}{4}}$$

(7)

where the $C_{pul}$ represents the per-unit-length capacitance between adjacent rings, $C_{pul}=2\pi r_2{\epsilon }_0{\epsilon }_r{d}_1/d$. ${\epsilon }_0$ denotes the permittivity of vacuum, and ${\epsilon }_r$ denotes the relative permittivity of the dielectric substrate. $L_{SRR}$ is the equivalent inductance of a circular ring of radius $\left(r_1+r_2\right)/2$ and ring width $\left(r_1-r_2-d_1\right)$.

The relationship between the equivalent capacitance and inductance of CSRR and SRR can be expressed as follows:

$$C_{CSRR}=4{\displaystyle \frac{{\epsilon }_0}{{\mu }_0}}{L}_{SRR}$$

(8)

$$L_{CSRR}={\displaystyle \frac{{\mu }_0}{{\epsilon }_0}}{C}_{SRR}$$

(9)

where ${\mu }_0$ denotes the permeability of vacuum.

The resonant frequency is ultimately expressed as follows:

$$f_{CSRR}={\displaystyle \frac{1}{2\mathsf{\pi }\sqrt{C_{\mathrm{CSRR}}{L}_{\mathrm{CSRR}}}}}$$

(10)

The values of the locations and sizes for Figure 6a are obtained with these formulas and CST optimization. The S-parameters results are presented in Figure 6c. In the first passband (24–25.5 GHz), S₁₁ remains below −12 dB with an insertion loss of 0.5 dB, while in the second passband (26.3–30 GHz), S₁₁ is maintained below −13.5 dB with the same 0.5 dB insertion loss. By loading the CSRR structure on the back of the filter, effective passband segmentation is achieved. Figure 6c presents the surface current of the filter with the loaded CSRR. At 26 GHz, the CSRR clearly interrupts current flow, which contrasts markedly with the unimpeded current propagation observed at 27.5 GHz within the passband. This provides direct evidence of the CSRR’s effect, correlating well with the S-parameter characteristics shown in Figure 6d. Ultimately, the desired dual-band performance has been successfully realized.

3.2.2. Tri- Sub-Bandpass Filter Loaded with Dual CSRR Structures

After realizing the dual-passband filter, this section introduces an additional CSRR with different parameters loaded on the back of the filter, following the same procedure. As illustrated in Figure 7a to obtain the third sub-passband and verify whether this method can achieve further band segmentation. The final structure of the filter is presented in Figure 7b. $mov{e}_{x3}$ = 14 mm and $mov{e}_{y3}$ =1.38 mm represent the distances from the CSRRs to the center point, while $r_3$ = 0.6 mm and $r_4$ = 0.4 mm denote the outer and inner radii of the newly added CSRR, respectively. $g_3$ = 0.1 mm specifies the opening width, and $d_2$ = 0.08 mm indicates the ring spacing. The detailed parameters of the new structure are summarized in

Table 2. Design parameters of the new structure in the filter (unit: mm).

Locations		Archimedean Spiral Parameters		CSRRs Parameters
movex1, movey1	8.5, 1.4	rArc1	0.63	r1, r2	0.65, 0.45
movex2, movey2	16, 1.45	rArc2	0.21	r3, r4	0.6, 0.4
movex3, movey3	14, 1.38	gArc	0.1	g2, g3	0.1, 0.1
				d1, d2	0.1, 0.08

, and along with the data in this table, all the parameters of the filters are provided. Considering the inherent discrepancies between theoretical simulations and actual measurements, the data in the tables have been optimized through parameter tuning with CST simulations to more accurately represent the device performance.

The S-parameter results for the tri-sub-bandpass filter are presented in Figure 7d. Within the 24 GHz–25.3 GHz frequency range, S₁₁ is below −13 dB with an insertion loss of 0.5 dB; in the 26 GHz–27.9 GHz range, S₁₁ is below −13.5 dB with an insertion loss of 0.7 dB; and in the 28.6 GHz–30 GHz range, S₁₁ is below −12 dB with an insertion loss of 0.8 dB. The loading of the two CSRRs splits the original single passband into three passbands, offering a feasible method to suppress unwanted signals in wireless communication systems and improve system stability. Figure 7c shows the surface current of the tri-bandpass filter at different frequency points. It can be observed that the proposed structure effectively suppresses current outside the upper and lower cutoff frequencies of the passbands, as well as in the frequency ranges segmented by the loaded CSRRs, while allowing current to pass freely within the three passbands. For example, at around 25.5 GHz and 28.5 GHz, the corresponding CSRRs exhibit significant resonance. Based on the S-parameter plots and surface current analysis, it is demonstrated that the design, built upon the SIW and comb-shaped SSPP structure, optimizes the passband and high-frequency cutoff characteristics by loading Archimedean spirals, while the loading of two types CSRRs enables tri-bandpass operation.

4. Measurement Results and Discussion

The wide-passband filters (both with and without the proposed tri-sub-band configuration) in this work were fabricated using standard PCB technology. The design was implemented on a 0.508 mm thick Rogers 5880 substrate (${\epsilon }_r$ = 2.2) with 0.035 mm thick copper, as shown in the fabricated prototype in Figure 8a,b. The overall dimensions are 35 mm × 6 mm, corresponding to 3.1 ${\lambda }_g$ × 0.53 ${\lambda }_g$, where ${\lambda }_g$ denotes the wavelength at the center frequency. Measurements were performed using a Keysight PNA N5247A vector network analyzer (Keysight Technologies, Santa Clara, CA, USA), with the test setup illustrated in Figure 8b. As demonstrated in Figure 8c,d, the simulated and measured S-parameters show good agreement, both with or without CSRR loading. For the tri-sub-passband filter, the measurement results indicate that within the 24 GHz–25.3 GHz frequency range, S₁₁ is below −12.5 dB with an insertion loss of 1 dB; in the 26.1 GHz–27.9 GHz range, S₁₁ is below –12 dB with an insertion loss of 1.5 dB; and in the 28.8 GHz–30.1 GHz range, S₁₁ is below −11.5 dB with an insertion loss of 2 dB. The single wide-passband filters yield better results. Minor discrepancies observed at certain frequency points can be attributed to fabrication tolerances and soldering variations, yet these deviations remain within acceptable ranges. This experimental validation confirms the validity of the design methodology.

To further objectively demonstrate the advantages and utility of the design,

Table 3. Comparison of the designed performances.

Ref.	Type	Passband Range (GHz)	Insertion Loss (dB)	Rejection Loss (dB)	Size (${\mathit{\lambda }}_{\mathit{g}}^2$)	High Frequency RL (dB)
[22]	SIW	8.24–8.76	1.7	10	1.155	35
[24]	SSPP	3.85–7.125	1.2	10	2.61	30
[26]	SIW + SSPP	8.1–12.1	3.5	10	1.005	35
[28]	SIW + CSRR	10.25–11.3	1.4	15	11.9	40
[29]	SSPP + CSRR	51.5–58.4 61.7–65.8	2.6	10	0.16	65
[30]	SIPF	7.4–8.8 9.01–9.72 10.01–12.5	1	10	1.83	53
Pro.	Filter 1	24–30	0.5	12	1.68	70
	Filter 2	24–25.5 26.3–30	0.5 0.5	12 13.5	1.68	70
	Filter 3	24–25.3 26–27.9 28.6–30	0.5 0.7 0.8	13 13.5 12	1.68	70

compares its performance with the results of previous studies. As can be seen in the table, Filter 1, Filter 2, and Filter 3 correspond to the single wide-bandpass filter, dual-sub-bandpass filter and tri-sub-bandpass filter in Section 3. The table compares key performance metrics for various types, including insertion loss, return loss, physical dimensions, and return loss characteristics beyond the high-frequency cutoff. The data in the table show that the structure presented in this paper achieves a multi-passband filter with low insertion loss, while ensuring compact size, multi-band capability, and low insertion loss. Furthermore, the S₁₁ parameter beyond the high-frequency cutoff can achieve −70 dB, which presents a notable advantage over other studies.

5. Conclusions

Novel wide-passband filters (with or without a triple-passband) based on SIW and SSPP structures are proposed, along with the design details, methodology and procedures. First, a single-passband filter operating at 24.25–29.5 GHz is realized by designing an SIW-SSPP unit cell with novel SSPP structure, where the upper and lower cutoff frequencies can be independently adjusted. Subsequently, loading an Archimedean spiral structure significantly enhances the filter performance, achieving lower insertion loss while maintaining compact dimensions. Moreover, the filter exhibits high out-of-band rejection above the upper cutoff frequency. To suppress unwanted signals in wireless communication systems, CSRR structures are incorporated to achieve dual-sub-bandpass and ultimately triple-bandpass filtering. The SIW-SSPP filter, loaded with both Archimedean spiral and CSRR structures, demonstrates significant advantages over existing designs in the literature. The final filter operates across 24.25–29.5 GHz, covering the 5G NR n257, n258, and n261 bands, exhibiting strong practical relevance and application potential.