High selective SIW bandpass filter with flexible bandwidth and transmission zero for 5G application

Abstract

This paper presents a novel design of an electric coupling structure for a substrate-integrated waveguide (SIW) bandpass filter, which exhibits flexible characteristics, sharp roll-off, and high out-of-band rejection, making it suitable for 5G applications. The filter structure is designed with a rectangular slot with a metallic cylindrical via and a narrow propagating path. The proposed design creates a transmission zero (TZ) and shows flexibility in terms of TZ and bandwidth. This structure can be used for both inline and cross-line SIW topologies. Two filters are simulated and fabricated to validate the design. The first filter is designed at 27.12 GHz frequency with 4.98% fractional bandwidth (FBW) and one TZ at a higher stopband using an inline filter topology. The second filter is centered at 27.46 GHz frequency and 4.11% FBW with two TZ at both sides of the passband in crossline topology.

Introduction

The Substrate Integrated Waveguide (SIW) structure offers a unique balance between conventional rectangular waveguides and planar transmission lines^1–3. While planar technologies, such as microstrip and stripline, are compact, low-cost, and easy to integrate with other circuits, they suffer from high losses, limited power-handling capability, and low quality factors at high frequencies. The microstrip filters generally do not experience significant leakage effects at lower frequencies (e.g., L, S, C, and X-bands)^4–6, these problems become increasingly severe as the operating frequency rises. In contrast, metallic waveguides offer excellent performance in terms of low insertion loss, high power handling, and very high Q-factors; however, they are bulky, expensive, and challenging to integrate with planar circuits. SIW technology effectively bridges this gap by utilising rows of metallic vias to emulate a rectangular waveguide within a planar substrate, thereby achieving low loss, high Q-factor, and good power-handling characteristics, while maintaining the compactness, low cost, and ease of fabrication benefits of planar PCB processes. These combined advantages make SIW an excellent choice for compact and high-performance microwave and millimeter-wave components, including 5G bandpass filters.

In the literature, most of the research on SIW filters is available in the L, S, and C bands. Still, the upper band of microwave frequency, such as the K and Ka bands, has very few research papers reported, so it needs further exploration as it is used in the 5G upper band and beyond. Bandpass filters (BPFs) in the K and Ka bands are more challenging compared to those at lower microwave frequencies due to their small size and fabrication limitations. To solve this problem, researchers have moved to a higher mode to implement BPF with a reasonably sized model^7,8. The TE₁₀₁ mode is preferred for designing a BPF at a lower frequency due to its spurious-free response in the lower stopband, and the only part that needs to be handled is creating the upper stopband. The design of the upper and lower stopbands presents a significant challenge when dealing with higher-mode filters. To solve this problem, a transmission zero (TZ) must be introduced on both sides of the passband. For this, magnetic and electric coupling are required to create the TZ, which also increases the selectivity of the filter and forms a passband.

The magnetic coupling can be formed by an inductive post within the cavity or by an iris window between adjacent cavities^9,10. However, in the magnetic coupling, the design is fixed, and only the length of the window can be changed here, or the radius of the cylinder can be changed in the case of the inductive post. Another challenge in only magnetic coupling is the creation of TZ at the desired position. Conversely, the electric coupling can be formed by etching the upper conductive layer in a rectangular or coplanar slot^11,12.

In slot formation, design flexibility is much higher as the length, width, and position of the slot within the cavity can be varied quickly. The slot is created on the top and bottom layers of the filter, and as a result, the performance of SIW is degraded due to packaging issues¹³. Similarly, defected ground structure (DGS)- based SIW filters^14,15 face surface-mount problems. To address this issue, one could improve by employing solely the top layer to create a slot cut, aligning it with a parallel of the surface current¹². The capacitive coupling is achieved through a multilayer structure, albeit at the cost of a complex design and increased losses^16,17. The single-layer design has the advantage of being easy to fabricate and having fewer fabrication errors, resulting in higher filter performance compared to multilayer SIW structures^18–20. Despite design flexibility, creating TZ with high selectivity has also been challenging using electric coupling. A novel diagonal coupling method is proposed in²⁶ using higher modes of propagation at the cost of a very complex design. The miniaturised SIW bandpass filter is proposed in^28,29. Reference²⁸ utilises Half-Mode Substrate Integrated Waveguide (HMSIW) technology, while²⁹ employs a hybrid technology (microstrip and SIW), resulting in a compact structure at the cost of a complex design. The literature mentioned above commonly faces problems in attaining a sharp roll-off, achieving good design flexibility, creating TZ, and maintaining wide stopband performance.

This paper proposes a novel electric coupling structure that incorporates a loaded inductive post within a single-layer substrate design. Design features with capacitive and inductive coupling enable it to implement TZ effectively at the desired frequency. On the other hand, design flexibility gives the researcher more freedom to design the required specifications of the filter. The filter achieves sharp roll-off, wide and high out-of-band rejection, flexible control over bandwidth and transmission zeros (TZs), and efficient signal transmission within the passband. Two filter prototypes are developed to demonstrate the versatility of the design: one with inline coupling and the other with cross-coupling. These implementations validate the proposed structure as a universal model capable of adapting to different SIW topologies—a challenging feat in filter design. Both filters exhibit transmission zeros, which significantly enhance selectivity. The fabricated prototypes closely match the simulated results, confirming the practicality and effectiveness of the design. The subsequent sections of the paper are organised as follows: “Design of bandpass filter” presents the bandpass filter design, Section “Parameter analysis” discusses the parametric analysis, and “Simulated and fabricated result discussion” introduces two filter models along with their simulated and fabricated results, followed by a discussion and an overview of the filter design steps. Finally, “Conclusion” concludes the work.

Design of bandpass filter

The initial step in the filter design process involves determining the cavity size according to the resonance frequency and propagating mode. The cavity size can be calculated by using Eq. (1) as given in²¹:

1

where is the cutoff frequency of mode m0n, c represents the speed of light, is the relative permittivity of the material, and are the SIW cavity width and length, respectively. It is defined mathematically as

2

3

where w and l are the width and length of the cavity, respectively, while d is the diameter of the via row and p is the centre-to-centre distance between two consecutive vias, as shown in Fig. 1F. In this work, the filter is designed to operate in the TE301 propagation mode, with a center frequency of 27.25 GHz. The initial cavity dimensions are calculated using Eq. (1), yielding approximate values of 8.5 mm and 13.4 mm. Once the cavity size is determined, key filter specifications, including the external quality factor, bandwidth, coupling structure, and coupling coefficient, are taken into consideration. The design is then simulated and iteratively tuned to achieve the desired performance, followed by fabrication and final measurement.

Fig. 1.

(A) filter structure in design step 1, (B) filter structure in design step 2, (C) filter structure in design step 3, (D) E-field at 25.44 GHz from design step 2, (E) E-field at 27.93 GHz from design step 3, (F) Proposed filter model-1 structure with design parameters and filter structure topology.

The proposed filter consists of two resonant cavities connected by a narrow propagation path, as shown in Fig. 1A, which represents Step 1 of the design process. This narrow inter-cavity path is inductively loaded to enhance magnetic coupling. In Step 2, each cavity features a slot cut into the top conductive copper layer, creating an electric coupling mechanism (Fig. 1B). A loaded inductive post is then introduced just before the rectangular slot, resulting in the final design of Model 1, illustrated in Fig. 1(C) as Step 3.

The cavities are excited in TE₃₀₁ mode, in which the electric field peaks at the center of the cavity. Consequently, the coupling slot is positioned horizontally at this maximum field region, while the inductive post is placed vertically at the leading edge of the slot. This configuration enables strong electric coupling, further enhanced by magnetic effects due to the loaded post. The electric field distribution for Step 2 is shown in Fig. 1(D), where the TE₃₀₁ mode appears at 25.44 GHz. In the final model (Step 3), shown in Fig. 1(E), the TE₃₀₁ mode shifts to 27.93 GHz due to the effect of the inductive loading, resulting in improved coupling and a wider passband.

The filter model, including detailed dimensions and coupling structure, is depicted in Fig. 1(F). In the coupling diagram, node-1 and node-3 correspond to resonating cavities 1 and 3, while node-2 represents the connecting path between these cavities. The source and load are directly linked to cavity-1 and cavity-3, respectively, whereas cavity-2 is connected to the other two cavities mainly through capacitive coupling.

The third resonance is most likely arising from the resonant behaviour of the central coupling section between the two main TE₃₀₁ cavities. This section, while primarily for coupling between the two main TE₃₀₁ cavities, can itself act as an effective third resonator, leading to a 3-pole filter response despite only two large TE₃₀₁ cavities being clearly created. The coupling is controlled by the physical dimensions and via the configuration of this central section. This central section not only provides the path between the two main cavities but also supports TE₁₀₁ mode, contributing as a third resonance in the passband formation. This connecting path is loaded with a couple of inductive via, and the distance between these via (p₁) is used to control the coupling.

Figure 2 A shows the S-parameter analysis across the design steps. The slot cuts induce capacitive coupling, creating a passband near 25.40 GHz associated with the TE₃₀₁ mode. However, the connecting path supports a TE₁₀₃ mode at 28.73 GHz, which negatively affects the stopband performance. To enhance the stopband and broaden the passband, design step 3 incorporates an inductive post. As seen in Fig. 2(A), this addition shifts the TE₃₀₁ mode from 25.44 GHz to 27.93 GHz, resulting in a wider bandwidth. Simultaneously, a transmission zero (TZ) emerges, suppressing the unwanted TE₁₀₃ mode of the connecting path. Thus, the inductive loading effectively improves bandwidth, reduces spurious responses, and enhances stopband performance in the final filter design.

Fig. 2.

(A) S-Parameters for design steps 1 to 3, (B) K versus l₁ with different values of w₁, (C) K versus l with different values of p₁, (D) Frequency of the mode and external quality factor (Q_e) versus parameter b_l.

The coupling of the filter response is extracted from the simulated response. The coupling coefficient (k) of the filter is given as²¹ Eqs. (4),

4

Here, f₁ and f₂ represent the coupled lower and higher resonant frequencies, respectively. The relationship between the coupling coefficient k and the parameters l₁ and l is illustrated in Fig. 2. Figure 2(B) shows how l₁ varies with different values of w₁. In the slot design, l₁ and w₁ correspond to the length and width of the slot, respectively, as depicted in Fig. 1. Consequently, the capacitance of the structure changes with variations in l₁ and w₁. When l₁ increases from 3.6 mm to 6.6 mm, the coupling coefficient k decreases from approximately 0.05 to 0.015 for a fixed w₁. In contrast, increasing w₁ results in an increase in k. Figure 2(C) presents the behaviour of k and l for different values of p₁. As l increases from 12.10 mm to 12.90 mm, k initially decreases from about 0.065 to 0.02, then slightly rises again. For p₁, as it grows from 1.5 mm to 1.7 mm, k first increases and then decreases. Both l and p₁ define the inductive post, so modifying these parameters influences the inductive coupling of the structure.

The external quality factor (Q_e) is the second critical parameter in the filter design. Q_e is extracted using the eigenmode solver in CST Microwave Studio, with results shown in Fig. 2(D). This figure plots Q_e and the filter’s coupled mode frequency against the parameter b_l. As b_l increases from 1.4 mm to 1.8 mm, Q_e decreases gradually from 156 to 28, while the mode frequency slightly decreases from 27.50 GHz to 27.48 GHz. These results indicate that Q_e can be effectively controlled by adjusting b_l, with minimal impact on the mode frequency.

Parameter analysis

This structure integrates a capacitive slot line, an inductive post load, and a narrow inductive path. For fine-tuning the filter, three key variables are considered: w₁, p₁, and l. While other parameters contribute to the filter design, these three have the most significant impact. Specifically, w₁ represents the width of the slot line, p₁ is the distance of the inductive post within the narrow path, and l denotes the distance of the inductive post load from the filter’s center, as illustrated in Fig. 1. These variables are crucial for adjusting the filter’s bandwidth (BW), center frequency (f_c), 3-dB cutoff frequencies ( and ), and transmission zero (TZ) frequency. The following discussion focuses on the design flexibility offered by tuning these three parameters.

BW and TZ tuning at constant

The parameter w₁ is used to control the width of the slot line, which in turn influences the capacitance of the structure. When w₁ is varied from 1.1 mm to 1.7 mm, BW increases from 1.25 GHz to 1.77 GHz, and TZ frequency increases from 28.6 GHz to 29.4 GHz at the same time, f_c shifts towards a higher frequency from 27.18 GHz to 27.38 GHz. The lower 3 dB cutoff frequency () remains nearly constant at around 26.5 GHz, while the upper 3 dB cutoff frequency () increases from 27.81 GHz to 28.28 GHz, as illustrated in Fig. 3A. Since w₁ primarily influences capacitive coupling, it allows tuning of the bandwidth (BW) and transmission zero (TZ) without affecting . In this design, the TZ is generated mainly by dominant capacitive coupling, whereas the lower stopband can be adjusted through the inductive effect, as explained in¹².

Fig. 3.

Filter response with (A) variation of w₁ parameter, (B) variation of p₁, (C) variation of l.

BW tuning at constant TZ

The parameter p₁ defines the position of the inductive post within the narrow propagation path. Adjusting p₁ changes the inductance of the structure, thereby affecting the filter’s response. As p₁ varies from 4.6 mm to 4.0 mm, the bandwidth (BW) decreases from 1.75 GHz to 1.38 GHz, and the center frequency (f_c) increases from 27.19 GHz to 27.62 GHz, while the transmission zero (TZ) frequency remains nearly constant at 29.15 GHz. The lower 3 dB cutoff frequency () increases from 26.32 GHz to 26.93 GHz, whereas the upper cutoff frequency () stays almost unchanged at 28.13 GHz, as shown in Fig. 3(B). In this case, only is affected because p₁ exclusively controls the inductive coupling of the structure. Therefore, BW tuning is achieved without impacting the TZ frequency.

BW and TZ tuning at constant

The parameter l determines the position of the inductive load relative to the center of the filter, as shown in Fig. 1. Changing l shifts the location of the inductive post in relation to the slot line, which affects both the inductance and the capacitive coupling of the structure. Figure 3(C) illustrates this variation: as l increases from 12.4 mm to 13.0 mm, the transmission zero (TZ) frequency decreases from 29.52 GHz to 28.50 GHz, and the bandwidth (BW) narrows from 1.77 GHz to 1.21 GHz, while the center frequency (f_c) remains nearly constant. Meanwhile, the lower cutoff frequency () rises from 26.39 GHz to 26.72 GHz, and the upper cutoff frequency () drops from 28.16 GHz to 27.93 GHz. Therefore, l is effectively used to tune the BW and TZ frequency without altering the center frequency. The tuning parameters mechanism in the summary form is further dictated in Table 1.

Table 1.

Summery of parameters tuning.

Parameter	Coupling effect	Mode	Cavity	Tuning
w₁	Capacitive	TE301	1 & 3	BW & TZ
p₁	Inductive	TE101	2	BW
l	Inductive	TE301	1 & 3	BW & TZ

Simulated and fabricated result discussion

The filter model can be used in inline and cross-coupled topologies. So here, two filter models are presented to validate novel structures to form filters.

Filter model-1 (inline topology)

Filter Model-1 is depicted in Fig. 1. The generalized coupling matrix of this filter has been optimized for an equiripple third-order design centered at 27.25 GHz, targeting a 30 dB return loss. This optimization was performed using the CST Filter Designer 3D simulator, as shown in Eq. (5). To determine the actual coupling values between the resonators, the coupling matrix is denormalized using Eq. (6), following the approach outlined in²¹

5

6

Using Eqs. (5) and (6), the coupling coefficients between the resonators and the external quality factor (Q_e​) for a fractional bandwidth (FBW) of 5% are determined as follows: K₁₂ = − 0.045, K₁₃ = 0.016, K₂₃ = − 0.045, and Q_e = 17.15.

The design parameters are: w₀ = 14, l₀ = 32, b_i=8, l = 12.6, l₁ = 5.7, p = 1.6, d = 1, r = 0.25, w_i=1.58, w₁ = 1.3, w = 0.5, b_l=1.6, and p₁ = 4.4 (all dimensions in millimeters). The dielectric material used is Rogers RT/Duroid 5880 with a thickness of 0.508 mm, relative permittivity of 2.2, and a loss tangent of 0.0009.

As discussed earlier, the most sensitive parameters that can be used to further tune filter response are w₁, p₁, and l. Where w₁ variation is used for upper cutoff frequency tuning, so that BW and TZ position are varied according to the change of w₁, as shown in Fig. 3 (A). The p₁ parameter is used for tuning the lower cutoff frequency, so that the bandwidth varies accordingly, as shown in Fig. 3(B). While l variation is used for both cutoff frequency tuning, so that BW and TZ position are varied according to the change of l, as shown in Fig. 3 (C).

Figure 4 compares the synthesized, simulated, and measured filter responses. The measured results show good agreement with the simulations. The measured minimum insertion loss (IL) is 1.79 dB, maximum return loss (RL) exceeds 24 dB, the center frequency (f_c​) is 27.12 GHz, bandwidth (BW) is 1.35 GHz, and a transmission zero (TZ) is observed at 28.86 GHz. The stopband attenuation is better than 10 dB from 28.2 GHz to 42.9 GHz. The simulated center frequency is 27.25 GHz, with an IL of 1.09 dB and a BW of 1.42 GHz. The roll off factor for lower and upper band is 15.21 and respectively. The slight differences between measured and simulated results are attributed to fabrication tolerances and input/output port losses.

Fig. 4.

(A) The synthesized, simulated, and measured results with the fabricated filter model-1, (B) the zoomed-in plot of the passband insertion loss.

Filter model-2 (crossline topology)

Filter Model 2 is introduced to demonstrate the versatility of the proposed Filter Model 1 design. Model 2 employs a cross-coupling topology combined with a combline design, as illustrated in Fig. 5. The structure shows cross-coupling between cavity nodes 1 and 4, with the cross-line path passing through the non-resonating node 3. According to the cross-coupling principle, when a signal travels via multiple paths, signal cancellation occurs, resulting in the formation of transmission zeros (TZ). To the best of the author’s knowledge, this is the first time a combline design has been integrated into a cross-coupled topology to create a bandpass filter using the proposed novel approach. This combination produces an additional TZ compared to Filter Model 1. With TZs on both sides of the passband, the filter achieves improved stopband performance and enhanced selectivity.

Fig. 5.

Filter model-2 and structure topology.

Filter Model 1 serves as the base design; thus, all parametric analyses presented in Sect. 3 apply to Model 2 as well. The flexibility in tuning the TZ and bandwidth is illustrated in Fig. 6A, B, with design steps similar to those used for Model 1. Equation (7) presents the normalized coupling matrix for Model 2, targeting a third-order equiripple response centered at 27.6 GHz with a fractional bandwidth (FBW) of 4.2%. Using Eqs. (6) and (7), the coupling coefficients are determined as , .

Fig. 6.

Filter response with (A) variation of l parameter, (B) variation of w₁ parameter.

The design parameters for Model 2 are: = 13.8, = 32, = 8, l = 12.5, l₁ = 6.4, p = 1.6, d = 1, r = 0.25, b_l = 1.8, = 4.4, w_i = 1.58, w = 0.5, w₁ = 1.4, w₂ = 3.2, w₃ = 4.6, b₁ = 11.2, b₂ = 12.8, all in millimeters. The dielectric substrate is Rogers RT/Duroid 5880, with a relative permittivity (ε_r) of 2.2 and thickness of 0.508 mm.

Figure 7 compares the synthesized, simulated, and measured responses of Filter Model 2. The measured minimum insertion loss (IL) is 1.6 dB, maximum return loss (RL) within the passband reaches 28 dB, the center frequency (fc) is 27.46 GHz, bandwidth (BW) is 1.13 GHz, with transmission zeros at 25.05 GHz and 28.4 GHz. The stopband attenuation exceeds 10 dB from 28.25 GHz to 31.70 GHz. The simulated values are fc = 27.6 GHz, IL = 1.28 dB, and BW = 1.16 GHz. The roll off factor for the lower and upper bands of model-2 is 15.89 and respectively. The slight differences between measured and simulated results are attributed to fabrication tolerances and input/output port losses. In particular, the performance at 27–27.5 GHz is highly sensitive to dimensional accuracy, and even small variations in substrate thickness, via diameter, or metallization quality can lead to increased conductor and dielectric losses.

Fig. 7.

(A) The synthesized, simulated, and measured results with the fabricated prototype of filter model-2, (B) the zoomed-in plot of the passband insertion loss.

A comparison with previously reported substrate-integrated waveguide (SIW) bandpass filters is presented in Table 2. The proposed Model 1 achieves high out-of-band rejection and low insertion loss with an FBW of nearly 5% on a single-layer substrate. Model 2 offers transmission zeros on both sides of the passband, low insertion loss, and an FBW greater than 4%, demonstrating enhanced selectivity and filter performance.

Table 2.

Comparison of this work with previously reported SIW filters.

R.N.	fc, FBW	RL, IL	TZ	SBR	DF	OBRR	Layer	Size ()
22	27, 7.4	15, 1.7	2	> 20	TZ	10dB @ 28–34 GHz*	M	NA
23	38.8, 5.92	15, 6.7	1	> 50	No	NA	S	1.66*2.55
24	27.96, 2.3	17, 2.01	2	> 25	TZ	20dB @ 28.3–44.7 GHz*	S	0.98*0.97
25	29.96, 4.03	16.6, 3.7	4	> 30	TZ, BW	20dB @ 31–35 GHz*	S	3.06*1.78
27	36.75, 4	15, 1.5	0	> 60	No	NA	M	1.31*1.85
Model-1	27.12, 4.98	13, 1.78	1	> 20	TZ, BW	10dB @ 28.2–42.9 GHz	S	3.16*1.54
Model-2	27.46, 4.11	15, 1.60	2	> 25	TZ, BW	10dB @ 28.25–31.7 GHz	S	3.2*2

R.N. reference number, f_c center frequency in GHz, FBW fractional bandwidth in %, RL return loss in dB, IL insertion loss in dB, TZ number of transmission zero, SBR stopband rejection in dB, DF design flexibility, S single layer, M multi-layer, *approximate data, NA not available, OBRR out of band rejection range.

The filter design utilizes higher-order modes, which require an oversized cavity. This approach enhances the reliability of PCB fabrication compared to compact designs and helps minimize fabrication errors.

7

The filter design process involves the following sequential steps:

1. Initially, critical filter specifications such as the operating frequency, bandwidth, maximum insertion loss, quality factor (Q), and filter order are precisely defined.

2. Based on these established specifications, individual resonant cavities are designed, followed by the determination of their optimal spatial arrangement within the filter structure.

3. A coupling matrix is then derived to accurately characterize and control the inter-resonator coupling coefficients.

4. Subsequently, the physical coupling structures are designed to facilitate the desired filtering characteristics and support the proposed novel design’s operational mechanism.

5. Extensive parametric analysis is conducted to iteratively refine the filter’s performance and achieve an optimal response.

6. Finally, once the desired performance criteria are met through the iterative design and optimization of the coupling structures, the filter’s dimensions are finalized, making it ready for fabrication and subsequent experimental validation.

Conclusion

This paper presents a novel coupling structure for designing single-layer substrate-integrated waveguide (SIW) filters. The proposed model features a wide stopband and offers significant design flexibility, particularly in tuning bandwidth and transmission zeros (TZ). It incorporates three independent parameters, each enabling distinct tuning capabilities. Two filter models are designed and validated: the first uses an inline coupling topology, while the second adopts a cross-coupling configuration. Both models demonstrate sharp roll-off and high selectivity, confirming the effectiveness of the proposed structure. The proposed SIW filter can be effectively applied in reconfigurable RF front-end modules, particularly within 5G NR mm Wave bands of FR-2 frequency allocation, such as n258 (24.25–27.5 GHz), enabling adaptive channel selection and dynamic frequency allocation. With its straightforward design and compatibility with standard PCB fabrication processes, the proposed filter provides a cost-effective and high-performance solution suitable for 5G applications.

Author contributions

Author Mr Govind Kumar Mishra conceived the original idea, simulated, fabricated, tested, and wrote the research paper. Authors Dr Hemendra Kumar Pandey and Dr Nagendra Prasad Pathak are investigating the original idea, feasibility of the novel work, reviewing the research paper and guiding all steps of the research work.

Data availability

All data generated or analyzed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.