Introduction
Modern wireless communication systems require compact and high-performance band-pass filters (BPFs). The components designed using substrate-integrated waveguide (SIW) technology can be advantageous due to its low cost, light weight, and ease of integration with planar microwave circuits [Reference Deslandes and Wu1, Reference Entesari, Saghati, Sekar and Armendariz2]. As SIW resonators suffer from higher-order spurious modes, it is difficult to design SIW filters with wide stopband. Thus, it is essential to suppress the spurious higher-order modes. Several methods have been proposed in the literature to obtain wider stopband. Various techniques are applied for harmonic suppression to obtain wide stopband rejection [Reference Wu, Zhou and Yin3–Reference Zhou, Zhou and Wu14]. Folded and ridge SIW BPFs with compact size and wideband rejection are reported [Reference Wu, Zhou and Yin3]. Using miniaturization techniqueswith half-mode SIW, quarter-mode SIW, eighth-mode SIW, and sixteenth-mode SIW resonators, 90–95% miniaturization is achieved as compared to using conventional SIW resonators [Reference Saghati, Saghati and Entesari4–Reference Azad and Mohan8]. In addition, band rejection of approximately up to 3f 0 is obtained, but the design procedure is complex. Mixed electric and magnetic coupling techniques are used in [Reference Azad and Mohan9–Reference Chu, Feng, Guo, Zhang, Yang, Liu and Wu12]. The higher-order TE102 mode is suppressed by mixed coupling, and TE202 mode is suppressed by weak coupling. In [Reference Zhu, Hong, Chen and Wu13–Reference Liu, Zhang, Tang, Deng and Zhou15], staggering of higher-order modes of substrate-integrated rectangular cavity resonators keeping fundamental frequency identical is used to suppress multiple spurious peaks to obtain a wide stopband. This technique needs a rectangular cavity, which requires larger dimensions, causing problems in high-density integration. A combination of SIW cavities and short-circuited coplanar line is utilized to create the passband with wide stopband [Reference Azad and Mohan16], but the rejection is limited to around 2f 0. In all of these designs, there is a possibility to obtain the wider stopband. Hence, it is a challenging task to design the SIW filters with ultrawide stopband characteristics.
In this paper, two circular SIW BPFs with ultrawide stopband characteristics are presented. The first design is a second-order multilayer SIW filter with orthogonal input/output feed, while the second design is a fourth-order multilayer SIW filter with similar feed technique. The proposed feeding technique and the placement of arc-shaped slots at strategic locations between the cavities enable the suppression of higher-order modes, and as a result, an ultrawide stopband rejection is obtained.
Design and analysis of circular SIW cavity BPF with wide stopband
Analysis of the circular SIW cavity
Figure 1 represents the circular SIW cavity resonator. The side walls of the cavity form a series of metallic vias having diameter d and separation s. The height of the cavity h is much smaller than its radius. Thus, only TMmn0 mode will be supported. The resonant frequency of the TMmn0 mode can be determined by [Reference Pozar17]:
\begin{equation}{{\it{f}}_{{\textrm{T}}{{\textrm{M}}_{{\it{mn}}0}}}}{\textrm{ = }}{{{{\it{J}}_{{\it{mn}}}}{\it{C}}} \over {{2\pi R}\sqrt {{{\mu }_{\textrm{r}}}{\epsilon _{\textrm{r}}}} }}\end{equation}
Figure 1. The front view and 3D view of circular SIW cavity.
where Jmn is the nth root of the mth-order Bessel function, R is the equivalent radius of the SIW cavity, c is the velocity of light in free space, µ r and ε r are the relative permeability and relative permittivity of the substrate, respectively. The cavity is designed on Rogers RT/duroid 5880 substrate having thickness 0.508 mm, dielectric constant 2.2, and loss tangent 0.0009. The diameter of the via-hole is d = 1 mm and their angular separation in s = 10°.
The electric field distributions of first 17 modes of the circular SIW cavity are plotted in Fig. 2. The circular cavity supports two variety of modes: (i) radially symmetric modes (TM010, TM020, TM030, etc.) and (ii) pair of degenerate modes (TM110, TM210, TM310, etc.). If the input and output ports are connected orthogonally at positions A and B, all radially symmetric resonant modes, namely, TM010, TM020, TM030, etc., will get excited. On the other hand, the resonant modes, namely, TM110-m1, TM110-m2, TM210-m1, TM310-m1, TM310-m2, TM120-m1, TM120-m2, TM410-m1, TM220-m1, TM510-m1, TM510-m2, etc., will not get excited because the electric field is nearly zero at position A or B or both.
Figure 2. Simulated electric field distributions of first 17 resonant modes of circular SIW cavity (radius of the cavity = 11 mm).
Figure 3 shows the configuration of the second-order multilayer circular SIW cavity filter. This filter is formed by stacking two circular SIW cavities named as Cavity 1 and Cavity 2. The cavities are fed through two orthogonally placed input/output ports designated as port 1 and port 2, respectively. Moreover, two arc-shaped slots named as Slot 1 and Slot 2 are introduced in the middle metallic layer to couple the cavities, as shown in Fig. 3. The dimension and position of the arc-shaped slots are appropriately chosen such that they allow the coupling of the fundamental TM010 mode, whereas the couplings of the higher-order modes of the cavities are minimum. As a result, the higher-order modes are suppressed, and an ultrawide stopband rejection is obtained.
Figure 3. The configuration of the proposed second-order circular SIW cavity filter.
The coupling strength can be controlled by varying the width W and angular length θ of the arc-shaped slots. The coupling for different modes namely TM010, TM020, TM030, TM210-m1, TM410-m1, and TM220-m1 of the cavities are plotted in Fig. 4(a). It can be observed that there is strong coupling intensity for TM010 mode, while the coupling strengths of TM020 and TM030 are weak. Hence, the arc-shaped slots only allow the coupling of TM010 mode and suppress the remaining higher-order modes. The external quality factor for different values of d s is plotted in Fig. 4(b). One can find that the external quality factor decreases with increasing d s.
Figure 4. (a) The coupling factor k against variation in θ and (b) external quality factor Qe against variation in ds.
To validate the proposed concept of higher-order mode suppression, two BPFs (second- and fourth-order) with wide stopband characteristics are synthesized and designed. The second-order filter (Filter I) and fourth-order filter (Filter II) are designed with Chebyshev response and 20 dB return loss in the passband.
Filter I: second-order circular SIW cavity filter
The first filter is a second-order circular SIW cavity filter (Filter I), as shown in Fig. 3. Filter I is designed with a ripple fractional bandwidth (FBW) of 2.5% centered at 7.9 GHz using the method described in [Reference Hong and Lancaster18]. The element values of the low-pass prototype filter are found as g 0 = 1, g 1 = 0.6667, g 2 = 0.5455, and g 3 = 1.2222. The required external quality factor and coupling coefficient are Q e = 26.7 and k 12 = 0.042. The final dimensions of the filter are d 1 = 22, d s = 5.2, W = 0.6, R 1 = 6.32, and θ = 35° (unit: mm). Figure 5 presents the simulated and measured frequency response of Filter I, and the photograph of the fabricated Filter I is depicted in Fig. 6. The simulated minimum passband insertion loss is about 1.1 dB and the passband return loss is 17 dB. The measured center frequency is 7.89 GHz with a 3-dB FBW of 3.8%. The minimum passband insertion loss is about 1.13 dB, and the return loss is better than 10 dB in the passband. The designed Filter I shows a rejection of 25 dB up to 40 GHz, i.e., 5.07f 0. The overall volume of the filter is 0.858λ g × 0.858λ g × 0.0398λ g, where λ g is the guided wavelength. There are some discrepancies observed in the measured results with respect to the simulated ones, and they are due to fabrication tolerances and errors in assembling the filters.
Figure 5. The simulated and measured S-parameters of Filter I.
Figure 6. A photograph of the fabricated Filter I.
Filter II: fourth-order circular SIW cavity filter
The second filter is a fourth-order circular SIW cavity filter (Filter II), as presented in Fig. 7. The filter consists of four circular SIW cavities stacked one over the other and named as Cavity 1, Cavity 2, Cavity 3, and Cavity 4. The first and fourth cavities are fed through two orthogonally placed input/output ports designated as port 1 and port 2, respectively. The fundamental TM010 mode of the cavities is coupled to each other through arc-shaped slots placed at the appropriate locations in the three middle metallic layers. Filter II is designed with a center frequency of 7.9 GHz and a ripple FBW of 2%. The element values of the low-pass prototype filter are found as g 0 = 1, g 1 = 0.9333, g 2 = 1.2923, g 3 = 1.5795, g 4 = 0.7636, and g 5 = 1.2222. The required external quality factor and coupling coefficients are Q e = 46.7, k 12 = 0.018, k 23 = 0.014, and k 34 = 0.018. The final dimensions of the filter are d 1 = 22, d s = 4.19, W 1 = 0.6, W 2 = 0.4, R 2 = 4.71, R 3 = 3.73, θ 1 = 35°, and θ 2 = 50° (unit: mm).
Figure 7. The configuration of the proposed fourth-order circular SIW cavity filter.
The simulated and measured frequency responses of Filter II are plotted in Fig. 8, and the photograph of the fabricated Filter II is shown in Fig. 9. The simulated minimum passband insertion loss is around 1.1 dB, and the passband return loss is 15 dB. In addition, two transmission zeros are observed in the lower stopband located at 7.36 and 7.58 GHz. The transmission zero (TZ)s are generated because of the mixed coupling between the cavities caused by the coupling slots. The mixed coupling creates multiple paths between the input and output ports, and signal cancellation takes place. The measured center frequency is 7.92 GHz with a 3-dB FBW of 3.2%. The minimum passband insertion loss is about 1.2 dB, and the return loss is better than 13 dB in the passband. The TZs are found at 7.37 and 7.57 GHz. Filter II exhibits a rejection of 20 dB up to 40 GHz, i.e., 5.05f 0. The overall volume of the filter is 0.861λ g × 0.861λ g × 0.0796λ g, where λ g is the guided wavelength. The discrepancies observed in the measured results compared to the simulated data are caused by the fabrication tolerances and errors in assembling the filters.
Figure 8. The simulated and measured S-parameters of Filter II.
Figure 9. A photograph of fabricated Filter II.
The proposed work is compared with the previously reported works in Table 1. It can be observed that the proposed filters exhibit compact size, low loss, comparable bandwidth, and ultrawide stopband rejection. It should be noted that scaling up the proposed methodology to higher-order filters may introduce several limitations and challenges on simulation, design complexity, fabrication tolerance, and manufacturing cost. However, advanced simulation tools, fabrication, and measurement setups may overcome these challenges and ensure successful scaling up of the methodology to higher-order filters. The design guidelines of the proposed filters are listed below.
(1) Decide the design frequency and the bandwidth of filter.
(2) Determine the radius of the circular SIW cavity based on the filter design frequency.
(3) Determine the desired coupling coefficients and external quality factor based on the filter bandwidth.
(4) Determine the values of the structural parameters for desired coupling coefficients and the external quality factor. It is suggested to place the input/output feedline orthogonally and choose the position of the arc-shaped slots appropriately to minimize the coupling of higher-order modes to achieve wide stopband attenuation.
(5) At last, the overall filter structure is tuned till the required frequency response is achieved.
Table 1. Comparison of the proposed work with reported works
Note: CF: center frequency, FBW: fractional bandwidth, IL: insertion loss.
Conclusion
In this paper, two multilayer circular SIW cavity BPFs with ultrawide stopband rejection are presented. The input and output feedlines arranged in orthogonal configuration are present at the top and bottom metallic layers, while the middle layers are used to couple the cavities through arc-shaped slots. To obtain an ultrawide stopband characteristic, higher-order spurious modes of the circular SIW cavities are suppressed with the help of orthogonal input/output feeds and arc-shaped coupling slots. Both filters are designed to operate at 7.9 GHz and allow the propagation of TM010 mode only. The second-order filter exhibits a stopband rejection of 25 dB up to nearly 5.07f 0, while the fourth-order filter shows a stopband attenuation of 20 dB up to nearly 5.05f 0. The proposed filters are suitable for wireless communication systems, point-to-point microwave links, spectrum monitoring and sensing, radio astronomy, and medical imaging.
Data availability statement
Data sharing is not applicable to this article as no data sets were generated or analyzed during this study.
Acknowledgements
The authors acknowledge the Department of Electronics and Communication Engineering, Indian Institute of Technology Roorkee, Uttarakhand, India, for providing equipment and laboratory facilities to carry out this work.
Funding statement
This research received no specific grant from any funding agency, commercial, or not-for-profit sectors.
Competing interests
The authors report no conflict of interest.
Amrita Medda is currently pursuing her Ph.D. from the Indian Institute of Technology Kharagpur, West Bengal, India. She received her B.Tech. and M.Tech. degrees in Electronics and Communication Engineering from Dr. B.C. Roy Engineering College, West Bengal, India, in 2014 and 2016, respectively. She has worked as junior research fellow at Indian Institute of Technology Kharagpur, West Bengal, India, before pursuing Ph.D. Her research interests revolve around the design of high-performance microwave band-pass filters and antennas tailored for modern wireless communication applications.
Amit Ranjan Azad received the B.Tech. degree in Electronics and Communication Engineering from West Bengal University of Technology, West Bengal, India, in 2010, the M.Tech. degree and Ph.D. degree in RF and Microwave Engineering from Indian Institute of Technology Kharagpur, West Bengal, India, in 2012 and 2019, respectively. From 2019 to 2022, he was a faculty member with the Department of Electrical and Electronics Engineering at Birla Institute of Technology and Science Pilani, Hyderabad Campus, Telangana, India. Since 2022, he has been a faculty member with the Department of Electronics and Communication Engineering at Indian Institute of Information Technology Kalyani, West Bengal, India. His research interests include the synthesis, analysis, and design of high-performance microwave band-pass filters and antennas for modern wireless communication applications.
Akhilesh Mohan received the B.Tech. degree in Electronics Engineering from Kamla Nehru Institute of Technology, Sultanpur, India, in 2002, the M.Tech. degree and Ph.D. degree in Microwave Engineering from Indian Institute of Technology Kanpur, Uttar Pradesh, India, in 2004 and 2009, respectively. From 2009 to 2010, he worked as a Scientist at Space Applications Center, Indian Space Research Organization, Ahmedabad, India. From 2010 to 2013, he was a faculty member with the Department of Electrical Engineering at Indian Institute of Technology Jodhpur, Rajasthan, India. From 2013 to 2020, he was a faculty member with the Department of Electronics and Electrical Communication Engineering at Indian Institute of Technology Kharagpur, West Bengal, India. Since 2021, he has been a faculty member with the Department of Electronics and Communication Engineering at Indian Institute of Technology Roorkee, Uttarakhand, India. Dr. Mohan has authored and co-authored more than 150 peer-reviewed international journals and conference papers. His research interests include the design of microwave filters, antennas, and absorbers for wireless communication systems.
Manoranjan Sinha is a Professor at Indian Institute of Technology Kharagpur, West Bengal, India, in the Department of Aerospace Engineering. He is the in-charge of Intelligent Systems Lab (ISL), which was born with a research focus on intelligent and autonomous systems with superior decision-making capabilities. He received his B.Tech. degree in Civil Engineering from the Indian Institute of Technology Delhi, New Delhi, India, in 1993 and subsequently received M.Tech. and Ph.D. degrees in Aerospace Engineering from the Indian Institute of Technology Kanpur, Uttar Pradesh, India, in 2001. In the following years, he worked as Post-Doctoral Fellow in the area of neural networks at the University of Saskatchewan, Canada, under the supervision of Prof. Madan M. Gupta and as an Assistant Professor at Birla Institute of Technology and Science Pilani, Rajasthan, India, and Indian Institute of Technology Bombay, Maharashtra, India. He joined the Department of Aerospace Engineering at the Indian Institute of Technology Kharagpur, West Bengal, India, in 2004. His research fields are neural networks, system identification, controls, flight dynamics, system health monitoring, vibration control, attitude dynamics, and formation flying.
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