Highly-Miniaturized Dual-Mode Bandpass Filter Based on Quarter-Mode Substrate Integrated Waveguide With Wide Stopband

This paper presents a novel design of a highly-miniaturized dual-mode bandpass filter (BPF) employing a quarter-mode substrate integrated waveguide (QMSIW). The QMSIW resonator is based on a square cavity with metallic vias along two sides, and open-ended edges at the remaining sides that contain orthogonal feed lines. An open slot is introduced along the two sides of the square cavity with metallic vias to form a magnetic wall. A single metallic via is assigned at the corner of the two open-edged sides to form an electrical wall, which produces different resonances. By loading a slot diagonally, the mode frequencies can be controlled independently, which allows us to realize a second-order BPF. The detailed design steps and a flowchart explaining the filter’s topology evolution are presented. The eigen-mode analysis, field distributions, coupling matrix, and full-wave simulation of the proposed QMSIW filter topology are used to determine the filter’s operating principle. To verify the proposed theory, a second-order BPF is realized, fabricated, and demonstrated experimentally. The BPF prototype exhibits excellent performance such as a small footprint of $0.019\lambda ^{2}$ , a wide passband of 34.8-percent, low insertion loss of 0.43 dB, and a wide stopband of $3.36f_{0}$ with a rejection level greater than 20 dB. Excellent consistency is found between the EM-simulated and measured responses of the device.


I. INTRODUCTION
Reduced-size high-performance bandpass filters (BPFs) with transmission zeros are critical in the development of modern wireless systems. Due to their advantageous features such as high quality factor, low loss, easy integration, and low cost, substrate integrated waveguides (SIWs) have attracted considerable attention in the recent years [1]- [2]. The SIW technology has been successfully applied to realize various BPFs [3]- [25]. A miniaturized BPF based on the SIW loaded with complementary split-ring resonators (CSRRs) has been designed in [3]. In [4], a three-pole BPF filter has been devised using a SIW triplet structure with frequency The associate editor coordinating the review of this manuscript and approving it for publication was Dušan Grujić . dependent cross-coupling. A wideband BPF using U-slotted SIW cavities has been designed in [5]. In [6], a three-pole BPF with controlled transmission zeros has been designed using a dual-mode circular SIW cavity. It has been found that bandpass filters based on full-mode SIW, therefore occupying larger areas, are not suitable for modern compact wireless systems. In order to reduce the size, half-mode SIW cavities are employed, whereas further size miniaturization can be achieved by applying quarter-mode SIW (QMSIW) cavities [7]- [15]. Especially, at low operating frequencies, the QMSIW could be a valuable solution for size-reduced filters of high performance.
Quarter-mode SIW cavities have been illustrated for the development of higher-order bandpass filters in [7]. In [8], half-mode SIW and co-planar waveguide (CPW) resonators VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ have been combined to realize an extended-doublet topology.
In [9], multi-layer full-mode SIW square resonators have been employed to design a filter. In [10], a multi-layer dualmode SIW has been used for the realization of the balanced filter. In [11], a bandpass filter has been designed based on a dual-mode SIW cavity with capacitive patches etched on the top conductor. In [12], a half-mode SIW (HMSIW) rectangular resonator with dual-mode characteristics has been employed for the development of a dual-band filter. A half-mode SIW cavity has been applied to design a dual-mode bandpass filter with two poles and two zeros [13].
In [14], dual-mode bandpass filters have been implemented based on full-mode SIW rectangular cavities. In [15], dualmode SIW filters with in-line ports have been realized featuring flexible responses. In [16], a third-order SIW lossy filter has been proposed based on complex coupling. In [17], two dual-mode, and one standard SIW cavities have been applied to design a five-pole filter. In [18], a hybrid topology has been developed using a dual-mode SIW and two CPWs to realize fourth-order BPFs. In [19], a tripleorder BPF has been proposed by employing the eighthmode SIW (EMSIW), and the QMSIW cavity. In [20], multi-layered dual-mode SIW with orthogonal feeding has been applied to design a wideband BPF. In [21], a miniaturized BPF with a wide stopband response has been developed using a mix of QMSIW and EMSIW cavities.
In [22], multi-layered SIW cavities have been employed to construct a BPF with a large upper stopband response. A wide stopband SIW filter has been obtained using a modified mode suppression approach in [23]. The use of dual-mode SIW rectangular cavities to create box-like BPFs with wide stopband response has been proposed in [24]. The combination of microstrip technology and SIW cavity has been used to build a compact BPF with a wide stopband response in [25]. Although size miniaturization has been achieved by using HMSIW/QMSIW, further and significant size reduction may be possible while retaining a high overall performance, based on the QMSIW cavity.
In this paper, a novel miniaturized second-order bandpass filter with low loss and wide stopband using QMSIW square cavity is proposed. A dual-mode resonance is realized by introducing a ring slot along the metallic vias, and a diagonal ring slot, which enables the design of a second-order Chebyshev filter. The eigen-mode analysis, coupling matrix, and electromagnetic simulation of the presented circuit are provided. The filter features compact size, low insertion loss, wide bandpass, and broad stopband rejection. In addition, two transmission zeros are realized by means of the diagonal ring slot, and a single metallic via. For the sake of demonstration, a compact size second-order BPF with wide bandpass, and low insertion loss is fabricated and experimentally validated. Figure 1 shows the proposed second-order filter topology, which consists of a square cavity, an open slot, a single metallic via, and a diagonally slot. A step-by-step design evolution of the filter topology has been shown in Fig. 2. First, a full-mode SIW (FMSIW) cavity operating at TE 110 mode is designed. The FMSIW is then divided into foursections, each called a quarter-mode SIW (QMSIW). Second, two orthogonal microstrip lines are used for feeding the QMSIW cavity. Subsequently, an open slot is introduced on the top of the QMSIW cavity to form a magnetic wall (MW). Next, a single metallic via is placed at the corner of the two open-edged sides to form an electric wall (EW). The open slot and the single metallic vias produce different mode resonances. Finally, a slot is inserted diagonally on the top of the QMSIW cavity to control the mode resonance frequencies, which allows for synthesizing a second-order BPF. Additionally, the electromagnetic leakage is prevented by the use of the ring slot and a single metallic via. The resonant frequency of the proposed QMSIW can be expressed as [2] f QMSIW mn0

II. DESIGN PROCEDURE
In order to reduce the leakage loss, the diameter d 1 and the distance S between the vias are chosen based on the conditions d 1 /λ ≤ 0.1 and d 1 /S ≥ 0.5 [2]. The eigen-mode solver is used to illustrate the different resonance modes. Figure 3 shows the E-field distributions of the QMSIW cavity without perturbation for different modes (TE 110 , TE 210 , and TE 120 ). It can be noted that the maximum field strength is   observed at the center, the middle of the open-edge sides, and a diagonal position for the TE 110 mode, TE 210 mode, and the TE 120 mode, respectively.. Figure 4 shows the E-field distribution of the proposed QMSIW filter for different modes (TE 110 , TE 210 , and TE 120 ), which are obtained by employing the eigen-mode solver. It is observed that the E-field distributions of the proposed QMSIW filter for TE 110 and TE 120 modes are different from the TE 110 and TE 120 modes of the QMSIW cavity without perturbation as shown in Figs. 3(a) and (c), respectively. On the other hand, the proposed QMSIW filter barely changes the E-field distribution for TE 210 mode due to the diagonal VOLUME 10, 2022 slot, which is placed at the null electric field of this mode as depicted in Fig 4(b). Figure 5 shows the surface current distribution for the three resonant modes (TE 110 , TE 210 , and TE 120 ). By introducing a diagonal ring slot, the resonant mode frequencies can be controlled independently. To demonstrate the influence of the slot, the variation of mode frequencies as a function of the slot length L c has been depicted in Fig. 6. Referring to Figs. 5(a) and 5(c), the surface current distributions for TE 110 and TE 120 modes are perpendicular to the diagonal ring slot, which results in a reduction of the resonant frequencies. From Fig. 5(b), it can be observed that the surface current distribution for TE 210 mode is parallel to the diagonal ring slot so that the ring has little influence on the TE 210 mode frequency. The resonant frequencies for the TE 110 and TE 120 modes are decreased by increasing the length of the diagonal ring slot, whereas a flat line is seen for the TE 210 mode. This feature helps to realize a second-order BPF by bringing the TE 110 and TE 120 modes closer, while shifting the TE 210 mode higher in frequency to achieve a wide stopband response.
The required source and load external quality factors Q S and Q L , and the coupling coefficient K i,i+1 can be extracted as follows [27] And where ω 0 and ω ±3dB are the center frequency and the 3dB bandwidth, respectively. f m1 and f m2 are defined as the mode frequencies. The bandwidth of the filter can be controlled by the length of the diagonal slot. The unloaded quality factor Q u can be computed by means of the eigen-mode analysis considering the total losses contributed due to the dielectric loss, conductor loss, and radiation loss.
For validation, a second-order Chebyshev filter centered at f 0 of 1.03 GHz with a passband ripple of 0.0218 (|S 11 | = −23 dB) and the fractional bandwidth of 14.6% is designed. According to [27], its lowpass filter parameters are defined as g 0 = 1, g 1 = 0.5521, g 2 = 0.4791, and g 3 = 1.0735. The external quality factor, the coupling coefficient, and the coupling matrix are calculated as [27]: Q S = Q L = 7.3, Q S , Q L , and K 12 are controlled by the length of the diagonal ring slot and the single metallic via. The proposed filter is realized using a quarter-mode cavity to ensure size reduction. The BPF is designed on a 0.8-mm-thick RT/Duroid 5880 substrate (ε r = 2.2, tanδ = 0.0009). The unloaded quality factor Q u of the QMSIW cavity resonator is calculated as 507.6 at the fundamental mode. The equivalent LC circuit models are generated for the proposed QMSIW filter as shown in Figure 7. The QMSIW cavity is treated as two-wire transmission-lines loaded with metallic vias, which are modelled as shunt inductors L v1 . The electric and magnetic couplings at the feed-lines are modelled as C c1 and L c1 . The QMSIW with the slot resonator is represented as shunt connected LC resonator (L sr and C sr ) with their mutual electric and magnetic couplings represented by C c2 and L c2 . This equivalent circuit is a simplified version, which is validated using the Keysight ADS simulator. Figure 8 shows the S-parameters obtained from the equivalent circuit model, coupling matrix and EM simulation. An identical response is observed in the passband and the stopband window. Two transmission poles are produced in the passband with a return loss of greater than 23 dB and insertion  loss better than 0.41 dB. In addition, two transmission zeros (TZs) are obtained at 2.06 GHz and 2.44 GHz due to the ring slot, and a single metallic via, which enables wide stopband response. It is observed that the transmission zeros can be controlled by the mutual and input couplings at frequencies: Figure 9 shows the variation of coupling coefficient (K 12 ) versus width (W c ) of the diagonal slot. The EM simulation is used to extract the coupling coefficients in the case of weak couplings in the transmission characteristic. It can be observed that the coupling coefficient decreases with the increase in the slot width. The variation of the external coupling coefficient (Q e ) is determined by varying the parameter L e as shown in Fig. 10. From the figure, it can be noted that the external coefficient Q e decreases as L e increased. Based on the above theoretical investigations, VOLUME 10, 2022  a detailed synthesis flowchart is provided for the realization of a highly-miniaturized second-order BPF applying QMSIW resonator as shown in Figure 11.

III. FABRICATION, RESULTS AND DISCUSSION
To demonstrate and exemplify the above analysis, a twopole QMSIW filter operating at 1.03 GHz has been fabricated using the same substrate material as mentioned in Section II. Figure 12 shows the photograph of the second-order filter prototype. The circuit size of the filter prototype is 0.14λ× 0.14λ (0.019λ 2 ). A vector network analyzer (Rohde & Schwarz) is used for the measurement. Figure 13 shows the EM simulated and measured S-parameters of the proposed two-pole QMSIW bandpass filters. The agreement between EM simulation and measurement data is overall excellent. However, a small deviation can be observed due to the connector loss and the fabrication tolerance. The measured operating frequency and the 3-dB fractional-bandwidth are 1.04 GHz and 34.8%, respectively. Two poles are located at 0.98 GHz and 1.08 GHz, respectively. Also, the two transmission zeros are located at 2.06 GHz and 2.44 GHz, respectively. The tested insertion loss and return loss are 0.43 dB and -22.97 dB, respectively. A wide stopband of 3.36f 0 is obtained with a rejection level better than 20 dB. Table 1 provides a comparative analysis and benchmarking of the proposed QMSIW filter with respect to the  state-of-the-art filter circuits from the literature [3]- [26]. The proposed filter exhibits the footprint area reduced by 49.8% over the smallest of the considered compact circuits (here, [26]). Compared with [3]- [26], the proposed filter achieves lower insertion loss, and a larger fractional bandwidth. Furthermore, the proposed QMSIW filter exhibits a better stopband rejection when compared with [3]- [21] and [23]- [25]. The above analysis indicates that the presented QMSIW BPF can be considered an attractive alternative over the previously reported filters.

IV. CONCLUSION
In this paper, we reported a novel design of a highly miniaturized dual-mode bandpass filter based on the QMSIW square resonator. Magnetic and electric walls are produced by placing an open slot along the metallic vias, and a single metallic via located at the corner of the two open-edged sides, which generates different mode resonances. A ring slot is etched diagonally on the top of the cavity to control the resonant mode frequencies. The working principle of the proposed QMSIW filter has been discussed in detail by using an eigen-mode solution, the coupling matrix, and EM simulation. Finally, a two-pole QMSIW filter with a wide stopband and two zeros has been fabricated and experimentally demonstrated. The circuit size of 0.019λ 2 is highly compact when compared to the state-of-the-art circuits. The measured in-band return loss and insertion loss are -21 dB and 0.43 dB, respectively. The 3-dB bandwidth of 34.8% and a wide stopband of 3.36f 0 with a rejection level better than 20 dB. Satisfactory agreement between the measured and EM simulated responses corroborates the validity of the presented design approach.