Bandpass Filter and Diplexer Based on Dual-Mode Dielectric Filled Waveguide Resonators

This paper presents the designs of a bandpass filter (BPF) and a diplexer based on the TM210 mode and the TM120 mode of the dielectric filled waveguide resonators (DFWRs). The DFWR is designed by integrating a dielectric main body and a printed circuit board (PCB) cover. The PCB cover is electrically connected with the top surface of the dielectric body. For each mode, metallized blind holes can be set at its maximum electric-field points to excite or extract it and the other mode will not be influenced. Microstrip lines on the PCB are utilized to connect different pairs of the metallized blind holes to form the internal and external coupling structures. For verification, a BPF and a diplexer are designed, fabricated and measured based on the DFWRs. In measurement, the BPF is with a frequency band of 2.515 GHz - 2.675 GHz, an insertion loss of 0.6 dB, and a return loss of 20 dB. The two frequency bands of the proposed diplexer are 3.3 GHz - 3.4 GHz and 3.7 GHz - 3.8 GHz. For the two frequency bands, the measured insertion losses are 0.9 dB/0.85 dB and the isolations are better than 40 dB/50 dB.


I. INTRODUCTION
Bandpass filter (BPF) is always one of the essential and crucial components in the wireless communication systems [1]- [5]. No matter what technology is used, miniaturization is an eternal topic in the BPF designs. Since the utilization of the dual-mode resonators could reduce the filter size to a half, it has been an effective and popular method to realize miniaturization. In recent years, many single-band BPFs based on different kinds of dual-mode resonators have been reported [6]- [15]. In [6], three identical quasi-lumped structures were loaded at a microstrip ring to form a dual-mode resonator, which is used to design a second-order BPF. Similarly, a dual-mode resonator was constructed by loading four step-impedance stubs at a microstrip ring and the use of the step-impedance stubs makes the implemented BPF with wide stopband performance [7]. The stub-loaded half-wavelength microstrip The associate editor coordinating the review of this manuscript and approving it for publication was Qi Luo . resonators also feature the dual-mode characteristics and have been widely utilized to design BPFs with compact sizes [8]- [10]. Although the above dual-mode resonators based on the microstrip technology merit compact size and light weight, their low quality factors usually make the designed BPFs with high losses. The dual-mode resonators with high quality factors have been proposed to design the BPFs featuring extremely low loss, such as the metal waveguide cavity (MWC) [11], [12] and the dielectric resonator (DR) [13]- [16]. However, these two kinds of resonators are heavy due to the employment of the metal cavities. For the applications in the 5G communication systems, the BPF is required to own a low loss and a light weight at the same time. Accordingly, the microstrip resonators, the MWCs and the DRs can no longer fulfil the requirements of the 5G applications. Dielectric filled waveguide resonator (DFWR) emerges as the most promising selection because of its merits of low loss and light weight [17]. Therefore, it is necessary and crucial to proposed dual-mode DFWRs to design miniaturized single-band BPFs.  Diplexer, which is also crucial in wireless communication systems, is usually composed of two BPFs with different working frequency bands. The diplexers based on different kinds of dual-mode or triple-mode resonators have been reported [18]- [25]. In [18], the dual-mode microstrip ring resonators were applied to design a diplexer with two close channels, where an open-ended stub was used to realize the impedance matching. One stub-loaded microstrip resonator could be used to split the signals to two different channels constructed by the resonators with different resonant frequencies, forming diplexers without extra matching circuits [19]- [21]. This idea was recently applied to designing the coaxial diplexers with the characteristics of low loss and high isolation [22]. Other dual-mode resonator with high quality factors, such as the MWC [23] and the DR [24], were also utilized to design the low-loss diplexers. Similar to the BPFs, the microstrip diplexers own high losses, while the diplexers by using the coaxial resonators, the MWCs or the DRs were heavy. Therefore, it is also important to design light and low-loss diplexers by using the promising DFWRs.
In this paper, the TM 210 mode and the TM 120 mode of the DFWR is studied and applied to the BPF and diplexer designs. According to the electromagnetic field distribution of the two modes, metallized blind holes are set at the maximum electric-field points of each mode to excite or extract the corresponding mode without influencing the other mode. A printed circuit board (PCB) is electrically connected with the top surface of the dielectric body, forming the DFWR. The microstrip lines on the PCB connect the metallized blind holes so that different types of coupling structures are constructed. For a square DFWR, the two modes are degenerate and an internal coupling structure between them is proposed for the dual-mode BPF designs. A fourth-order BPF is designed with a frequency band of 2.515 GHz -2.675 GHz by using only two square DFWRs. For a rectangular DFWR, the two modes are separated from each other and utilized to design a diplexer, whose two frequency bands are 3.3 GHz -3.4 GHz and 3.7 GHz -3.8 GHz, respectively. The designed BPF and diplexer are fabricated and measured for verification. For the BPF, an in-band insertion loss of 0.6 dB and an in-band return loss better than 20 dB are obtained. Its size is about 30% smaller than the BPF using the fundamental mode. For the diplexer, the measured insertion losses are around 0.9 dB and the isolations are better than 40 dB for both frequency bands.

II. BPF BASED ON DUAL-MODE SQUARE DFWRS A. MODE ANALYSIS
The DFWRs can be in various shapes, such as square, rectangle, circle and so on. Fig. 1 shows the diagram of the square DFWR. The dielectric material of the DFWR is with a relative permittivity of 20.3 and a loss tangent of 1.5×10 −4 . The outer surfaces of the DFWR are metallized by plating silver. The TM 210 mode and the TM 120 mode are found to be degenerate and closest to the fundamental TM 110 mode. If the edge a of the square DFWR is 26 mm, the resonant frequency of the TM 110 mode is about 1.8GHz, while the resonant frequencies of the TM 210 mode and the TM 120 mode are around 2.6 GHz. It means that a dual-mode DFWR employing the TM 210 mode and the TM 120 mode is about 30% smaller than two singlemode DFWRs using the TM 110 mode. For a given order, therefore, the BPF using the proposed dual-mode DFWR will be about 30% smaller than that using the single-mode DFWR. The electric-field distributions of the TM 210 mode and the TM 120 mode are shown in Fig. 2. It can be seen that the two maximum electric-field points of each mode are located at the quarter and three-quarter positions along the center line. Besides, the maximum electric-field points of the TM 210 mode correspond to the nearly-minimum electric-field points of the TM 120 mode and vice versa. The metallized blind holes can be set at the maximum electric-field points to independently excite or extract the two modes. As shown in Fig. 3, the positions namely A1 and A2 are for the TM 210 mode, while those named as B1 and B2 are for the TM 120 mode.

B. COUPLING STRUCTURES
Based on the above-mentioned metallized blind holes, two coupling structures, i.e. the internal coupling structure between the two modes of a single DFWR and the external coupling structure between two adjacent DFWRs, are proposed for the BPF designs.
As shown in Fig. 4, a piece of PCB is stacked on the DFWR and they are electrically connected by soldering. The substrate of the PCB is the Rogers 4003C with a relative permittivity of 3.55 and a thickness of 0.813 mm. Two metallized blind holes are set on the top surface of the DFWRs A length of microstrip line connects the two metallized blind holes, providing an internal coupling path between the TM 210 mode  and the TM 120 mode of the DFWR. This internal coupling is related not only to the width of the microstrip line but also to the depth of the metallized blind holes.
The external coupling structure between two adjacent DFWRs are exhibited in Fig. 5. It is also realized by utilizing a length of microstrip line to connect two metallized blind holes for the TM 120 mode. Similarly, the width of the microstrip line and the depth of the metallized blind holes will also be the main parameters those control the external coupling.

C. DUAL-MODE BPF DESIGN
A fourth-order BPF is constructed by two dual-mode DFWRs, as shown in Fig. 6. In Fig. 6, kh 1 , kh 2 , kh 3 and kh 4 are the depths of the corresponding metallized blind holes, while cx 1 , cx 2 , cy 1 and cy 2 define their positions. Its working principle is described as follows. Firstly, the TM 210 mode will be excited in the DFWR 1 through Port 1. Secondly, the TM 210 mode will be coupled to the TM 120 mode by the internal coupling structure. Thirdly, the TM 120 mode will be coupled from DFWR 1 to DFWR 2 through the external  coupling structure. Then, in DFWR 2, the TM 120 mode will be coupled to the TM 210 mode by the internal coupling structure. Finally, the TM 210 mode will be extracted from the DFWR 2 through Port 2. Accordingly, the coupling route of the proposed fourth-order BPF is as shown in Fig. 7. The M SL in Fig. 7 represents the source-to-load coupling that is caused by the parallel microstrip lines at the two ports. This coupling is much smaller than the main couplings. Therefore, it will generate two transmission zeros far away from the passband and will only slightly influence the passband performance. Moreover, the simulated un-loaded quality factor of the DFWR is about 1200, which is large enough to obtain low insertion loss.
The target BPF is required to own a center frequency of 2.594 GHz, a fractional bandwidth (FBW) of about 6%, and an in-band return loss of 20 dB. According to the coupled   resonator theory [26], the following steps could be conducted to design the target BPF.
1. Based on the specifications of the BPF, the normalized coupling matrix can be synthesized as where the negative values represent the capacitive couplings and the positive values are the inductive couplings.   (1), the external quality factor (Q e ) and the couplings can be calculated to be

According to
3. To determine the desired Q e and coupling coefficients, they are extracted for the corresponding physical parameters. The Q e changes after the depth (kh 1 ) of the metallized blind hole for feeding, as plotted in Fig. 8.
4. Based on Fig. 8, kh 1 is defined to be 5.2 mm to obtain the desired Q e in (2). To maintain the symmetry of the DFWR, kh 2 , kh 3 and kh 4 are all fixed to be 5.2 mm for simplification. 5. Fig. 9 and Fig. 10 indicate that both the internal and external couplings vary after the widths of the connecting microstrip line. Accordingly, c w1 and c w2 can be determined to be 2.6 mm and 0.65 mm so that the desired main coupling coefficients in (3) can be realized, respectively. Because the source-to-load coupling is much smaller than the main couplings, it is not considered in the design.
6. The fourth-order BPF is constructed and simulated in the ANSYS Electromagnetic Simulator. After a simple fine-tuning process, the optimized physical parameters are attained and listed in Table 1. The simulated and synthesized results are shown in Fig. 11, in which good agreements are observed.
In simulation, the boundary conditions of the proposed BPF are set to be as consistent with the practical boundary  conditions as possible. The metal surfaces of the DFWRs are set to be silver. The metal surface of the PCB is set as cooper. An air-filled radiation boundary condition, which is also known as an absorbing boundary condition, is set at the top of the PCB.

III. DIPLEXER BASED ON RECTANGULAR DFWRS
The TM 210 mode and the TM 120 mode of the square DFWR used in the last section have the same resonant frequencies.
If the DFWR becomes rectangular, the two modes will split from each other. In this section, the rectangular DFWR will be applied to the diplexer design.
The electric-field distributions of the TM 210 mode and the TM 120 mode of the rectangular DFWR are similar with those of the square DFWR. The difference is that the resonant frequencies of the two modes are split due to the change of the dimensions. As shown in Fig. 12, the positions A1 and A2 are for the TM 210 mode, while those identified as B1 and B2 are for the TM 120 mode. For a diplexer, there should be a common port that can excite both modes to support the two channels. A metallized blind hole at the positions C1, C2, C3 or C4 could achieve this function.
The proposed DFWR diplexer is shown in Fig. 13, where five DFWRs are employed. Among them, DFWR 1 is shared by the two channels. To excite both the TM 210 mode and TM 120 mode of shared DFWR 1, a metallized blind hole should be set at the positions C1, C2, C3 or C4 in Fig. 12.  DFWR 2 and DFWR 3 are to support one channel, while DFWR 4 and DFWR 5 are to support the other channel. Its coupling topology is given in Fig. 14. The design process of the diplexer is similar to that of the BPF. The main difference lies in the control of the Q e s for the TM 210 mode and the TM 120 mode of the common DFWR. The extracted Q e s for both modes are plotted in Fig. 15, where the position parameters dx and dy are defined in Fig. 12. The depth of the corresponding metallized blind hole is fixed in the extraction. For the TM 210 mode, the Q e enlarges when dy increases and reduces when dx increases. For the TM 120 mode, the Q e almost remains unchanged when dy changes but enlarges when dx increases. Therefore, the Q e s for the two modes can be controlled independently. Moreover, the depth of the metallized blind hole could also be an alternative of adjusting the Q e s for both modes.
A third-order diplexer with two frequency bands of 3.3 GHz -3.4 GHz and 3.7 GHz -3.8 GHz is designed. Fig. 16 plots the simulated and synthesized results of the designed diplexer. As it can be seen, the isolation of the upper channel is about 45 dB, which can be improved by generating a transmission zero. As shown in Fig. 17, two microstrip lines attached at the microstrip lines in the coupling structure are  employed. As a result, the isolation of the upper channel is improved to be better than 60 dB, as shown in Fig. 18.

IV. MEASUREMENT AND DISCUSSION
For verification, the designed BPF and diplexer are fabricated, assembled and measured. The measurement is conducted by the Agilent N5230C vector network analyzer. Fig. 19 shows the photographs of the fabricated fourth-order BPF. The measured and simulated results are shown in Fig. 20, where good accordance is observed. In measurement, the working frequency band is from 2.515 GHz to 2.675 GHz.   The in-band insertion loss is around 0.6 dB and the in-band return loss is better than 20 dB. The comparisons of the proposed dual-mode BPF with previous prototypes are outlined in Table 2. As compared with the reported PCB dualmode BPFs, the proposed one features much smaller in-band insertion loss and better in-band return loss. Although the in-band insertion loss of the proposed BPF is at the same level as the MWC or DR ones, it features lighter weight and compacter size because no metal cavity is employed. In a word, the proposed BPF using dual-mode DFWRs features a small insertion loss, a light weight and a medium size simultaneously.   The photographs of the fabricated DFWR diplexer are given in Fig. 21. Fig. 22 plots its measured and simulated results. In measurement, the frequency bands of the two channels are 3.3 GHz -3.4 GHz and 3.7 GHz -3.8 GHz, respectively. The measured insertion losses in the two channels are found to be 0.9 dB and 0.85 dB. The measured isolations are 40 dB and 50 dB for the lower and upper channels, respectively. Discrepancies between the simulated  and measured results are observed. It is mainly because that the angle α in Fig. 21(a) is slightly bigger than 90 • . The performance of the proposed DFWR diplexer is compared with the reported diplexers in Table 3. It can be summarized that the proposed diplexer owns a low insertion loss and a light weight at the same time since the DFWR technology is used. Besides, its isolations are also excellent for many practical applications.

V. CONCLUSION
In this paper, the TM 210 mode and the TM 120 mode of the DFWRs are investigated. Metallized blind holes are set at the maximum electric-field points of the two modes so that each mode can be excited or extracted independently. A dualmode BPF is realized by using the square DFWRs, where the number of the resonators used can be reduce by half. Besides, the rectangular DFWRs are utilized to design a diplexer. Both the proposed BPF and diplexer own a low loss and a light weight simultaneously, making them the promising candidates for the basestation applications in the 5G and future wireless communication systems.