Precise Design of an 11-Pole TM₀₁₀ Mode Dielectric Resonator BPF with Novel Capacitive Coupling Structures

Fan LIU, Zhewang MA, Masataka OHIRA, Dongchun QIAO, Guosheng PU, Masaru ICHIKAWA

Summary :

In this paper, a precise design method of high-order bandpass filters (BPFs) with complicated coupling topologies is proposed, and is demonstrated through the design of an 11-pole BPF using TM₀₁₀ mode dielectric resonators (DRs). A novel Z-shaped coupling structure is proposed which avoids the mixed use of TM₀₁₀ and TM_01δ modes and enables the tuning and assembling of the filter much easier. The coupling topology of the BPF includes three cascade triplets (CTs) of DRs, and both the capacitive and inductive couplings in the CTs are designed independently tunable, which produce consequently three controllable transmission zeros on both sides of the passband of filter. A procedure of mapping the coupling matrix of BPF to its physical dimensions is developed, and an iterative optimization of these physical dimensions is implemented to achieve best performance. The design of the 11-pole BPF is shown highly precise by the excellent agreement between the electromagnetic simulated response of the filter and the desired target specifications.

• Publication: IEICE TRANSACTIONS on Electronics Vol.E107-C No.11 pp.472-478
• Publication Date: 2024/11/01
• Publicized: 2024/03/22
• Online ISSN: 1745-1353
• DOI: 10.1587/transele.2023ESP0003
• Type of Manuscript: Special Section PAPER (Special Section on Recent Advances in Simulation Techniques and Their Applications for Electronics)

1.  Introduction

Dielectric resonators (DRs) are favored in modern communication systems due to their low loss, small size, light weight, and temperature-stable property. Many kinds of microwave components, such as antennas [1], [2], filters and duplexers [3], [4], as well as power dividers [5], [6] have been developed by using DRs. High-performance bandpass filters (BPFs) using DRs are crucially important in many RF front-end systems, and have been gathering continuous attentions for long years [7], [8].

The most commonly used DR BPFs are those using TE\(_{01\delta}\) mode DRs [9]-[15] and TM\(_{01\delta}\) (or TM\(_{010}\)) mode DRs [16]-[18]. The main reasons are that these single mode DRs are easy to excite and are easy to realize independently controlled couplings among DRs. Early papers reported DR BPFs with Chebyshev responses, which were simple in circuit configuration and design, but poor in frequency selectivity [9], [12], [16]. More recent papers described DR BPFs with elliptic or quasi-elliptic responses, which are better than the Chebyshev ones in terms of frequency selectivity [13], [14], [17], [18]. In the design of elliptic or quasi-elliptic BPFs, complicated circuit topologies with cross-couplings among DRs are employed in order to produce transmission zeros (TZs) and improve thereby the frequency selectivity of the BPFs. Typical coupling topologies include cascade triplet (CT) of resonators and cascade quadruple (CQ) of resonators with capacitive and/or inductive couplings [19]. Techniques on realizing cross-couplings in various types of BPFs have been described in numerous papers [20]-[30].

In recent years, the rapid development of wireless communications systems has put more severe design specifications on microwave BPFs, including very sharp passband skirt and extremely large attenuations in the stopband. To meet these requirements, high-order BPFs with multiple controllable TZs should be developed. However, this is actually a very difficult task to accomplish. The difficulty comes mainly from two aspects. First, when the order of the DR BPF, i.e., when the number of DRs is large, there are a big number of structural parameters of the filter which make both the design and tuning of the filter too complicated to achieve acceptable frequency response of the filter. Second, to realize multi-controllable TZs not only means complicated coupling topologies among the resonators, but also requires clear understanding of their coupling mechanisms and requires finding appropriate approaches to implement individual control of each of these couplings. Most previous papers reported low-order DR BPFs [13], [14], [16], [20], [29], and few publications on the successful design of high-order DR BPFs with complicated coupling topologies are available. Therefore, precise design methods of high-order DR BPFs are strongly demanded, which will not only provide guidelines for both the design and fabrication of the filters, but also shorten the development cycle of the filters, cutting thereby the cost of the products.

In our previous paper [30], we reported a design of an 11-pole DR BPF with three controllable TZs. The paper is significantly revised and extended in this article. The main revision and extension include the following two aspects.

First, a novel capacitive coupling structure is proposed in this paper, which avoids the mixed use of TM\(_{010}\) and TM\(_{01\delta}\) modes as in [30] and makes both the design and fabrication of the filter much easier. In [30], two dumbbell-shaped metal probes were used to introduce capacitive cross-couplings in two CTs of resonators and produce thereby two TZs on the lower side of passband. To enhance the capacitive coupling, a small gap should be introduced between the DR and its top metal lid. As a result, the TM\(_{010}\) mode in the DR is changed to TM\(_{01\delta}\) mode [30]. In the current paper, instead of the dumbbell-shaped metal probes, a novel Z-shaped metal structure is proposed to realize capacitive coupling between DRs in the CT structures. There is no need to introduce a small gap between the DR and its top metal lid, so TM\(_{01\delta}\) mode is avoided and only TM\(_{010}\) mode DRs are used in the BPF. Moreover, assembling difficulties of the DR BPF due to the small gap between the DRs and the top metal lid is also avoided.

Second, in this paper, a precise design method for high-order BPFs by mapping the coupling matrix to physical dimensions of BPFs is proposed and fully described through the example of an 11-pole DR BPF with three TZs. The design is shown highly precise by the excellent agreement between the electromagnetic (EM) simulated response of the filter and the desired target specifications.

2.  Specifications and Design Procedures of the BPF

The design specifications of the BPF are given in Table 1. The BPF operates at a center frequency of \(f_{0}=1.84\) GHz and is aimed at applications in mobile communication base stations. With the assistance of the commercially available simulator, CST Filter Designer 3D, it is found that a BPF with a minimum order of 11 poles and three TZs can satisfy the specifications. The coupling topology with three CT structures of the 11-pole BPF is shown Fig. 1 (a), and its theoretical response is given in Fig. 1 (b), which meet the specifications highlighted in blue and yellow. Three TZs located at 1.775, 1.784 and 1.918 GHz is required, as shown in Fig. 1 (b). The corresponding coupling-matrix of the BPF is given in Fig. 1 (c).

Table 1  Specifications of the proposed BPF

Fig. 1  (a) Coupling topology of the filter, (b) filter response satisfying the specifications, and (c) corresponding ideal coupling-matrix of the filter.

Before describing the following design process of the 11-pole DR BPFs in detail, we provide in Fig. 2 our flowchart of the design of high-order BPFs. The design procedures can be summarized in four steps.

1) Determine the minimum number of reflection poles and TZs of the filter by using a circuit simulator, e.g., the CST Filter Designer 3D, based on the design specifications. Choose the coupling topology of the BPF, and calculate its coupling-matrix, as well as the ideal synthesized response of the filter. From the coupling matrix, we obtain the external quality factors \(Q_{e}\) for the input/output structure of the filter, and the self-couplings coefficients \(m_{ii}\) and inter-coupling coefficients \(m_{ij}\) between the resonators, from which the physical dimensions of the filter can be determined as described later.

2) By using an electromagnetic simulator, e.g., HFSS, design the appropriate DR cavity according to the required cavity size and unloaded \(Q\)-factor \(Q_{u}\) at \(f_{0}\). Then, design the DRs, the I/O structure, and inter-couplings between DRs, according to the above coupling-matrix.

3) Determine physical dimensions of the BPF and simulate its response by using HFSS. Extract the corresponding coupling-matrix of the BPF from the simulated S-parameters, and compare the extracted coupling-matrix with the ideal coupling-matrix obtained in Step 1).

4) Exam and minimize the deviation of each element of the extracted coupling-matrix from the ideal one by tuning the corresponding physical dimensions of the BPF until the filter response satisfies the target specifications.

Fig. 2  Flowchart for the design of high-order BPFs.

The first step described above for the design of our 11-pole DR BPF is done readily with the assistance of the CST Filter Designer 3D, and the result is given in Fig. 1 (a)-(c). The next three steps are more important and much more difficult, and are described in detail below.

3.  Precise Design of the 11-Pole DR PBF

As stated above, from the obtained coupling matrix, we get the external quality factors \(Q_{e}\), the self-couplings coefficients \(m_{ii}\), and inter-coupling coefficients \(m_{ij}\) between the resonators. From these parameters, we will design the DR cavities, the input/output (I/O) structures of the filter, and inter-coupling structures for the DRs, and obtain finally the physical dimensions of the filter. Below are detailed descriptions of the design of each part of the BPF, as well as an iterative procedure to optimize these dimensions and achieve a BPF response satisfying the design specifications.

3.1  The TM\(_{010}\) Mode Dielectric Ring Resonator

As shown in Fig. 3, the proposed cylindrical dielectric ring with an inner and an outer radius of \(r_{h}\) and \(r_{d}\), respectively, is mounted inside a cubic metal cavity with dimensions of \(h_{c} \times w_{c} \times l_{c}\). The TM\(_{010}\) mode is selected for the filter design due to a trade-off between the cavity size and the value of \(Q_{u}\) at \(f_{0}\), as shown in Table 1. It is seen that the dielectric ring resonator is short-circuited at both its bottom and top surfaces which ensures that the TM\(_{010}\) is the fundamental mode. In the following design, the dielectric constant is chosen as 45.0 and the loss tangent \(5.0 \times 10^{-5}\). The metal cavity size is given as \(h_{c} = w_{c} = l_{c} = 22.0\) mm.

Fig. 3  Proposed dielectric ring resonator loaded cavity with a metal tuning screw. (a) Top view. (b) Side view.

The electric and magnetic field distributions of the TM\(_{010}\) mode, as obtained by HFSS, are shown in Fig. 4 (a) and 4 (b), respectively. According to the electric field, a metal screw with a radius of \(r_{s}\) and a height of \(h_{s}\) is inserted at the center of the dielectric ring resonator to adjust the resonant frequency of TM\(_{010}\) mode. Figure 5 plots the variation of the resonant frequency and \(Q_{u}\)-value of the TM\(_{010}\) mode versus the screw height \(h_{s}\) while the radius \(r_{s} = 1.5\) mm. The figure shows that when the size of the metal cavity is fixed, the increase of the height \(h_{s}\) will reduce both the resonant frequency and the \(Q_{u}\)-value of the TM\(_{010}\) mode. Therefore, the height \(h_{s}\) can be used to control readily the resonant frequency of TM\(_{010}\) mode.

Fig. 4  (a) Electric and (b) magnetic field distributions of the TM\(_{010}\) mode dielectric ring resonators form perspective view.

Fig. 5  Variation of the resonant frequency and unloaded \(Q_{u}\) versus the screw height \(h_{s}\) while the radius \(r_{s} = 1.5\) mm.

3.2  Design of the I/O Coupling Structure

The I/O coupling is implemented by mounting a short-circuited loop structure, which can improve the strength of external coupling, as illustrated by the inset of Fig. 6. It is seen from Fig. 6 that the \(Q_{e}\) reduces with the increase of the height \(h_{f}\) of the loop when other parameters are fixed. Therefore, the height of the loop can be adjusted to obtain the designated I/O coupling.

Fig. 6  Variation of the external \(Q_{e}\) versus the height \(h_{f}\) of the external coupling loop.

3.3  Design of the Inter-Resonator Couplings

The coupling topology of the filter in Fig. 1 (a) shows that the filter make use of three CTs of resonators with cross-couplings to produce three controllable TZs. The inductive cross-coupling \(m_{24}\) is used for introducing the TZ\(_{3}\) on the upper side of the passband. In this design, by adjusting the iris width and tuning screw between two adjacent cavities [7], the desired strengths of inductive coupling can be obtained to meet the requirements.

On the other hand, other two capacitive cross-couplings in Fig. 1 (a) are needed to yield two TZs on the lower side of the passband. In order to realize the capacitive cross-coupling, a Z-shaped metal connector with one end short-circuited on bottom wall and the other end short-circuited on top lid of the cavity is introduced, as shown in Fig. 7 (a). The capacitive cross-coupling can be simply achieved by the proposed Z-shaped metal connector, which obviates the need to provide special capacitive coupling devices and avoid changing the mode TM\(_{010}\) to TM\(_{01\delta }\) of the relative resonators to strengthen the capacitive cross-couplings for the required strengths in [29], [30]. Figure 7 (b) shows the coupling coefficient \(m_{57}\) as function of the gap \(g_{1}\) between the Z-shaped metal connector and resonator when other parameters are fixed. It is observed that negative values of \(m_{57}\) can be obtained, and \(m_{57}\) is decreased as \(g_{1}\) become larger. This property indicates that the proposed structure can substitute the conventional capacitive coupling devices in [29], [30]. Therefore, the capacitive coupling coefficient can be simply achieved and controlled by the proposed novel capacitive coupling structure.

Fig. 7  (a) The configuration of the proposed Z-shaped metal connector. (b) Coupling coefficient \(m_{57}\) versus the gap \(g_{1}\).

3.4  BPF Optimization and Discussion

After the above investigation, the configuration of the 11-pole DR BPF is determined and shown in Fig. 8. The initial physical parameters of the BPF are also obtained, with which, the initial response of the filter is simulated by HFSS and drawn in Fig. 9 (a). It is seen that this response is far from the target specifications. After 36 iterated simulations with combined use of HFSS and CST, the final response of the BPF is achieved as shown in Fig. 9 (d).

Fig. 8  The physical configuration of the proposed 11-pole BPF. (a) Top view. (b) Perspective view.

Fig. 9  Simulations of the proposed 11-pole CT BPF. (a) Initial design. (b) Iteration = 8. (c) Iteration = 16. (d) Iteration = 32.

A comparison between the finally optimized result and the synthesized performance of the BPF is shown in Fig. 10 (a). Here, dielectric and conductor losses of the BPF are not considered in the EM simulation. It is seen that the filter operates at 1.84 GHz with a bandwidth of 75 MHz at 20 dB. Within the passband, 11 poles are clearly observed, and the return loss is better than 20 dB. In the stopband, three TZs, TZ\(_{1}\), TZ\(_{2}\), and TZ\(_{3}\) are produced at the pre-assigned frequencies, 1.775, 1.784 and 1.92 GHz, ensuring the design specifications well satisfied. The out-of-band rejections near the lower and upper side of the passband are as large as about 120 dB and 110 dB, respectively. The EM simulated responses of the filter match very well with the synthesized theoretical responses of the filter shown by dot-lines in Fig. 10 (a).

Fig. 10  (a) Comparison between the finally optimized result and the ideal synthesized performance of the 11-pole BPF. (b) Comparison of the simulated responses of the BPF using HFSS and CST in a wide frequency range.

Finally in Fig. 10 (b), the EM simulated wideband frequency response of the BPF is given. It is seen that in addition to the above described TZ\(_{1}\), TZ\(_{2}\), and TZ\(_{3}\) near the passband, multiple extra TZs, like the TZs at 2.25, 2.5, 2.59 and 2.7 GHz are also observed due to other extra cross-couplings among the 11 resonators. These extra TZs are far away from the passband and contribute positively to improve the stopband property of the BPF, like widening the stopband and increasing the attenuations in the passband.

To verify the simulation results by HFSS, another well-known EM simulator, CST, is also used to simulate the designed BPF, and its simulation results are added in Fig. 10 (b) in broken lines. It is observed that the simulation results by HFSS and CST agree well, and this proves again our design method and the simulated response of the BPF.

4.  Conclusion

A precise design method of high-order BPFs with complicated coupling topologies is demonstrated by an 11-pole BPF having three CTs of TM\(_{010}\) mode DRs. The design includes the determination of the coupling matrix of the filter by using the circuit simulator included in the CST software, and the mapping of the coupling matrix to physical dimensions of the BPF, as well as an iterative optimization procedure to achieve best performance of the BPF. The newly proposed Z-shaped coupling structure avoids the occurrence of TM\(_{01\delta}\) modes, and simplifies significantly the design and fabrication of the filter. Three controllable TZs near the passband are obtained due to the independently tunable inductive and capacitive cross-couplings in the CTs of DRs. The EM simulated response of the 11-pole BPF shows very sharp passband skirt and extremely large attenuations in the stopband, and meets the target specifications very well.

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Authors

Fan LIU
  Saitama University,Changsha University of Science and Technology

Zhewang MA
  Saitama University

Masataka OHIRA
  Saitama University

Dongchun QIAO
  HUAWEI Technologies Japan K.K

Guosheng PU
  HUAWEI Technologies Japan K.K

Masaru ICHIKAWA
  HUAWEI Technologies Japan K.K

Keyword

bandpass filter,  dielectric ring resonator,  TM₀₁₀ mode,  cross-coupling,  cascade triplets,  transmission zero,  precise design