Miniaturized Dual-Band Dual-Mode TM-Mode Dielectric Filter in Planar Conﬁguration

This paper reports a new class of compact inline dual-band bandpass ﬁlters using TM-mode dielectric resonators in planar conﬁguration. Thanks to the employment of the dielectric-loaded TM-mode waveguide conﬁguration and the dual-mode TM 120 and TM 210 resonances, substantial size miniaturization and volume saving ( > 70%) can be obtained in comparison with conventional waveguide technology. Ad-ditionally, the planar topology of the presented concept offers highly desirable advantages for industry and mass production including the ease of manufacturing, assembly, and tuning. Furthermore, the resonating doublets and the nonresonating TM 110 mode are effectively utilized to introduce and control both inter-band and outer-band transmission zeros, advantageously increasing the isolation between the two passbands and enhancing the outer-band rejection regions. The general design procedure of the proposed ﬁlter is discussed in detail. A three-pole C-band dual-band dual-mode TM-mode dielectric ﬁlter is designed, implemented, and measured to validate the proposed conﬁguration.


I. INTRODUCTION
The Current rapid development of multi-channel/multistandard RF and satellite communications have urged the demand for more efficient, compact, and lightweight multiband payloads and subsequent filtering units. Often, those essential requirements cannot be effectively fulfilled using the conventional single-band filter structures, and more efficient multi-band designs are needed [1]. Accordingly, various dualband bandpass filters were introduced in the literature using different technologies and configurations [2]─ [12]. Whereas the majority of the presented dual-band bandpass filters are developed using compact planar microstrip and SIW structures as presented in [2] and [3], they are not favorable in satellite and high-performance communications due to the high losses and limited power handling capabilities. Therefore, high-Q and high-power compatible waveguide cavities have gained more interest in the implementation of dual-band BPFs [4]─ [6]. For example, [4] introduced a new class of waveguide dual-band bandpass filters in an in-line configuration using dual-mode TE 101 /TE 011 modes for size reduction.
However, a special milling machining is required to realize such structures, and cross-couplings cannot be introduced to generate additional transmission zeros (TZs). Folded sidecoupled dual-band dual-mode TE 11m mode elliptical cavity filters were presented in [5] to facilitate the cross-coupling and TZs' creation. Nevertheless, the proposed filters suffer from many unwanted spurious resonances and inflexibility in controlling the transmission zeros' positions. In addition to the aforementioned limitations of empty-cavity waveguide dual-band filters, more size reduction and lighter weight are still required. This motivated the introduction of more compact dual-band coaxial and dielectric-loaded waveguide filters [7]─ [12]. Work performed by [9] presented a 3rd-order dual-band filter using an open-circuited-stub-loaded quarterwavelength coaxial resonator. The bandpass filter operates at 0.9 GHz and 2 GHz bands with a single uncontrolled inter-band transmission zero. A third-order dual-band filter was introduced in [10] using dielectric resonators to offer a more compact size and higher Q u than the other configurations. However, specially customized dielectric resonators and This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ assembly processes are needed to implement the filter. Besides, the filter suffers from close spurious modes and limited selectivity due to the difficulty in the introduction and control of transmission zeros. All of these drawbacks limit the extension of the proposed dual-band DR filter to higher orders and also to use in industry.
TM mode dielectric resonators are particularly favorable in filter applications due to their substantial size miniaturization, mechanical stability, high Q u , and wider spurious-free band [13]. To take the advantage of all these desirable features with considering the limitations of the aforementioned dual-band filter structures, the authors in [11] introduced a new highly compact dual-band dual-mode TM mode dielectric filter with more than 90% reduced volume than the conventional waveguide structures. The dual-band response is realized through properly modifying the transverse doublet structure. Additionally, the coupling scheme is adjusted to move at least one transmission zero between the two passbands to enhance the inter-band isolation. However, this transversal configuration has many drawbacks including difficult tuning, sensitivity to TZs locations, and precise selection of iris locations. Additionally, since the filter is built out of separated transversal blocks, this leads to more assembly time and cost, and can also increase the related losses. Therefore, alternative dualband TM-mode dielectric-loaded configurations are required to benefit from the TM mode DR advantages and overcome the challenges of the transversal topology.
A new miniaturized C-band dual-band dual-mode TMmode dielectric filter is presented in this paper. The filter is designed in planar configuration for the purposes of easy tuning, manufacturing, and assembly. Additionally, enhanced interband isolation and outer-band rejection are realized through flexibly positioned transmission zeros. The following sections discuss the design procedure of the proposed topology and report the measured results of a three-pole dual-band dual-mode TM-mode dielectric resonator filter.

II. CONCEPT AND DESIGN A. DUAL-RESPONSE DUAL-MODE TM-MODE DIELECTRIC RESONATOR
The basic doublet block was introduced earlier in [14] and employed to design a dual-mode dielectric filter using TE mode dielectric resonators in [15]. Similarly, dual-mode TM-mode DR configurations were introduced in planar topology for miniaturized single-band fixed and tunable filters applications [16], [17]. For instance, in [17], a dual-mode filter is designed using the two orthogonal degenerate modes TM 120 and TM 210 in a single resonator structure. The resonant frequencies of the orthogonal modes are adjusted primarily through the cavity length (C L ) and width (C W ) where each mode is mainly propagating and more sensitive in a corresponding dimension. Herein, the cavity length and width are set equal in order to obtain the desired dual-mode passband (C L ≈C W ). Alternatively, the dual-mode configuration can be altered to a dual-passband response by shifting any of the degenerate resonant frequencies away from the other one as depicted in Fig. 1. This is basically done by changing the respective dimension of any of the resonant modes (C L ࣔC W ). As can be seen in Fig. 1(c), both TM 120 and TM 210 resonate at the same central frequency (4.58 GHz) when C L = C W = 26 mm, while f TM210 increases and moves away from f TM120 with the reduction of the cavity width creating a dual-band response. The separation of the two passbands is proportionally related to the ratio between the cavity length and width (C L /C W ). Similar to conventional doublet configurations [15], the input and output feeding probes are rotated to excite both modes with angles θ 1 = 45°and θ 2 = −45°, respectively. If the rotation equals to 45°, then the IO probes are coupled to both orthogonal TM 120 and TM 210 modes equally. If θ is less than 45°, then the IO probes are more coupled to TM 210 while in contrary, they'll be more coupled to TM 120 when θ is larger than 45°. θ 1 and θ 2 are related to the coupling coefficients using: The angular distance between the dielectric resonator and the IO probes (D) controls the coupling strength to both modes. Fig. 2 demonstrates a dual-response cavity using a dual-mode TM-mode dielectric resonator with three different coupling routes and S parameter responses. The H-fields of the resonating TM 120 , TM 210 , and nonresonating TM 110 modes are also included. The cavity length is set larger than the width to move f TM210 away from f TM120 , therefore, creating a dual-band response at 4.98 GHz and 4.66 GHz, respectively. Based on (1), the input probe is positioned at an angle θ 1 = 45°(M S2 = M S1 ), and the output pin is rotated to an angle θ 2 = −45°(M 2L = −M 1L ). The first path S-1-L corresponds to the lower channel (f TM120 ) and the second route S-2-L represents the upper band (f TM210 ). The blackline represents the basic dual-response configuration with Chebyshev characteristics (M S2 = M S1 , M 1L = −M S1 , M 2L = M S2, M SL = 0). Also, both inter-band and outer-band TZs can be easily introduced and flexibly controlled which provides high isolation between the two bands and also improves the out-of-band rejection level. The appearance of an inter-band transmission zero in the second case (redline) is due to phase reversal of the orthogonal modes at the output port with respect to the input side (M S2 = M S1 , M 1L = −M S1 , M 2L = −M S2, and M SL = 0). This is realized by rotating the output probe to an angle θ 2 = −135°to change the sign of M 2L . While in the third case (blueline), the bypass coupling caused by the nonresonating mode (NRM) TM 110 mode creates a pair of outer-band transmission zeros (M S2 = M S1 , M 1L = M S1 , M 2L = −M S2, M SL < 0) [11], [14]. In this case, the output pin is rotated to an angle θ 2 = −225°. All of these interesting capabilities of the proposed concept can be effectively applied to filter's configurations and will be discussed in the following sub-section.

B. DUAL-BAND DUAL-MODE TM-MODE DIELECTRIC FILTERS
The generalized coupling mechanism of the proposed miniaturized dual-band dual-mode TM-mode DR filters is depicted in Fig. 3. It is comprised of two coupling paths that are composed of directly coupled doublet blocks. Each doublet block exhibits two orthogonally resonating modes (TM 120 , TM 210 ) at two different frequencies which create a dual-passband response. Also, in particular configurations, the nonresonating fundamental TM 110 mode is employed to create a bypass source-load coupling path that introduces additional transmission zeros [18]. The general design procedure begins with the synthesis and extraction of the corresponding coupling scheme and parameters of each passband individually which has been then optimized and applied to the overall dual-band response and any additional transmission zeros [19]. The coupling matrices in this paper are extracted following simple steps: 1) A good start point is by using the standard synthesis method [20] to extract the coupling matrix of every single passband individually (f 1 , ABW 1 ), (f 2 , ABW 2 ) with an order of N/2 for each band. 2) Normalize both channels to a single-band N-order filter using the pre-synthesized values from the first step. The 1, 2, 3, ….N/2 resonators from the first and second single-band filters represent 1, 3, 5, …..N-1 path and 2, 4, 6, ….N channel, respectively, and constitute the initial coupling coefficients of the overall matrix (M i,j_0 ). The chosen channel has a centre frequency f 0 = (f 1 +f 2 )/2, and an absolute bandwidth ABW 0 = ABW 1 . Note that f 0 , ABW 0 , and normalized coupling coefficients can also be chosen arbitrarily [19]. The mutual and selfcouplings are calculated using: where Q ext_1 and Q ext_2 are the calculated external quality factors from the coupling matrices of the single-band filters from the first step. Next, the required physical coupling coefficients (K) and external quality factors (Q ext ) for the lower passband (f 1 ) and higher passband (f 2 ) are calculated using the corresponding f 0 and bandwidth (ABW 0 ) as follows: Afterward, the dual-band bandpass filter is realized using the presented dual-mode TM mode dielectric resonators.  employed with a high dielectric constant of 45 to provide more volume reduction. Considering the fields' coupling nature of the two orthogonal modes, the required dual-band response cannot be obtained with conventional coupling irises configurations because they cannot provide the required isolation between the two modes. Therefore, inductive rectangular posts are effectively employed to obtain the required inter-resonator couplings and provide bands' isolation and separation. The IO feedings are rotated to excite both orthogonal modes at the same time as discussed earlier. Fig. 4 demonstrates a 2nd-order dual-band filter of the proposed structure operates at 4.65 GHz and 4.79 GHz with a narrow bandwidth of 12 MHz at both passbands. The coupling topology and optimized matrix are provided in Fig. 4(a) following the aforementioned procedure. The simulated S-parameter responses are also included in Fig. 4(a) with excellent agreement with the required specifications. The simulated Q u for the first passband is 3440 and 3330 for the higher band. Fig. 4(b) shows the realized dual-band BPF using dual-mode TM-mode DR in planar configurations. The TM 120 mode constructs the lower passband (f 1 ) while the higher channel (f 2 ) is formed by the orthogonal TM 210 mode. As shown earlier, the separation between the resonant frequencies of the two modes is mainly controlled by the cavity length/width ratio. In this example, the two channels are closely-spaced with 140 MHz separation. The required inter-resonator couplings of both passbands (K 13 , K 24 ) are realized using common inductive irises with side and central inductive posts. The relation between the coupling coefficients (K) of TM 120 (K 13 ), TM 210 (K 24 ) channels and the central and side posts is depicted in Fig. 5. The interresonator coupling of the first passband is more controlled by the side posts (Ls) since the TM 120 mode resonates mainly in sides and it is less distributed in the centre of the cavity (see Fig. 1(c)). In contrast, the coupling bandwidth of the upper passband is more related to the central post (Lp) as the TM 210 mode is more distributed in the centre of the cavity than the sides. Furthermore, as the central post is located close to the maximum of the TM 210 mode, the post width (Wp) can be altered to push the TM 210 channel further away from the TM 120 mode passband as can be seen in Fig. 6. All these capabilities advantageously provide a more relaxed degree-of-freedom to the designers towards getting different/similar bandwidths at the two passbands with extended spacing. Tuning screws can be introduced easily and utilized effectively in this planar structure to compensate for various tolerances and retain the required response. The inter-resonator couplings of both passbands can be tuned through T4 and T5, while T1 is used to  tune the resonant frequency of both bands at the same time (frequencies will move up with tuning [17]). Furthermore, T2 and T3 can be employed to tune the lower (TM 120 ) and upper (TM 210 ) bands independently (frequencies will decrease with tuning). Similarly, T6 can be added to control the IO coupling.
The desired external quality factors Q ext_1 (TM 120 ), Q ext_2 (TM 210 ) are realized using inductive probes rotated with an angle θ . The dependence of Q ext_1 and Q ext_2 on the rotation angle of the IO probe is presented in Fig. 7. As shown, Q ext_1 of TM 120 increases with smaller angles whereas Q ext_2 of TM 210 is decreasing, and vice versa.
The introduced dual-band filter has Chebyshev outer-band response and inter-band isolation at 22 dB level. These two aspects need to be enhanced for high-performance applications. Therefore, the introduction of inter-band and outer-band TZs is importantly needed to improve the isolation between the two channels and the outer-band selectivity. [21] presented a detailed overview of the TZs' generation in multi-path coupling structures. Similarly, [22] showed that a TZ can be created between the passbands through the proper orientation of the feeding waveguides to cause a phase reversal between the signals traveling through different paths. The same concept can be employed effectively and more flexibly in  (Fig. 4). the proposed dual-band TM-mode DR filter configuration. In the original structure in Fig. 4, the input and output probes are in aligned configuration with the same angle (θ 2 =θ 1 ). The phase change diagram of the presented filter is demonstrated in Fig. 8. All couplings are inductive with reference to the corresponding coupling topology in Fig. 4. As can be seen in Table 1, the signals of both bands are in-phase to each other, hence, no inter-band transmission zero can be introduced. An inter-band TZ is generated if the output probe is rotated by 90 • for phase reversal between the two modes. Fig. 9   FIGURE 10. Outer-band transmission zeros relation to the IO feeding angle.

TABLE 1. Total Phase Shifts for the Two Paths of the Two-Pole Dual-Band Filters
depicts the phase-reversed IO configuration of the presented filter with its corresponding coupling route and simulated S parameters. As can be seen, inter-band transmission zero is effectively generated. As the output probe is rotated by 90 • , the sign of M 3L changes to negative causing the two channels to be coupled out-of-phase as shown in Table 1. Thus, a transmission zero is introduced between the two passbands enhancing the isolation to more than 50 dB. In addition to the creation of the inter-band transmission zero, the 90 • rotation of the output probe also excites the non-resonating fundamental TM 110 mode creating a source-load (S-L) coupling path (M SL = −0.0004) introducing two asymmetrical transmission zeros below and above the filter passbands at 4.1 GHz and 5.1 GHz, respectively. The introduction and control process of the transmission zeros due to the nonresonating modes are well explained in [23] at transversal TM-mode structures. In principle, multiple inter-band and outer-band transmission zeros can be introduced and controlled in the proposed planar configurations. However, this is practically challenging since the IO probes will need to be rotated close to/inside the coupling irises unlike the transversal configurations [11] where the IO feedings can be rotated freely 360 • . This limits the flexibility of controlling the outer-band transmission zeros in the presented filter. Fig. 10 shows the dependence of the transmissions zeros on the feeding angle (θ ). As can be seen, both transmission zeros are controlled towards the same direction [23]. Referring also to Fig. 7, when θ decreases, M S1 /M SL increases and M S2 /M SL decreases resulting-in a decrease in the zeros' frequencies and vice versa. To locate both TZs closer to the passbands, the transferred energy through the nonresonating TM 110 mode should increase with respect to the coupling of the resonating TM 120 , TM 210 modes [18]. A possible straight-forward option is by pushing the nonresonating TM 110 mode to a higher frequency closer to the resonating TM 120 , TM 210 modes. This can be done at the first design steps with the selection of the DR and its dimensions. Another design example of a three-pole dual-band TMmode DR filter is demonstrated in Fig. 11 to Fig. 14. The filter here is designed to operate at 4.77 GHz and 5.11 GHz with fractional bandwidths of 1.1% and 1.3%, respectively. The generalized corresponding coupling matrix is stated FIGURE 12. Phase shift diagram of the presented 3rd-order dual-band filter in phase-reversed configuration (Fig. 11).
Structures and corresponding responses of the phasereversed and in-phase configurations are demonstrated in Fig. 11 and Fig. 13, respectively. Here in these designs, the cavity length/width ratio is set larger than in the previous twopole examples to obtain wider spacing between the two passbands (350 MHz). The simulated unloaded-Q for the lower passband is 3200, while in the upper passband is 3000. Similar to the two-pole designs, inter-band and outer-band TZs can be positioned effectively by controlling the I/O orientation. Fig. 11 depicts one configuration of the proposed third-order dual-band filter with an inter-band transmission zero having a high isolation level >70 dB. As discussed earlier, the appearance of this TZ is due to the phase reversal between the  two paths of the filter as can be seen from the phase shift diagram in Fig. 12 and Table 2. Since each cavity causes a 180 • phase shift to the signals (3 × 180 • ), the output probe is rotated 90 • to keep the sign of M 5L positive. Consequently, the NRM bypass coupling is not excited and no outer-band TZs are obtained (M SL = 0). The case is the opposite in the second dual-band filter example shown in Fig. 13. When the input and output ports are aligned, the sign of M 5L changes to negative and both signals become in-phase. As a result, the inter-band transmission zero cannot be introduced. On the other hand, the NRM bypass coupling is excited and creates two asymmetrical TZs at both edges (M SL < 0 = −0.00021). Conceptually, the source-load coupling strength can be changed to control the positions of the TZs as can be seen in Fig. 14. Here, good isolation > 30 dB is obtained between the two passbands but with no inter-band TZ.
It should be noted that the design procedure and control process of the TZs of the presented 2nd and 3rd order filters extend and apply the same to all other multiples of even and odd cavities. Also, the proposed planar configuration can be utilized effectively to implement other miniaturized TM-mode DR components (e.g., diplexers, tunable filters). For example, a 3-pole ultra-compact TM-mode diplexer can be introduced by just modifying the output feeding mechanism of the proposed 3-pole dual-band dual-mode DR filter. All dimensions and passbands' specifications are the same as the dual-band filter. The only adjustment needed here is to modify the output structure to receive each channel separately unlike in the dualband configuration. This can be done easily since the TM 120 , TM 210 modes are orthogonally distributed. Then, as shown in Fig. 15, the input probe (port 1) is positioned with 45°angle to excite both modes. On the other side, port 2 is positioned at an angle (θ =0 • ) to only excite the TM 120 mode and receive only one channel corresponding to the lower passband of the dual-band filter. Similarly, port 3 is positioned orthogonally at 90 • angle to only excite the TM 210 mode and receive just the upper channel of the dual-band filter. As can be seen in Fig. 15, the passbands' specifications of the ultra-compact diplexer are ideally identical to the dual-band channels.

III. EXPERIMENTAL RESULTS AND COMPARISON
A three-pole C-band dual-band TM-mode dielectric resonator filter is manufactured and measured to validate the concept of the proposed planar configuration. A photograph of the implemented filter is shown in Fig. 16. The TM-mode dielectric resonator that has been used is an E6045 (ε r = 45, Q u = 8000 @ 5 GHz) from EXXELIA [24] with the same dimensions stated in the above section. The TM-mode dielectric resonators are then soldered in a compact metallic housing milled out of copper. Fig. 17 and Fig. 18 depict the measured responses of both the in-phase and phase-reversed configurations. Measurement results generally agree with simulations in the bandwidth specifications and the transmission zeros that have been created and controlled. A shift in the passband frequencies from simulated ones is noticed mainly due to the tuning process and uncertainty of the dielectric constant of   the DRs (100 MHz in the first passband, and 190 MHz in the upper band). The frequencies in simulations were then re-optimized to resemble the measured results. Fig. 17 shows the measured S parameter responses in comparison with the optimized simulations. The first passband operates at a centre frequency of 4.86 GHz with a 53.5 MHz of bandwidth compared to a bandwidth of 53.8 MHz in the simulated one (both at 15 dB level of S 11 ). The measured insertion loss is ≤1.1 dB and the return loss is better than 19 dB. The upper band has a  central frequency of 5.3 GHz with 77.2 MHz BW compared to 78.2 MHz of the simulated one. The mid-band insertion loss is lower than 0.9 dB and the return loss is better than 17 dB. Measurements and simulations have a good agreement in the lower passband frequency, while the measured higher passband has a slight shift of 50 MHz from simulations. This could be due to the sensitivity of this band (TM 210 ) to the central post as aforementioned, especially since the resonators are positioned very close to the central post and the cavity. Fig. 18 depicts the measurements of the implemented filter in both in-phase and out-of-phase configurations obtained by the rotation of the output probe. As can be seen, an inter-band TZ provides high isolation between the two passbands up to 60 dB in the out-of-phase case, while two outer-band TZs are introduced in the in-phase configuration. Silver-plated tuning screws (shown or located where the empty holes in Fig. 16) were added similar to those in Fig. 4(b) to tune both frequencies or each one independently, inter-resonator couplings, and the IO couplings. The extracted unloaded Q factor is better than 1040 (≈ 35% of the simulated ones). Silver-plating and larger dielectric resonators can be considered to increase the Q u up to 3000. The filter has a compact size of 41.3 × 36 × 5.9 mm 3 offering more than 70% volume reduction than the conventional waveguide structure. Fig. 19 exhibits the measured wideband response of the implemented filter. As shown, the filter has a good spurious-free band of 1.5 GHz at the lower side, 1.7 GHz to the next higher unwanted spurious frequency. Table 3 summarizes a comparison between the proposed compact inline dual-band dual-mode TM mode BPF and similar designs. The filter has a good spurious-free band ≥1.5 GHz which is better than the other configurations. Also, the proposed filter offers the advantage of effective introduction and control of inter-band and outer-band transmission zeros. Despite that the transversal configuration in [11] is able to introduce multiple inter-band and outer-band TZs, those TZs are sensitive to many parameters and cannot be effectively controlled. Contrary, the generated inter-band TZ in the proposed planar configuration is controlled just through the phase shift between the two signal paths and it is not affected by any other parameters. Additionally, whereas the structure must be folded in [5] to introduce both inter-band and outerband TZs at both sides, out-of-band rejection characteristics of the inline filters in [10] and [11] need to be improved either at one or both edges. While the presented configuration has shown the capability of obtaining and controlling inter-band and outer-band TZs at both edges to provide higher out-ofband rejections. Nevertheless, it should be mentioned that the positioning of the outer-band TZs closer to the passband is not easy and the coupling ratio of the nonresonating TM 110 mode should be considered carefully. Another attractive advantage of the proposed planar topology is that it makes the assembly and tuning process easier and more feasible than the transversal configurations resulting-in better responses and less implementation effort. Post-tuning is even more important in such designs where each of the two signals needs to properly couple and excited in the same single cavity with the same IO feedings. Advantageously, the introduced planar configuration allows the designer to introduce tuning screws to efficiently control all resonant frequencies, bandwidths, and IO couplings.

IV. CONCLUSION
A miniaturized dual-band dual-mode TM-mode dielectric filter is presented in planar configuration for the first time. The use of the TM-mode DRs and the orthogonal degenerate TM 120 and TM 210 modes effectively provide substantial compactness with high Q u and good spurious-free response. Also, high inter-band isolation and outer-band rejections are obtained through the introduction of flexibly controlled transmission zeros. The proposed planar configuration brings various advantages in comparison with the transversal configuration including easier tuning, assembly, and production. All these features strongly promote the employment of the presented planar design in other ultra-compact components (e.g., tunable filters, diplexers). A prototype has been manufactured and the measurements allow for the design approach to be verified.