Dual-Band Dielectric Resonator Filters Employing TE01δ Mode and Degenerate HEH11 Modes

This article presents a novel dual-band bandpass filter based on cylinder dielectric resonators, where the dielectric mode TE01δ is exploited to generate the first passband, and the two degenerate modes HEH11 are used to generate the second passband. In order to achieve the needed couplings between the input/output port and the TE01δ/HEH11 modes, a probe with both a straight and a curved section is designed. The needed inner couplings between modes of contiguous cavities are instead obtained by using inductive irises and capacitive probes. A systematic design procedure is provided for achieving the center frequencies and bandwidths with large design freedoms. To validate the methods, a dual-band filter working at 2.249 GHz and 2.607 GHz with bandwidths of 32 MHz, is designed and fabricated. The Filter shows low insertion loss, high rejection and compact dimensions. Measured results demonstrate the feasibility of the proposed approach.


I. INTRODUCTION
Recently, the increasing requirement for wireless communication has bring the development of dual-mode or multi-mode transceivers or systems that can support two or more communication standards and networks.Therefore, dual-band filters have attracted many researchers' attention.
Dual-band bandpass filters in industry are often realized with two filters which share the same input and output ports, similar to the topology in [1] which uses two sets of resonators and two extra diplexing impedance matching networks, becoming redundant in circuit and bulky in dimension.Dualmode resonators like stepped-impedance resonators (SIRs) [2], stub-loaded resonators (SLR) [3] in planar forms can provide required frequency ratio between the first two modes by varying the characteristic impedances ratio and electrical length ratio, and can be used to construct dual-band filters, however, it is hard to independently control the two bandwidths, since the design freedoms for internal and external couplings are inadequate.Microstrip and defected ground structure (DGS) resonators [4] implemented on two layers of a substrate can also be used to realize two passbands.Planar technology performance in terms of losses and power handling is very low and this makes this technology not suitable for some applications, as for example in base-station RF-frontends.In such cases, the use of technologies with higher performance, as cavity resonator filter technology, is often needed.
Cavity resonators are indeed capable of high quality factors (Q factors) and high-power handling and allow a proper control of couplings, this resulting in an easy bandwidth control.In [5], a dual-band bandpass filter has been synthesized by using a transformation from lowpass to dual-band bandpass, but the filter is implemented using the dominant mode of the coaxial cavity resonators, and the passbands cannot be widely separated because the frequency space is limited by the realizable maximum coupling coefficient between every two resonators.In [6], a dual-band bandpass filter has been realized with capacitively loaded cavity resonators, but with limited freedom in controlling the bandwidths.A tripleconductor TEM dual-mode resonator has been proposed [7] and dual-band bandpass filter with low insertion loss have been designed.In [8], a so-called E-plane dual-band bandpass filter has been designed but the insertion loss is high because of the use of stripline resonators.A stepped impedance coaxial resonator has been used as dual-mode resonator for realizing dual-band bandpass response but with low freedom in bandwidth assignment [9].
Dielectric loaded cavity resonators allow for small dimensions while maintaining very high quality factors and can be exploited for low loss bandpass filters [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20] with very high power handling capability and very low frequency shift in a large temperature range.Dual and multiple resonating modes can be combined to realize single passband with sharply reduced dimension [16], [17], [18], [19], [20], and can also be exploited to obtain dual-and multi-passband, respectively [21], [22], [23], [24].In [21], a dielectric dual-band bandpass filter is realized by using degenerate TM modes, and multiple transmission zeros are realized by introducing nonresonant modes.The use of degenerated modes to obtain the two filtering bands however limits the distance between the two passbands.Triple-mode waveguide resonators and dielectric loaded cavity resonators are used respectively to realize triple-band bandpass filters with controllable bandwidths and advanced features [22].In [23], two rectangular ceramic pieces are attached together for providing two modes, used for obtaining two passbands with controllable bandwidths.In [24], two dual-mode dielectric resonators are assembled in the same cavity for realizing two passbands.In [25], dual-mode half-cut dielectric resonators are used for dual-band filter design with compact dimensions.A differential dual-band filter is realized by employing the half-TE 01δ modes of dielectric resonators which has a dielectric puck directly mounted on the metal ground.Commonly, as the resonating modes are non-periodic and not widely separated, the ability in assigning the center frequencies of waveguide and dielectric dualband bandpass filters is weaker than solutions in microstrip forms.
In this article a dual-band bandpass filter is presented by using the TE 01δ and degenerate HEH 11 modes which are commonly the lowest two modes with high quality factors.In particular, TE 01δ mode are used to obtain the lowest passband, while both degenerate HEH 11 modes are used to obtain the higher pass-band.This results in a steep rejection slope for the second passband.

II. RESONATOR STRUCTURE AND FILTER DESIGN METHOD A. DIELECTRIC RESONATOR AND RESONATOR MODES
Fig. 1(a) and (b) give the structure of traditional high-Q dielectric resonator consisting of a high-permittivity and low loss-tangent ceramic puck centered to the cavity and mounted on a low-permittivity dielectric support (placer).
Commonly, in a large value range of diameter/height ratio, the fundamental modes with lowest resonating frequencies of the dielectric resonator are TE 01δ mode and degenerate HEH 11 modes, with the electric field distributions shown in Fig. 1(c)-(e).According to the figures, the electric field distribution of the TE 01δ mode shows a circular symmetry, whereas the two HEH 11 modes are orthogonal to each other, and we refer to them as HEH 11// and HEH 11 according to their polarization directions.In Fig. 2 the resonant frequencies of TE 01δ and HEH 11 modes varying with the dielectric height H are plotted.Here the dielectric puck has a permittivity of 45 and a tanδ of about 1/16000, whereas the alumina support has a permittivity of about 10.In that figure, HEH 11 mode resonant frequency is always higher than that of the TE 01δ mode.The quality factors of the TE 01δ mode and degenerate HEH 11 modes are comparatively high among all resonating modes, making them suitable for low loss filter design.Considering H = 6.45 mm and silver-plating on the inner walls, the simulated resonating frequencies and Q-factors of TE 01δ and HEH 11 modes are:

B. INPUT/OUTPUT COUPLING SCHEMATIC
For realizing dual-band bandpass filters with independent bandwidths, the input/output coupling structures should meet the following requirements: 1) Each port should be coupled to one of the two degenerate HEH 11 modes (We take HEH 11 for example) and the TE 01δ mode.2) The two couplings can be independently controlled.3) The coupling to the other HEH 11 mode (Here it is HEH 11// mode) should be small and negligible, as traditional filter.
To fulfill all three requirements, the structure shown in Fig. 3(a) and (b) has been adopted, that, a coupling probe with a straight section of length H c and a curved section with a radius of R c and an angle of is positioned under the dielectric puck.We can observe that the straight section is parallel to the field polarization of the HEH 11 mode and the curved section is in the direction of the TE 01δ mode polarization, thus the straight and curved sections are coupled to the HEH 11 mode and TE 01δ mode, respectively.However the whole probe is perpendicular to the electric field of the HEH 11// mode, and the coupling of the probe to the HEH 11/ mode is very weak.Fig. 3(c) gives the direction relationship between the probe the mode polarizations.
Commonly we use external quality factor Q e to represent the coupling strength from a port to a certain resonating mode, and larger Q e means weaker input coupling.The Q e of a specific mode can be simulated using eigen-mode solver of Ansys HFSS [27] after loading the dielectric resonator with the probe and assigning a 50 load impedance to the coaxial port, as shown in Fig. 3(a) and (b).The simulation method strictly follows the physical definition of external Q e , and all the external quality factors of the concerned modes can be computed simualtaneously, especially helpful for the cases that the modes are close.
In Fig. 4, we give the simulated Q e curves of TE 01δ , HEH 11 and HEH 11// Modes when H c and angle vary, and the corresponding field distributions of the modes are also plotted.TE 01δ mode is mainly excited by the curved section as we can observe high electric field along the curved section but much weaker electric field along the straight section.As a result, we can see the Q e value of TE 01δ decreases when the angle increases.Moreover, the Q e decreases when H c is smaller, because smaller length of the straight section can result in larger radius of the arc, as shown in Fig. 4(a).
The HEH 11 mode is mainly excited by the straight section as we can see from Fig. 4(b) that the electric field along the straight section is stronger than along the curved section, and Q e of HEH 11 mode can be decreased when H c is increased.However, as the angle also affects the total length of the probe, larger will result in weaker voltage distribution along the straight section and decreases input coupling to HEH 11 mode.
In Fig. 4(c) we can see the Q e of HEH 11// is always several thousands and much higher than those of the other two modes, demonstrating that the input coupling to HEH 11// is very weak and even negligible by using this probe.
The position H in of the probe of course influences the couplings: The closer the probe to the dielectric puck, the stronger the couplings and smaller the Q e values.
Proper selection of H c , and H in can provide needed input/output couplings for both the two passbands, simultaneously.As can be observed from Fig. 4(a)-(c), the field distribution and the corresponding field symmetry of each mode are primarily maintained when the probe is inserted into the resonator.

C. INTERNAL COUPLING STRUCTURES
To realize a dual-band dielectric filter, we need to introduce coupling structure in every cavity for two degenerate HEH 11 modes, and coupling structure between adjacent cavities for the couplings between HEH 11 modes and between TE 01δ modes in two cavities.
In-cavity coupling can be achieved by using a coupling screw inserted from the top cover into the cavity.According to Fig. 5(a), the coupling screw is positioned along the diagonal of the squared section of the cavity to obtain the intra-coupling between the two degenerate HEH 11 modes.The field perturbation introduced by the screw splits the resonant frequency of the HEH 11 into two resonating frequencies ( f HEH11,e and f HEH11,o ), which can be computed with the eigen mode solver of Ansoft HFSS.The coupling coefficient is then calculated as: The coupling coefficient k increases when the screw length L T increases and the screw approaches the dielectric puck surface, as shown in Fig. 6(c).
The second kind of coupling structure is positioned between two adjacent cavities.According to Fig. 6(a), this coupling structure consists of a window iris with a capacitive  probe.This structure allows for the independent control of two different couplings: the coupling between TE 01δ modes and between HEH 11// modes in adjacent cavities (see Fig. 6(b)).
The capacitive probe is mounted on a Teflon support and consists of a center metal pin connecting two metal rectangular plates.It is mainly used for the coupling between the two HEH 11// modes, whose polarizations are aligned to the probe.Its contribution to the couplings between the HEH 11 modes and between the TE 01δ modes is instead negligible, because of their field distributions are orthogonal to the direction of the capacitive probe.The window iris will introduce couplings between TE 01δ modes and between HEH 11// modes, whereas the coupling between HEH 11 modes will be comparatively weak due to the field polarization, and will act as weak cross coupling, which may introduces transmission zeroes as a bonus.
In Fig. 7 the coupling coefficients of TE 01δ modes and of HEH 11 modes versus the iris width are plotted.Coupling coefficients have been calculated by using the HFSS eigen mode solver to find even and odd resonant frequencies and then by applying (1).Fig. 7(a) shows that the coupling between TE 01δ modes increases when the iris width increases, but, as expected, it remains almost unchanged when the length of the probe changes, demonstrating that the contribution of the probe is very weak.Fig. 7(b) shows that the coupling between HEH 11// increases when the length of the capacitive probe increases and when the iris width increases.Besides, a tuning screw is used for fine tuning of the coupling coefficients.Note that this coupling mechanism allows for the independent control of both couplings.
As shown in Fig. 7(c), the coupling between HEH 11 modes which are parallel in polarization is much weaker (<0.001), and can not be sufficiently increased by increasing the iris width or increasing the probe length.The curves are not smooth because the frequency difference between the even/odd HEH 11 modes is small and comparable to practical simulation errors of the frequencies.
It is possible to introduce stronger coupling between the HEH 11 modes by adding an inductive loop [28] which is close to the side wall, as shown in Fig. 8.As can be seen, the coupling increases rapidly when Lc is increasing and the loop is approaching the surfaces of the dielectric pucks.Of course, the introduction of the inductive loop will greatly affect the couplings of other modes, and reduce the width range of iris as it will occupy an area near the side-wall.ng

D. FILTER TOPOLOGY AND COUPLING MATRIX
In Fig. 9, the routing scheme of a four-cavity dual-band bandpass filter exploiting dielectric resonators is shown.In each dielectric resonator, the TE 01δ mode and degenerate HEH 11 modes are exploited to form the lower and higher passbands, respectively.The two signal paths are connected to the same input and output ports.Since the frequency separation between the two passbands is large enough, no interaction is present between the two signal paths and the two passbands can be designed separately.For the lower single-mode passband, port 1 and port 2 are coupled to TE 01δ modes of the first and last cavity, meanwhile the TE 01δ modes in two adjacent cavities are coupled directly with each other.
For the higher dual-mode passband, each port is mainly coupled to one HEH 11 mode (e,g.HEH 11 ) whose polarization is align with the coupling probe direction, as the coupling to the other HEH 11 mode is much weaker.In every cavity the two perpendicular modes are coupled.Furthermore, modes with the aligned polarizations in adjacent cavities are coupled too.The couplings between the modes with parallel polarizations (e.g., the HEH 11 modes of DR1 and DR2) are parasitic and relatively weaker and we represent the couplings with dashed lines in Fig. 9, however they will introduce cross couplings to the filter topology and introduce transmission zeros to the high passband.
Thanks to the negligible interaction between the two passbands, the coupling matrix of each band can be separately synthesized by using classic single-band bandpass filter synthesis technique [23].As an example, we consider a four-cavity dual-band bandpass filter with bands centered at 2.249 GHz and 2.607 GHz.For both passbands, a bandwidth of 32 MHz is considered.By using four cavities we obtain a 4th order filter that exploits TE 01δ modes and an 8th order filter that exploits degenerate HEH 11 modes.Coupling matrices ( 2) and ( 3), shown at the bottom of this page, implement the lower and upper passband Chebyshev response with return loss of 20 dB by omitting the parasitic and weak cross couplings in synthesis stage.
The denormalized coupling coefficients between adjacent resonators are computed from the coupling matrix coefficients by using Formula (4): obtaining the following values: The external Q factors representing the input/output couplings are instead obtained by using the (5): obtaining the following values:

A. FILTER IMPLEMENTATION AND RESULTS
A 4-cavity and 12-pole dual-band filter has been designed with the filter geometry shown in Fig. 10(a) and (b).Port 1 and port 2 are coupled to dielectric resonators DR1 and DR4, respectively, via the compounded probes shown in Fig. 4.
For the tuning of the resonant frequency of the TE 01δ mode, four ceramic disks (namely T1, T2, T3 and T4) having dielectric constant ε r = 45, mounted on alumina screws and positioned above the DRs are used.Two metal screws for each dielectric resonator (T5, T6, T7, T8, T9, T10, T11 and  T12) are instead used for tuning the HEH 11 mode resonant frequencies.
Metal screws positioned along cavity diagonals (T13, T14, T15 and T16) are instead used for realizing the internal couplings, k H  12 , k H 34 , k H 56 , k H 78 for the high passband.Couplings between modes in adjacent cavities are realized with the probes and irises, and the metal screws T17, T18 and T19 are for fine tuning of the couplings.
The filter has been manufactured and tuned with its response is shown in Fig. 11.In Fig. 11(a) the measured response is compared to the equivalent circuit response of both upper and lower passbands.As can be seen, the measured center frequencies and bandwidths match the specifications very well.
The highest insertion losses of the lower and higher band are 1.0 dB and 1.1 dB respectively, while the lowest insertion losses within the bands are instead 0.6 dB and 0.75 dB.The higher loss at the higher passband is mainly due to the larger filtering order and smaller relative bandwidth.The ILs are a little bit higher than expected, and this is probably due to the losses introduced by the lossy glue used for assembling the ceramic pucks, and by the lossy metal tuning screws.The return loss over the passbands are better than 20 dB.
As can be seen in Fig. 11(a) and (b), the rejections outside the two passbands reach values larger than 70 dB.Transmission zeros close to the higher passband increase the transition slope, making the higher frequency filter more selective.Such transmission zeros are due to two possible reasons: 1) For every two adjacent cavities, there exists a weak cross coupling (presented by dashed connecting line in Fig. 9) between the two HEH 11 modes whose field polarizations are parallel to each other, introducing transmission zeros.The cross couplings can not be independently controlled without affecting the in-line couplings, which are presented with solid connecting lines in Fig. 9, as they all the same coupling irises and capacitive probes, thus the capability of controlling the introduced transmission zeros is weak.Although there is possility of controlling the cross coupling by introducing inductive loop from the lid, as shown in Fig. 8, however the iris width will be reduced, decreasing the design freedom of TE 01δ coupling, and the design complexity will be increased.2) Frequency-dependent couplings may be generated by mixed inductive and capacitive coupling structures.The iris couplings and the probe couplings are inductive and capacitive in nature, respectively, and will cancel each other out at certain frequencies, introducing transmission zeros.In Fig. 11(b) the wideband plot of the filter response is shown.A lot of spurious passbands can be observed, which are generated by higher modes of the dielectric puck and by the couplings structure like the external coupling metal loops.The first spurious frequency due to higher order modes appear around 3 GHz, but with a transmission lower than -40 dB.Until 3.5 GHz spurious passbands appear with insertion loss higher than 15 dB.If necessary, such spuriouses can be easily removed by using a lowpass filter, which commonly has very low insertion loss.Coaxial cavity resonators may be incorporated into this design for getting broad upper stopband [30].For example, two coaxial cavity resonators working at the two passbands may be combined, acting like a dual-mode resonator, which are coupled to one port and to two modes of the first dielectric resonator, and the large spurious-free bandwidth of the coaxial resonators may be applied to the filter.
In Fig. 12 the photograph of the manufactured filter with silver-plated aluminum cavities is shown.The filter dimensions are 80 mm × 80 mm × 38 mm.

B. DISCUSSIONS
Table 1 compares this filter with some published dielectric resonator dual-band filters in performances.
Considering the obtained high performances, such as the low insertion loss and superior rejection slope, this filter has a relatively compacter structure compared to previous works listed in Table 1.The high rejection is mainly attributed to the exploiting of three modes (TE 01δ mode and two HEH 11 modes) for realizing two passbands, including a dual-mode filtering passband, while the former works only apply two modes for realizing two single-mode passbands.Moreover, the introduced multiple transmission zeros also add to the outof-band ejection.The three modes are all high-Q resonating modes, and low insertion losses are therefore achieved.
The filter structure provides enough design freedoms in controlling the center frequencies and bandwidths.The input/output coupling probes have design parameters, like the length of the straight section, the radius and radian of the curved section, enabling to achieve the required external quality factors for two passbands simultaneously.The screw on the diagonal line of a cavity can efficiently control the in-cavity coupling between two HEH11 modes.As to the coupling structure between two cavities, the width of the iris and the dimensions of the capacitive probe are the two design freedoms, enabling simultaneous control of the coupling coefficients of the TE 01δ modes and the aligned HEH 11 modes.Moreover, in every cavity, there are two metal screws and one dielectric screw, tuning all the three resonances independently.As a result, all the resonances and couplings in the topology of Fig. 9 can be independently designed and tuned, introducing fully controllable center frequencies and bandwidths.
Technical breakthrough of ceramic materials in 1970s and 1980s has result in very stable temperature performance for dielectric resonator filters [28], and the proposed filter is possible to achieve much lower frequency shift over temperature for both the two passbands than coaxial-cavity filter solutions.Considering vibration issue, the metal lines used to make the internal and external coupling structures should have considerable large diameters (at least 2 mm), and gaps between screws and resonators should not be too small, for better structural stability and for avoiding large frequency shift and return loss deterioration.In practice, the bandwidths are commonly designed with small margin, which is slightly larger than temperature frequency shift.
As the resonators are in a planar topology, all the tuning elements can be arranged on the surface of the cover lid, allowing for convenient tuning and fast fabrication.
Due to the fact, that, TE 01δ mode is always lower than HEH 11 modes in frequency, the lower passband is always single-mode filtering passband, with lower frequency selectivity than the higher passband.
From the mode chart given in Fig. 2, when changing the diameter of the ceramic puck, the center frequency separation varies from 300 MHz to 400 MHz, while the center frequencies are between 2 GHz and 3 GHz.The small passband separation perhaps is a common design limitation for all dielectric resonator dual-band filters [21], [22], [23], [24], [25], [26].
It is possible to employ more resonating modes, like HEE 11 modes and other higher-order modes, for realizing three and more passbands.For getting needed frequency distribution of the modes, the dimensions (especially the ratio between diameter and height), and even the structure of the ceramic puck need to be designed and optimized.The difficulty will be the design of coupling structures, which should provide needed coupling coefficients for all passbands.

IV. CONCLUSION
A new class of dual-band dielectric filters exploiting TE 01δ mode and degenerate HEH 11 modes has been presented.The design method together with a detailed description of the coupling mechanisms have been shown.
The new configuration allows for very compact structures, whereas the high Q-factor of the resonant modes allow for passbands with low insertion loss.A peculiarity of such filters is that the two passbands have different orders: the passband obtained by exploiting degenerate HEH 11 modes has a number of poles double than that obtained by exploiting the TE 01δ mode.A dual-band filter with two identical bandwidths of 32 MHz, 4th order lower passband and 8th order higher passband has been designed and manufactured.Measured results demonstrate the feasibility of the proposed structure.

FIGURE 3 .
FIGURE 3. Input/output coupling schematic of dual-band bandpass filter: (a) Down view; (b) side view; (c) electric field distribution of resonant modes and input coupling probe geometry.

FIGURE 5 .
FIGURE 5. Coupling structure of degenerate HEH 11 modes within a cavity: (a) Downward view; (b) side view; (c) plot of k vs length of tuning screw.

FIGURE 6 .
FIGURE 6. Coupling structure between two cavities: (a) Structure; (b) relationship between the coupling structure and the E-field distribution of modes.

FIGURE 9 .
FIGURE 9. Schematic topology of a four-cavity dual-band bandpass filter.

FIGURE 11 .
FIGURE 11. S parameters of the dual-band bandpass filter: (a) Comparison between measured and theoretical S parameters; (b) wide frequency range measurement.