3-D Printed Slotted Spherical Resonator Bandpass Filters With Spurious Suppression

In this paper, a third-order waveguide bandpass filter (BPF) based on slotted spherical resonators with a wide spurious-free stopband is presented. The resonator consists of a spherical cavity with slots opened at the top and bottom. Compared with a non-slotted spherical resonator, the slotted resonator suppresses the two spurious modes (TM211 and TE101) whilst maintaining the fundamental TM101 mode. The unloaded quality factor of the TM101 mode is not significantly degraded. This is achieved by interrupting surface current and radiating the unwanted spurious modes with the slots. The BPF is designed at a center frequency of 10 GHz with a fractional bandwidth of 1%. Two filter prototypes are fabricated, one using metal-based selective laser melting (SLM) and the other by polymer-based stereolithography apparatus (SLA) techniques. The slots also facilitate the copper electroplating process for the SLA-printed filter. The measured results show that the average passband insertion losses of the SLM- and SLA-printed filters are 0.33 and 0.2 dB, respectively. The corresponding passband return losses are better than 22 and 20 dB. The filters demonstrate excellent passband performance and wide spurious-free stopbands up to 16 GHz with stopband rejections of over 20 dB.


I. INTRODUCTION
Microwave resonators are the building blocks of passive microwave devices such as filters and multiplexers.Rectangular and cylindrical resonators [1]- [3] have been widely used because they can be readily fabricated by using conventional manufacturing technologies.In recent years, additive manufacturing, also known as 3-D printing, has been reported in the fabrication of microwave devices.Complex geometries can be 3-D printed to enhance the performance of microwave devices [4]- [15].A good example is the 3-D printed spherical resonator with intrinsically high unloaded quality factor (Qu).In [4] and [5], spherical resonators were 3-D printed to construct waveguide bandpass filters (BPFs).The BPF in [4] exhibited a very low passband insertion loss (IL).However, the spherical resonator suffered from spurious modes spectrally close to the fundamental mode.This degraded the stopband performance of the filter.The stopband rejection was improved by using the 90°-twisted coupling geometry in [4] to minimize coupling strength of the spurious TM211 mode.Another example is the mathematically defined super-ellipsoid resonators presented in [6] and [7] showing excellent filtering performance.However, except for [6] and [7], there has been little work in spurious suppression for the filters.VOLUME XX, 2017 In this work, we focus on improving the spurious-free region of the spherical resonator BPFs.A new approach aiming to maximize the spurious suppression through slotting the cavities is presented.The spurious TM211 and TE101 modes of the spherical resonator are effectively suppressed without compromising the high Qu of the fundamental TM101 mode.This significantly enlarges the spurious-free stopband.This is achieved by interrupting surface current of the spurious modes with slots.The slots are appropriately arranged on the cavity shells to ensure that the spurious TM211 and TE101 modes are suppressed and the TM101 mode is not disturbed.The proposed method of slotting for spurious resonance suppression significantly enhances the spurious-free region as compared to the filter in [5].Application of the proposed slotting method is possible for other types of air-filled cavity resonators.In the following sections, a third-order waveguide BPF based on slotted spherical resonators will be demonstrated.

II. SLOTTED SPHERICAL RESONATORS
When an air-filled spherical resonator is fed with a rectangular waveguide, as demonstrated in [4], the first and second excited spurious modes are TM211 and TE101 modes.With a fundamental mode (TM101) at 10 GHz, the resonant frequencies of the TM211 and TE101 modes are 14.08 and 16.39 GHz, respectively.The surface current distributions of these modes are illustrated in Fig. 1.In order to suppress the spurious modes, a rectangular slot in the spherical cavity, as illustrated in Fig. 2(a), is proposed.The suppression is realized by interrupting surface current of the spurious modes with the slots, so these modes radiate.As can be seen from Fig. 1 and Fig. 2(a), the slots are along the directions parallel to the TM101-mode surface current, but intersect the currents of the spurious modes.In addition, the slots are placed in the region with a low current density for the fundamental mode, but relatively large current densities for the spurious modes.Therefore, the TM211 and TE101 modes are suppressed through radiation without significantly interfering with the TM101 mode.This is verified by investigating the responses of the resonator model in Fig. 2(a).The transmission coefficient (S21) obtained from electromagnetic (EM) simulation in CST [16] is plotted in Fig. 2(b).It is shown that the spurious resonances at 14.08 and 16.39 GHz have been effectively eliminated after the slots are introduced whilst the TM101-mode resonance is not affected.It should be mentioned that the spurious TM311 mode at 18.08 GHz has a similar current distribution with the TM101 mode.So, suppression of the TM311 mode and others beyond without affecting the TM101 mode can be difficult.
EM-simulated transmission responses of the slotted spherical resonator under different slot dimensions are graphically compared in Fig. 3.The results show that the suppression level is mainly determined by the slot length l.As the length l is increased from 9 to 13 mm, the suppression of the TM211 and TE101 modes is significantly enhanced, as ) shown in Fig. 3(a).This is because in the slotted region the current for the spurious modes is concentrated and longer slots interrupt the current more effectively.The suppression is also affected by the slot width s, as shown in Fig. 3(b), but in a much less significant way.
It is important to quantify the influences of the slots on the TM101-mode resonance.This is accomplished by simulations as follows.The loaded quality factor (QL) and unloaded quality factor (Qu) of the slotted spherical resonator in free space can be expressed as [17] 1 Here Qe is the external quality factor associated with the coupling aperture between the feeding rectangular waveguide and the resonator.Qr and Qc are the radiation quality factor and conductor quality factor, respectively.We are interested in finding Qr due to the slots for the TM101 mode and comparing it with Qc.The calculation of the quality factors of the slotted spherical resonator, with s = 1.21 mm and l = 11.91 mm, is exemplified as follows.Firstly, to find Qe we use an unslotted spherical resonator with the coupling aperture set to be 2.5 mm by 10.16 mm.In this case, we make the material a perfect electrical conductor (PEC), hence there is no radiation loss or conductor loss.From (1) this gives QL = Qe, which by simulation turns out to be 1.67 × 10 7 .Now the slotted resonator is simulated with PEC, giving a value of QL = 1.5 × 10 6  .From (1) and the previously calculated Qe, the Qr value can be calculated as 1.64 × 10 6 .Next, the material is changed from PEC to copper with an electrical conductivity of 5.96 × 10 7 S/m and the simulation of the slotted resonator produces a QL of 1.42 × 10 4 .Knowing the values of QL, Qe, and Qr in equation ( 1) allows the calculation of Qc resulting in Qc = 1.43 × 10 4 .Since Qe and Qr are at least two orders of magnitude larger than Qc, they have little influence on QL in this case.It should be noted that this calculation is only an approximation, but it is good because of the large differences in the Q values.It allows us to conclude that Qr has virtually no influence on the TM101 mode as Qc << Qr.Using the calculated Qc and Qr, the Qu value of the slotted spherical resonator is obtained from (2) as 1.42 × 10 4 .This value is very close to the Qu (1.44 × 10 4 ) of a non-slotted spherical resonator.
Using the above method, TM101-mode quality factors of the slotted spherical resonator under different slot dimensions  are calculated and plotted in Fig. 4. The simulated result shows that increasing s or l only reduces Qc and Qu by less than 1.5% over the inspected region of the dimension.This shows that negligible conductor loss is introduced from the enlarged slots.In contrast, Qr decreases by over 40%.However, it is still much higher than Qc (~10 4 ), indicating very little radiation loss for the TM101 mode.From (2), it is known that the degraded but large Qr has little effect on Qu.

III. SLOTTED SPHERICAL RESONATOR FILTER DESIGN
To validate the spurious passband suppression for BPFs using the slotted spherical resonators, a third-order waveguide filter was designed.The constituent slotted spherical resonators of the filter were configured with an inline coupling geometry as illustrated in Fig. 5 GHz are suppressed and the spurious-free stopband is greatly extended.

IV. FILTER FABRICATION
It would be very difficult to make the filter by conventional means due to the complex geometry.Therefore, additive manufacturing technology was used.To demonstrate the capability of 3-D printing, the metallic selective laser melting (SLM) and polymer-based stereolithography apparatus (SLA) were used to produce two filter prototypes.The first prototype was SLM-printed with an aluminumcopper-based alloy (92 weight percent (wt.%) aluminum, 5 wt.% copper, and 3 wt.% others) in a powder form supplied in 15-53-µm particle size.A printing orientation, as illustrated in Fig. 8(a), was selected to ensure that no metallic support is required inside the cavities.Any internal metallic support would be very difficult to remove.After the printing process was completed, the metallic support structure outside the filter was removed manually.
The second prototype was SLA-printed with an Accura Xtreme resin [18] under a printing resolution of 50 μm.The orientation for the printing is illustrated in Fig. 8(b).For SLA, it is easier to remove resin support, so that the orientation can be selected more flexibly.After the resin curing process, a 10-μm thick copper was electroplated onto the printed resin using the same process as in [4] and [5].This thickness of copper was subtracted from the filter model before the 3-D through the input and output waveguide sections for the same purpose.

V. MEASUREMENT AND DISCUSSION
The RF performance of the 3-D printed filters were measured using a Keysight network analyzer E8362C under a two-port waveguide thru-reflect-line calibration.The frequency responses at X and Ku bands were measured separately.For the Ku-band measurement, a pair of X-to-Ku-band waveguide tapers were used, and the network analyzer was calibrated at Ku band.The EM-simulated and RF-measured frequency responses of the prototype I are compared in Fig. 9, showing good agreement.The measured passband IL and RL are averagely 0.62 dB and greater than 22 dB, respectively.The IL is 0.4-0.5 dB VOLUME XX, 2017 higher than the simulated value.Assuming the IL increment is only attributed to the surface roughness of the printed alloy, this corresponds to an equivalent root mean square roughness (Rq) of about 2.5 μm.The re-simulated S21 parameter taking into account the 2.5-μm surface roughness agrees better with the measured one, as shown in Fig. 9(a).The measured Qu for the slotted spherical resonator is estimated to be 2830.The measured frequency shift (Δf) is about 0.5% and is caused by the volume shrinkage of the metal-printed cavities.Shrinkage is usually induced during the laser melting process because of the phase transformation and the contraction of solids when cooling from the solidification temperature to ambient temperature [19].The shrinkage induced a small error in the size which could be minimized by performing a structural compensation before the printing.
To further reduce the passband IL, a vibration grinding process was performed on the metal-printed filter.The fabricated filter was immersed in the vibration grinding machine tank filled with water and abrasive materials, as shown in Fig. 10(a).The inner and outer surfaces of the filter were polished.This improved the effective electrical conductivity of the 3-D printed aluminum alloy and thus decreased the associated conductor loss.The control of the polishing time was very important.Experiments showed that when the structure was grinded for too long, the improvement in the surface finish would not be as significant as at the beginning.Even worse, some critical geometries may be worn out, deteriorating the filter's RF performance.In this work, the filter was measured after 2 and 8 hours of polishing.The measured passband responses are plotted in Fig. 10(b) and compared with the one before the polishing.As can be seen, the measured passband IL of the filter is decreased with the increasing time of polishing.After 2 hours, the passband IL is reduced to around 0.5 dB.The IL is further reduced to around 0.33 dB after 8 hours, approaching the simulated IL value of 0.25 dB.Assuming all the loss is due to the roughness, the corresponding equivalent Rq is improved to 1 μm.The measured Qu of the slotted spherical resonator is improved to be 4060, about 43% higher than the value before the polishing.The measured reflection response after polishing shows little difference from the one before The EM-simulated and RF-measured frequency responses of the prototype II are compared in Fig. 11, showing much better agreement in terms of the passband IL and a negligible Δf, as compared with the metal 3-D printed prototype.In the passband, the measured average IL and minimum RL are 0.2 and 20 dB, respectively.The measured IL is only 0.05 dB higher than the simulated one.The measured Δf is as small as 0.04% (4 MHz), indicating accurate reproduction of the structure.Noteworthy is that shrinkage also occurs in SLA process and can be induced by phase transformation of the resin from liquid to solid [20].However, it is much less prominent because of the different materials and a high temperature is not involved in SLA process.As can be seen from Figs. Fig. 12 shows the loss factor in the filters calculated by (1 -|S11| 2 -|S21| 2 ).This provides information on losses due to the metal as well as the radiation.It can be seen that at the higher spurious mode frequencies the loss is very high due to the enhanced radiation.Within the passband, the loss is mainly caused by the conductor loss, and the loss (~0.2 dB) in the filter II is much smaller than the loss in the filter I (0.23-0.7 dB).This indicates a higher electrical conductivity of the plated copper than that of the aluminum alloy.Furthermore, within the passband the simulated loss difference between the non-slotted and slotted filters is less than 0.05 dB from Fig. 12(b), validating the negligible passband radiation.The impact of stopband radiation to external circuits can be mitigated by attaching microwave absorbers to the slots.The measured results of the filters with the absorbers attached show no significant difference to the one in Figs. 9 and 11 in terms of both the passband and the stopband responses.Finally, a comparison of the filters to previous related work is summarized in Table II.The filters reported here exhibit extended spurious-free stopbands compared to previous filters in [4], [5], and [8].The proposed method of slotting can be extrapolated to higher order filters with flexible slot patterns to further enhance the stopband performance.

VI. CONCLUSION
A high-Q slotted spherical resonator is proposed to suppress spurious passbands of the BPF.The spurious TM211 and TE101 modes are eliminated, and an extended spurious-free stopband (f1/f0 > 1.7:1) is realized without significantly compromising the RF performance of the fundamental-mode passband.The filters made by two 3-D printing techniques, i.e., SLM and SLA, demonstrate good process flexibility.The excellent passband performance of the fabricated filters validates the capability of the utilized 3-D printing process for microwave waveguide devices.

FIGURE 1 .FIGURE 2 .FIGURE 3 .
FIGURE 1. Simulated surface current distribution (top views) of the resonant modes in a two-port weakly coupled air-filled spherical resonator.(a) The TM101 mode.(b) The TM211 mode.(c) The TE101 mode.The parameter a is the width of the feeding rectangular waveguide's broad wall.

FIGURE 4 .
FIGURE 4. Simulated TM101-mode quality factors of a slotted spherical resonator under different slot dimensions.(a) The quality factors versus slot width s.(b) The quality factors versus slot length l.

FIGURE 5 .
FIGURE 5. A geometrical illustration of the third-order X-band BPF based on the slotted spherical resonators.(a) A 3-D view.(b) A side view (i = 1, 2, and 3 for the radius ri of the i th resonator, respectively).

6 .FIGURE 8 .
FIGURE 8. Illustrations of the orientations of the BPF models under 3-D printing, (a) for SLM printing and (b) for SLA printing.The red arrows indicate the printing direction.
9(b) and 11(b), both filter prototypes demonstrate wide spurious-free stopbands with rejections over 20 dB up to 16.2 GHz.The first spurious passband appears beyond 17 GHz.Photographs of the fabricated filters are included in the insets of Figs.9(b) and 11(b).