диафрагмированные волноводные фильтры / 5d9cef98-28d0-43f8-b1e9-a672e70c24fd

I. INTRODUCTION

Terahertz (THz) domain, loosely de ned as 100 GHz 10 THz, has great potential applications in wireless communications [1], imaging radars [2], astrophysics and planetary science. Terahertz heterodyne receivers and arrays [3], [4] have provided higher sensitivity, greater detecting speed, and large-scale mapping ability in these scienti c and practical applications. There is a recently growing interest in passive components for performance improvement of advanced terahertz instruments [1] [4], such as antennas [5], polarimeters [6], orthomode transducers [7], couplers [8], [9], twists [10] and lters [11], ect. terahertz lters, as one of the key devices, play an invaluable role in communication systems and spectrum detectors, blocking unwanted, harmonic or mirrored waves. Therefore, the development of essential terahertz bandpass lters (BPFs) with easy-packaging and high-performance is still of particular importance.

Comparing with the substrate-based microstrip lines and coplane waveguides [12] with signi cant losses in high THz

The associate editor coordinating the review of this manuscript and

approving it for publication was Giovanni Angiulli .

band, the metal sealed waveguides can exhibit advantages of low loss (high Q-factor), power handling, easy assembling and interconnection, which are preferred transmission medium to realize components and systems from W-band up to THz band [1] [11]. Because of waveguide lters working in THz band suffer from ne dimension drawback, various micro-machining technologies with high precision have been employed for fabrications, such as laser sintering [13], silicon based MEMS [14] [18] and thick SU-8 photoresists [19], [20], especially for the components working from 300 GHz and beyond. Currently an expensive clean-room and an additional metal coating process are required for such micro-machining, which makes them cost effective only for large-scale production [20]. Besides, micro-machined waveguide lters are usually dif cult to exhibit great insertion loss due to additional xtures, connection or misalignment problems [21]. Among them, two transmission zeros (TZs) were achieved based on quasi-TM110 mode elliptic cavity and speci c angle coupling [17], which are really dif cult to be implemented with general processing method.

The well-established approach for building terahertz active systems is adopting waveguides for main circuitry blocks in

FIGURE 1. Simulated resonant frequencies (f0) variation of TE101- and TE102-mode resonators as function of dimensional deviation (1d ).

combination with lithographic chips [22]. Thus, the current computer numerical control (CNC) technique is still utilized for producing terahertz waveguide components and blocks through a split-block way to strengthen physical robustness while simplify assembling and interconnection, such as the WR-3 band [11] and even WR-1.5 band [6] lters. However, the conventional coupling irises, which are indispensable in most terahertz waveguide lters, will be too accurate to acquire, degenerate the physical robustness of blocks or even increase packaging dif culty.

In this work, two 3rd-order quasi-elliptical waveguide bandpass lters working on the WR-2.2 band are evaluated based on CNC-milling. Speci c transmission zeros can be motivated based on mixed-mode exciting method and physical cross coupling. Oversized resonators and H-plane offaxis couplings without any fragile irises are fully adopted to simplify the packaging and strengthen architecture robustness. Details of designing procedures, excitation principles of transmission zeros, machining tolerance effects and performance comparisons are discussed.

II. COMPARISON OF TE101 AND TE102 RESONATORS

Large enough cavities are always desired in terahertz waveguide components, as they can permit a less stringent tolerance lead to easy the fabrication. High-order TE102-mode cavity, with almost twice area of TE101-mode one, is thus preferred for terahertz lter designs. The sensitivities to dimensional errors (1d) of both TE101 and TE102 mode resonators are calculated by using ANSYS HFSS [23], as compared in Fig. 1. The variable 1d is assumed to be simultaneously changed on three axes of the resonant cavity. It is evidently clear that TE102-mode cavities can weaken the resonant frequency sensitivity to the dimensional errors comparing with the TE101-mode ones.

The Q factors of TE101- and TE102-mode cavities with different surface roughness have been additionally simulated, as contrasted in Fig. 2. The Groiss model [24] can be used to calculate the correction factor by using the formula (1), and then the equivalent conductivity ( rough) corresponding from roughness can predict the Q properties.

FIGURE 2. Calculated unloaded quality factors of TE101- and TE102-mode resonators as function of the surface roughness ( is the skin depth at 400 GHz).

where S is the surface roughness, is the skin depth, is the conductivity. The Q factors of TE101- and TE102-mode resonators with smooth gold boundary are about 1100 and 1220 respectively, as well as will be rapidly degraded to about one half due to a 1 @400GHz surface roughness. Even if the roughness is increased up to 4 , the Q factor of TE102-mode is still larger than 600. It is obvious that Q factors of TE102-mode are always higher than TE101-mode ones with the same roughness, which is also consistent with the lter insertion loss claims. Therefore, TE102-mode resonators, that feature dimensional insensitivity and high Q factor, can be a good candidate for terahertz waveguide lters design.

III. DESIGN OF 400 GHz WAVEGUIDE FILTERS

In this section, two 3rd-order quasi-elliptical waveguide l- ters based on TE102-mode are developed according to the following speci cations:

1)Center frequency f0 400 GHz;

2)3 dB bandwidth is about 10%;

3)In band return loss better than 15 dB;

4)Insertion loss: as low as possible;

5)High out-of-band rejection.

Higher-order TE102-mode resonators with oversized cavities and H-plane offset couplings without irises are meanwhile used to build both 400 GHz lters to weaken the machining complexity in such high terahertz frequencies.

A. FILTER-I DESIGN

A 3rd-order waveguide lter (Filter-I) is initially proposed to verify the usefulness of TE102-mode resonators, as shown in Fig. 3 (a). This geometric con guration is comprised with standard WR-2.2 waveguide (a b D 0.56 mm 0.28 mm), a TE101-mode and two TE102-mode resonators. For a waveguide resonator utilizing the TE101or TE102-mode as the dominant resonance, cavity sizes (ai, li) should satisfy the following equations (2):

where a and l are width and length of waveguide resonators along the propagation direction (y-axis). Fig. 3 (b) displays the corresponding schematic diagram of the magneticeld distributions and the couplings of dominant resonances, which can help to understand this working principle. The adjacent resonators, namely R1&R2 and R2&R3, are directly magnetic couplings, which are implemented by H-plane offsetting (t12 and t23) without any fragile irises. There is a weak cross-coupling between R1 and R3 through an evanescent waveguide (w13 and l13). According to the magnetic coupling directions on the main path, this cross-coupling is turned out to be negative, as clearly pointed in Fig. 3 (b). As a result, the negative cross-coupling in this 3rd-order lter will lead to one transmission zero at the upper sideband based on the coupling matrix theory [25], [26].

Using the coupling matrix method, the lter speci cation is rst translated into coupling matrix elements, which are then transformed into physical dimensions according to the procedure developed in [25], [26]. The matrix elements including external quality factors and un-normalized non-zero coupling coef cients for this Filter-I can be synthesized as: QS1 D Q3L D 8.6, M12 D M23 D 0.097, M13 D 0.038. The extracted Qe is carry out by using the formula (3), where f0 and 1f 90 can be obtained through full-wave simulating phase and group delay responses of S11 for a singly loaded TE102-mode resonator in ANSYS HFSS [22]. Fig. 4 (a) gives the extracted Qe curve, which is a non-monotonic function of offset size (tS1) due to this higherorder TE102-mode response. Nevertheless, Qe can be adjusted by tS1. While the coef cients Mij could be roughly calculated from the formula (3), where fi and fj are extracted from the S21 responses of two off-axis coupled resonators. As can be seen clearly in Fig. 4 (b), the coupling coef cients (strengths) M12 or M23 are controlled by the off-axis coupling lengths (t12 D t23).

Based on the above discussion, the initial design geometry parameters can be obtained. Because of the frequency shifting

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FIGURE 5. (a) Top view of the 3rd-order Filter-II with dimensions marking,

(b) The magnetic field distribution of the dominant resonances in the Filter-II.

caused by the mutual couplings when three resonators are cascaded together, an additional ne-tuning optimization procedure is therefore needed to obtain the satisfactory performance based on ANSYS HFSS [22]. The nal full-wave responses of the Filter-I are shown in Fig. 9. The simulated 3-dB fractional bandwidth (FBW) is 11% and one transmission zero at the upper sideband (around 460 GHz) is clearly demonstrated. The physical dimensions of Filter-I are listed in Table 1. The vertical corners in the model have beenlleted with a 0.1-mm radius (r), which is necessary for such high frequency lter considering the non-negligible drill size, as shown in Fig 3.

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B. FILTER-II DEVELOPMENT

In order to develop a terahertz waveguide lter based on full oversized TE102-mode resonators to further simplify the machining, an additional 3rd-order Filter-II is proposed in Fig. 5 (a). Comparing with the previous Filter-I, this resonator-2 is selecting the TE201-mode resonance, and then the I/O ports are moved to the side near R2 position to enhance couplings. TE102 and TE201-mode with the same resonant frequencies can be separated according to the wave propagating direction (y-axis). Fig. 5 (b) draws the magnetic eld distributions and the couplings of dominant resonances in this Filter-II. A positive cross-coupling between R1 and R3 is demonstrated due to the magnetic transformation property of TE201-mode, and thus will produce one transmission zero at the lower sideband based on the same coupling matrix theory. The coupling matrix for this Filter-II can be synthesized as: QS1 D Q3L D 8.6, M12 D M23 D 0.087, M13 D 0.066. The Qe and Mij extracted by the similar method are shown in Fig. 4 too (blue short dotted line).

After optimization by ANSYS HFSS [22], this Filter-II response is displayed in Fig. 10. The physical dimensions of Filter-II are also listed in Table 1 for comparison. The simulated 3-dB FBW is about 8.5% and three transmission zeros on the out-of-band are produced. TZ1 is generated by the positive cross-coupling between R1 and R3. The reason of generation of two extra TZs is the concept of bypass coupling existed in the R1 or R3, which has been discussed in [27] [29]. When TE102-mode resonance in R1 is regarded as passband, TE101-mode resonance in R1 is viewed as spurious response, and the coupling window with offset size t12 is treated as output port, TZ2 will be produced [27], [28]. Moreover, TZ3 can be generated while higher order TE103-mode resonance in R1 is regarded as passband and TE101-mode resonance is considered as spurious mode [29].

C. TOLERANCE ANALYSIS OF FILTER-II

In order to analyze the performance sensitivity of Filter-II to the current CNC-milling uncertainties, a lot of simulations are carried out based on ANSYS HFSS, as shown in Fig. 6 (a-h). Changing the width (a1) of cavity R1 and the offset size (tS1) will mainly shift the TZ3 position, as exhibited in Fig. 6 (a, g). From Fig. 5 (b), the length (l1) of cavity R1 has a great in uence on the frequency response including the passband and all TZs locations. As can be seen in Fig 6(c, f), the lter performance is almost independent of the width (a2) of cavity R2 as well as the length (l13) of cross-coupling window. The length (l2) of cavity R2 can slightly adjust the TZ2, as shown in Fig. 6 (d). It is clear that TZ1 is independently controlled by the width (w13) of cross-coupling window, as given in Fig. 6 (e). Furthermore, the in uence of chamfering with r D 100 m can be neglected at such design, as obviously displayed in Fig. 6 (h). Above tolerance analyses have made clear that the current CNC machining within 10 m errors [6] [11], [29], [30] can well meet the technological requirements of this 400 GHz waveguide lter design.

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FIGURE 6. Simulated frequency response of Filter-II with 20 m tolerances.

FIGURE 7. (a) The machined half blocks integrating with straight waveguide, Filter-I and Filter-II together. (b) Photograph of the measurement setup.

IV. FABRICATION AND MEASUREMENT

It is well known that the optimum split-block alternative is in the E-plane since no surface currents of the fundamental mode are interrupted [30]. However, the E-plane split way, which will result in a higher depth-to-width ratio considering such oversized cavities, is dif cult to be applied for these folded structures. Nevertheless, if a good electrical contact in the H-plane split-block is guaranteed, some advantages such as low cost, easy alignment, high aspect ratio on the waveguide cross-section can be gained [30]. In this paper, the geometric architecture integrating with a straight waveguide having 8 mm length, Filter-I and Filter-II has been manufactured in aluminum based on the H-plane splitting along one of the broad sides by the CNC-milling technology, as shown in Fig. 7 (a). The radius of minimum drill is 0.1 mm during the milling process. It should be kept in mind that a small surface roughness must be guaranteed to achieve a good electrical contact. Gold plating with 2- m-thick is the nal step to minimize conductor losses.

Measurements of the fabricated block are carried out by the R&S R ZVA24 Vector Network Analyzer connecting

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FIGURE 10. The comparison between the measured and simulated results of Filter-II, and details of insertion loss in passband. The inside view is

E-filed distribution at 400 GHz. An equivalent conductivity of 4:1 106 (S/m) is used in simulation.

with the exception of frequency shifting. The simulated 3-dB FBW is 11% from 375 to 420 GHz, whereas the measured 3 dB FBW is 12% from 365 to 414 GHz. The measured return loss is mainly better than 15 dB, which is a bit degraded comparing to the simulation. For this actually acquired quasi-elliptical response, one transmission zero is evidently existed at about 440 GHz. The simulated E- led distribution at 400 GHz inside Filter-I has been revealed in illustration of Fig. 9, which can make clear that the TE102-mode resonances in R1&R3 serve as the passband. As the magni ed losses are at the same level in passband (as shown in Fig. 9 top), an insertion loss of about 1.5 dB and an equivalent conductivity of 4:1 106 (S/m) have been achieved in this Filter-I prototype.

C. FILTER-II RESULTS

Fig. 10 exhibits measurements together with simulations of the Filter-II. The minimum 1.5 dB insertion loss in passband has the same level with the simulation using the same effective conductivity of 4:1 106 (S/m). The simulated 3-dB FBW is 8.5% from 386 to 420 GHz, while the measured bandwidth is 9% from 376 to 412 GHz. Three TZs at around 355 GHz, 370 GHz and 480 GHz on the out-of-band are clearly observed to demonstrate the quasi-elliptical response. The characteristics (S21&S11) are matched well in full WR- 2.2 band except the frequency shifting too. The TE102-mode resonance in R1&R3 and TE201-mode resonance in R2 are monitored in 400 GHz E- led distribution.

D. DISCUSSION

There is a frequency shifting of 10 GHz (about 2.5% f0) on measured results of both lters, and that will lead to a bit wider FBWs than the expected ones. This band shifting towards low frequency is mainly due to the positive physical tolerances (less than C10 m), especially for the dimension l1, as discussed in Fig. 6 (b). Some important dimensions of the fabricated lters have been measured on the order of magnitude m using KEYENCE VHX-2000 three

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dimensional microscopic system, as listed in Table 1. From the performance comparison of two proposed lters, Filter-II has more transmission zeros at the cost of existing a spurious TE101-mode at the low 320 GHz. Both spurious response peaks at 500 GHz nearby are caused from the higher order mode resonances.

E. PERFORMANCE COMPARISON

A performance comparison between our proposed lters and some other similar reported ones is demonstrated in Table 2. It can be seen that low loss, broad bandwidth and transmission zeros have been achieved for both lters. Although the micromachining can be used to manufacture waveguidelters operating at higher frequencies [14] [19], our lters based on oversized resonators exhibit simple constructions, which can be milled by automatic drills. Comparing with the analogous lters developed by state-of-the-art CNC technologies at VDI [6] and NAOJ [33], two developed lters have comparable loss performance while owning transmission zeros. Besides, both values of losses are of the same order in magnitude through comparing with the E-plane cases in [6], [33], meaning a good electrical contact between two halves for this H-plane case. The aforementioned results have indicated that our proposed lters based on mixedmode and off-axis couplings are still suited for the delicate CNC-machining restrictions in such high WR-2.2 band.

VI. CONCLUSION

Two 3rd-order waveguide bandpass lters working on WR-2.2 band have been designed and evaluated based on oversized mixed-mode resonators and physical off-axis couplings. High performance including 1.5 dB low loss, 10% wideband and quasi-elliptical response have been achieved in two workable prototypes, which indicates that the technological requirements can still be met by the current CNCmilling for such high WR-2.2 band. Both malleable designs can also be scaled up to WR-1 band through employing the advanced CNC-milling with 850 m drill [33] and frequency band above 1 THz by using the micro-machining technologies [36], [37]. It is highly possible that such 3rd-order architectures, mixed-mode resonators and H-plane off-axis couplings would have great potential in terahertz waveguidelter designs.

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JIE WANG was born in Jiangsu, China, in 1986. He received the M.Sc. degree in signal and information processing from the University of Chinese Academy of Sciences, Beijing, China, in 2013, and the Ph.D. degree in signal and information processing from the Science and Technology on Microwave Imaging Laboratory, Institute of Electronics, Chinese Academy of Sciences, University of Chinese Academy of Sciences, in 2015.

Since 2017, he has been with the School of Electronic and Information Engineering, Nanjing University of Information Science and Technology. His research interests include radar waveform designing and processing, joint wireless communication and radar sensing, and novel radar imaging techniques, such as MIMO, OFDM, and THz SAR systems.

YUN ZHAO was born in Jiangsu, China, in 1987. She received the M.S. and Ph.D. degrees in information and communication engineering from the Nanjing University of Science and Technology, Nanjing, China, in 2012 and 2017, respectively.

She is currently a Lecturer with the Nanjing University of Information Science and Technology. Her major research interests and activities include microwave and terahertz antenna technology, design and analysis of wideband, and low-pro le antennas.

JIANG-QIAO DING was born in Jiangsu, China, in 1987. He received the M.S. and Ph.D. degrees in electromagnetic eld and THz technology from the Nanjing University of Science and Technology, Nanjing, China, in 2012 and 2017, respectively.

He is currently a Lecturer with the Nanjing University of Information Science and Technology. His research interests include the design of THz waveguide components and Schottky-based multipliers, and mixers for radio-astronomy receivers.

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