I. INTRODUCTION

Terahertz (THz) wave, which is de ned from 0.3 to 3THz, has great potential in ultra-fast wireless communications, atmospheric monitoring, medical imaging, and other applications [1], [2]. As an indispensable component of front-ends in THz systems, bandpass lters (BPFs) with low insertion loss (IL) and high selectivity are desired. Due to small dimensions of THz devices, different micromachining techniques, such as low-temperature co red ceramic (LTCC) technology [3], Si deep reactive ion etching (DRIE) [4] [6], and SU-8 photoresist technology [7] [9], have been developed and reported for fabrication of THz lters. In [4], a 400GHz silicon micromachined elliptic cavity waveguide lter with two transmission zeros (TZs) on both sides of the passband is presented. The measured 3-dB fraction bandwidth (FBW)

The associate editor coordinating the review of this manuscript and approving it for publication was Lei Zhao.

is 7.52%, and the minimum IL is 2.84 dB. A micromachinedlter at 450 GHz with 1% fractional bandwidth and unloaded Q beyond 700 is also proposed in [5] recently. In [8] and [9], two WR-3 band lters using SU-8 technology have been fabricated. The measured IL is about 1.6 dB and 0.5dB, respectively.

On the other hand, with the accuracy improvement of conventional computer numerical control (CNC) milling technology, waveguide BPFs based on this technology have been extended to 700 GHz [10] and widely used in THz systems due to their advantages of lower IL, simpler fabrication and easier inter-connection [9], [11] [14]. In [9], a WR-3 band BPF with one TZ in upper sideband is presented. The measured IL as low as 0.41dB. In [11], two high-performance pseudoelliptic lters with a pair of TZs are proposed in WR-3 band. The fabrication tolerance of both lters is better than10 m, the measured 3-dB FBW is 8.77% and 9.83%, the IL is around 0.7dB and 0.5dB, respectively. A seventh-order

Chebyshev lter is introduced in [13] to achieve sharp stopband rejection. However, such high order lter will increase the IL and in uence the THz system performance.

In addition to the challenge of processing, high frequency selectivity is also a research hotspot for THz BPFs. Elliptic and pseudoelliptic lters with TZs at nite frequencies offer optimal solutions for achieving sharp cutoff skirts and low IL, simultaneously, with lower lter order. There are many approaches to realize pseudoelliptic response. In [15] [17], one or two TZs are introduced by allowing cross-coupling in cascaded doublets (CDs), cascaded triplets (CTs), and cascaded quadruplets (CQs). In [18], the concept of ``Singlet'' is rst introduced, which is a rst-order structure with one resonator and one TZ at a real frequency. Because the position of TZ can be controlled by the dimensions independently, singlet has widely used in pseudoelliptic lter design in [11], [12]. However, limited by the inherent structure oflters above, passband characteristics are quite sensitive to changes of each TZ position. Recently, an advanced synthesis technique for extracted pole is proposed in [19]. By introducing a general circuit topology, the traditional extracted pole and nonresonating node (NRN) lters can be designed precisely. However, all calculations in this paper are based on narrowband and do not consider the in uence of adjacent spurious passbands, this technique is not suitable for designing broadband lter.

In this paper, a novel THz pseudoelliptic BPF with two TZs respectively based on a singlet resonator and an extracted pole resonator is proposed. In order to realize broadband responses and high selectivity in lower stopband, a fthorder lter which is symmetry about the geometric center of the singlet is designed rst. The extracted pole resonator is then loaded at the lter terminal to improve selectivity in the upper stopband. By tuning the dimensions of these two resonant cavities, the location of TZs can be controlled independently. For demonstration, the proposed BPF is manufactured by CNC milling, and experimental results show a good agreement with the simulation ones. To the best of the author's knowledge, the proposed BPF has the highest 30dB rectangular factor with such wide fractional bandwidth compared to other THz waveguide BPFs in open literature.

II. ANALYSIS OF TRANSMISSION ZEROS GENERATION

In this paper, a THz waveguide BPF is designed based on a singlet and an extracted pole resonator to generate a pair of TZs. In this Section, mechanism of TZs generation are analyzed in detail and their position are predicted precisely.

A. THE PROPOSED SINGLET

A simple low-pass circuit model of the singlet, as shown in Fig. 1, is used to illustrate the mechanism of TZ generation. It is mainly composed of dominant resonance (R), spurious resonance (Rsp) and two separate paths. The dominant resonance is used to implement the passband characteristics, while the spurious resonance affords another bypass path for signal. b1, b2 are represented by unit capacitors in parallel

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FIGURE 1. Low-pass circuit topology of the TE301 singlet. S: Source. L: Load. R: Dominant resonance. RSP: Spurious resonance.

with constant reactance jb1 and jb2. The source and load are unit conductance jBS and jBL , respectively. According to Kirchhoff's current law, the admittance matrix [Y] of

In particular, the position of TZ (!z), which is equal to the

jb1j jb2j. jM1M2j jM3M4j, because the external quality factor (Qe) of the dominant resonance is obviously higher than that of the spurious resonance. Therefore, (2) can be simpli ed as:

For a given singlet, the sign of b2 is xed. Therefore, equation (3) illustrates that the position of TZ is determined by the signs of M1M2M3M4, which is related to the relativeeld distributions of the dominant resonance and the spurious resonance in the singlet. In conclusion, a TZ can be formed in singlet when two conditions are satis ed. 1) The dominant resonance and spurious resonance have same amplitudes. 2) Two resonances have proper relative phase for cancellation (i.e. satisfaction (3)).

The dimensions of singlet based on TE301 mode should

where a is the width of the resonator, l is the length of the resonator along the propagation direction. By changing dimensions of a and l, the position of TZ can be controlled correspondingly. In this paper, the singlet where aD1.54mm, lD0.8mm is introduced to achieve sharp cutoff skirt in low stopband. For this singlet, the reactance element b2 has a negative sign (f102 > f301). The magnetic eld distributions of TE301 mode and TE102 mode are shown in Fig. 2.

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FIGURE 2. Magnetic field distribution of the TE301 resonances and the TE102 resonances in the proposed singlet.

The tangential magnetic eld components of these two modes around input and output coupling apertures have different signs. Thus, M1M2M3M4< 0;!z < 0. According to (3), a TZ is introduced lower than TE301 resonance at 338.5GHz, as shown in Fig. 3. And the geometry of the singlet is also shown in bottom right corner in Fig. 3. Here, other resonance modes (TE101, TE103, TE302, et al.) are not analyzed because they are farther away from the fTE301 and have little effect on the passband.

FIGURE 4. (a) Two structures of the proposed extracted poles: The traditional structure (left). The proposed structure (right). (b) Low-pass prototype of the extracted poles.

which is directly related to the phase of electromagnetic wave. In this lter, we are more concerned about the extracted pole resonator equivalent as a one-half open-circuit resonator to generated TZ. When signal propagates a half wavelength along transmission direction, the re ected and incident wave are cancelled out due to their equal amplitudes and antiphases, a TZ is produced thereby. Besides, the mechanism of quarter-wavelength short-circuit resonator can be explained in this way either.

The waveguide wavelength can be calculated by:

where c is cutoff wavelength. Therefore, the upper TZ (TZ1 at 379GHz) is produced by the extracted pole resonator where aepD0.564mm and lepD0.524mm, as shown in Fig. 5. It can be seen that another TZ (TZ2 at 401GHz) are also obtained as quarter-wavelength resonators. Furthermore, this structure also has good low-pass characteristics which shows great advantages on producing TZ in upper stopband.

B. THE PROPOSED EXTRACTED POLE RESONATOR

In order to meet the high cut-off rate in upper stopband, the other TZ is produced by the extracted pole resonator, and its geometry is shown in Fig. 4(a). Compared with traditional ones, there are some small improvements to make fabrication easier. This structure can be respectively regarded as a one-half wavelength open-circuit resonator and quarterwavelength short-circuit resonator at different TZs, and both type of resonator equivalent circuit is shown in Fig. 4(b). aep controls the height of the re ecting surface and determines the correspondence between the resonator type and TZ. lep is the length of the resonator along the propagation direction,

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FIGURE 5. Simulated results of the extracted pole resonator.

III. DESIGN OF THE PROPOSED FILTER

According to the above analysis, a sixth-order lter, which is composed of an extracted pole resonator and a singlet with four TE101-mode-based resonators, is proposed using the standard techniques in [20]. Fig. 6(a) shows the whole structure and critical dimensions of the proposed lter. The initial low-pass circuit topology is illustrated in Fig. 6(b). In this design, R1-R2-Singlet-R4-R5, which is symmetry about the

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FIGURE 6. (a) The structure of the proposed filter. The critical dimensions of the proposed filter are listed as: l1 D l4D0.355mm, l2 D l3D0.368mm,

t1 D t6D0.52mm, t2 D t5D0.239mm, t3 D t4D0.190mm,

w1 D w6D0.385mm, w2 D w5D0.370mm, w3 D w4D0.353mm,

aTE301l1 D l4 D 0:355mmD1.54mm l2 D l3 D 0:368mm, lTE301D0.80mm, aepD0.564mm, lepD0.523mm w1 D w6 D 0:385mm. (b) Initial coupling

scheme of the proposed filter. (c) Adjusted equivalent coupling scheme of the filter.

FIGURE 8. Simulated results of some critical parameters. Influence of

(a) aTE301, (b)lTE301.

geometric center of the singlet, is designed rst to implement the passband characteristic and generate a TZ in the lower stopband. Meanwhile, due to the good symmetry, the spurious passband of BPF is restrained effectively. As to the upper TZ, it can be controlled independently with little in uence on in-band characteristics because it is uniquely linked to the extracted pole resonator R6, as shown in Fig. 7. Therefore, a less sensitive network is obtained. The whole structure of the proposed BPF is symmetric in relation to the E-plane, which will reduce fabrication complexity and be good for system integration and minimization.

In order to extract the standard coupling matrix, spurious resonance can be regarded as a cross-coupling path, and the cross-coupling coef cient (MSL) from the input port to output port can be calculated as [21].

According to (6), the low-pass circuit topology of this lter can be simpli ed as shown in Fig. 6(c), where kij represents the coupling coef cients between the ith and jth resonators. It can be seen that the cross-coupling coef cient k24 depends on the spurious resonance TE102. Using the synthesis techniques in [22] or [23], the normalized coupling matrix of

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FIGURE 9. Simulated results of some critical parameters. Influence of

(a) aep, (b) lep.

low-pass circuit prototype can be written as:

To demonstrate the in uence of some critical parameters in proposed lter. Fig. 8-10 show the simulated results which

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are carried out by using software package HFSS. It can be seen from Fig. 8(a), (b), the position of lower TZ is controlled independently by dimensions of singlet, and it is more sensitive to aTE301 , which is consistent with (4). Similarly, when changing the dimensions of extracted pole resonator, the position of the lower TZ remains xed, while the upper one is shifted, as shown in Fig. 9(a), (b). lep is mainly controls the position of TZ because it directly related to the phase of electromagnetic wave, which is also agreement with analysis of Section II. Interestingly, when aepD0.604mm (blue dash line in Fig. 9(a)), the TZ caused by quarter-wavelength resonator fall at 388GHz, which exhibits that aep affects the distance between two TZs when lep isxed. From Fig. 10(a), (b), w1 and t1 has little in uence on inband transmission responses and TZs position, which show the good tolerance and modularity property of the proposedlter.

IV. FABRICATION AND MEASUREMENT

The proposed lter is fabricated in the E-plane spilt block by CNC milling with 2 m thick gold plating process for metallizing the whole blocks (i.e. the conductivity of waveguide wall is 4.10 107 S/m). The minimum radius of the drill used in the process is 0.1mm. Fig. 11(a) exhibits the photomicrograph of the internal structures of the lter. The inner surface of the cavity is fairly smooth. The photograph of the lter after assembling is shown in Fig. 11(b), and volume dimensions of the lter block are W H LD20mm 20mm 14mm.

FIGURE 13. (a) Simulated and measured frequency responses of the propose BPF. (b) Details comparisons of the insertion loss between the measured and simulated results. represents the conductivity of waveguide wall.

For the measurements, R&S ZVA40 vector network analyzer with two frequency expansion network Z500 converters are used to obtain the S-parameters of the fabricatedlters. The measurement scene is shown in Fig. 12. Good agreements between the measured and simulated results are achieved as shown in Fig. 13(a). Fig. 13(b) compares the measured in-band insertion loss with the simulated one in detail. In Fig. 13(a) and (b), six transmission poles are clearly visible, the measured insertion loss is around 0.7dB, 3dB fractional bandwidth is 9.9%, and the in-band return loss is better than 14dB. High selectivity is achieved by introducing two TZs at 336.5GHz and 379GHz, respectively. Due to good

agreement between simulated and measured insertion loss in Fig. 13(b), the equivalent conductivity of 4.10 107 S/m can be obtained in this prototype. The frequency of the lower TZ is 2GHz lower than the simulated one is mainly caused by the fabrication deviation of the singlet. Besides, tolerance analysis on the proposed lter is also carried out, as shown by the gray lines in Fig. 13(a).

Comparison of performances between the proposed l- ter and some other similar reported ones is demonstrated in Table 1. It can be seen that the proposed lter exhibits excellent performances with low insertion loss and ultrahigh frequency selectivity. In [4], [8], two WR-2.8 bandlters respectively based on DRIE and SU-8 technique are proposed. However, the insertion loss and selectivity of those two lters are poor. Although, a higher order lter is proposed in [13], the BW3dB/BW30dB is still lower than ours, and its insertion loss is much higher. In [11], [12], each lter has two TZs in the vicinity of passband, and their performances are comparable with this work. However, they are designed in a lower band, and the proposed lter in this paper exhibits the highest rejection among all comparisons.

V. CONCLUSION

This paper presents a novel THz pseudoelliptic BPF with low insertion loss, high selectivity and broadband response using CNC milling. By utilizing the singlet resonator and extracted pole resonator, two TZs are obtained, and the measured results are in good agreement with simulation ones. Compared with similar previous works, this THz bandpass lter has the highest 30dB rectangular factor with such wide fractional bandwidth. Due to simple and symmetrical structure, the method used in this paper is especially desirable for highfrequency applications. This simple and high-performance BPF would have a great potential in THz applications.

[3]S. W. Wong, K. Wang, Z.-N. Chen, and Q.-X. Chu, ``Electric coupling structure of substrate integrated waveguide (SIW) for the application of 140-GHz bandpass lter on LTCC,'' IEEE Trans. Compon., Packag., Manuf. Technol., vol. 4, no. 2, pp. 316 322, Feb. 2014.

[4]J.-X. Zhuang, Z.-C. Hao, and W. Hong, ``Silicon micromachined terahertz bandpass lter with elliptic cavities,'' IEEE Trans. THz Sci. Technol., vol. 5, no. 6, pp. 1040 1047, Nov. 2015.

[5]C. A. Leal-Sevillano et al., ``Silicon micromachined canonical E-plane and H-plane bandpass lters at the terahertz band,'' IEEE Microw. Wireless Compon. Lett., vol. 23, no. 6, pp. 288 290, Jun. 2013.

[6]O. Glubokov, X. Zhao, J. Campion, U. Shah, and J. Oberhammer, ``Micromachined lters at 450 GHz with 1% fractional bandwidth and unloaded Q beyond 700,'' IEEE Trans. THz. Sci. Technol., vol. 9, no. 1, pp. 106 108, Jan. 2019.

[7]Q. Chen, X. Shang, Y. Tian, J. Xu, and M. J. Lancaster, ``SU-8 micromachined WR-3 band waveguide bandpass lter with low insertion loss,'' Electron. Lett., vol. 49, no. 7, pp. 480 482, Mar. 2013.

[8]X. Shang, M. Ke, Y. Wang, and M. J. Lancaster, ``WR-3 band waveguides and lters fabricated using SU8 photoresist micromachining technology,'' IEEE Trans. THz. Sci. Technol., vol. 2, no. 6, pp. 629 637, Nov. 2012.

[9]H. Yang et al., ``WR-3 waveguide bandpass lters fabricated using high precision CNC machining and SU-8 photoresist technology,'' IEEE Trans. THz. Sci. Technol., vol. 8, no. 1, pp. 100 107, Jan. 2018.

[10]D. Koller, E. W. Bryerton, and J. L. Hesler, ``WM380 (675 700 GHz) bandpass lters in milled, split-block construction,'' IEEE Trans. THz. Sci. Technol., vol. 8, no. 6, pp. 630 637, Nov. 2018.

[11]J.-Q. Ding, S.-C. Shi, K. Zhou, Y. Zhao, D. Liu, and W. Wu, ``WR-3 band quasi-elliptical waveguide lters using higher order mode resonances,'' IEEE Trans. THz Sci. Technol., vol. 7, no. 3, pp. 302 309, May 2017.

[12]Y. Xiao, P. Shan, K. Zhu, H. Sun, and F. Yang, ``Analysis of a novel singlet and its application in THz bandpass lter design,'' IEEE Trans. THz Sci. Technol., vol. 8, no. 3, pp. 312 320, May 2018.

[13]W. Cheng, L. Bin, L. Jie, and D. Xianjin, ``140 GHz waveguide H ladder bandpass lter,'' in Proc. Int. Conf. Microw. Millim. Waves Technol., Shenzhen, China, May 2012, pp. 1 4.

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[15]S. Amari and U. Rosenberg, ``The doublet: A new building block for modular design of elliptic lters,'' in Proc. Eur. Microw. Conf., vol. 2, Milan, Italy, Sep. 2002, pp. 123 125.

[16]R. Levy and P. Petre, ``Design of CT and CQ lters using approximation and optimization,'' IEEE Trans. Microw. Theory Techn., vol. 49, no. 12, pp. 2350 2356, Dec. 2001.

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YINIAN FENG was born in Inner Mongolia, China, in 1993. He received the B.E. degree in electronic engineering from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2012, where he is currently pursuing the Ph.D. degree in electronic engineering. His research interests include microwave, millimeter-wave, and terahertz solid-state circuits.

BO ZHANG (M'07 SM'15) received the B.E. degree, M.S. degree, and Ph.D. degree in electromagnetic eld and microwave technology from the University of Electronic Science and Technology of China, Chengdu, China, in 2004, 2007, and 2011, respectively. He is currently a Professor with the School of Electronic Science and Engineering, University of Electronic Science and Technology of China. His research interests include terahertz solid state technology and systems.

YANG LIU received the B.E. degree in electromagnetism and wireless technology from the University of Electronic Science and Technology of China, Chengdu, China, in 2016, where he is currently pursuing the Ph.D. degree in terahertz solid-state circuit technology. His research interests include nonlinear circuit technology, terahertz communication, and terahertz monolithic technology.

JIAWEI LIU received the B.E. degree in electrical engineering from Southwest Minzu University, Chengdu, China, in 2017. He is currently pursuing the Ph.D. degree in electrical engineering with the University of Electronic Science and Technology of China (UESTC). He is currently with the Extra High Frequency Key Laboratory of Fundamental Science, UESTC. His research interests include RF/microwave, and mm-wave circuits and systems.

ZHONGQIAN NIU was born in Luoyang, Henan, China, in 1991. He received the B.E. degree in electronic science and technology from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2014, where he is currently pursuing the Ph.D. degree in terahertz solid-state devices and systems with the School of Electronic Science and Engineering. His research interests include terahertz high speed communication systems, terahertz mixers, and other terahertz devices.

KE YANG was born in Changde, Hunan, China, in 1993. He received the B.E. degree from the School of Electronic Engineering, University of Electronic Science and Technology of China (UESTC), Chengdu, China, where he is currently pursuing the M.S. degree in terahertz communication systems and terahertz solid-state devices.

YONG FAN received the B.E. degree from the Nanjing University of Science and Technology, Jiangsu, China, in 1985, and the M.S. degree in microwave technology from the University of Electronic Science and Technology of China, in 1992. He is currently a Professor and the Dean of the School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China. His research interests include millimeter wave, and terahertz technology and systems.

XIAODONG CHEN (F'14) received the B.Sc. degree in electronic engineering from the University of Zhejiang, Hangzhou, China, in 1983, and the Ph.D. degree in microwave electronics from the University of Electronic Science and Technology of China, Chengdu, China, in 1988. In 1988, he joined the Department of Electronic Engineering, King's College, University of London, London, U.K., as a Postdoctoral Visiting Fellow. In 1990, he was a Research Associate with the

King's College and was appointed to an EEV Lectureship later on. In 1999, he joined the School of Electronic Engineering and Computer Science, Queen Mary University of London, where he is currently a Professor. He has authored and coauthored many publications (book chapters, journal papers, and refereed conference presentations). His research interests include wireless communications, microwave devices, and antennas.