диафрагмированные волноводные фильтры / d80e7e56-cc7a-48ca-8b62-bb7c60e39e1d

Abstract— In this article, resonators based on air-filled rectangular cavity consisting of one perfect magnetic conductor (PMC) wall and the rest of walls as the perfect electric conductor (PEC) are proposed. The proposed cavity can be engraved in the top or bottom metal plate of a gap waveguide structure, and the PMC wall is realized by the periodic metallic pins located within the gap waveguide geometry. The resonant frequency and electromagnetic (EM) field distribution of the cavity are investigated, and it is shown that the electric field is horizontally polarized with respect to the wave propagation direction. Two bandpass filters are designed by inserting the proposed cavity in the cutoff region of the gap waveguide, on the top and bottom plates. In the latter case, all pins are the same, and the cavities and coupling structure are easily implemented by engraving the top plate. Therefore, by using this concept, a common pin plate can be used to implement different passive millimeter-wave devices. For instance, three different filters working at 60, 65, and 70 GHz with a common bottom pin plate are designed and fabricated. The measured results show a minimum insertion loss of 1.4, 1.1, and 1.1 dB with 0.83%, 1.4%, and 1.8% fractional bandwidth for the three bandpass filter designs, respectively, with aluminum as metal.

Index Terms— Antenna system, gap waveguide, millimeterwave filter, perfect magnetic conductor (PMC).

I. INTRODUCTION

THE antenna systems including radiator elements, feeding network, filter, diplexer, and active circuits are a critical part of transceivers [1], [2]. The high-performance antenna

systems with low loss at the millimeter-wave frequency band, in particular, frequencies higher than 40 GHz in which the propagation losses is large, are required. The realization and fabrication of such antenna systems can be encountered with some problems such as high insertion loss, difficult packaging and leakage issues, and high fabrication cost. To overcome these problems, it is needed to integrate all consequent of

Manuscript received November 7, 2019; revised January 24, 2020; accepted March 3, 2020. This work was supported in part by the Swedish Governmental Agency for Innovation Systems within the VINN Excellence Center Chase and in part by the Swedish Research Council VR. (Corresponding author: Morteza Rezaee.)

Morteza Rezaee is with the Department of Electrical Engineering, Hakim Sabzevari University, Sabzevar 9617976487, Iran (e-mail: morteza.rezaee@ hsu.ac.ir).

Ashraf Uz Zaman is with the Antenna Group, Department of Signals and Systems, Chalmers University of Technology, 412 96 Gothenburg, Sweden (e-mail: zaman@chalmers.se).

Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMTT.2020.2986111

components of the RF system on a unique high-performance physical platform. Recently, to avoid the drawbacks of conventional waveguides in the realization of multilayer millimeterwave antenna systems, the gap waveguide technology is proposed, in which there is no need for electrical contact between two consisting metallic parts [3], [4]. In this platform, a parallel-plate bandstop structure is realized using a periodic structure such as periodic metallic pins and mushrooms [5]. This periodic structure is located between two metallic parallel plates, and a guiding wave structure is usually realized as a groove [6], ridge [7], or microstrip ridge [8] along with the perfect electric conductor (PEC)/perfect magnetic conductor (PMC) environment, which acts as a channel for wave propagation. The wave propagation in this platform is studied in [3] and [8]–[10]. Among different types of gap waveguide, groove gap waveguide operates similarly to the conventional rectangular waveguide and supports TE10-like mode, and its propagation characteristics below and above the cutoff frequency are studied in [3]. By using this platform, an antenna system including antenna array, feeding network, and diplexer is presented in [2]. Furthermore, a complete gap waveguide-based E-band radio front-end has been demonstrated in [11]. The separate gap waveguide passive devices such as feeding networks of antenna [12], [13], filters [14]–[21], couplers [22], [23], diplexers [24], [25], and packaging of active circuits [26]–[30] are also presented.

Usually, in order to design a gap waveguide filter, similar to conventional rectangular waveguide filters, TE101 mode vertically polarized (with respect to the wave propagation direction) groove gap waveguide cavities are used as the filter resonators [14], [17]–[21]. In these filters, in order to implement the filter resonators or coupling mechanism between cavities, usually, the position or height of pins located between two adjacent cavities is selected, properly. In [19], by using periodic metal pins as the walls of the cavity, the rectangular resonators coupled through inductive irises are realized, and thereby, a vertically polarized or H-plane groove gap waveguide filter is designed. In the filter presented in [17], the inductive irises are realized by inserting two pins with different dimensions with the other periodic pins. Furthermore, the control of coupling between adjacent vertically polarized cavities by the height of pins is proposed in [18]. In all these designs, filers were implemented in vertically polarized groove gap waveguide.

In this article, horizontally polarized groove gap waveguide cavities are proposed to realize the bandpass and bandstop behavior. It is shown that by inserting a horizontally polarized resonator in the bandstop area of the structure, a bandpass filter can be realized, and by inserting this cavity in waveguiding path, a bandstop filter can be realized. In the proposed filter, the cavities or coupling structures are realized on the top or bottom metal plates, and there is no need to change the regularity of periodic pins which adds extra flexibility in the manufacturing of these filters. The regular lattice of pins can be fabricated easily by using a cost-effective approach such as metal milling and metal die casting, and also it will be possible to have a common pin plate for different filters operating at different frequencies. Moreover, the proposed filter using cavities on the top plate occupies a smaller area than conventional vertical polarized gap waveguide filters. This article is organized as follows. In Section II, the horizontally polarized cavity is introduced, and its behavior when located at the bandstop or bandpass area of the structure is investigated. In Section III by inserting the cavity on the bottom plate, a bandpass filter at the center frequency of 65 GHz with a transmission zero (TZ) in the stopband is designed and in Section IV, and this filter is investigated by inserting the cavity on the top plate.

II. HORIZONTALLY POLARIZED GAP

WAVEGUIDE RESONATOR

A. Resonator Structure and Its Resonant Frequency

A gap waveguide structure including a parallel metallic plate and a periodic pin structure located on the bottom plate is shown in Fig. 1(a), in which there is a bandgap for wave propagation between two parallel plates. As presented in [17], a frequency bandgap from 40 up to 92 GHz will occur when the dimensions of pins are selected as it is shown in Fig. 1(a). As shown in Fig. 1(a), there is an air gap of g between the top of metallic pins and the top metallic layer, which differentiates the gap waveguide with the conventional waveguide. A common way to implement the groove gap waveguide resonator is removing a few rows of pins through the periodic structure to realize the rectangular cavity [14], [18]. In this case, a groove gap waveguide resonator with the fundamental resonance of TE101-like mode is realized, in which, similar to the conventional rectangular waveguide cavities, the electric field is vertically polarized with respect to the wave propagation direction.

In order to reduce the area of the resonator, the cavity can be implemented vertically inside the bottom plate or top plate, as it is shown in Fig. 1(b) and (c), respectively. In the following, the resonant frequency of the proposed resonator is studied. The metallic pins located on the pin plate with the height of almost equal to λ/4 generate a high impedance surface which can be considered as a perfect magnetic conductor (PMC) when one looks toward the top surface of periodic pins [3], [5]–[7]. Therefore, the proposed cavity can be modeled as an air-filled cavity with PEC on five sides and one side being PMC, as shown in Fig. 2. It should be noted that when the cavity is created inside the bottom plate as shown in Fig. 1(b), the top wall of the cavity can be

Fig. 1. (a) Gap waveguide structure including a parallel plate and a bed of

periodic pins (h = 1.5 mm, g = 0.25 mm, p = 1.3 mm, dpin = 0.5 mm, and hpin = 1.25 mm). Proposed resonator realized in (b) bottom plate and

(c) top plate.

Fig. 2. Equivalent cavity of the proposed resonator.

considered as a PMC due to periodic structure and five other sides are PEC. Furthermore, the PMC boundary condition can be assumed valid as long as d is close to h.

The simulated electric and magnetic field of the fundamental mode in the proposed resonators on a surface at the middle of cavity is shown in Fig. 3(a) and (b), which are obtained by using the eigenmode analysis of HFSS software. As can be seen, half of the electromagnetic (EM) fields exist inside the carved cavity, and the other half is trapped between the periodic pins. The excited mode is a TE101-like mode rotated by 90◦ with respect to the fundamental resonant mode of vertically polarized resonators. In order to realize a filter, these cavities are excited later thorough the groove gap waveguide, where the fundamental propagating mode is TE10. By assuming the longitudinal direction where the TE10

Fig. 3. Electric and magnetic fields on a surface at the middle of cavity at the fundamental resonant mode. (a) Cavity realized in the bottom plate.

(b) Cavity realized in the top plate. (c) Resonant frequency comparison of the proposed cavity and the equivalent rectangular waveguide with the height of (d + h).

inside the groove gap waveguide is propagating as a reference, the mode resonating inside the cavity is a TM mode. Since the PMC condition is exploited at the center of the mode, then the resonant mode would be TM110 half-mode. Based on the method used to obtain the resonant frequency of the conventional rectangular cavity [31], the resonant frequency of the fundamental mode of the proposed cavity is obtained as follows:

The above relation is similar to the f101 mode of conventional rectangular waveguide resonators but with required half-length in the z-direction to have an equal resonant frequency.

Fig. 4. Cavity located at the passing path of signal in (a) bottom plate and

(b) top plate. (c) Transmission response of the structure with and without inserting the cavity (a1 = 4 mm and d1 = 1.4 mm).

A comparison between the resonant frequency of the cavity and the equivalent rectangular waveguide cavity, which has equal dimensions except its height (d+h), is shown in Fig. 3(c) which shows an overall similarity. The difference between the resonant frequencies is due to the nonideal behavior of the PMC wall realized by the periodic pins in all frequencies. The simulated unloaded quality factor of the proposed cavity is around 1770 at 65GHz, whereas a similar rectangular waveguide cavity has a quality factor of around 2100 when aluminum is considered as metal.

B. Bandstop and Bandpass Behavior of the

Proposed Resonator

To discuss further about the horizontally polarized resonator realized in the groove gap waveguide structure, two different cases are studied in this section. In the first case shown in Fig. 4(a) and (b), the resonator is placed in the area of the structure that passes the signal, i.e., the groove area, on the top or bottom plate. The simulated transmission response of the structure with and without inserting the cavity is shown in Fig. 4(b). A wideband bandpass response is seen when there is no cavity with an insertion loss of around 0.4 dB, whereas when the cavity is considered, a TZ is generated at around 65 GHz with an insertion loss of 50 dB. Similar to the conventional rectangular waveguide bandstop filters, the resonator works as a λ/4 short-circuited stub connected to the waveguide in series [32], and therefore, by generating an open circuit in the guiding path of signal, the TZ is generated.

In the second case shown in Fig. 5(a), two rows of pins are inserted in the propagating path of groove gap waveguide structure to realize a bandstop region. As it is expected, around 35-dB insertion loss is seen in the transmission response shown in Fig. 5(b) because of bandgap behavior of the periodic pins. Now, by inserting a horizontally polarized cavity on the bottom or top plate of the structure, as it is seen in the transmission response of Fig. 5(b), a bandpass response is obtained against the bandgap phenomena. Actually, since the λ/4 short circuit stub is located on the PMC surface, it works as a λ/2 short circuit stub and so the bandpass behavior is obtained. In comparison to the λ/2 stub, the depth of the carved cavity is reduced by half. This issue is important, especially when the filter is used as a building block of a multilayer antenna system. In this case, the thickness of the top or bottom layer is reduced. A similar concept is used in [33] to realize the bandpass response of an SIW filter, in which the frequency range lower than the cutoff frequency of SIW structure is used as the bandstop of wave propagation. Then, by loading a complementary split-ring resonator (CSRR) on the top metal layer of the SIW substrate with a resonant frequency below cutoff frequency, the bandpass behavior of filter is provided.

III. GROOVE GAP WAVEGUIDE FILTER USING

HORIZONTALLY POLARIZED RESONATOR

ENGRAVED IN THE BOTTOM PLATE

In this section, as a proof of concept, a third-order Chebychev filter is designed and realized using the resonator shown in Fig. 1(b). The center frequency of the filter is 65 GHz with 1.17% FBW and return loss better than 20 dB at

Fig. 6. (a) Coupling between two the horizontally polarized cavities and simulated coupling coefficient Mi j versus distance s. (b) Input coupling structure and simulated coupling coefficient versus height of pins t.

the passband. The conventional coupling matrix approach is used to synthesize the frequency response [34] which is independent of filter physical platform. The appropriate coupling coefficient between two adjacent resonators, M12 and M23, is 1.03 and input/output coupling coefficient, MS1 and M3L , is 1.082. Fig. 6(a) shows the 3-D and top view of two coupled horizontally polarized cavities with a distance of s. As it is seen in order to take account the effect of milling tool in the fabrication process, the corners of the cavities are rounded with the radius of 0.5 mm. In Fig. 6(a), the obtained coupling coefficient between two resonators versus s based on the following equation [34] is also depicted:

where f1 and f2 are the resonant frequency obtained from eigenmode analysis of the structure. As is it seen in the graph of Fig. 6(a) by increasing the distance, an intercavity coupling increases. Indeed, when some pins are inserted in the groove section, evanescent modes are excited, and when two sets of pins corresponding to two resonators are separated, the evanescent modes will couple to the basic TE10 mode with lower loss; therefore, the coupling between adjacent cavities will be increased. In order to obtain the input coupling coefficient, a horizontally polarized resonator is fed by two ports as it is shown in Fig. 6(b), in which the coupling is controlled by using the height of pins t located beside the resonator. The simulated coupling coefficient of MS1 obtained from the following equation is also illustrated versus height of pins [34]:

where GDS11 is the group delay of S11 at resonance, and Qext is the external quality factor of input cavity. By decreasing t, as it is expected, the coupling to the cavity will be increased. Using two design graphs of Fig. 6, the required all-pole Chebychev filter can be realized.

As a proof of concept, a TZ in the stopband of the filter at 68 GHz is realized by integrating the cavity in the propagating path of the filter in order to improve the isolation between TX and RX ports if the filter is used as part of a diplexer. However, the generation of the TZ should not affect the bandpass response of the filter. Although by using the engraved resonator through the groove as shown in Fig. 5(a) or (b), the TZ can be generated, as it is shown in Fig. 5(c), the relatively wide stopband will degrade the passband response of the filter at nearby frequencies. A narrower bandstop can be obtained by moving the cavity toward the regular pins, i.e., by applying an offset. Fig. 7 shows a comparison between the stub with and without off-center. As it can be seen, without off-center, a wide stopband can be obtained, but based on S11 response, it will affect a wide frequency range around the TZ.

Fig. 8(a) shows the designed Chebychev filter with a TZ at 68 GHz, and Fig. 8(b) shows the simulated frequency response. As it is seen if the other band of a diplexer is located at 68 GHz, by inserting the TZ, the isolation will be improved around 25 dB. Required transitions from WR-15 to the groove gap waveguide are also designed and included in the filter structure, in which a wide aperture with a suitable

Fig. 8. (a) Proposed third-order Chebychev filter with a TZ in the stopband including needed transitions to WR-15. (b) Simulated frequency response of the filter (s1 = s2 = 4.73 mm, t1 = t3 = 1.13 mm, t2 = 1.25 mm, d1 = d3 = 1.88 mm, d2 = 1.775 mm, and depth of TZ cavity d = 2 mm).

distance with the end of groove gap waveguide is considered to have a wideband and high-performance input impedance matching. It should be noted that when the filter is used as part of a groove gap waveguide antenna system, there is no need for the transitions. The simulated minimum insertion loss of the filter when aluminum is assumed as metal is around 0.56 dB with the return loss better than 19 dB and FBW of 1.2%. In comparison with the previous articles presented in [17, Section III], actually a carved slot on the pin plate is used in [17] to destroy the bandgap effect of periodic pins. By using this phenomenon, the coupling between two adjacent vertically polarized TE101 cavities is controlled. While in the proposed filter shown in Fig. 8(a), the horizontally polarized resonators are located in the bottom plate, and the distance between them controls the coupling between the neighboring resonators.

IV. GROOVE GAP WAVEGUIDE FILTER USING

HORIZONTALLY POLARIZED RESONATOR

ENGRAVED IN THE TOP PLATE

A problem with implementation of the horizontally cavities on the bottom plate is that it needs a long length milling tool.

Fig. 9. (a) Coupling between the two horizontally polarized cavities and simulated coupling coefficient Mi j versus iris width w assuming d = 1.5 mm.

(b) Input coupling structure and simulated coupling coefficient versus opening section k..

Due to small diameters of milling tool and also small pins besides the cavities, the milling tool or pins may become challenging during fabrication. Moreover, to control the input or output coupling, a different height for pins is required. Horizontally polarized cavity located on the top plate shown in Fig. 1(c) does not have these issues. In order to realize a filter using this cavity, intercavity coupling mechanism between adjacent cavities located on the top plate shown in Fig. 9(a) is used. In this coupling mechanism, a slot of width w

controls the coupling between two cavities. As it is seen in the coupling graph, by increasing w, the coupling is increased. To control the input coupling, the cavity is extended in the middle as it is shown in Fig. 9(b). The extended section is a cube with a depth equal to the depth of cavity, d, width of k, and length of 0.5 mm, in which its corners are rounded. This extended section opens the way of fields to couple to the cavity, and by broadening its width k, the coupling will be increased as it is seen in the corresponding graph.

As a proof of concept, a third-order filter similar to that of Section III is realized using the design graphs shown in Fig. 9. The structure of the designed filter is shown in Fig. 10(a) which consists of a regular pin plate with a similar height of all pins and an engraved top plate. The simulated frequency response of the filter is shown in Fig. 10(b), which shows that the simulated insertion loss of the filter is around 0.61 dB with the return loss better than 20 dB and FBW of 1.1%.

An interesting advantage of the proposed filter is that in order to design and implement different gap waveguide filters, it is just needed to focus on the pattern which should be engraved on the top plate, and there is no need to change the periodic pins. Based on this concept, similar filters at the center frequencies of 60, 65, and 70 GHz are designed with different depth of engraved cavities on the top plate with a common pin plate. The detailed dimensions of these three filters are shown in Table I. The top plate of three filters and common pin plate are fabricated using conventional machining technique, as shown in Fig. 11(a). Furthermore, the simulated and measured insertion and return loss results are shown in Fig. 11(b) and (c), where a good agreement between the simulated and measured results is seen. The simulated minimum insertion loss is 0.88, 0.6, and 0.48 dB, respectively, at the center frequency of 60, 65, and 70 GHz, and the return loss is better than 20 dB at three filters. Furthermore, the measured results obtained by using a N5290A PNA show a minimum insertion loss of 1.4, 1.1, and 1.1 dB, respectively. The measured return loss of the filters is almost better than 13.5, 12.5, and 11.5 dB, respectively. The degradation of the return loss in measurement can be due to fabrication tolerance that is around ±20 μm, the variation of gap size between pins and top plate, and also misalignment of the top plate with respect to the bottom plate. The unloaded quality factor from the measured data can be obtained from the following equation [18], [35]:

Fig. 10. (a) Proposed third-order Chebychev filter by using horizontally polarized cavities located on the top plate. (b) Simulated frequency response of the filter (w1 = w2 = 1.68 mm, d1 = d3 = 1.47 mm, d2 = 1.67 mm, and k = 1 mm).

Fig. 11. (a) Photograph of the fabricated prototype bottom layer with three top plates. Insertion loss (solid line) and return loss (dashed line) results of different filters. (b) Simulation results. (c) Measurement results.

where gi is the element value of equivalent normalized low-pass filter, and N is the order of filter. By using this formula, Qu of the resonators is obtained around 766 from

measured results. The quality factor of a similar vertically polarized groove gap waveguide filter presented in [19] is reported around 800. A comparison between the proposed filter

8

and other V-band filters with different technologies is shown in Table II.

Using a common bottom plate and different top plates opens a new way to solve the problems with the fabrication process of gap waveguides. Indeed, a regular pin plate can be fabricated by cost-effective approach of molding easily, and then by creating different patterns on the top plate, different millimeter-wave filter devices can be realized.

V. CONCLUSION

In this article, a horizontally polarized cavity loaded on the gap waveguide structure has been proposed. One wall of this rectangular cavity is PMC wall, whereas the other walls are PEC. The periodic metallic pins in the gap waveguide structures realize a bandgap where no wave can propagate in the frequency bandgap. It is shown that in this article, by loading the horizontally polarized cavity on the bottom plate or top plate of the gap waveguide structure, a bandpass behavior can be realized, and based on this concept, two types of filter at the V-band have been designed. On the other hand, if the horizontally polarized cavity inserted in the wave propagating region of the gap waveguide structure (such as groove region in this article), a bandstop behavior is seen that can be used to generate a TZ in the stopband of filter. By using the concept of realizing bandpass behavior by loading the horizontally cavities on the top plate and keeping all pins the same and regular, the pin plate can be manufactured by costeffective methods such as molding, and the passive devices can be realized by engraving a suitable pattern on the top plate. Moreover, different passive devices (such as filters with different center frequencies in this article) can be implemented by using a common pin plate.

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Morteza Rezaee received the Ph.D. degree in electrical engineering from the Ferdowsi University of Mashhad, Mashhad, Iran, in 2015.

He was a Visiting Researcher with the Antenna Group, Chalmers University of Technology, Gothenburg, Sweden, in 2014, where he started contributing to the development of filters and diplexers in the gap waveguide technology for 60 GHz. He was also in collaboration with the Sun-Air Research Institute, Ferdowsi University of Mashhad, in 2016. He is currently an Assistant Professor with Hakim

Sabzevari University, Sabzevar, Iran. His research interests are in millimeterwave devices, microwave filters, microwave sensors, antenna design, and passive and active microwave devices.

Ashraf Uz Zaman (Member, IEEE) was born in Chittagong, Bangladesh. He received the B.Sc. degree in electrical and electronics engineering from the Chittagong University of Engineering and Technology, Chittagong, and the M.Sc. and Ph.D. degrees from the Chalmers University of Technology, Gothenburg, Sweden, in 2007 and 2013, respectively.

He is currently an Associate Professor with the Communication and Antenna Systems Division, Chalmers University of Technology. His current

research interests include high-gain millimeter-wave planar antennas, gap waveguide technology, frequency-selective surfaces, microwave passive components, RF packaging techniques, and low-loss integration of monolithic microwave integrated circuits (MMICs) with the antennas.