Frequency Scanning Single-Ridge Serpentine Dual-Slot-Waveguide Array Antenna

This paper presents a novel one-dimensional (1D) frequency scanning dual-slot-waveguide array antenna with versatile advantages such as large scan volume, high frequency sensitivity, low cross-polarization and low sidelobe. Electromagnetic waves radiate through the leaky-wave dual slots, machined on the side chambers of the single-ridge serpentine waveguide. By properly designing the serpentine waveguide, which plays the role of delay line, such 1D frequency scanning array antenna can achieve 39° scanning over a frequency range from 9.7 GHz to 10.3 GHz, and high frequency sensitivity of 65°/GHz. The dual slots with all the adjacent monomers inclined in same direction are designed to acquire low cross-polarization and avoid high-order mode radiation. The cross-polarization is 45 dB lower than the corresponding co-polarization over the whole working band. Taylor aperture distribution is employed to achieve a low sidelobe (−21 dB). The nonresonance VSWR is below 1.2, and meanwhile the resonance VSWR remains a low level, around 2.5. Furthermore, our proposed 1D array as a building block can compose a novel 2D electric scanning array, with frequency scanning in one dimension and phase scanning in the orthogonal dimension. A 2D array consisting of three waveguide elements is simulated to predict the phase scanning performance, and the results indicate that a 120° scanning performance can be obtained. At last, a 1D serpentine dual-slot-waveguide array antenna is fabricated, whose measurements show good agreement with simulations.

Then with the development of patch antennas, a lot of research has been done on frequency scanning microstrip antennas [11], [12]. A microstrip FSA for imaging applications is proposed in [13], where the radiating patches are feed by a main delay line. A 50 • scanning range is obtained with a frequency sensitivity of 11.67 • /GHz. The printed FSAs have the advantages of low profile, small volume, light weight and convenient processing. However, the gain and efficiency are quite low due to the losses of the microstrip line.
As a member of traveling-wave antennas, LWA has also been intensively investigated due to its frequency scanning capability and simple feeding network. The uniform LWA whose dominant mode is a fast wave that therefore radiates whenever the structure is open. The most common example of such an antenna is a rectangular waveguide with a continuous slit cut along its side [14]. While the radiation from this type of LWA is limited to the forward quadrant. The second type of LWA is periodic LWA, in which some periodic modulation of the guiding structure is introduced, and -1 order mode is used most frequently for leaky-wave radiation. Microstrip line [15] and waveguide [5] are the common used guiding structures. Reference [16] proposed a lowprofile FSA based on substrate integrated waveguide (SIW), which achieved a wide scanning range of −30 • ∼30 • and a maximum gain of 10 dB. The SIW technology provides a reasonable tradeoff between the dielectric-filled metallic waveguide and microstrip technologies, which have the advantages of relatively low loss, low profile and ease in integration. Composite right/left-handed (CRLH) metamaterial based LWAs have been a research hotspot over the past decades due to their backfire to endfire scanning ability, including the broadside direction [17]- [19]. By using the balanced transmission line, the open-stopband problem [20] usually occurred in the periodic LWAs has been overcome. However, the aperture distribution of this type of LWA is difficult to control, thus usually leading to high sidelobe level in the radiation patterns. In addition, due to the small changes of the propagation constant, wideband frequency resources are usually required to achieve large scanning angles.
The ridge gap waveguide (RGW) is considered a new technology to build different kinds of microwave components [21], [22]. A LWA based on RGW with nonresonant slots is first constructed with a scanning capability of 17 • [23]. However, except the small scanning angle, it suffer from undesirable grating lobes. A split slots array in RGW is proposed to suppress the grating lobes, while the radiation beam can only scan in one side of the boresight [24]. In addition, the width of the RGW is more than half of a wavelength, thus the grating lobe will appear when building a 2D array. The strengths of the RGW technology are its low loss and high-power handing ability with minimal complexity by avoiding any kind of waveguide connectivity. It's a very competitive choice for high frequency applications, especially for millimeter wave band, while may not be necessary at low frequency when compared with the simple rectangular waveguide.
In this paper, we cast our eyes on the air-filled metal waveguide. Its advantages of low loss, good stability and reliability, and high power handling capability are highly valued for many specific outdoor applications, such as airfield control radar and harbor surveillance control radar. Thus we propose a novel one-dimensional (1D) frequency scanning dual-slot-waveguide array antenna. The slow-wave structure as well as the radiating elements are studied comprehensively to obatian large scan sector, high frequency sensitivity, low cross-polarization and low sidelobe level (SLL). The radiating elements, consisting of two inclined slots, directly located on side chambers of the serpentine waveguide. The radiating slots have different tilting angles, forming desired aperture distribution. The feed network involved here is that all the slots are excited by the single-ridge serpentine waveguide. As a slow-wave structure, the serpentine waveguide provides expected phase delay to the slots, which radiate electromagnetic fields by cutting the currents in the waveguide. Such 1D array antenna can work alone, or as a subarray element to compose a 2D array via putting tens of waveguides together. The 2D array can scan in frequency along the waveguide, while scan in phase along the perpendicular direction with phase shifters. When applied to the previously mentioned scenarios, such 2D array can be installed on the radar tower.
This paper is organized as follows. Section II shows the design of single-ridge serpentine dual-slot-waveguide array (SSDA) in detail, including the serpentine waveguide, dual slots and array design. Section III presents the simulation and analysis results. Section IV demonstrates the fabrication of prototype array and the measurement results. Finally, conclusions are drawn in V.

II. ANTENNA STRUCTURE AND DESIGN
The configuration of the frequency scanning SSDA is illustrated in Fig. 1(a), which is composed of six dual-slots. The radiating slots on the waveguide are an integral part of the feed system, which is the waveguide itself. When the slots are cut into a waveguide wall and it interrupts the flow of current, power is coupled from the waveguide modal field through the opening to free space. This antenna is fed by a connector through a waveguide coaxial junction on the left, and terminated by a matched load on the right to eliminate reflection (not shown). Fig. 1(b) is the top view of the SSDA, all the dual slots are inclined in the same direction, while monomers within the dual slots incline oppositely towards the perpendicular direction of the waveguide line. A 2D array is shown in Fig. 1(c), composed of six stacked SSDAs, which can realize frequency and phase hybrid electronically scanning. With that configuration, the azimuth plane is scanned by frequency, while the elevation plane scanned by phase using phase shifters. And the top-right inset of Fig. 1 gives the zoomed view of the waveguide cross-section.

A. SINGLE-RIDGE WAVEGUIDE DESIGN
The SSDA can be divided into two parts by the horizonal dotted line in Fig. 1(a). Within the two parts, the radius (r 1 ) of the upper transition is small, while that (r 2 ) of the lower transition is larger. In order to leave more space between the radiation slots and the waveguide transition, we make the radius r 1 small, giving enough length to attenuate high-order modes; the large radius r 2 is aimed at reducing the reflection and also maximizing the space usage.
Meanwhile, the radii r 1 and r 2 are key parameters for reflection performance of the single-ridge serpentine waveguide. Fig. 2(a) plots the structure chart of the unit for the single-ridge serpentine waveguide, and Fig. 2(b)-(c) show the simulation results of different r 1 and r 2 for the unit, respectively. The voltage standing wave ratio (VSWR) is very sensitive to r 1 and r 2 , and thus small changes of the radii will have a remarkable influence. We can see that r 1 mainly effects the low frequency performance of VSWR [ Fig. 2  the r 1 and r 2 are chosen as 1.0 mm and 5.4 mm, respectively. Thus a very low VSWR(<1.1) for the single ridge serpentine waveguide has been obtained.
To obtain good performance, it is important to design the slow-wave structure well, for it also determines the frequency bandwidth, the range of scanning angles, the loss of the antenna, etc. The inset in Fig. 1(a) shows the cross section of the serpentine waveguide, whose width and height are a and b, respectively. The ridge's width and height are s and b − d. The phase and frequency scanning angles are mainly determined by the width (a) and height (b) of the waveguide, respectively [25]. The phase scanning angle satisfies: The frequency scanning angle satisfies: where And the loss of the waveguide is mainly determined by both the width (s) and height (b − d) of the ridge. To avoid the grating lobes during phase scanning, the single-ridge waveguide instead of the standard rectangular waveguide is used to get a smaller element spacing a + 2t. As we can see, since individual characteristics are usually controlled by many parameters, it's difficult to separate them apart. The relations between the parameters and the performance of the array are listed detailedly in Table 1. Therefore we should consider all of the relations above before designing the arrays. It's worth noting that there is a main difference between the side-chamber dual slots and the narrow-wall inclined slots. As shown in Fig. 3(a), the current distribution of a rectangular waveguide, is completely transverse throughout the narrow wall; and that on the side chamber of a single-ridge waveguide, shown in Fig. 3(b), not only contains a transverse current, but also a lateral one throughout the chamber. When the  slots are not inclined, the narrow-wall slot wouldn't radiate, and thus the equivalent conductor would be zero. However, the dual slots would remain on radiating because of the lateral currents. Fig. 4 shows the equivalent conductor of narrowwall slot of rectangular waveguide and side-chamber slot of single-ridge waveguide for three different structures. We can see that for a narrow-wall slot, the equivalent conductor decreases as the inclined angle does, and tends to 0; but for the side-chamber slot, the conductor has a similar behavior as the narrow-wall one, except for tending to a nonzero value. These may provide some good insights towards designing waveguide slot antennas. If low side-lobe level is required, structure of the serpentine waveguide must be carefully adjusted to get the minimal lateral current on the side chamber. Our study shows that the current distribution on the side chamber is mainly affected by the ratio of b to d. When the ratio becomes larger, the lateral current decreases; and the lateral current is negligible when it exceeds 4. Besides, in our design, the Taylor aperture distribution is used for the slot array synthesis by adjusting the inclined angles of the dual slots.

B. DUAL SLOTS
Waveguide slot antenna is a kind of aperture antenna, and the slots interrupt some of the wall current associated with the fundamental mode. This current interrupts induce an electric field distribution in the slot, which can be viewed as the radiation source. When radiating, the disturbed current on the wall of the waveguide will flow around the slots, thus the slots can be equivalent as the magnetic current sheets.
The dual slots, consisting of two opposite inclined slots located respectively on the side chambers, would be radiating by cutting the transverse currents. As illustrated in Fig. 1(b), monomers within the dual slots incline oppositely towards the perpendicular direction of the waveguide line. This exquisite design is to suppress the crosspolarization by radiation cancellation. The co-polarization, along the waveguide line, is enhanced by adding the horizontal electromagnetic field component of the dual slots together. While the cross-polarization, perpendicular to the waveguide line, is counteracted by the vertical field component of the dual slots. Furthermore, all the dual slots incline in same direction to suppress the unwanted high-mode radiation.
To show the merits of our dual-slot design, Fig. 5 gives three configurations of slot arrays and their corresponding radiation patterns. Among them, Fig. 5 (a) is a mono-slot array, Fig. 5   Generally, adjacent alternately slots and oppositely inclined slots are used to reduce the cross-polarization of the traveling wave slot array. As shown in Fig. 5(d), the adjacent alternately mono-slot array can reduce the crosspolarization about 10 dB, which would be the same as the co-polarization without alternated the adjacent slots. And the opposite inclined dual slots can reduce the cross-polarization about 40 dB. But for such waveguide structures, the adjacent alternately slot array will radiate the high-order radiations, leading to undesirable grating lobes; see Fig. 5(d) and (e). After considerable research, the dual slots, inclined in same direction, are chosen to be the radiating elements, as shown in Fig. 5(c). The radiation patterns in Fig. 5(f) show the best performance compared to two other. The array will have the same results when all the dual slots are inclined in the opposite direction to that in Fig. 5(c), because of the symmetry of the current distribution on the side-chamber of the structure. Fig. 6(a) gives an equivalent model of the single-ridge dualslot-waveguide array with six dual slots. The single-ridge waveguide can be considered as a serpentine transmission line which transmits guided waves, and dual-slots are radiators coupling the fields inside the waveguide into free space. As seen in Fig. 6(a), the length of the slow-wave serpentine line and the distance between the two adjacent radiation elements are l and d s , respectively. Then the interelement and space phase shifts can be expressed respectively as

C. ARRAY DESIGN
where λ g is the guided wavelength in the serpentine guide, λ 0 the vacuum wavelength and θ the beam-scanning angle. When it satisfies we can substitute Eq. (4) and Eq. (5) into Eq. (6), and go straight to the beam-scanning angle = arcsin β k 0 .
Here β = [(2πl)/λ g −2mπ]/d s is the equivalent propagation constant in the slow-wave structure, and m is the rounded number of l λ g , deciding the frequency sensitivity. The length of the meandering waveguide will be longer with the increase of integer number m. For a longer l, the interelement phase will change greater with the frequency, and the scanning angle of the structure will be more sensitivity to the frequency. But when the meandering waveguide becomes longer, the loss will be greater. So m is set to 4 to balance the sensitivity and loss. Fig. 7 plots the simulated dispersion diagram of the β and the attenuation constant α versus frequency of the SSDA. Similar to the CRLH LWAs, the value of β goes from negative to positive, indicating the backfire to endfire scan ability including the broadside direction. The attenuation constant is depressed around the resonant point, which is because of the coherent superposition of the reflection at the feed point. But the lowest value of α near the resonant point is not zero. Thus the open stop band of the structure is mitigated slightly, the structure can still radiate at the resonant point.
As seen in Fig. 6(b), it is an equivalent circuit of the dual-slot-waveguide array [26]- [28]. The dual-slot can be equivalent to a shunt admittance, thus we can use the circuit theory to obtain the dual-slots' admittance according to the Tayor aperture distribution. The meanings of the symbols in Fig. 6(b) are: The Normalized admittance of the i-th dual slots; The Normalized admittance seen from the right of the i-th dual slots to the load; The Normalized admittance seen from the left of the i-th dual slots to the load; • P ri : The power radiate by the i-th dual slots; • P + i : The power transmit from the right of the i-th dual slots to the load; • P − i : The power transmit from the left of the i-th dual slots to the load. The dual slots can be thought of as working in the resonant case, hence the susceptance can be neglected. The admittance of the i-th dual slots can be written as: Because of the travelling wave situation and matched load, G + i is approximate to 1. We need to obtain the value of P + i , if we want to get the G i . According to the conservation of VOLUME 8, 2020 energy, we have: where q is the specific loss of the single ridge serpentine guide. P is the gross power that transmit to the SSDA. N is the total number of the slots. N is 6 in Fig. 6(b) for clarity. Combining Eq. (9) and Eq. (8), we can get: where we use the following relations Here E ri is the aperture excitation coefficient, determined by the aperture distribution, and η is the antenna efficiency. Once the aperture distribution and antenna efficiency are selected, then the conductance of the dual slots can be determined accordingly. Meanwhile, we can use the simulation software to obtain the relation between the conductance and slot parameters (inclined angle θ and cut-depth d c ) by digging ten or more same dual slots into the SSDA to consider the slot coupling. Using the calculated conductance and fitting curves from the simulation results, we can determine the dual slots parameters. Fig. 8 shows the fitting curve of the relation between the conductance and the inclined angle, and that of the relation between the cut-depth and the inclined angle, respectively.

III. ANALYSIS AND SIMULATION
Because of the long waveguide slow-wave line, the structure is complicated and electrically large. And thus it's time-consuming to simulate the whole two-dimensional scanned array. Therefore, in this paper, we just present the simulation results of an SSDA and three stacked SSDAs to validate the frequency-scanning and phase-scanning performance.
The design frequency and side lobe level of the SSDA are 10 GHz and −25 dB, respectively. The period of the dual slots in an SSDA is 21.2 mm, while that of SSDAs is 16 mm. As for the scanning angle, the array, actually several stacked SSDAs, can scan 45 • along the waveguide in frequency and 120 • perpendicular to the waveguide in phase without grating lobe.

A. SIMULATION RESULTS OF AN SSDA
In order to meet the aforementioned requirements, the parameters of the structure should be chosen carefully. After the parameter optimization, the width and height of the guide are chosen to be 14 mm and 6 mm, and those of the ridge to be 3.75 mm and 4.2 mm, repectively. In order to get fine frequency sensitivity, integer m is set to be 4. And we simulated 30 dual slots to validate the low sidelobe level. The slot width is 1.5 mm, and the detailed parameters of the slots are list in Table 2. The total length of an SSDA is about 0.7 m.
The simulation results of an SSDA are shown in Fig. 9, where (a) plots the co-polarization and cross-polarization radiation patterns at 10 GHz, respectively. We can see that the first sidelobe of the pattern (−1 dB) is about 21 dB lower than the main lobe (20 dB), and the cross polarization is below −40 dB. The radiation patterns of scanning frequency from 9.  array shows the same behavior; see (d). Here the resonant point means that the inner spacing of the radiators is an integral multiple of the half guided wavelength. In this case, the backscattering of the radiators will interfere in phase at the feed port. This phenomenon will deteriorate the refection and gain.

B. SIMULATED ARRAY PERFORMANCE OF THREE STACKED SSDAs
In order to validate the array performance of the SSDA, we simulated the array consisting of three stacked SSDAs. The E-plane and H -plane radiation patterns of an SSDA and active pattern of the central subarray of three stacked SSDAs are shown respectively in Fig. 10. It can be seen from Fig. 10(a) that there is no difference between the E-plane radiation patterns. As a result, we can infer that adjacent SSDA doesn't have much influence on the performance of frequency scanning. As plotted in Fig. 10(b), the beam-width in H -plane of the central subarray of the stacked waveguide, about 120 • with 4 dB gain drop, is wider than that of one waveguide. This indicates the maximum steering angle can be ±60 • in the plane perpendicular to the waveguide, leading to good array characteristics of such an SSDA.

IV. FABRICATION AND EXPERIMENTAL RESULTS
An sample of such SSDA is shown in Fig. 11, fabricated by CNC machining. Fig. 11(a) shows an oblique view of the SSDA, whose dimensions are 686 mm × 16 mm × 100 mm. Details of the dual slots are given in Fig. 11(b), where two opposite inclined slots are located on the two side chambers respectively. The coaxial-to-waveguide junction, a fourth-order Chebyshev impedance adapter here, is shown in Fig. 11(c) with the cover board removed to show the internal structure. The measurement and implementation setup of the SSDA is shown in Fig. 11(d). What should be pointed out is that in the fabricated structure, we didn't mill off the excess metal (Al) outside the serpentine line to reduce the processing time, making the sample look quite different from the schematics. The hollow serpentine waveguide is actually on the inside.
Far-field patterns of the SSDA are measured in a compact anechoic chamber. Thus it's kind of difficult to align the detector with the main beam of the SSDA, specifically about 2.5 • width in E-plane. Fig. 12(a) plots the measured radiation patterns for both co-and cross-polarizations at 10 GHz. It's measured that the first sidelobe of the pattern (−0 dB) is VOLUME 8, 2020   Fig. 9, respectively. about 18 dB lower than the main lobe (18 dB), and the crosspolarization is below −25 dB, which have subtle differences with the simulations as shown in Fig. 9(a). The sidelobe difference stems from the scattering errors in the measurement environment. And a higher cross-polarization over the band is mainly due to processing errors, making the dualslot monomer asymmetric. Since high cross-polarization of the array is completely eliminated when the oppositely inclined dual-slot monomers are machined perfectly, thus it's quite sensitive to symmetry of the dual-slot configuration. Fig. 12(b) and (c) give the measured co-and crosspolarization patterns over the 9.7-10.3 GHz band. Except for some inevitable deviations in gain, the measured main beams coincide well with the simulated ones shown in Fig. 9. Measured VSWR of the sample is shown in Fig. 12(d), where the whole profile agrees well with the simulation. Here, the main difference that small ripples occur is due to the different frequency steps between measurement and simulation. The measured main beam angles of the designed SSDA are plotted in Fig. 13, which agrees well with the theoretical predictions and the simulation results. Beam-steering range from −23 • to +16 • is realized when the frequency scans from 9.7 GHz to 10.3 GHz, which indicates the high frequency sensitivity of 65 • /GHz. Fig. 14 shows the realized gain and radiation efficiency of this frequency scanning SSDA. As seen in Fig. 14(a), the measured maximum gain is 19 dB. The maximum discrepancy between the simulated and measured gains is 2 dB. That is due to machining and welding errors, which makes the loss of the actual structure higher than ideal one. The measured gain is more than 12 dB within the whole frequency range. The measured maximum efficiency is about 60%, as shown in Fig. 14(b). The notches in the gain curve and the radiation efficiency curve are in accordance with the aforementioned resonance phenomenon. What can be noted, however, is that the radiation efficiency at both ends of the frequency band is a little lower. The low efficiency of the band ends is because of the narrow resonance bandwidth of the slots. Therefore, most of the energy is absorbed by the terminated load. The long slowwave structure and the low sidelobe aperture distribution are also the factors leading to this situation. Fortunately, designers have the flexibility to adjust the sidelobe level, frequency  Features of this paper are compared with other references in Table 3. It is clear that the proposed frequency scanning SSDA has high frequency sensitivity, low cross-polarization, low sidelobe level, as well as acceptable scanning range and antenna size. Moreover, the SSDA is advantageous in terms of good stability and reliability, long life and high power handling capability. However, it should be pointed out that the profile of our structure (H ) is a little higher than the planar arrays. This is due to the use of meandering slow-wave structure in the height direction. Thus our structure is suitable for specific outdoor applications, which value good stability and reliability, and high power handling capability more than compact size.

V. CONCLUSION
A frequency scanning dual-slot-waveguide array is studied in this paper. For an SSDA, it scans from the backfire to the endfire in a narrow bandwidth resource with a frequency sensitivity of 65 • /GHz. A −21 dB or even lower first sidelobe is obtained. The cross-polarization is also kept at a very low value (−45 dB) or much lower. As for three stacked SSDAs, it realize a 120 • phase-scanning, with no influence on the frequency-scanning of the individual 1D subarray. Compared to the conventional 2D phased arrays, our frequency-scanning waveguide-line structure uses much less phase shifters. It is much simpler and cheaper so that it will have a broad application in civilian fields. Last but not least, it should be pointed out that the array still suffers from the common problem in periodic LWAs, that when the inner spacing of the radiators is an integral multiple of the half wavelength (called resonant point), the backscattering of such radiators will interfere constructively at the feed port. This phenomenon would deteriorate the reflection, leading to a peak in S 11 curve (about −6 dB in our structure). In the future work, we could use random dual-slots and add reflection-cancelling structure to break constructive interference, thus reducing the return loss at the resonant point.