Wide beam reflector antenna with cosecant-squared pattern

Journal Pre-proofs Regular paper Wide Beam Reflector Antenna with Cosecant-Squared Pattern Hadi Ahmadabadi, Sadjad Mallahzadeh, Abdorreza Torabi PII: DOI: Reference:

S1434-8411(19)32142-9 https://doi.org/10.1016/j.aeue.2020.153064 AEUE 153064

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International Journal of Electronics and Communications

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24 August 2019 1 January 2020

Please cite this article as: H. Ahmadabadi, S. Mallahzadeh, A. Torabi, Wide Beam Reflector Antenna with Cosecant-Squared Pattern, International Journal of Electronics and Communications (2020), doi: https://doi.org/ 10.1016/j.aeue.2020.153064

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Wide Beam Reflector Antenna with Cosecant-Squared Pattern Hadi Ahmadabadia, Sadjad Mallahzadehb,*, Abdorreza Torabic Faculty of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran

a

Department of Future Technology, University of Turku, Turku,Finland, [email protected]

b,*

School of Engineering science, College of Engineering, University of Tehran, Tehran, Iran

c

Abstract In this paper, a reflector antenna with a cosecant-squared and wide beam pattern is presented. The cosecant-squared antennas with different structures were reported to achieve a pencil beam area in azimuth direction but in this paper, a cosecant-squared antenna with a half beam angle of 33˚ was successfully synthesised. Such a wide beam pattern at the azimuth plane provides an appropriate coverage area for detection. A particle swarm optimization algorithm is used to synthesis the reflector surface of the antenna with respect to obtaining the desired cosecant-squared pattern. Tuning and finalizing the antenna structure have been done by using numerical full wave simulation. Finally, the designed antenna has been fabricated and tested in the far-field measurement setup. There is a good agreement between simulation and measurement results.

keywords: Reflectror antennas; Cosecant-squared-type antenna; Particle swarm optimisation

1. Introduction Shaping of an antenna pattern is considered as an important treat to illuminate the power in certain angles and distances in communications [1, 2]. The pattern with cosecant-squared shape is commonly used for this purpose. This pattern illuminates the radiated energy at higher angles in the elevation direction. The realization of the cosecant-squared pattern can be done by using different types of antenna, such as reflector [3], Lens [4], leaky-wave [5], and reflect array [6]. Previous studies have indicated that the reflector antenna is the only antenna structure that not only operates in a wideband frequency spectrum but also offers a straightforward and inexpensive manner of the production process. The reflector antenna surface is usually shaped by using optimization techniques. Genetic algorithm [7],

invasive weed optimization [3, 8], and particle swarm optimization (PSO) algorithm [9] have been reported to be applicable to shape the reflector antennas. As it was mentioned in the previous work [9], the PSO algorithm would be a simple and fast candidate to find the geometrical properties of the desired reflector antenna, specifically in the cases that the appropriate initial values are available. In this paper, a doubly curved reflector antenna with a cosecant-squared pattern in the elevation plane is synthesized. As a specific feature, this antenna has a wide-beam radiation pattern in azimuth direction in comparison with that of previous cosecant-squared antennas containing a pencil beam in the azimuth plane. In this paper, as our antenna is designed specifically for an application within the frequency band of 12-13 GHz, both simulation and measurement results are reported in the same frequency range. However, it should be noted that the antenna could be operated in a wider range of frequencies. After the design parameters of the antenna are set according to the PSO algorithm, a full-wave simulation of the designed antenna is done using the CST simulator package. In the end, the simulated results are compared with the measured ones of the fabricated antenna.

2. Antenna design Fig. 1 shows a schematic view of the doubly curved reflector antenna and its feed. The surface of the reflector could be created by sweeping a vertical curve (intersection of reflector surface with the x-z plane) along the horizontal curve (intersection of reflector surface with the y-z plane), and vice versa. These two curves should be appropriately designed with respect to the desired pattern because they are determinative to form radiation patterns in both elevation and azimuth directions. As the first step of the design process, the vertical one-dimensional curve of the reflector is modeled with a 5th order polynomial equation. The polynomial equation is: 1 z  x   P5x5  P4 x 4  P3x3  P2 x 2  Px 1  P0

D1 / 2  x  D1 / 2

(1)

Where Pi (i= 1, …, 5) is the coefficient that is determined iteratively by an optimization algorithm. In each iteration of the optimization procedure, a solver is needed to analyze the geometry of the reflector to obtain the radiation pattern. The analyzing approach should be accurate and fast to decrease the time of the optimization process. The physical optics (PO) method is chosen in this study for the analysis of the designed reflector.

Fig. 1. Schematic view of the doubly curved reflector antenna and feed.

For a reflector with electric current J on its surface, the radiated electric field could be calculated by equation (2) which is the same as equation (15-1) presented in [10]

E(r)  

j



[(J.) k J]g(R)dS 2

'

(2)

 jkR

g(R)  e 4 R



(3)



g(R)  jk  1 g(R)Rˆ R

(4)









(J.)g(R)  k 2(J.Rˆ )Rˆ  3 jk  1  (J.Rˆ )Rˆ  1 jk  1 J  g(R)  R R R R  (5)

R=r  r, R | R |, Rˆ  R R

(6)

In the preceding expressions, k is the free space wave number, and as it is depicted in Fig. 1, r and r  are the position vectors of observation and reflector points respectively. Surface integral (2) could be derived using the concept of vector potentials [11], which is applicable for both the near-field and farfield zones. Following approximation for far-field zones

R | r  r |  r  rˆ. r

(7)

And further simplification of Eq. (2) allow us to obtain the next well-known expression for the radiated field in the far-field zone:

E(r)  

jk 2





ˆˆ) Je jk rˆ.rdS ' g(r)(I  rr

(8)

By just focusing on the vertical one-dimensional curve, the surface integral (8) turns into a line integral, where the surface element dS ' must be replaced by dl ' . If H i is considered as an incident magnetic field, in the PO method, the surface current on the reflector can be calculated by J  2nˆ  H i , where nˆ is the unit vector normal to the reflector surface [12]. It is necessary to find H i for calculation of E(r) in Eq. 8. In this paper, the feed antenna is considered as an idealized feed which its radiation pattern is described as [10]:

ˆCE   cos  ˆCH   sin   e jkr .  ˆCE   sin  ˆCH   cos   r

Hi r   

 x polarized   y polarized

Where CE    (cos  ) qE and CH    (cos  ) qH . If q changes, beam-width, and gain of the feed antenna will vary consequently. Antenna gain can be obtained as following: G  10 log(4q  2) dBi . To find the best values for geometrical parameters of the reflector curve, an optimization process should be applied. In this study, a PSO approach is used and a cost function is defined for antenna radiation pattern:

(9)

 CF  1  N



 G     GDesired      0.5  X  X     2 2



2

(10)

Others

where G( ) is the antenna normalized gain calculated by numerical simulation, N is the number of points for the far-field calculation, and by considering the desired values of the side lobe level (SLLDesired), X can be obtained by the following equation: X=G(θ)-SLLDesired. The desired shape of the pattern and side lobe level are depicted in Fig. 2.

Fig. 2. The desired pattern for antenna in vertical plane.

The cosecant-squared pattern is in the range of 20    60 and the maximum gain should be realized for a theta within 4    10 and it must be more than 17 dBi. To obtain wide beam-width in the azimuth plane, the horizontal curve is chosen to be a sector of a circle whose center is at the back of the reflector as shown in Fig. 3 The radius of the circle (a) determines the beam-width of the pattern in the azimuth plane. The center of the circle is positioned at

(0,0,  F 

(H )2  a) . 4F

Fig. 3. Schematic view of the designed reflector antenna and a corrugated horn antenna as the feed.

3. Numerical results The initial values of the antenna parameters are listed in Table 1. The unshaped reflector with these dimensions has a gain of 38 dBi. Since the shaped pattern of the reflector antenna should be the same for both vertical and horizontal polarizations, the beam of feed antenna must be symmetrical in both Eplane and H-plane ( qE  qH ). In this work, the corrugated horn antenna is chosen as the feed antenna. This antenna has low edge diffraction, improved pattern symmetry, and low cross polarization. The gain of designed corrugated horn antenna is about 19 dBi and its 10 dB beam-width is 40 . The 10dB beamwidth is corresponding to qE  qH  19 . The high gain of the feed antenna reduces the minor lobes of the radiation pattern at the back side of the reflector antenna. Table 1. Initial values of the antenna parameters to start the optimization

parameter value

λ 2.4 cm

H 15 λ

F 24 λ

D1=D2 30 λ

a 75 λ

The optimization procedure starts by choosing randomly generated initial particles for the PSO algorithm. Then, the coefficients Pi are iteratively updated by means of PSO. The algorithm must be executed until the termination criterion is met. We consider the maximum number of iterations as a termination criterion. Setting the initial values for one of the particles with Pi corresponding to the parabolic and unshaped reflector increases the speed of convergence to reach the best solution. The

selected values for PSO parameters are listed in Table 2. More details for PSO algorithm is presented in [13]. The behaviour of the cost function values versus iteration numbers is shown in Fig. 4(a) the optimization procedure was repeated three times, due to the random nature of the PSO algorithm. As it is depicted in Fig. 4(a), the convergence of all the three optimization procedures have the same behaviour through 80 iterations, thus this number of iteration could be considered as an appropriate termination criterion.

Table 2. PSO algorithm parameters

Parameter Cognitive parameter Social parameters Swarm size Maximum number of iterations

Value 1.5 1.5 Twice of number of coefficients 250

The final values of coefficients Pi are given in table 3. Since the coefficient P5 is approximately zero, therefore a fourth-order polynomial is sufficient for modeling the vertical curve of the reflector in order to obtain the desired pattern illustrated in Fig. 2 As Fig. 4(b) also indicates, the obtained patterns approach to the defined one as the number of iteration limits increases.

Fig. 4. (a) Cost function value versus iteration numbers (b) elevation pattern for different iteration limits. Table 3. Final optimum values of the coefficients Pi

coefficient

P5

P4

P3

P2

P1

P0

value

-6.6×10-14

-9.5×10-7

-1.02×10-4

1.17×10-2

0.175

-51.48

The dimensions of the finally designed antenna are shown in Fig. 5 where Fig. 5(a) and (b) demonstrate the dimensions of the reflector and the position of the feed antenna respectively. A detailed view of the corrugated horn antenna is illustrated in Fig. 5(c). The feed antenna is connected to a WR75 standard waveguide through a transition of a cylindrical waveguide to WR75 and then it is fed by an SMA connector using a waveguide to coaxial line adapter. The length of D1 is 72 cm based on the optimization results, but in the final design it was extended to 80 cm in order to reduce the back lobe of antenna caused by spill-over of the feed radiation and also to achieve a slight increase in the antenna gain. It should be noted that the cosecant-squared shape of the radiation pattern was not affected by this increment in length of D1 .

Fig. 5. Dimension of antenna. (a) side view (b) front view (c) cross section view of horn antenna.

The PO method is used to analyse the electromagnetic problem of the shaped reflector for each particle of the PSO approach. This method is not sufficiently accurate to find all features of the designed antenna such as side lobe level. Therefore, the finally designed antenna with the parameter values extracted from the PSO algorithm is simulated numerically in CST Microwave Studio using an integral equation method. Fig. 6 shows a schematic view of the designed antenna and its gain pattern.

Fig. 6. Schematic view of the designed antenna and its Far-field pattern of gain at frequency of f=12.5 GHz

Two-dimensional pattern of the antenna gain in the elevation and azimuth planes are demonstrated in Fig. 7(a) and (b) respectively, while the antenna is exposed to horizontal illuminations at the frequency of f=12.5 GHz. The radius of horizontal circular curve is 75  180cm. The corresponding beam-width to this radius in the azimuth plane is 33 . As mentioned, the radius of curve affects the beam-width in the azimuth plane. For example, the reflectors with aperture width of D2  30 and radius of a  35 ,

50 , 75 and 100 produce patterns with beam-widths of 47.2, 39.8, 33, and 31, respectively. However, an additional increase in the radius of curvature does not change beam-width significantly. This can be anticipated since for a large value of radius, a sector of a circle is very similar to a straight line.

Fig. 7. Two-dimensional pattern of antenna gain in (a) elevation plane and (b) azimuth plane.

Fig. 8 shows the fabricated antenna with its feed and holder. The designed reflector antenna was fabricated by using resin and composite material. The feed antenna and holder structure were made by aluminium. The feed holder allows the selection of desired polarization. The far-field pattern of the antenna was measured for both vertical and horizontal polarizations. Fig. 9(a) and (b) illustrate the twodimensional pattern of gain at the frequency of 12.5 GHz in the elevation plane for horizontal and vertical polarizations, respectively. The measured patterns are compared with the simulation ones and they are in a fair agreement.

Fig. 8. The fabricated antenna with its feed and holder in the test field.

Fig. 9. Measured radiation pattern at the frequency of 12.5 GHz in the elevation plane and comparison with the simulation results for (a) horizontal and (b) vertical polarizations.

The radiation patterns of the fabricated antenna have been measured at a free space site where the distance between the transmitter and receiver is approximately 150 meters. This distance resulted in a high free space loss, and although high gain amplifiers were used during the measurement, the received signals strength at side and back lobes of the antenna were still below the sensitivity level of measurement equipment. Therefore, the normalized measured power at the side and back lobes regions have roughly constant values corresponding to the lowest measurable power at the receiver. The only 

detected side lobe can be seen in Fig. 9(b) at   100 with a level higher than that of simulated one. The observed difference could have occurred because of fabrication error, edge diffraction from reflector body, measurement error, or a superposition of all these effects. A similar comparison for the azimuth plane is presented in Fig. 10. The beam-width of the simulated pattern is similar to that of measured pattern. The squint of measured pattern is caused by the misalignment of transmitter and receiver positioners in the free space measurement setups.

Fig. 10. Measured radiation pattern at the frequency of 12.5 GHz in the azimuth plane and comparison with the simulation results for (a) horizontal and (b) vertical polarizations.

Since the antenna has a frequency band from 12 GHz to 13 GHz, Therefore, in addition to the center frequency, the radiation patterns of the antenna have been also measured at both lower and upper ends of the frequency band. Fig. 11 shows the results for measurements of radiation patterns at frequency of 12 GHz for both vertical and horizontal polarization in elevation and azimuth planes. Similar measurement results for the frequency of 13 GHz are presented in Fig. 12, and the corresponding simulated ones are also illustrated in Figs. 11 and 12. As it could be observed, there is a good agreement between measurement and simulated results. The cosecant-squared shapes of patterns are also quite similar to the shape of the radiation pattern at 12.5 GHz. The details of the characteristics of both simulated and measured radiation patterns at frequencies 12, 12.5 and 13 GHz are given in Table 4. which are confirming again a good agreement between measured and simulated results. The slight differences between the simulated and measured beamwidth can be attributed to the error in alignment of the antenna under test and the reference antenna (a horn antenna as the standard transmitting antenna in the measurement setup).

Fig. 11. Measured and simulated radiation pattern at the frequency of 12 GHz. (a) elevation plane, horizontal polarization, (b) elevation plane, vertical polarization, (c) azimuth plane, horizontal polarization, (a) azimuth plane, vertical polarization.

Fig. 12. Measured and simulated radiation pattern at the frequency of 13 GHz. (a) elevation plane, horizontal polarization, (b) elevation plane, vertical polarization, (c) azimuth plane, horizontal polarization, (a) azimuth plane, vertical polarization.

Table 4. Radiation pattern characteristics

Freq(GHz) 12 12.5 13

Horizontal polarization 3dB-BW 3dB-BW

Vertical polarization 3dB-BW 3dB-BW

(measured)

(simulated)

(measured)

(simulated)

(measured)

17.1 17 17

32.7 32.9 32.6

33.7 33.6 33.4

30.3 30.7 30.5

32.2 33.2 31.3

Gain

Gain

(simulated)

17.2 17.1 17.4

The conventional reflector antennas are determined to have inherent wideband characteristic. And however the antenna performance has been already studied at 12 to 13 GHz as the desired frequency bandwidth, but in order to evaluate the bandwidth performance of our presented new shaped reflector antenna, the radiation pattern stability of the antenna was also studied at a frequency range wider than that of our desired application. Thus, simulation results were also reported at 10 GHz and 15 GHz as the lower- and upper-end frequencies of the recommended frequency range for the WR75 standard waveguide, which is also the same feed antenna operational bandwidth. As it can be seen in Fig. 13, the designed antenna maintains its cosecant-squared pattern through a wide frequency range.

Fig. 13. Simulated radiation pattern at the frequency of 10, 12.5 and 15 GHz.

4. Conclusion In this paper, we synthesized a reflector antenna with the cosecant-squared pattern and wide beam shapes in both elevation and azimuths planes, respectively. While the previously presented antennas with the cosecant-squared pattern had narrow beams in the azimuth plane, our synthesized antenna has a wide beam with an angle of 33 degrees for 3 dB beam-width. This wide-beam pattern in the azimuth plane provides maximum coverage in order to reach maximum accessibility. The synthesized reflector surface with the PSO algorithm is simulated by the CST software package. Furthermore, the antenna with the corrugated feed is fabricated and tested in the far-field situation. The measured and simulated results are compared and except for the SSLs, they comply well with each other.

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