Vol 17, No 5 (2017) / Wang

An adjustment method for active reflector of large high-frequency antennas considering gain and boresight

An adjustment method for active reflector of large high-frequency antennas considering gain and boresight

Wang Cong-Si1, 2, , Xiao Lan1, 3, Wang Wei1, Xu Qian2, Xiang Bin-Bin2, Zhong Jian-Feng4, Jiang Li5, Bao Hong1, Wang Na2

Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi’an 710071, China
Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, China
Huawei Technologies Co., Ltd., Shenzhen 518129, China
Nanjing Research Institute of Electronics Technology, Nanjing 210039, China
CETC No.39 Research Institute, Xi’an 710065, China

† Corresponding author. E-mail: congsiwang@163.com


Abstract: Abstract

The design of the Qitai 110 m Radio Telescope (QTT) with large aperture and very high working frequency (115 GHz) was investigated in Xinjiang, China. The results lead to a main reflector with high surface precision and high pointing precision. In this paper, the properties of active surface adjustment in a deformed parabolic reflector antenna are analyzed. To assure the performance of large reflector antennas such as gain and boresight, which can be obtained by utilizing an electromechanical coupling model, and satisfy them simultaneously, research on active surface adjustment applied to a new parabolic reflector as target surface has been done. Based on the initial position of actuators and the relationship between adjustment points and target points, a novel mathematical model and a program that directly calculates the movements of actuators have been developed for guiding the active surface adjustment of large reflector antennas. This adjustment method is applied to an 8 m reflector antenna, in which we only consider gravity deformation. The results show that this method is more efficient in adjusting the surface and improving the working performance.

Keywords: telescopes;methods: analytical;techniques: miscellaneous



1 Introduction

Reflector antennas have been widely used in various fields such as radio astronomy, satellite communication and object tracking, and rely on a typical mechatronic structure (Rahmat-Samii & Haupt 2015 ; Wang et al. 2016 ). Mainly operating as a receiving antenna, its reflector must be “large” and “precise” (see the example in Figure 1). “Large” refers to “large dishes” which means that there is a large diameter and a big aperture area to receive weak signals, in order to observe deeper space. “Precise” incorporates two major points: one is to have very high surface accuracy and the other is to have very high pointing accuracy, so that the telescope can work at a higher frequency and receive a narrow beam for obtaining high resolution images.

Fig. 1 The 100 m Green Bank Telescope, a large high-frequency antenna.

However, because it operates in a complex environment, a large antenna is affected by many factors such as gravity, solar radiation and wind, which can produce structural deformation and rotation during observations. These result in a time-varying surface topography of the antenna. In addition, random errors are also present from sources like manufacture and installation (Wang 2015 ), which lead to deterioration in antenna performance, such as deflection of beam pointing, lower gain, raised sidelobe, etc. These problems are predicted to also occur in the Qitai 110 m Radio Telescope (QTT) which is proposed to be built in Qitai, Xinjiang, China. It is necessary for the antenna to compensate the performance by adjusting the spatial position and changing the geometrical shape of the distorted reflector surface. An implementation of active surface adjustment is shown in Figure 2, which is the most effective way to compensate performance of the antenna (Hans & Jacob 2014 ; Zhang et al. 2012 ).

Fig. 2 Active surface of a large high-frequency antenna: (left) active surface adjustment, (right) a close up of one actuator.

Literature related to performance compensation in a large antenna (Leng et al. 2011 ; Gonzalez-Valdes et al. 2013 ; Wang et al. 2013 , 2014 , 2007 ; Xu et al. 2009 ; Zhang et al. 2016 ) is almost all based on a traditional antenna structure to compensate the antenna performance by matching the feed position, moving and adjusting the alignment of the subreflector and azimuth-elevation rotation adjustment method of the whole antenna, or other approaches like the array method which uses a feed array or a subreflector array for compensating reflector surface distortion as shown in Figure 3.

Fig. 3 Two kinds of the array methods: (a) feed array and (b) sub-reflectarray.

Figure 3(a) shows a diagram of two types of reflector antennas with feed arrays. Figure 3(b) shows that a microstrip reflector array is used as a subreflector, illuminated by a primary single feed. By properly adjusting the radiated phase front provided by the array method, the aperture phase errors caused by surface distortions in the main reflector can be compensated (Rahmat-Samii 1988 ; Xu et al. 2009 ). It may be possible to improve the working performance of the antenna, but all of these methods are indirect compensation methods that incorporate complicated processes. There are still rigid deformations in the antenna structure and it is still impossible to make up for the antenna gain loss, which does not solve the main problem. Moreover, real-time compensation of a large antenna will be a difficult ideal to achieve. In addition, intelligent truss like application of an active surface can improve the antenna performance by aiming to generate the minimum displacement in the antenna structure, optimal surface precision or the best antenna boresight, by applying various optimization methods and implementing the optimal control problem of antenna structure and surface shape.

Therefore, a new performance compensation that eliminates rigid deformations in the antenna structure and transforms the reflector surface through active surface adjustment is proposed and a quick calculation of an adjustment value is introduced in the following sections.

2 Electromechanical Coupling Adjustment Method That Considers Antenna Performance

The electromechanical coupling adjustment method that considers antenna performance is introduced in this section, based on simulation using the computer-aided engineering software ANSYS. This simulation includes gravity deformation combined with the structural design form of the antenna and the active surface adjustment method of panels that are supported and controlled by four actuators in each corner which is replaced by four short poles in ANSYS. With the antenna finite element model (FEM model) in the simulation, it provides information on the gravity deformation and the overall deformation of the paraboloid reflector is known. With this information, we can analyze the target surface to improve antenna gain and boresight, and use it to calculate the adjustment value directly for moving and rotating the panels.

Figure 4 shows the flow chart of the adjustment method. In total, there are four key parts in the developed adjustment method:

Fig. 4 The flowchart of this adjustment method that considers the electrical performance of the antenna.

First, confirm the antenna structure and record the installed positions and the initial stroke of the actuators. Correct the actual initial positions of the active surface panels and then generate the FEM model which is close to the actual state and determine the actuator nodes. If the working performance of the deformed antenna meets the requirements, there is no need to adjust and the adjustment value of the actuators is zero. Then compute the deflection of the paraboloid and generate a least squares fit.

Second, use the formulas in the adjustment to compute the root mean square (RMS) error of the deformed paraboloid and verify whether the antenna gain is satisfied or not. Then determine the target surface by considering gain and boresight.

Third, which is the core part of the adjustment method, when the antenna performance deteriorates beyond requirements, it will be adjusted according to the calculated value. The specific means of active adjustment are described later.

Fourth, calculate the antenna far field pattern with an electromechanical coupling model and verify whether the antenna pointing accuracy is satisfactory or not.

This article emphasizes simulating gravity deformation of the antenna, which is repeatable. Through the simulation of gravity deformation and calculation of the adjustment value, an effective database can be constructed by all the adjustment values for the active surface, which can be embedded in the surface control system of the active antenna and used to directly operate the actuators when the antenna is in service. We aim to implement movements in the antennaʼs panels to make adjustments in real time in order to compensate the antennaʼs performance and to guide active adjustment for a large reflector antenna like the QTT.

3 Four Key Steps in the Developed Adjustment Method

3.1 Fitting the Distorted Surface

Antenna performance is closely connected with reflector surface and, to a great extent, is restricted by deviation, size and shape of the reflector surface. When the surface deforms under load, it causes phase error in the planar aperture, which influences the antenna performance. The phase error is determined by the relative error of each point between each other on the surface (Wang 2015 ), so the goal is to find the paraboloid with minimum RMS relative to the deformed surface. That is, establishing the equation describing the distorted reflector antenna surface is important for calculating antenna performance.

This article utilizes the software ANSYS to perform FEM analysis of the antenna structure. Based on an explicit FEM, ideal coordinates of the sampling nodes can be determined as . Then, include gravitational acceleration and simulate gravity deformation. On the basis of information about deformation, we can calculate the node on the distorted surface. By analyzing the displacement of nodes on the reflector and based on the least squares method, a mathematical expression for a distorted parabolic reflector can be derived accurately. Meanwhile, the RMS of normal errors associated with sample nodes in the whole aperture is minimized (Wang 2004 ). The corresponding equation of the distorted reflector is as follows

in which

Assuming that is on the BFP which corresponds to the sample node along the normal direction of the deformed surface, the normal error associated with sample nodes on the deformed surface with respect to the BFP is

The normal error of the whole deformed surface is

After that, we can make a quick calculation of the gain in the distorted reflector antenna (Wang 2015 )

in which

Fig. 5 The positional relationship diagram representing antenna surface adjustment for an ideal surface, target surface, BFP and distorted surface.

3.3 Calculating the Adjustment Value

The specific methods used for active surface adjustment are: (a) Determine target surface with optimal working performance according to the antenna boresight. (b) Make sure the relationship between target points and adjustment points is correct, and then calculate the adjustment values, which correspond to movements of actuators for fitting and rotating panels on the deformed surface. (c) Change the positions of reflector panels and update the structure FEM of the antenna, thus improving the antenna performance.

It should be mentioned that there are some assumptions made in all calculations in this article. We assume that there are four actuators that can adjust each panel, the neighboring corners of four panels are supported by one actuator simultaneously and each actuator moves the corners in the normal direction (Yang et al. 2011 ). It is easy to understand the properties of axial direction adjustment or that four actuators displace four panel corners independently, which can be calculated in a similar way. After determining the target surface with optimal working performance, we can directly calculate the adjustment value of panels that form a distorted paraboloid antenna and the calculation process is written as follows.

Because the magnitude of the deformation in antenna structure caused by its own weight is very small compared to the size of the antenna aperture, the normal direction cosine of the sample node , which is supported by an actuator on the ideal surface, is considered to be the same as the normal direction cosine of the node , supported by the same actuator on the distorted surface, as shown in Figure 6. So, is

Fig. 6 A diagram that illustrates locally calculating the adjustment value from distorted surface to target surface.

With the sample node and the normal direction cosine , we can obtain a normal equation as follows

Those are the equations we have to solve. As is well known, there is a line through a node outside the curved surface along the normal direction and the line must intersect the curved surface at a point or two. It is easy to discard the farther point which cannot be the target point to adjust to. Consequently, the coordinate of the intersection node can be obtained after solving the above equations. Then it is time to compute the normal deviation between on the distorted surface and on the target surface using the following equation

The sign function can be determined, which depends on the relative position of and . When is located along the normal direction of pointing to the inner side of the actual surface, equals 1; otherwise, equals . With and , the adjustment value of actuators can be written as

In addition, when there is an inclined angle (IA) for the actuator installation, which means movement of actuators in our program deviates from the normal direction of the panels during adjustment, the adjustment values should be divided by cos(IA), and we can get the final adjustment values.

3.4 Computing the Electrical Performance

The idea of active surface adjustment is to actively change the positions of the panels on an antenna surface by electromechanical actuators, which moves the corners of the panels in such a way as to compensate for deformations (Orfei et al. 2004 ), so that it meets the electrical requirement at their operating frequency. Therefore, active surface adjustment can be considered as a coupling problem between the associated mechanical and electrical properties (Duan & Wang 2009 ). According to an approximate expression given by DUAN Baoyan’s team from Xidian University to compute the antenna radiation pattern shown in Figure 7, which is called the electromechanical coupling model, we can easily obtain the antenna gain and boresight.

Fig. 7 The diagram of reflector surface error in the electromechanical coupling model.

The actual pointing direction of the antenna is the direction of maximum gain. It depends on the direction of the axis of the BFP and on the relative positions of the primary reflector, subreflector and feed (Antebi et al. 1998 ). However, this article focuses on the reflectorʼs surface deformation due to the great weight of the antenna. Let us assume that this is the only deformation. In this situation, the expression of the electromechanical coupling model is as shown

The directive gain is obtained as

where the function is the electric field of the feed and r 0 is the distance from the feed to the reflecting surface. and represent the influence of deformation in the reflector surface due to systematic error and random error, respectively, on the aperture phase distribution. represents the displacement of the antenna structure and β is a design variable associated with the antenna structure, including structure size, shape, topology and type. γ is random error due to manufacture and installation, A is projected area of the reflector on the XOY-plane and is wavenumber.

4 Simulation Results and Discussions

In this simulation, the object is a Gregorian reflector antenna pointing to the sky with diameter of 110 m and focal length of 36.3 m, as illustrated in Figure 8 (Wang et al. 2007 ). The antenna FEM model is shown in Figure 9. The beam element is beam118, the shell element is shell63 and the others are link8. All the mechanical information about the antenna model is listed in Table 1.

Fig. 8 The QTT antenna ProE model (ProE means Pro/Engineer, which is 3D CAD/CAM/CAE feature-based solid modeling software).
Fig. 9 The 110 m antenna FEM model.
Part Material Elasticity Modulus (MPa) Density (kg cm−2) Thickness (mm)
Structure Steel
Panels Aluminum 4

Table 1 Antenna Parameters used in the FEM Model

With the antenna FEM model and after extracting the node information about the distorted parabolic reflector, all the formulas used in the adjustment can be programmed and computed. Finally, by implementing the electromechanical coupling model in a high speed, high accuracy framework, we can analyze the electrical performance.

Figure 10 displays the reflector displacement nephogram in the vertical direction generated using ANSYS software. Also, Figure 11 provides the far field pattern of the ideal situation, and cases with gravity deformation and active adjustment.

Fig. 10 The Z-axis displacement nephogram generated using ANSYS.
Fig. 11 The far field pattern of antenna for the ideal situation, and cases including gravity deformation and active adjustment.

Table 2 is a comparison of the performance related to loss in antenna gain and pointing accuracy in three different situations. It can be seen that loss in antenna gain for the deformed antenna is –2.367 dB and pointing deviation is . However after active adjustment, the loss in antenna gain becomes –0.138 dB, which is an improvement of 2.229 dB or about 90%. The pointing deviation of the adjusted antenna is , an improvement of or almost 98%. In this case, the reflector antenna gain and boresight are much better than before. The sidelobe of the antenna is also reduced. In conclusion, the electrical properties of the antenna are effectively improved when the adjustment method is applied.

Ideal Gravity Deformation Active Adjustment Improvement Value
(dB) 0 –2.367 –0.138 2.229
Pointing ( ) 0 17.8974 0.3462 17.5512

Table 2 Comparison of Antenna Performance

The simulation result also demonstrates that, after applying the adjustment value obtained in this article to correct the positions of panels that are part of the deformed reflector antenna, the precision of the main reflector can be effectively enhanced. Table 3 lists adjustment values for actuators connected to panels in the radial direction.

No. Value No. Value No. Value No. Value
1 –0.381 24 0.321 47 1.715 70 0.797
2 0.123 25 0.257 48 0.463 71 0.516
3 0.252 26 0.366 49 0.412 72 1.463
4 –0.267 27 0.168 50 0.559 73 1.143
5 –0.298 28 0.226 51 1.003 74 1.051
6 0.094 29 0.411 52 0.692 75 1.470
7 0.060 30 0.936 53 0.691 76 1.121
8 0.117 31 0.825 54 0.807 77 1.494
9 –0.058 32 0.536 55 1.292 78 0.630
10 0.243 33 0.503 56 1.263 79 1.269
11 0.413 34 0.900 57 0.758 80 1.012
12 –0.243 35 1.064 58 0.543 81 0.936
13 0.208 36 0.148 59 0.887 82 1.458
14 0.095 37 0.785 60 1.309 83 1.173
15 0.268 38 0.568 61 0.612 84 0.925
16 0.473 39 0.855 62 1.149 85 1.285
17 –0.160 40 0.697 63 1.546 86 1.702
18 0.505 41 0.245 64 1.166 87 1.483
19 0.273 42 0.446 65 1.566 88 1.882
20 0.066 43 0.338 66 1.586 89 1.303
21 0.678 44 0.287 67 0.935 90 1.069
22 0.114 45 0.445 68 0.479 91 0.919
23 0.581 46 0.718 69 1.376 92 1.445

Table 3 Adjustment Values of Some Actuators for Panels in the Radial Direction

Figures 12 and 13 show the 23 different kinds of panels that are part of the 110 m antenna in the radial direction and their actuator nodes in ANSYS.

Fig. 12 The 23 different kinds of panels that are part of the 110 m antenna.
Fig. 13 Some actuator position nodes in ANSYS.

5 Conclusions

Based on simulation and analysis of the antenna FEM model, this active adjustment method can guarantee high gain and high pointing accuracy with optimal working performance in the distorted reflector antenna:

Based on the active surface that is incorporated in the design of the large antenna structure, we undertake research about active surface adjustment, which results in a new target surface that can enhance reflector antenna gain and boresight. Then combined with the electromechanical coupling model, we can compute electrical performance with high speed and high accuracy. This active adjustment method has many advantages, such as a short total distance needed for actuators, better precision in antenna reflector, optimal working performance with antenna gain and, last but not least, obviously improved pointing direction.

Another important aspect of this article is to calculate the adjustment value for the active surface’s actuators. A direct calculation of the adjustment value to correct the position of panels has been derived and the calculation method is simple. With the simulation, it can be demonstrated that the calculated value can significantly improve the antennaʼs performance. This kind of calculation is a new fast way to implement corrections for antenna deformation and can also be applied to different target surfaces. In addition, it should be noted that in this article all the data are produced by simulation.

This article emphasizes simulating the gravity deformation of the antenna ahead of time. Generating all the adjustment values and the associated large database of compensation values for gravity deformation associated with the antenna can be implemented for the active surface control system to control actuators directly when the antenna is in service. These efforts can contribute to advancing research for the QTT antenna, which will be the largest steerable antenna in the world.


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Cite this article: Wang Cong-Si, Xiao Lan, Wang Wei, Xu Qian, Xiang Bin-Bin, Zhong Jian-Feng, Jiang Li, Bao Hong, Wang Na. An adjustment method for active reflector of large high-frequency antennas considering gain and boresight. Res. Astron. Astrophys. 2017; 5:043.

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