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1

Merkle, Fritz. "Active Control and Adaptive Optics for Optical Interferometers." Highlights of Astronomy 8 (1989): 565–66. http://dx.doi.org/10.1017/s1539299600008364.

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Long baseline interferometry requires the full phasing of a telescope array. Especially for future arrays with large unit telescopes active control systems are mandatory. Adaptive optics can be applied for real-time phase compensation of the individual pupils due to atmospheric distortions. Additional to phasing of the individual pupils of independently mounted telescopes, the whole array has to be phased, including pupil position corrections due to pupil foreshortening and shift effects in order to reach a reasonable phased field-of-view.
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2

Mailloux, R. "Phased array architecture for millimeter wave active arrays." IEEE Antennas and Propagation Society Newsletter 28, no. 1 (1986): 4–7. http://dx.doi.org/10.1109/map.1986.27839.

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3

Milyakov, D. A., V. S. Verba, V. I. Merkulov, and A. S. Plyashechnik. "Quadcopter active phased antenna array." Procedia Computer Science 186 (2021): 628–35. http://dx.doi.org/10.1016/j.procs.2021.04.185.

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4

Park, Daesung, Juho Yun, Youn Kwon Jung, Donghyeok Jang, Keum Cheol Hwang, and Jaehoon Choi. "Active Phased Array Antenna Calibration Using Skeleton Array." Journal of Korean Institute of Communications and Information Sciences 45, no. 11 (November 30, 2020): 1843–46. http://dx.doi.org/10.7840/kics.2020.45.11.1843.

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5

Aminev, A. M., A. V. Gilev, D. Yu Grishin, V. E. Zaytsev, and V. N. Sergeev. "Automated active phased array control stand software." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 4 (December 30, 2019): 93–102. http://dx.doi.org/10.38013/2542-0542-2019-4-93-102.

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The study suggests using a software platform for multidimensional data cubes in automated active phased array control stands. The application of the platform greatly facilitates and accelerates the display and analysis of very large volumes of data coming from large-aperture active phased arrays during the measurement process, so that the end user can make spontaneous data requests. The study shows the prospects of using this platform for radar systems as a whole.
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6

Patrick, William. "Active noise control using phased-array active resonators." Journal of the Acoustical Society of America 105, no. 1 (1999): 24. http://dx.doi.org/10.1121/1.424716.

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7

Nishio, T., Hao Xin, Yuanxun Wang, and T. Itoh. "A frequency-controlled active phased array." IEEE Microwave and Wireless Components Letters 14, no. 3 (March 2004): 115–17. http://dx.doi.org/10.1109/lmwc.2004.825188.

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8

Chintawongvanich, Prasan. "Active acoustic phased array antenna system." Journal of the Acoustical Society of America 113, no. 3 (2003): 1193. http://dx.doi.org/10.1121/1.1567091.

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9

Daryoush, A. S., and B. Choe. "Optically reconfigured active phased array antennas." Microwave and Optical Technology Letters 1, no. 9 (November 1988): 344–48. http://dx.doi.org/10.1002/mop.4650010910.

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10

Gavrilova, S. E., A. N. Gribanov, G. F. Moseychuk, and A. I. Sinani. "Features of excitation reconstruction in flat multielement phased antenna array face using dynamic directional patterns." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 4 (December 30, 2017): 32–39. http://dx.doi.org/10.38013/2542-0542-2017-4-32-39.

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The study focuses on reconstructing the amplitude-phase distribution of flat multielement passive and active phased antenna arrays with the use of dynamic radiation patterns, measured with electronical scanning without mechanical rotations and antenna movements. The paper describes the measurement settings of dynamic radiation patterns, necessary for reconstructing the amplitude-phase distribution. Findings of the research show that to reconstruct the amplitude-phase distribution according to dynamic radiation diagrams, there is no need for increased computational resources due to the use of Fourier transformation algorithms. After the method was experimentally verified on the specific samples of active phased antenna arrays, its high efficiency was established. The paper gives the examples of reconstructing the amplitude-phase distribution from dynamic radiation patterns in the presence of malfunctions in active phased array antennas.
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11

Li, Xiao-Yan, Zhang-Zhao Yang, Yi-Fan Zhu, Xin-Ye Zou, and Jian-Chun Cheng. "Broadband acoustic phased array with subwavelength active tube array." Applied Physics Letters 112, no. 9 (February 26, 2018): 093503. http://dx.doi.org/10.1063/1.5009661.

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12

Birring, Anmol. "Optimizing Probe Active Aperture for Phased Array Weld Inspections." Materials Evaluation 79, no. 8 (August 1, 2021): 797–804. http://dx.doi.org/10.32548/2021.me-04220.

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Phased array ultrasonic testing (PAUT) has become a popular nondestructive technique for weld inspections in piping, pressure vessels, and other components such as turbines. This technique can be used both in manual and automated modes. PAUT is more attractive than conventional angle-beam ultrasonic testing (UT), as it sweeps the beam through a range of angles and presents a cross-sectional image of the area of interest. Other displays are also available depending on the software. Unlike traditional A-scan instruments, which require the reconstruction of B- and C-scan images from raster scanning, a phased array image is much simpler to produce from line scans and easier to interpret. Engineering codes have incorporated phased array technology and provide steps for standardization, scanning, and alternate acceptance criteria based on fracture mechanics. The basis of fracture mechanics is accurate defect sizing. There is, however, no guidance in codes and standards on the selection and setup of phased array probes for accurate sizing. Just like conventional probes, phased array probes have a beam spread that depends on the probe’s active aperture and frequency. Smaller phased array probes, when used for thicker sections, result in poor focusing, large beam spread, and poor discontinuity definition. This means low resolution and oversizing. Accurate sizing for fracture mechanics acceptance criteria requires probes with high resolution. In this paper, guidance is provided for the selection of phased array probes and setup parameters to improve resolution, definition, and sizing of discontinuities.
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13

Yue, Xinan, Weixing Wan, Baiqi Ning, and Lin Jin. "An active phased array radar in China." Nature Astronomy 6, no. 5 (May 2022): 619. http://dx.doi.org/10.1038/s41550-022-01684-1.

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14

Richarz, Werner G. "Phased array active noise controller for ducts." Journal of the Acoustical Society of America 80, S1 (December 1986): S11. http://dx.doi.org/10.1121/1.2023607.

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15

Agrawal, A. K., and E. L. Holzman. "Active phased array design for high reliability." IEEE Transactions on Aerospace and Electronic Systems 35, no. 4 (1999): 1204–11. http://dx.doi.org/10.1109/7.805438.

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16

Jablon, A., and A. Agrawal. "Optimal number of array faces for active phased array radars." IEEE Transactions on Aerospace and Electronic Systems 42, no. 1 (January 2006): 351–60. http://dx.doi.org/10.1109/taes.2006.1603428.

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17

Kondratieva, Svetlana, Pavel Shmachilin, and Natalia Anosova. "Fault-tolerant active phased array antenna with neural network." ITM Web of Conferences 30 (2019): 05004. http://dx.doi.org/10.1051/itmconf/20193005004.

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A model and architecture for an active phased array antenna with a neural network control unit has been developed, which provides correction of the amplitude-phase distribution depending on the quality of work of individual array modules. The possibility of adapting the system to failures of individual modules is shown.
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18

Shi, Wei, Jun Zhou, Zuping Qian, and Ya Shen. "Analysis and experimental studies of compact polarization tracking modules for Ku band phased array antennas." International Journal of Microwave and Wireless Technologies 5, no. 5 (July 2, 2013): 629–36. http://dx.doi.org/10.1017/s1759078713000603.

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Detailed analysis of the polarization tracking modules for Ku band active phased array antennas is presented. The proposed transmitter (14.0–14.5 GHz) and receiver (12.25–12.75 GHz) modules are based on the low temperature co-fired ceramic (LTCC) technique, containing orthogonal dual channels with different phases controlled by phase shifters. The effect of amplitude and phase inconsistency between two channels on polarization tracking performance is analyzed. The validity of the analysis is verified by the measurements of the manufactured prototypes. The measured patterns of the active phased array antenna are given to illustrate the effects of the modules on polarization agility, which may be used for Ku band satellite antennas on mobile terminals.
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19

Li, Jian, and Petre Stoica. "The Phased Array Is the Maximum SNR Active Array [Lecture Notes." IEEE Signal Processing Magazine 27, no. 2 (March 2010): 143–44. http://dx.doi.org/10.1109/msp.2009.935418.

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20

Alekseytsev, S. A., A. P. Gorbachev, and Y. N. Parshin. "An investigation of novel active phased array components." IOP Conference Series: Materials Science and Engineering 1019 (January 21, 2021): 012099. http://dx.doi.org/10.1088/1757-899x/1019/1/012099.

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21

WANG, Congsi. "Development of Spaceborne Deployable Active Phased Array Antennas." Journal of Mechanical Engineering 52, no. 5 (2016): 107. http://dx.doi.org/10.3901/jme.2016.05.107.

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22

Yun, Juho, Daesung Park, Youn Kwon Jung, Donghyeok Jang, and Keum Cheol Hwang. "Active Phased Array Antenna Calibration Using Mutual Coupling." Journal of Korean Institute of Communications and Information Sciences 44, no. 9 (September 30, 2019): 1678–81. http://dx.doi.org/10.7840/kics.2019.44.9.1678.

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23

Whicker, L. R. "Active phased array technology using coplanar packaging technology." IEEE Transactions on Antennas and Propagation 43, no. 9 (1995): 949–52. http://dx.doi.org/10.1109/8.410211.

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24

Agrawal, A. K., and E. L. Holzman. "Beamformer architectures for active phased-array radar antennas." IEEE Transactions on Antennas and Propagation 47, no. 3 (March 1999): 432–42. http://dx.doi.org/10.1109/8.768777.

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25

Bolandhemmat, H., M. Fakharzadeh, P. Mousavi, S. H. Jamali, G. Z. Rafi, and S. Safavi-Naeini. "Active Stabilization of Vehicle-Mounted Phased-Array Antennas." IEEE Transactions on Vehicular Technology 58, no. 6 (July 2009): 2638–50. http://dx.doi.org/10.1109/tvt.2008.2012159.

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26

Seong, Nak-Seon, and Seong-Ook Park. "A radiator element for active phased array antenna." Microwave and Optical Technology Letters 48, no. 12 (2006): 2393–95. http://dx.doi.org/10.1002/mop.21971.

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27

Kuznetsov, Grigory, Vladimir Temchenko, Maxim Miloserdov, and Dmitry Voskresenskiy. "Modifications of active phased antenna arrays near-field diagnosis method based on compressive sensing." International Journal of Microwave and Wireless Technologies 11, no. 7 (July 18, 2019): 568–76. http://dx.doi.org/10.1017/s1759078719000989.

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AbstractThis paper presents two modifications of compressive sensing (CS)-based approach applied to the near-field diagnosis of active phased arrays. CS-based antenna array diagnosis allows a significant reduction of measurement time, which is crucial for the characterization of electrically large active antenna arrays, e.g. used in synthetic aperture radar. However, practical implementation of this method is limited by two factors: first, it is sensitive to thermal instabilities of the array under test, and second, excitation reconstruction accuracy strongly depends on the accuracy of the elements of the measurement matrix. First proposed modification allows taking into account of thermal instability of the array by using an iterative ℓ1-minimization procedure. The second modification increases the accuracy of reconstruction using several simple additional measurements.
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28

Joo, Taehwan, Chanho Hwang, Juman Park, Kichul Kim, and Jaesoo Jung. "Design of a Tile-Type Rx Multi-Beam Digital Active Phased Array Antenna System." Journal of Electromagnetic Engineering and Science 22, no. 1 (January 31, 2022): 12–20. http://dx.doi.org/10.26866/jees.2022.1.r.55.

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This paper details the design, manufacture, and performance test results of a highly integrated Rx multi-beam active phased array antenna for aerial communications. The proposed Rx phased array antenna comprises three tile-phased array antennas consisting of array antennas, radio frequency, and beamforming units. A performance test of the Rx antenna system revealed the system achieved gain-to-noise temperature of -6 dB/K and beam pointing accuracy of below 0.4° with four independently operable multi-beams. It is designed with compact size and less weight for various platforms.
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29

Xiao, Rui, Shouli Jianga, and Jianfeng Zhongb. "Status and Development Trend of Active Sub-arrays Structure Design in Active Phased Array Antenna." IOP Conference Series: Materials Science and Engineering 914 (September 19, 2020): 012038. http://dx.doi.org/10.1088/1757-899x/914/1/012038.

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30

Qu, Shi-Wei, De-Jun He, Shiwen Yang, and Zaiping Nie. "Novel Parasitic Micro Strip Arrays for Low-Cost Active Phased Array Applications." IEEE Transactions on Antennas and Propagation 62, no. 4 (April 2014): 1731–37. http://dx.doi.org/10.1109/tap.2013.2262071.

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31

Lu, Junqi, and Yongxin Guo. "Compact Planar Sparse Array Antenna with Optimum Element Dimensions for SATCOM Ground Terminals." International Journal of Antennas and Propagation 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/806981.

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A novel antenna array architecture for low-cost and compact SATCOM mobile terminal is presented. Based on equal-amplitude aperiodic phased array with fewer active chain numbers, it possesses advantages including lower weight, less cost, and higher power efficiency compared to conventional periodic phased arrays. It is implemented with printed patch antenna so that it guarantees compactness. The elements position and dimensions are jointly designed, with an effective sparse array synthesis strategy that takes actual patch antenna design constraint into consideration, to obtain a maximum array aperture efficiency. Executable and practical approach for variable dimension patch antenna designing, including defect substrate element and small scale array, is introduced and utilized to implement proposed sparse array. Full-wave simulation results demonstrate the advantages of proposed array antenna as well as the effectiveness of corresponding design approach.
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32

Gong, Yinghui, Robert Wang, and Pei Wang. "Improved Phase-Encoding Calibration for Active Phased-Array Antennas of SAR." IEEE Geoscience and Remote Sensing Letters 13, no. 6 (June 2016): 767–71. http://dx.doi.org/10.1109/lgrs.2016.2542104.

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33

Ryu, Han-Cheol, Su-Jae Lee, Seung Eon Moon, Min-Hwan Kwak, Mun-Cheol Paek, Kwang-Yong Kang, and Seong-Ook Park. "A Phased Array Antenna Using Ferroelectric CPW Phase Shifter Active Modules." Ferroelectrics 407, no. 1 (November 2010): 45–53. http://dx.doi.org/10.1080/00150193.2010.484707.

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34

Bhattacharjee, Samaresh, Ashish Kumar, and Manish Naja. "Array Factor Optimization of an Active Planar Phased Array Using Evolutionary Algorithm." International Journal of Antennas 2, no. 3 (July 30, 2016): 01–11. http://dx.doi.org/10.5121/jant.2016.2301.

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35

Aleshin, Victor S. "EVALUATION OF THE FEASIBILITY OF AN ACTIVE PHASED ARRAY ANTENNA IN THE TERMINAL OF THE EXPRESS-RV SATELLITE COMMUNICATION SYSTEM." T-Comm 15, no. 8 (2021): 13–21. http://dx.doi.org/10.36724/2072-8735-2021-15-8-13-21.

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The basic principles of building a promising domestic regional satellite communication system “Express-RV”, based on the highly elliptical orbit “Molniya” and intended for broadband access of civil sector subscribers to various public communication networks, in particular to the Internet, are considered. The main technical requirements for the antenna systems of mobile mobile satellite communication terminals of the Express-RV system are formulated. The necessity of using active phased array antennas for a number of types of such terminals is justified. A brief overview of the principles of implementation and examples of the design of microstrip active phased array antennas, including their elementary emitters and individual modules, are given. The problem of the occurrence of the blinding effect inherent in flat microstrip gratings made on dielectric substrates is noted; measures to compen-sate for this effect are considered. The possibility of expanding the maximum scanning angle of a narrowly directed beam of an active phased array antenna by using a magnetically controlled scattering dielectric lens, as well as creating segment-dome structures of antenna systems in relation to mobile terminals of mobile satellite communications of the “Express-RV” system, is shown. Simple analytical relations are derived that allow us to estimate the number of elementary emitters required for the implementation of a receiving-transmitting active phased array antenna with specified technical characteristics: gain and maximum scanning angle; the corresponding dependencies are given. The cost of creating an antenna system based on an active phased array is estimated.
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36

Wang, Lu, Zhihai Wang, Congsi Wang, Guozhou Li, and Lei Yin. "Multiobjective Optimization Method for Multichannel Microwave Components of Active Phased Array Antenna." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/5398308.

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Multichannel microwave components are widely used and the active phased array antenna is a typical representative. The high power generated from T/R modules in active phased array antenna (APAA) leads to the degradation of its electrical performances, which seriously restricts the development of high-performance APAA. Therefore, to meet the demand of thermal design for APAA, a multiobjective optimization design model of cold plate is proposed. Furthermore, in order to achieve temperature uniformity and case temperature restrictions of APAA simultaneously, optimization model of channel structure is developed. Besides, an airborne active phased array antenna was tested as an example to verify the validity of the optimization model. The valuable results provide important reference for engineers to enhance thermal design technology of antennas.
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37

Jung, Jinwoo, and Taehwan Joo. "Initial Beam Forming for Active Phased Array Antenna Systems." Journal of Korean Institute of Electromagnetic Engineering and Science 31, no. 8 (August 2020): 677–87. http://dx.doi.org/10.5515/kjkiees.2020.31.8.003.

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38

HASTURK, Ahmet, Nursel AKCAM, and Funda ERGUN YARDIM. "S-Band Active Phased-Array RF Beam Forming Networks." GAZI UNIVERSITY JOURNAL OF SCIENCE 32, no. 4 (December 1, 2019): 1185–94. http://dx.doi.org/10.35378/gujs.457458.

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39

Han, Jae-Seob, Young-Wan Kim, Jong-Gyun Baek, and Jong-Pil Kim. "Design of Ka-band Planar Active Phased Array Antenna." Journal of the Korean Society for Aeronautical & Space Sciences 47, no. 2 (February 28, 2019): 143–52. http://dx.doi.org/10.5139/jksas.2019.47.2.143.

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40

Constantinides, Antonios, and Haris Haralambous. "A Compact Wideband Active Two-Dipole HF Phased Array." Applied Sciences 11, no. 19 (September 26, 2021): 8952. http://dx.doi.org/10.3390/app11198952.

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The design and construction of an upgraded HF quarter-wavelength two-dipole active array with 90° difference feed was implemented in the course of a research project to perform a directional (azimuthal) investigation of interference at HF. The lack of affordable compact antennas to meet the project requirements was the incentive to develop a compact unidirectional antenna, with the maximum possible front-to-back ratio at frequencies of 20–30 MHz, where the dimensions of traditional passive antennas are enormous. By installing a low-noise very-high-input impedance amplifier in each dipole of the array, the effect of the mutual coupling between the two dipoles was reduced, improving the front-to-back (F/B) ratio over a wide frequency range. Electronic steering, easy polarization adjustment, and fast and easy deployment were the key requirements for the construction of the antenna. Therefore, a light and compact design was of the utmost importance to meet the space limitations at the monitoring site, which did not allow the deployment of a traditional HF directional antenna that employs a very long boom and elements.
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41

Wei, Xinyuan, Enming Miao, Yangyang Chen, and Wei Wang. "Thermo-Mechanical Coupling Modeling of Active Phased Array Antennas." International Journal of Precision Engineering and Manufacturing 20, no. 11 (August 17, 2019): 1893–904. http://dx.doi.org/10.1007/s12541-019-00206-w.

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42

Holloway, J. "Design considerations for adaptive active phased-array 'multifunction' radars." Electronics & Communication Engineering Journal 13, no. 6 (December 1, 2001): 277–88. http://dx.doi.org/10.1049/ecej:20010605.

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43

Sheehan, P. G., and J. R. Forrest. "Satellite-borne active phased array techniques for mobile communications." IEE Proceedings F Communications, Radar and Signal Processing 133, no. 4 (1986): 339. http://dx.doi.org/10.1049/ip-f-1.1986.0057.

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44

Sanagi, Minoru, Kenji Yano, Kazuhiro Fujimori, and Shigeji Nogi. "Active phased array antenna radiating second harmonic output wave." Electronics and Communications in Japan (Part II: Electronics) 89, no. 4 (2006): 39–50. http://dx.doi.org/10.1002/ecjb.20168.

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45

Jung, Young-Bae. "A Compact Active Channel Module Design for Active Phased Array Antenna System." Journal of IKEEE 17, no. 4 (December 30, 2013): 393–97. http://dx.doi.org/10.7471/ikeee.2013.17.4.393.

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46

Yue, Jian, Anqi Cui, Fei Wang, Lei Han, Jinguo Dai, Xiangyi Sun, Hang Lin, Chunxue Wang, Changming Chen, and Daming Zhang. "Design of Monolithic 2D Optical Phased Arrays Heterogeneously Integrated with On-Chip Laser Arrays Based on SOI Photonic Platform." Micromachines 13, no. 12 (November 30, 2022): 2117. http://dx.doi.org/10.3390/mi13122117.

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In this work, heterogeneous integration of both two-dimensional (2D) optical phased arrays (OPAs) and on-chip laser arrays based on a silicon photonic platform is proposed. The tunable multi-quantum-well (MQW) laser arrays, active switching/shifting arrays, and grating antenna arrays are used in the OPA module to realize 2D spatial beam scanning. The 2D OPA chip is composed of four main parts: (1) tunable MQW laser array emitting light signals in the range of 1480–1600 nm wavelengths; (2) electro-optic (EO) switch array for selecting the desired signal light from the on-chip laser array; (3) EO phase-shifter array for holding a fixed phase difference for the uniform amplitude of specific optical signal; and (4) Bragg waveguide grating antenna array for controlling beamforming. By optimizing the overall performances of the 2D OPA chip, a large steering range of 88.4° × 18° is realized by tuning both the phase and the wavelength for each antenna. In contrast to the traditional thermo-optic LIDAR chip with an external light source, the overall footprint of the 2D OPA chip can be limited to 8 mm × 3 mm, and the modulation rate can be 2.5 ps. The ultra-compact 2D OPA assembling with on-chip tunable laser arrays using hybrid integration could result in the application of a high-density, high-speed, and high-precision lidar system in the future.
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47

Han, Min-Seok, Ju-Man Kim, Dae-Sung Park, Hyoung-Joo Kim, and Jae-Hoon Choi. "Dual Polarized Array Antenna for S/X Band Active Phased Array Radar Application." Journal of electromagnetic engineering and science 10, no. 4 (December 31, 2010): 309–15. http://dx.doi.org/10.5515/jkiees.2010.10.4.309.

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48

WANG, Yan, and Jiaguo LU. "From active phased array antenna to antenna array microsystem in post-Moore era." SCIENTIA SINICA Informationis 50, no. 7 (July 1, 2020): 1091–109. http://dx.doi.org/10.1360/ssi-2019-0247.

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49

Alonso, José, Santiago Pavón, Juan Vidal, and Manuel Delgado. "Advanced Comparison of Phased Array and X-rays in the Inspection of Metallic Welding." Materials 15, no. 20 (October 13, 2022): 7108. http://dx.doi.org/10.3390/ma15207108.

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The most common nondestructive weld inspection technique is X-rays and, since a few years ago, the ultrasound-based phased array. Their comparison has been done from the top view of both, with the result that the phased array is much more efficient in discovering flaws. From the last studies of the authors, a welding flaw can be three-dimensionally reconstructed from the sectorial phased array information. The same methodology is applied to compare quantitatively X-rays and phased array on 15 metal inert/active (MIG/MAG) welding specimens covering pores, slag intrusion and cracks. The results can be summarized in the correlation of the top views and in the correlation profiles between the X-ray top-view and the reconstructed top-view at the depths from phased array in the weld. The maximum correlation is the depth when the flaw in the X-ray looks like that in the phased array records at some depth, leading to an effective quantitative comparison of X-rays and phased array.
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50

Gribanov, A. N., S. E. Gavrilova, O. V. Pavlovich, G. F. Moseychuk, and A. N. Titov. "Method of forming and scaling phased array expanded beams." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 3 (September 30, 2019): 19–29. http://dx.doi.org/10.38013/2542-0542-2019-3-19-29.

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The paper focuses on the phase synthesis of one-dimensionally expanded phased array beams. In the study we used the fan partial diagram method. By this method and applying the known amplitude distribution in the aperture and the desired beam shape, we were able to unambiguously determine the desired phase distribution by means of simple calculations. The method is applicable for a phased antenna array and an active phased antenna array with linear and flat apertures. The study is the first to discuss the scaling properties of expanded beams, which allow one to obtain many synthesis options from only one option by multiplying the phase distribution by the scaling factor. Four important properties of scaling are formulated and proved, which must be taken into account when scaling. The paper gives the results of mathematical simulation and experimental measurements, proving the efficiency of the method
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