Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 61901086), the Postdoctoral Innovation Talents Support Program of China (Grant No. BX20180057), the China Postdoctoral Science Foundation (Grant No. 2018M640907), and the Fundamental Research Funds for the Central Universities (Grant Nos. ZYGX2019J101, ZYGX2019Z016)
Received Date:04 November 2020
Accepted Date:17 December 2020
Available Online:23 April 2021
Published Online:05 May 2021
Abstract:At present, researchers generally believe that the change of maximum directivity of planar phased arrays in beam scanning process conforms with the cosine law, so that the wide-range beam scanning from broadside to end-fire is impossible to realize. There are three main factors that affect the scanning range of the planar phased array antenna: 1) array factor; 2) element pattern; 3) port impedance matching. Scholars have done a lot of researches on the element pattern and the port impedance matching. About the array factor, Elliott, a famous phased array scholar, made a theoretical study on the directivity of the linear array and the planar array in 1963 and 1964, concluding that the variation of directivity of planar phased array conforms with the cosine law. However, the above conclusion came from an approximate formula under certain conditions: 1) the element pattern in the half-space is omnidirectional; 2) the beam of a large array is narrow enough; 3) the beam cannot scan a range of several beamwidths close to end-fire. To make clear the scanning beam’s change law of planar arrays, the law of directivity changing with scanning angle of linear array and planar phased array with different sizes are analyzed by using the strict formula of array factor, and the directivity’s change law derived from strict formula of array factor is compared with the cosine law. The results show that 1) the variation law of the directivity of a linear array depends on the spacing between elements. When the spacing between elements is equal to half a wavelength, the directivity of the array does not change with the scanning angle. When the spacing between elements is less than half a wavelength, the directivity of the array increases with scanning angle increasing. 2) The directivity of a finite array decreases with scanning angle increasing. However, the scanning beam’s maximum directivity of a finite planar phased array does not satisfy the cosine law and it is not zero in the end-fire range. Based on the above conclusions, the idea that the change of array factor’s directivity is compensated for by element beamforming is further proposed, which points out a direction for realizing the ultra-wide-angle-range beam scanning of planar phased arrays. Keywords:planar array antenna/ wide-angle scanning/ array factor/ element beamforming
为了定量分析一维阵列阵因子大角度扫描的规律, 分析了不同阵列规模、不同单元间距的阵列在不同扫描角度时阵因子的最大方向性系数, 如图2所示. 在实际的大角度扫描阵列中, 为了避免栅瓣, 阵元间距一般都小于0.5λ, 因此本文不讨论阵列间距大于0.5λ的情况, 此处 λ为自由空间波长. 为了方便对比, 图2中的方向性系数曲线都按照对应阵列在单元间距为0.5λ时侧射波束的方向性系数进行了归一化. 图中90°为侧射方向, 0°为端射方向. 从图2可以看出, 当单元间距为0.5λ时, 其方向性系数不随扫描角度变化. 当阵元间距为0.1λ, 0.2λ, 0.3λ, 0.4λ和0.489λ时, 一维阵因子的方向性系数均会随着扫描角度的增加而增加. 特别地, 当阵元间距小于0.4λ时, 一维阵因子的方向性系数在端射方向均比边射方向约大3 dB, 只有当阵元间距接近0.5λ时(0.489λ), 该数值才会发生明显变化. 这表明, 要利用阵因子弥补单元方向图在端射附近的增益下降, 并不需要非常小的阵元间距, 这对线阵实现超大角度扫描非常有利. 并且, 当单元间距小于等于0.5λ时, 直线阵方向性系数的变化都与余弦规律无关, 这和Elliott关于线阵的分析是吻合的[20]. 从图2的结果来看, 对于直线阵来说, 阵因子并非限制阵列大角度扫描特性的因素, 只要单元方向图波束宽度足够, 端口阻抗随扫描角度变化较小, 就能够实现大角度扫描, 现已有诸多研究基于上述思路实现了线阵的大角度扫描, 甚至超大角度扫描[11,13]. 因为很多文献将扫描范围大于 ±45°的阵列都称为大角度扫描阵列, 为了加以区分, 本文将具有从侧射扫描到近端射方向能力的阵列称为超大角度扫描阵列. 图 2 一维阵因子在不同阵元间距扫描时的归一化方向性系数随扫描角度的变化 (a) 一维阵列尺寸为8λ; (b) 一维阵列尺寸为16λ; (c) 一维阵列尺寸为32λ; (d) 一维阵列尺寸为64λ Figure2. Normalized directivity of the linear array factor varies with different element spaces and different scanning angles: (a) The size of the linear array factor is 8λ; (b) the size of the linear array factor is 16λ; (c) the size of the linear array factor is 32λ; (d) the size of the linear array factor is 64λ.