Distortion Generated in Angle-Modulation Systems by Phased Arrays

The case of linear, uniformly weighted phased arrays is examined via time and frequency domain analyses. Bounds that must be placed on array length, modulation frequency, modulation index ?, and scan angle relationships if excessive distortion is to be avoided in wideband angle-modulated communication systems are established. Distortion is shown to consist of odd harmonic terms. It is also shown that, for one class of equivalent RF signals, phased arrays produce approximately three times as much distortion in frequency-modulation (FM) systems as in phase-modulation (PM) systems. Graphs of distortion plotted as functions of signal and array parameters show that, for practical array sizes, distortion is a monotonically increasing function of the product of L and sin ? where L is the length of the array expressed in modulation wavelengths ?m and ? is the scan angle. In PM systems, distortion also increases monotonically with the modulation index ?. Plots of distortion versus L sin ? show that even relatively small arrays can produce intolerable distortion levels in wideband systems; e.g., an FM system having ? = 3,L = 0.35?m, and ? = 60 degrees exhibits approximately 20 percent distortion.