The effect of amplitude control and randomness on strongly coupled oscillator arrays

THE EFFECT OF AMPLITUDE CONTROL AND RANDOMNESS ON STRONGLY COUPLED OSCILLATOR ARRAYS Name: Jiang, Hai University of Dayton Advisor: Dr. Robert P. Penno Phased arrays have many applications such as Radar Communication, Satellite Communication, and Wireless Local Area Networks (WLAN). For the traditional phased array, a phase shifter is used with each antenna element to establish a constant phase progression along the antenna array. A constant phase progression will force the electromagnetic wave to add up so that the energy would radiate at a particular angle with respect to the array. However, it is difficult to integrate the bulky phaseshifters in the monolithic module, especially when the application involves a large number of elements. This dissertation studies an alternative phase beam-scanning technique using arrays of coupled oscillators (COA), which avoids the use of phase shifters. This technique of COA may reduce the complexity of phase control circuits and provide for a phased array of lower volume and weight. Consequently, it simplifies the architecture of the T/R module and reduces the overall cost. iii In this work, dynamic equations of the nonlinear COA with arbitrary coupling networks are derived using both time and frequency domain methods. From the dynamic analysis, it is shown that the phase distribution along the array, and hence the beam scanning angle of the array, can be controlled by free running frequencies of the coupled oscillators. The stability and nonlinear behaviors of synchronized coupled oscillators are studied via the nonlinear control theory and applied to radar beam scanning arrays. Analysis indicates that a stable, unique equilibrium point exists when choosing a specific set of free running frequencies, and it is associated with the desired phase shift but within a given range. By means of previous dynamic analysis, effects of amplitude dynamics are studied for COAs with uniform, triangular and Chebyshev amplitude distributions. The array with different coupling strengths, nonlinear parameters, and synchronization frequencies are considered. Results demonstrate that beam shapes and SLLs can be controlled for the coupled oscillator array using strong coupling. The influence of the random, free-running frequency distribution of the phase error in COAs, which causes the phase shift error and hence the error of main beam scanning angle (EMBSA), is also investigated through a Monte Carlo analysis. It is found that strongly COAs are more robust than weakly COAs under the same level of randomness in free running frequencies. Furthermore, when random deviations become larger, the robustness of strongly COA is especially obvious.