Nonlinear Oscillation Based Synchronized Coupling Oscillator Array: Phased Array without Individual Phase Shifters

Based on synchronized coupling oscillators, we present a nonlinear antenna array. A self-resonating circuitry is related to the nonlinear Van der Pol(VDP) differential equation and its perturbation solution is provided. The corresponding stable limit cycles for different nonlinear indies are plotted. The equivalent negative admittance is adapted for single-transistor oscillation(STO) and the Kurokava resonant criteria are enforced to build the oscillator. When several phased oscillators with slightly different self-resonating frequencies and random initial phases are grouped into a system, every unit oscillator has rapidly synchronized at the centroid frequency, forming a system of coupled oscillator phased array(COPA). The time-domain mechanics of the COPA are solved by fourth-order Runge-Kutta method. A seven-element COPA is designed and simulated by Keysight advance design systems(ADS). In the system, amplitudes of individual oscillators are about the same, while the progressive phase delay of each unit can be precisely predicted and controlled in the precision of picosecond. Good agreement is observed between the Runge-Kutta and ADS solutions. Two single-transistor oscillators(STOs) are combined by the Wilkinson combiner, yielding a unit of push-push double-transistor oscillator(DTO), which may augment scanning angle by 75%. Substrate integrated cavity backed antennas are used for the load. Finally the STO- and DTO- based COPAs of seven-element will be compared, built and tested.