Analysis of coupled phase-locked loops with independent oscillators for beam control active phased arrays

Phase dynamics and phase noise of N coupled phase-locked loops (PLLs) with N independent oscillators are analyzed. The phase noise of coupled PLLs with independent oscillators is analyzed by using the signal flow graph and Mason´s gain rules. The near-carrier phase noise of PLL elements in the array can be reduced to 1/N that of a single independent (without coupling) VCO of the PLL element, and return to its free-running phase noise far from the carrier frequency, provided the coupling network is reciprocal, the feedback loop gain of the PLL elements is large, and the phase detector and amplifier noise are neglected. The phase dynamics and noise improvement of coupled PLL arrays are verified by using two coupled PLLs with independent GaAs MESFET oscillators operating at X-band.