Injection Locking in Concurrent Dual-Frequency Oscillators

In a separate paper, the authors show that a nonlinear active core with a fourth-order resonator can generate two stable independent frequencies simultaneously. In this paper, the effect of injecting two frequencies into such a concurrent dual-frequency oscillator is analyzed and experimentally verified. It is shown that, for weak injection, the effect of injection at one frequency is decoupled from the effect of injection at the other frequency. The differential equation describing the effect of injection at either of the two frequencies is similar to the Adler's injection-locking equation for single-frequency oscillators. A theoretical analysis for a linear array of coupled concurrent dual-frequency oscillators is provided. It is shown that a linear phase progression at both frequencies can be achieved independently by detuning the array's end elements. Dual-frequency quadrature signal generation using two coupled concurrent dual-frequency oscillators is also demonstrated. To verify the theoretical derivations, an integrated circuit in a 0.18-$mu$m SiGe BiCMOS process is designed and fabricated. Measurement results closely match the theoretical predictions. The application of concurrent coupled oscillator array in dual-frequency beam forming with steering capability is also demonstrated.