Quadrature Van der Pol oscillators using second harmonic coupling

A new coupling mechanism is used to synchronize two Van der Pol oscillators. This coupling uses the second harmonic appearing in common mode current of each oscillator. The common mode current is measured by a current mirror, and is amplified by a current amplifier. The amplifier introduces negative feedback, so that the current in the current mirror measuring diode of the first oscillator is nearly equal to the common mode current of the second oscillator, hence the coupling is established. It is shown that the system of two oscillators is described by two differential equations where the coefficients in one equation have the perturbations defined by the second oscillator, and vice versa. The coupling amplifier gain is defined. The developed concepts are demonstrated on a 5 GHz CMOS LC oscillator with quadrature outputs. The oscillator phase noise is lower than -116 dBc/Hz at 1-MHz offset