Theory of cross-coupled RF oscillator for multi- and quadrature-phase signal generation

We proved in this paper that, a system composed of identical sub-systems that are cross-coupled in certain manner is capable of generating multi- or quadrature-phase oscillation signals under specified conditions. Based on the theory, an RC multi-phase oscillator is proposed as an example, for which the condition for maintaining stable oscillation is also deduced. Moreover, a detailed numerical result is presented, particularly for a four-phase, namely quadrature oscillator, which is in accordance with the proposed theoretical analysis.