The effect of mismatch and disturbances on the quadrature relation of a cross-coupled relaxation oscillator

Cross-coupled relaxation oscillators are capable of producing two stable and highly accurate, quadrature output signals. We present a complete high-level model of the cross-coupled relaxation oscillator in terms of circuit parameters, from which we obtain explicit expressions for duty-cycle, oscillation frequency and output phase relation. They predict the influence of mismatches and other disturbances such as delays, at circuit level. The results provide useful guidelines for the design of a high performance circuit of such an oscillator. The theoretical results are confirmed by simulation and by experiment