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We present a comprehensive nonlinear analysis of coupled oscillators and examine the trade-off between phase-noise of the oscillator and the quadrature precision. We show that asymmetry gives rise to amplitude and phase imbalance which are proportional to the inverse and inverse square, respectively, of the relative coupling strength. It is shown that the level of AM-PM is determined by the nonlinearity of the coupling transconductance. The 3dB noise reduction in close-to-carrier phase-noise in quadrature oscillators due to mutual coupling is lost to the extra AM-PM noise for large coupling strengths. The additional contribution of the internal noise sources in the coupling circuit together with the AM-PM noise contribution explains why the 3dB noise reduction is rarely seen in measurements of this particular circuit.