We present an analytical calculation of the response of a driven Duffing oscillator to low-frequency fluctuations in the resonance frequency and damping. We find that fluctuations in these parameters manifest themselves distinctively, allowing them to be distinguished. In the strongly nonlinear regime, amplitude and phase noise due to resonance frequency fluctuations and amplitude noise due to damping fluctuations are strongly attenuated, while the transduction of damping fluctuations into phase noise remains of order 1. We show that this can be seen by comparing the relative strengths of the amplitude fluctuations to the fluctuations in the quadrature components, and suggest that this provides a means to determine the source of low-frequency noise in a driven Duffing oscillator.

我们提出了驱动 Duffing 振荡器对共振频率和阻尼的低频波动的响应的分析计算。我们发现这些参数的波动表现得很明显，可以区分它们。在强非线性状态下，谐振频率波动引起的幅度和相位噪声以及阻尼波动引起的幅度噪声被强烈衰减，而阻尼波动到相位噪声的转换仍然保持在 1 阶。我们表明，这可以通过比较幅度波动与正交分量波动的相对强度，并表明这提供了一种确定驱动杜芬振荡器中低频噪声源的方法。