Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
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二次和三次非线性对完美调谐参数放大器的影响
DOI：
10.1016/j.jsv.2016.09.013
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发表时间：
2017
影响因子：
4.7
通讯作者：
J. J. Thomsen
中科院分区：
文献类型：
--
作者：
S. Neumeyer;V. Sorokin;J. J. Thomsen
我们考虑的参数放大器的性能与完美的调谐（二比一的参数和直接激励频率之间的比例）和二次和三次非线性。以一个带有二次非线性项的受迫Duffing-Mathieu方程为模型系统，利用变幅法得到了系统的近似解析稳态解和相应的稳定性。纯二次，混合二次和三次非线性参数放大的一般影响。特别是，混合的二次和三次非线性的影响可能会产生额外的振幅-频率的解决方案。在这种情况下，与纯二次或三次非线性的情况相比，获得了增加的响应和更相位敏感的幅度（激励频率之间的相位）。此外，跳跃和双稳定的幅相特性的预测，支持以前报道的实验观察。
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi-stability in the amplitude–phase characteristics are predicted, supporting previously reported experimental observations.