反并联二极管对LC电路的非线性阻尼
Nonlinear Damping of the LC Circuit using Anti-parallel Diodes
摘要：
我们研究了一个简单的变化的串联RLC电路中，反并联二极管取代电阻。这导致具有非线性阻尼项的阻尼谐振子，该非线性阻尼项在零电流处最大，并且对于远离零的电流以逆电流关系减小。一组非线性微分方程的振荡器电路推导和集成电路测量比较数值。该协议是非常好的瞬态和稳态响应。与标准RLC电路不同，该电路的行为是幅度相关的。特别地，对于瞬态响应，振荡器从欠阻尼行为过渡到过阻尼行为，并且对于被驱动振荡器，随着驱动源幅度增加，谐振响应变得更尖锐和更强。该设备价格便宜，并且在高级物理实验室中很常见。
英文摘要：
We investigate a simple variation of the series RLC circuit in which anti-parallel diodes replace the resistor. This results in a damped harmonic oscillator with a nonlinear damping term that is maximal at zero current and decreases with an inverse current relation for currents far from zero. A set of nonlinear differential equations for the oscillator circuit is derived and integrated numerically for comparison with circuit measurements. The agreement is very good for both the transient and steady-state responses. Unlike the standard RLC circuit, the behavior of this circuit is amplitude dependent. In particular for the transient response the oscillator makes a transition from under-damped to over-damped behavior, and for the driven oscillator the resonance response becomes sharper and stronger as drive source amplitude increases. The equipment is inexpensive and common to upper level physics labs.
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