噪声扰动下RLC串联谐振电路随机共振的数值研究

Numerical simulation for stochastic resonance of a RLC series resonant circuit under noise disturbance

采用四阶Runge-Kutta算法,以信噪比增益和谱功率放大率为随机共振测度指标,研究了电容参数和激励信号均受高斯白噪声扰动时RLC串联谐振电路的随机共振现象。研究表明,欠阻尼RLC串联谐振电路在适当的电路参数、激励信号频率和噪声参数条件下,信噪比增益和谱功率放大率是噪声强度和输入信号频率的非单调函数,且其值均大于1,电路中存在随机共振现象;而在临界阻尼或过阻尼情况下尽管信噪比增益在一定条件下也是噪声强度和输入信号频率的非单调函数,但谱功率放大率取值小于1,电路发生了随机共振现象,改善了信噪比,信号能量却并未得到加强。这一结论使得将欠阻尼RLC串联谐振电路应用于微弱信号检测成为可能。

The stochastic resonance of a RLC series resonant circuit whose capacitance parameters and excitation signal were disturbed by Gaussian white noise was studied using Fourth-order Runge-Kutta algorithm, and taking signal to noise ratio（SNR） gain and spectral power magnification as indicators for stochastic resonance（SR） measurements. The results showed that it an underdamped RLC series resonant circuit has appropriate system parameters, noise parameters and excitation signal frequencies, its SNR gain and spectral power magnification are non-monotonic functions of noise intensity and frequency of input signal, and their values are greater than 1, stochastic resonances occur in the circuit; while in critical damping or overdamped case, although the SNR gain under a certain condition is also non-monotonic function of noise intensity and input signal frequency, the spectral power magnification value is less than 1; the occurrence of stochastic resonance improves SNR, but signal energy is not enhanced. This conclusion made application of an underdamped RLC series resonant circuit in weak signal detection possible.