Wu Yichun, Wang Lingzhi, Cai Yuanfeng, Wu Cunqiao
College of Energy, Xiamen University, Xiamen 361102, China.
College of Physics and Information Engineering, Minnan Normal University, Zhangzhou 363000, China.
Rev Sci Instrum. 2015 Aug;86(8):085109. doi: 10.1063/1.4928061.
A novel method based on logarithmic derivative is introduced to analyze multi-lifetime decay. As the discharge voltage signal of a RC circuit is a special kind of multi-lifetime exponential decay, the logarithmic derivative method can be used to measure single capacitance and multiple capacitances. With the logarithmic derivative method, a log(t) curve strongly peaked at precisely log(τ) is obtained, where the lifetime τ equals to RC. In a measurement system, if the resistance R is known, then the capacitance under test can be calculated. A logarithmic derivative curve fitting method is also presented, which has better anti-noise capability than the method that simply finds the maximum data on the peak. The curve fitting method can also be used for multiple capacitors measurement. To measure small capacitances, a large enough time window of the measuring instrument is required. Based on a field programmable gate array and a high speed analog-to-digital converter, a measurement system is developed. This system can provide the 16-bit resolution with sampling rate up to 250 MHz, which has a large enough time window for measuring lifetime shorter than 10(-8) s. To reduce the amount of data needed to be stored and the noise due to the derivative treatment of transient data, the interpolation and noise-filter algorithms are employed. Experiments indicate that the logarithmic derivative method and system are suitable for the measurement of capacitances discharge and other exponential decay processes.
介绍了一种基于对数导数的新方法来分析多寿命衰减。由于RC电路的放电电压信号是一种特殊的多寿命指数衰减，对数导数法可用于测量单个电容和多个电容。使用对数导数法，可以得到在精确的log(τ)处强烈峰值的log(t)曲线，其中寿命τ等于RC。在测量系统中，如果已知电阻R，则可以计算被测电容。还提出了一种对数导数曲线拟合方法，该方法比简单地在峰值处找到最大数据的方法具有更好的抗噪声能力。曲线拟合方法也可用于多个电容器的测量。为了测量小电容，需要测量仪器有足够大的时间窗口。基于现场可编程门阵列和高速模数转换器，开发了一种测量系统。该系统可提供16位分辨率，采样率高达250 MHz，具有足够大的时间窗口来测量短于10(-8)s的寿命。为了减少需要存储的数据量以及由于瞬态数据的导数处理而产生的噪声，采用了插值和噪声滤波算法。实验表明，对数导数法和系统适用于电容放电及其他指数衰减过程的测量。
