Logarithmic derivative method and system for capacitance measurement.
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.
College of Energy, Xiamen University, Xiamen 361102, China.
Yichun
Y
Wu
College of Physics and Information Engineering, Minnan Normal University, Zhangzhou 363000, China.
Lingzhi
L
Wang
College of Energy, Xiamen University, Xiamen 361102, China.
Yuanfeng
Y
Cai
College of Physics and Information Engineering, Minnan Normal University, Zhangzhou 363000, China.
Cunqiao
C
Wu