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.