On Supercapacitors Time-Domain Spectroscopy. C/R Characteristic Slope
Abstract
A novel time-domain technique for supercapacitor characterization is developed, modeled numerically, and experimentally tested on a number of commercial supercapacitors. The method involves momentarily shorting a supercapacitor for a brief duration, denoted as τ, and measuring first ∫ Idt and second ∫ I2dt moments of current along with the potential before and after shorting. The effective C(τ) and R(τ) are then obtained from charge preservation and energy dissipation invariants. A linear behavior in [R(τ),C(τ)] parametric plot is observed by several orders of τ. This gives a C/R characteristic slope: how much C we can ``gain'' if we are ready to ``lose'' R in internal resistance. The C/R characteristic slope characterizes possible energy and power properties of the device in terms of materials and technology used, this is a measure of supercapacitor perfection. The technique has been proven with experimental measurements and then validated through computer modeling, analytic analysis, and impedance spectroscopy on a number of circuit types: transmission line, binary tree, etc., a new n-tree element (nTE) is introduced. The approach offers an alternative to low-frequency impedance spectroscopy and methods outlined in the IEC 62391 standard. It provides valuable insights into the performance and characteristics of supercapacitors.