On Supercapacitors Time-Domain Spectroscopy. C/R Characteristic Slope
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 $\int Idt$ and second $\int I^2dt$ 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 $ΔC$ we can ``gain'' if we are ready to ``lose'' $ΔR$ 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.