Determination of supercapacitor metrics using a magnitude-only method

Impedance spectroscopy is a powerful tool to study the frequency behavior of supercapacitors, but it comes with pricy hardware and postprocessing routines. Here we present a non-impedance method to extract the fractional-order model parameters (R
_s
, C
_α
, α) of a supercapacitor-assumed to be equivalent to a series association of a resistance with a constant phase element-using the magnitude response of a measurement circuit consisting of a large bandwidth operational amplifier with negative feedback. The theory behind the measurement circuit, along with the extraction method of the model parameters, and validation within 1% error using simulated and experimental results from a commercial supercapacitor are presented and discussed.