Characterization and Modeling of High-Value Inductors in ELF Band Using a Vector Network Analyzer

Characterization and modeling of high-value inductors (hundreds to thousands of henrys) are complex problems, exacerbated when working in the extremely low frequency (ELF) range. This paper details the measurement and characterization of inductors using a vector network analyzer that has a bottom operating frequency of 5 Hz. Using this device, we establish a strategy for measuring the impedance of high-inductance coils—with or without a high-permeability core—and propose a mathematical model that can explain the behavior of these high-inductance coils, which incorporate long lengths of winding wire, as a function of working frequency. These inductors were constructed as part of a research project on ELF electromagnetic fields. The importance of making a complete characterization derives from the need to exploit the largest possible amount of energy captured by the coil, which acts as a sensor. We propose a mixed model of concentrated and distributed parameters that fits the experimental results with an error of about 2% for the frequency range of 5–500 Hz, as part of the characterization process. The effects of the magnetic core on inductance and winding resistance, as a function of frequency, have been characterized in terms of concentration of the magnetic field.