Two-port Equivalent Circuits Deduced from S-parameter Measurements of NaCl Solutions

Abstract

We deduced two-port equivalent circuits related to molar concentrations M (0–1 mol/L) of NaCl solutions by measuring S-parameters S 11 and S 21 at frequencies from 1 to 100 MHz, using a portable vector-network-analyzer (NanoVNA) and two-port coaxial probes. The deduced two-port equivalent circuits of the NaCl solutions consist of three sub-CR circuits. Resistances R n and capacitances C n comprising the sub-CR circuits were calculated using the molar concentrations M related to solute-ions of Na+ and Cl− and relative dielectric constant of solvent H2O. The electrical conductivity of the two-port equivalent circuits reflected drift mobility of the solute ions and rotation and vibration of polar molecules of the solvent H2O. Input impedances Z in and transmission coefficients S 21 calculated from the deduced two-port equivalent circuits of the NaCl solutions were consistent with the measured S-parameters.