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 S₁₁ and S₂₁ 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 S₂₁ calculated from the deduced two-port equivalent circuits of the NaCl solutions were consistent with the measured S-parameters.