Complex Permittivity of NaOH Solutions Used in Liquid-Metal Circuits

Gallium alloys are liquids at room temperature, and are suitable as conductors in electronic circuits. Furthermore, gallium-based liquid metals immersed in a water-based electrolyte such as sodium hydroxide (NaOH) can be electrically actuated, enabling reconfigurable electronics such as RF switches, tunable filters, and tunable antennas. However, NaOH in liquid-metal reconfigurable electronics also causes RF losses that should be minimized by careful design and simulation. To accurately simulate the effects of NaOH at microwave frequencies, the complex permittivity of NaOH is required over the operating frequency range. Here, the complex dielectric permittivity of aqueous NaOH solutions is determined from 0.2 to 20 GHz by dielectric spectroscopy. NaOH solutions with concentrations of 0.01 moles/liter (M), 0.1 M, 0.25 M, 0.5 M, 0.75 M, 1.0 M, 1.25 M, and 1.5 M are investigated at 20 °C. The complex permittivity spectra are fitted by a Cole-Cole relaxation time distribution. In addition, the fitting parameters, including static permittivity <inline-formula> <tex-math notation="LaTeX">$\varepsilon _{s} $ </tex-math></inline-formula> and relaxation time <inline-formula> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> are reported, along with the distribution parameter <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>. The measured permittivity of NaOH is used to simulate two liquid-metal RF components using NaOH. The measured RF performance are in good agreement with the simulated results that include the effects of NaOH.