Modeling and simulations of the amplitude–frequency response of transmission line type resonators filled with lossy dielectric fluids

Stub resonators can be used to assess the dielectric properties of fluids. The resonance frequencies, determined from the amplitude versus frequency (AF) response of such resonators, are mainly determined by the permittivity of the fluid while damping arises from dielectric losses. Even though this methodology has been extensively reported in the literature, without almost any exception these studies refer to (near) ideal behavior regarding for example, geometry and negligibly low conductivity of the fluid studied. Online stub resonator-based sensors (i.e., flow-through) in use for industrial applications, however, quite often suffer from high dielectric losses, non-ideal material choice of the conductors from an electrical point of view and unconventional resonator geometry. Therefore, in order to ensure correct data interpretation, a straightforward model accounting for the effects of dielectric losses, conductor losses (skin effect) and impedance mismatches on the AF response is highly desirable. In addition, such a model can help to optimize future sensor designs. Here, we present a lumped parameter model, essentially based on telegrapher's equations, that accounts for the skin effect, dielectric losses and impedance mismatches between the transmission lines to the resonator and the resonator respectively. The adequacy of the method, even in the case of impedance mismatch, is demonstrated by comparing these model simulations with experimentally obtained AF curves for both flow-through coaxial stub resonators and microstrip resonators immersed in the fluid under investigation