Probing the Theoretical Ultimate Limit of Coaxial Cable Sensing: Measuring Nanometer-Scale Displacements

Open-ended coaxial probes have been widely explored and commercialized for dielectric spectroscopy at microwave frequencies over the past decades. The working principle of the probes relies on the dependence of the fringing field on the complex permittivity of the material in front of the open end. In this article, inspired by the optical fiber extrinsic Fabry-Perot interferometer, we propose a novel sensing scheme based on an open-ended hollow coaxial cable resonator (OE-HCCR). The resonator is constructed using two reflectors along the coaxial line. The first reflector is a metal post at the RF input end, shorting the inner and outer conductors. The second reflector is the open end, where a metal plate is placed parallel and near the open end. The resonance frequency of the open-ended coaxial resonator depends strongly on the gap distance between the metal plate and the open end of the coaxial cable, due to the modulation of the phase of the reflection coefficient that characterizes the open end. Thus, by correlating the resonance frequency to the gap distance between the metal plate and the open end (or the movement of the metal plate), the OE-HCCR can be used as a displacement sensor device. Importantly, the displacement measurement resolution of the OE-HCCR is three orders of magnitude greater than that of the existing coaxial-cable-based displacement sensors within a certain dynamic range (~0.11 mm), affording a resolution that is comparable to fiber-optic sensors. The mathematical model of the OE-HCCR is discussed in detail, followed by a proof of concept for displacement measurements. The novel OE-HCCR device is suitable for sensing applications in harsh environments and will advance the field of physical/chemical sensing.