Abstract
In this paper, angular displacement and angular velocity sensors based on coplanar waveguide (CPW) transmission lines and S-shaped split ring resonators (S-SRRs) are presented. The sensor consists of two parts, namely a CPW and an S-SRR, both lying on parallel planes. By this means, line-to-resonator magnetic coupling arises, the coupling level being dependent on the line-to-resonator relative angular orientation. The line-to-resonator coupling level is the key parameter responsible for modulating the amplitude of the frequency response seen between the CPW ports in the vicinity of the S-SRR fundamental resonance frequency. Specifically, an amplitude notch that can be visualized in the transmission coefficient is changed by the coupling strength, and it is characterized as the sensing variable. Thus, the relative angular orientation between the two parts is measured, when the S-SRR is attached to a rotating object. It follows that the rotation angle and speed can be inferred either by measuring the frequency response of the S-SRR-loaded line, or the response amplitude at a fixed frequency in the vicinity of resonance. It is in addition shown that the angular velocity can be accurately determined from the time-domain response of a carrier time-harmonic signal tuned at the S-SRR resonance frequency. The main advantage of the proposed device is its small size directly related to the small electrical size of the S-SRR, which allows for the design of compact angular displacement and velocity sensors at low frequencies. Despite the small size of the fabricated proof-of-concept prototype (electrically small structures do not usually reject signals efficiently), it exhibits good linearity (on a logarithmic scale), sensitivity and dynamic range.
Highlights
Transmission lines loaded with electrically small resonators, such as split ring resonators (SRRs) or complementary split ring resonators (CSRRs), have been applied to the implementation of metamaterial-based or metamaterial-inspired circuits where dispersion and impedance engineering play a key role in their designs [1]
We have demonstrated that shaped split ring resonators (S-SRRs)-loaded coplanar waveguide (CPW) transmission lines are useful for the implementation of compact angular displacement and angular velocity sensors
For miniaturization purposes, it is necessary to consider electrically small resonators, such as the S-SRR, which by virtue of its large inductance is electrically much smaller than other resonant particles which have been proposed for angular displacement and velocity sensors
Summary
Transmission lines loaded with electrically small resonators, such as split ring resonators (SRRs) or complementary split ring resonators (CSRRs), have been applied to the implementation of metamaterial-based or metamaterial-inspired circuits where dispersion and impedance engineering play a key role in their designs [1]. A novel approach for the implementation of microwave sensors, based on the disruption of symmetry in transmission lines loaded with electrically small resonators, was proposed [21] In this strategy, which is considered here and which may be referred to as coupling-modulated resonance, the sensors are designed to be symmetric in the non-actuated (unperturbed) state. Transmission line based sensors might not satisfy the size requirements of many applications, unless the sensing elements are electrically very small In this regard, the S-shaped split ring resonator (S-SRR) [32,33,34], the considered sensing element in this work, is a very convenient resonant element, since it is by far electrically smaller than other resonant elements previously utilized to build up angular displacement and velocity sensors, such as the split ring resonator (SRR) [35] or the electric-LC (ELC) resonator [36]. This topology is disregarded here because sensor performance is expected to be degraded to a considerable extent (an extremely low attenuation is expected due to the excessive increase in the resonator capacitance produced by the broadside electric coupling)
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