# Planar Microwave Resonant Sensors: A Review and Recent Developments
## 4 Prototype Examples
### Coupling Modulation Sensors  
As discussed in Section 2, coupling modulation sensors are implemented by symmetrically loading a transmission line with a symmetric resonator. The symmetry planes of the line and resonant element should be of different electromagnetic sort, i.e., one should be a magnetic wall and the other one an electric wall. Figure 12 illustrates the working principle of coupling modulation sensors, by considering a CPW loaded with a SRR [47]. The line exhibits a magnetic wall at the axial symmetry plane for the fundamental CPW mode, whereas the symmetry plane of the SRR is an electric wall at the fundamental resonance. For perfect symmetry, the electromagnetic field generated by the line is not able to excite the SRR, and the structure is all-pass in the vicinity of the SRR fundamental resonance. This situation is preserved if the SRR is symmetrically loaded with a dielectric material. However, if symmetry is truncated, e.g., by means of an asymmetric dielectric load, as depicted in Figure 12, then the resonator is driven by the line (i.e., line-to-resonator coupling is activated), and a notched response (bandstop-type) appears. Although this type of sensor can be used for dielectric characterization or for comparison purposes by exploiting their electromagnetic symmetry properties, most coupling modulation sensors have been applied to the implementation of linear or angular displacement and velocity sensors [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 48]. The reason is that a relative linear or angular displacement between the line and the resonant element also truncates symmetry (except if the resonant element displaces linearly in the direction of the line axis). Thus, in this subsection, this sensing approach is illustrated by means of two examples, to be discussed next. Figure 11: Real (**a**) and imaginary (**b**) part of the complex dielectric constant of water–methanol solutions as a function of the water content, inferred from the data of Figure 10 and the mathematical model developed in [46]. From [46], reprinted with permission. In the first example [22], an angular displacement and velocity sensor based on a circular-shaped CPW loaded with a movable circular ELC resonator is reported. The ELC resonator is a bisymmetric particle, exhibiting orthogonal electric and magnetic walls. Thus, significant variation of line-to-resonator coupling by ELC rotation can be achieved, and this is interesting in terms of the output dynamic range. Figure 13 shows the picture of the CPW and ELC resonator, as well as the experimental set-up used for measuring the angular displacement and velocity. Figure 12: Illustration of symmetry disruption by means of square-shaped inclusions in a CPW loaded with a SRR. From [47], reprinted with permission. Figure 13: Set-up for the angular displacement and velocity measurement. (**a**) Cross section view, (**b**) photographs of the rotor (circular ELC resonator) and stator (CPW), and (**c**) photograph of the step-motor providing rotor motion and zoom view of the stator-rotor. From [22], reprinted with permission. By rotor motion with regard to the stator, the transmission coefficient at \(f_{0}\), the resonance frequency of the ELC, experiences a roughly linear variation with the rotation angle, as can be appreciated in Figure 14. Thus, the output variable for measuring angular displacement is the magnitude of the transmission coefficient. The sensitivity is reasonable, but the dynamic range is restricted to \(90^{\circ}\), as it can be explained from obvious symmetry considerations. To measure the (average) angular velocity, the strategy proposed in [22] is based on an amplitude modulation (AM) scheme. By feeding the line with a harmonic signal tuned to the resonance frequency of the ELC, the amplitude at the output port is expected to be modulated due to the time-varying coupling between the line and the resonant element, and two pulses of the envelope function per cycle are expected.