# Planar Microwave Resonant Sensors: A Review and Recent Developments
## 4 Prototype Examples
### Coupling Modulation Sensors
Thus, from the time distance between adjacent pulses, the angular velocity can be inferred. The envelope function can be simply obtained by means of an envelope detector, preceded by an isolator (implemented by means of a circulator) in order to protect the CPW line against mismatching reflections from the diode (a highly nonlinear device). The schematic diagram of the approach is presented in Figure 15. Figure 16 depicts a pair of recorded envelope functions (visualized in an oscilloscope in [22]), corresponding to different angular velocities of the rotor (particularly, 1 rpm and 50 rpm). The measured envelope functions reveal that the method is useful to provide the angular velocity. However, it is not possible to obtain instantaneous velocities with this approach, as only two pulses per cycle are generated. Namely, only the average angular speed corresponding to time lapses between adjacent pulses can be measured. In order to improve this limitative aspect, a very large number of pulses is necessary (like in optical encoders [92; 93; 94]). Thus, a different approach for the measurement of angular displacements and velocities was reported in [28], where a completely different configuration (edge configuration), providing hundreds of pulses per revolution, was implemented. Figure 14: Transmission coefficient at \(f_{0}\) as a function of the rotation angle. From [22], reprinted with permission. Figure 15: Sketch of the system for the measurement of angular velocities based on an AM modulation scheme. In the rotation sensor of Figure 13, the axis of the resonator coincides with the axis of the rotor (axial configuration). In [28], a rotor consisting of a circular chain of resonant elements etched along its edge was proposed as a means to boost the number of pulses (see Figure 17). The working principle is indeed very similar to the one used to infer the angular velocity with the sensor based on the axial configuration. Namely, by rotor motion, the amplitude of the feeding harmonic signal is modulated, but at least as many pulses as resonators in the chain can be generated per each revolution. Indeed, it was demonstrated in [29; 30] that by conveniently choosing the frequency of the feeding signal, up to two pulses per resonant element can be achieved, and the sensor reported in [30] exhibits 1200 pulses per revolution (i.e., 600 resonators), which is a relevant figure of merit. Moreover, this sensor is equipped with a resonator's chain devoted to detect the motion direction (see details in [30]). Note that in this sensor based on the so-called edge configuration, the working principle is coupling modulation as well. By this means, the transmission coefficient of the line at the frequency of the feeding signal periodically varies with time, generating a pulsed AM signal at the output port of the line. However, coupling modulation is achieved by the consecutive crossings of the resonant elements of the chain over the axis of the line (stator), when the rotor is in motion. The working principle is very similar to the one of optical encoders, with apertures in a metallic disc. In such encoders, the apertures are detected by means of an optical beam (when an aperture lies in the path between the source and the detector, a pulse is generated). By contrast, in the sensor based on the edge configuration, the resonators are detected by means of an electromagnetic signal. Therefore, such sensors can be designated as electromagnetic (or microwave) rotary encoders. Figure 16: Measured envelope functions. (a) 1 rpm; (b) 50 rpm. From [22], reprinted with permission. Figure 17: Sketch of the rotation sensor based on the edge configuration. From [29], reprinted with permission. Figure 18 depicts the sketch of the sensor with a double chain of resonators to measure the angular speed, and an additional non-periodic chain to discriminate the motion direction.