Microwave Sensors Based on Symmetry Properties of Resonator-Loaded Transmission Lines

This review paper is focused on the design of microwave sensors using symmetry properties of transmission lines loaded with symmetric resonators. The operating principle of these sensors is presented and then several prototype devices are reported, including linear and angular displacement sensors and rotation speed sensors. The main advantage of the proposed sensors is the robustness against changing environmental conditions.


Introduction
The microwave sensors based on symmetry properties presented in this review paper are inspired by resonant-type metamaterial transmission lines [1][2][3][4][5][6][7][8], a subclass of metamaterial transmission lines (see the books [9][10][11][12][13] for an in-depth study of these artificial lines), where a host line is loaded with electrically small resonators and, habitually, with additional lumped or semilumped reactive components (inductors and/or capacitors).Figure 1 depicts the first reported resonant-type metamaterial transmission line [1], implemented by means of a coplanar waveguide (CPW) loaded with split ring resonators (SRRs) [14] and shunt connected inductive strips.If the fundamental resonance frequency of the SRRs is smaller than the cut-off frequency of the high pass filter that results by loading the CPW only with the inductive strips, then the SRR/strip-loaded CPW exhibits a band pass response, and wave propagation in the first allowed band is left handed (LH), or backward [1].Backward wave propagation means that the phase and group velocities are antiparallel; namely, the wave fronts propagate to the direction opposite to energy flow, that is, towards the source.This unconventional type of propagation, due to the combined effect of the SRRs and inductive strips, is caused by the simultaneously negative effective permeability and permittivity in that band [15] and is related to the presence of SRRs and strips, respectively [1].Indeed the SRR/strip-loaded CPW is the planar counterpart of the one-dimensional bulk LH metamaterial reported in [16], where an array of SRRs is combined with metallic posts (the incident radiation must be polarized with the magnetic field axial to the SRRs and the electric field parallel to the metallic posts).In both media, the simultaneous negative sign of the effective permeability and permittivity does not preclude wave propagation, as follows from inspection of Maxwell's equations; however, wave propagation is not forward, but backward.
If the strips are removed, the pass band switches to a stop band, which can be interpreted as being due to the negative effective permeability related to the presence of the SRRs (see Figure 2).In the vicinity of the SRR fundamental resonance, the SRRs are excited by the magnetic field generated by the line.Above that frequency, the structure exhibits a negative effective permeability in a narrow band, and, below that frequency, the effective permeability is highly positive, resulting in a stop band.However, the stop band behavior of a CPW loaded only with pairs of SRRs can also be interpreted from circuit theory.Namely, the SRRs are resonators magnetically coupled to the host line, and the injected power is reflected back to the source if the signal frequency is in the vicinity of SRR resonance.
Microwave sensors based on the variation of the resonance frequency, phase, or quality factor of resonator-loaded lines have been reported [17][18][19][20][21][22][23].These resonator parameters may be influenced by environmental changes (temperature, moisture, etc.) [24], and hence proper calibration is required, in general, before sensing (exceptions may be sensors based on differential measurements).Otherwise, measurements are likely to be affected by random errors as a result of changing ambient factors.Alternatively, a novel sensing principle, where the symmetry properties of transmission lines (host line) loaded with symmetric resonators are exploited, has been pointed out recently [25].The resulting sensors are robust against variations of environmental conditions and especially suitable for alignment purposes since alignment is a geometrical property invariant to these conditions.Prototypes of linear and angular displacement sensors [25][26][27][28][29][30][31][32][33][34] as well as angular velocity sensors [33,34] have been demonstrated.The purpose of this paper is to describe the operation principle of these sensors and to report some examples.It is also worth mentioning that some immunity to variable ambient conditions can also be attained using pairs of identical resonators (i.e., differential measurement).On the basis of this approach (beyond the scope of this paper), displacement sensors [35] and sensors for dielectric characterization [36] have been proposed by means of symmetry rupture.Other microwave and metamaterial based sensors can be found in [37][38][39].

Sensing Principle
The CPW structure of Figure 2 is loaded with pairs of SRRs.Regardless of the orientation of the SRRs, the magnetic field generated by the line is able to drive each resonant element of the pair, resulting in a stop band in the vicinity of the SRR fundamental resonance.Let us now consider that the CPW is loaded with a single SRR oriented with its symmetry plane aligned with the symmetry plane of the line (Figure 3(a)).Under these conditions, there is not a net axial magnetic field able to excite the particle, and the structure is transparent.The coupling between the transmission line and the resonator is therefore effectively canceled.However, if symmetry is broken (Figure 3(b)), such perfect cancelation of magnetic field lines no longer holds; the particle is coupled to the line, and it is excited causing a notch in the transmission coefficient.The magnitude of the notch is dependent on the net coupling and hence on the level of asymmetry.Accordingly, the notch magnitude may be used for sensing purposes.Note that, with this sensing strategy, calibration for alignment measurements is not needed, since symmetry is not affected by environmental conditions.On the other hand, several types of variables, able to produce symmetry disruption, may be sensed, including linear and angular displacement, velocity, or variations in the composition (and hence dielectric permittivity) of a sample loaded to the structure.
Despite the fact that the operating principle of the proposed sensors has been explained with regard to a specific host line (CPW) and resonant element (SRR), the key aspect is to achieve transparency (total transmission) when the considered structure (host line plus resonator) is perfectly symmetric and resonance (i.e., a transmission zero) when symmetry is disrupted.A sufficient condition to achieve transmission line like behavior if symmetry is satisfied is that the symmetry planes of the line and resonator are of different electromagnetic nature (one of them a magnetic wall and the other one an electric wall).Note that this is the case of the CPW and SRR; that is, the CPW exhibits a magnetic wall at its symmetry plane for the fundamental even (CPW) mode, whereas the SRR exhibits an electric wall at its symmetry plane at the fundamental resonance.There are other combinations of transmission lines and resonators satisfying the above requirement, including CPWs and microstrip lines loaded with stepped impedance resonators (SIR) [40], or CPWs loaded with bisymmetric resonators, such as the electric-LC resonator (exhibiting an electric and a magnetic wall simultaneously in orthogonal symmetry planes) [41], or differential microstrip lines loaded with complementary split ring resonators (CSRRs) [2].The SIR, like the SRR, exhibits an electric wall at the fundamental resonance, whereas the CSRR exhibits a magnetic wall at its symmetry plane.Some illustrative different combinations of transmission lines and resonators are depicted in Figure 4.

Examples
In this section, two different examples of microwave sensors based on symmetry properties are included: (i) a twodimensional position sensor [27] (ii) and an angular velocity sensor [33].

Two-Dimensional Position
Sensor.The two-dimensional (2D) position sensor reported in this subsection is based on a right angle bended CPW loaded with a pair of SRRs in each transmission line section.For the implementation of a two-dimensional position sensor, able to measure the relative displacement between two surfaces, the SRRs must be etched on a different (movable) substrate.However, here we report a proof-of-concept where the SRRs are all etched in the back substrate side of the CPW transmission line.Therefore, we  have fabricated several samples where the relative position of the SRRs with regard to the CPW transmission line has been modified.The layout of the designed sensor is depicted in Figure 5.As discussed in [25], narrow substrates are necessary to boost the sensitivity.The vias and backside strips are used to connect the ground plane regions and thus prevent the appearance of the CPW parasitic slot mode.
For a better comprehension of the principle of operation of the proposed sensor, let us consider the four different displacements indicated in Figure 6 from the aligned structure, that is, right, left, up, and down displacements.The resonance frequencies of the four SRRs are denoted as  Δ ,  Δ ,  ± , and  ± (see Figure 5).It can be seen that both direction and magnitude of the displacements in the ±and ±-direction can be detected (by means of the resonators SRR ± and SRR ± ) and measured (by the resonators SRR Δ and SRR Δ ), respectively.Namely, the resonators SRR ±,± are only excited if their position is shifted towards the CPW central strip, and hence it is possible to distinguish between up and down displacement, or between left and right.Indeed, such resonators act as a flag that determines the direction of motion, but not the magnitude.The magnitude of relative displacement is given by the resonators designated as SRR Δ,Δ , since these resonators are symmetrically loaded to the CPW in the unperturbed state (i.e., the one corresponding to Figure 5).Any other linear displacement is a combination of the previous ones, and hence it can also be detected and measured.As an illustration, Figure 7 shows the obtained transmission coefficient for Δ = 0.3 mm and Δ = 0.25 mm.As mentioned before, the position sensing structure was validated by considering several proof-of-concept prototypes with different displacements, by measuring the frequency responses, and by representing the notch magnitude of the different involved resonance frequencies (Figure 8 shows a photograph of the device for the case Δ = Δ = 0).In order to validate the proposed approach, we considered positive and negative displacement in the -direction (horizontal shift), as well as in the  = -direction (diagonal shift), although here we report only the results corresponding to the horizontal shift.
Figure 9 depicts the dependence of the notch magnitude (simulated and measured) with displacement in the ±direction.As expected, for positive displacements, the SRR ± is activated as is manifested by a clear increase in the notch at  ± , whereas the specified −3 dB threshold level is not exceeded for negative displacements (indicating that the shift is in the negative direction).The dependence of the notch magnitude for  Δ is similar and roughly linear in both directions, with a measured value of approximately −20 dB for Δ = ±0.3mm, which is indicative of a significant sensitivity of roughly 65 dB/mm (average value).On the other hand, the notch corresponding to  Δ is approximately 0 dB, which indicates that the structure is aligned with the axis (for Δ = 0.3 mm the notch is slightly beyond −3 dB because for this sample the -axis position sensing resonators are somewhat misaligned due to fabrication tolerances and underetching).The results of the relative displacement in the diagonal orientation (Δ = Δ), not shown, indicate that the resonators SRR ±,± are activated if the displacement is positive.
In comparison to other two-dimensional displacement sensors based on the resonance frequency of split ringloaded transmission lines [17], the proposed sensors based on symmetry properties are more robust against environmental conditions.Indeed, the alignment measurement is immune to (uniform) changes in the properties of the constitutive materials of the sensors as well as those properties of the surrounding medium.

Angular Displacement and Velocity
Sensors.The angular displacement and velocity sensors reported in this subsection are based on a CPW transmission line loaded with an electric-LC (ELC) resonator.The topology of this resonant particle (for a rectangular geometry) is depicted in Figure 10.At the fundamental resonance frequency, the currents in the two loops flow in opposite directions (one is clockwise and the other is counterclockwise), as depicted in that figure.The particle exhibits two symmetry planes, that is, an electric wall and a magnetic wall, as indicated.Hence, according to the sensing principle pointed out in Section 2, it follows that a CPW transmission line loaded with a symmetrically   11 with different resonator rotation angles.The angles 0 ∘ and 90 ∘ correspond to the extreme cases of orthogonally oriented magnetic walls and perfectly aligned magnetic walls, respectively.From [28], reprinted with permission.
etched ELC is transparent if the line axis is aligned with the electric wall of the particle, and a notch is expected to appear if the magnetic wall of the ELC is aligned with the symmetry plane of the line (also a magnetic wall).These two extreme situations are depicted in Figure 11.The frequency response corresponding to these two orientations is shown in Figure 12, where the response for other intermediate angles is also depicted.As expected, the notch magnitude increases with the rotation angle.
A circular geometry for both the ELC resonator and the CPW transmission line is convenient in order to improve sensitivity, dynamic range, and linearity.Thus, we have designed a circular-tapered (nonuniform) CPW transmission line with a characteristic impedance of 50 Ω.By designing a circular ELC whose diameter extends beyond the slot regions of the CPW, it is expected that the above sensor parameters are optimized.The ELC has been etched in a different substrate, which has been attached to a rotating cylinder made of Teflon.Rotation can be achieved by means of a step motor.The designed CPW transmission line, ELC resonator, and the experimental setup to measure the rotation angle are shown in Figure 13.After a 3D spatial calibration between the CPW and the resonator by means of manual positioners, the measured notch magnitude and frequency as a function of the rotation are plotted in Figure 14.The results are very similar to those obtained with a suspended substrate and reported in [28].In comparison to [28], the notch frequency has experienced a slight decrease of 30 MHz due to the Teflon slab, while the change in the notch depth is negligible.These results indicate that the notch magnitude exhibits not only rather robustness, but also less sensitivity than frequencybased sensors to variations or tolerances on the substrate properties (the former may be conditioned to environmental factors).The output dynamic range is 23.7 dB, and the average sensitivity is 0.26 dB/ ∘ .Therefore, by sensing amplitude levels, remarkable robustness against environmental factors is expected, although noise may degrade the measurements.
The setup of Figure 13 was also used for the measurement of angular velocities.To this end, the CPW transmission line is fed by a harmonic signal (carrier) tuned at the notch frequency of the ELC resonator (actually, the notch frequency slightly depends on the orientation (angle) of the ELC resonator; therefore, the carrier frequency is chosen in the vicinity of the average value).At the output port of the CPW the amplitude of the carrier signal is modulated by the effect of the rotating ELC; that is, the amplitude is maximum each time the electric wall of the ELC is aligned with the symmetry plane of the line (this occurs twice per cycle).Therefore, by capturing the envelope of the modulated signal through an envelope detector, the distance between adjacent peaks gives the rotation speed.In order to avoid unwanted reflections caused by the envelope detector, a circulator is cascaded between the output port of the CPW transmission line and the input of the envelope detector, as depicted in Figure 15(a).The typical waveform of the envelope signal obtained through an oscilloscope, for a rotation speed of 50 cycles per second, is depicted in Figure 15(b).The pronounced peaks allow for the measurement of angular velocities with high accuracy (errors less than 1% have been obtained).Since the carrier frequency is very high, it is obvious that very high angular velocities can be measured with this approach.The microstrip version of this angular velocity sensor was reported in [34].
As stressed before, the main advantage of the proposed symmetry-based sensors is their inherent immunity to changing ambient conditions.By contrast, angular sensors based on the shift of resonance frequency may be affected by environmental factors [22].In addition, as compared to spatial sensors with mechanical friction (e.g., rotary potentiometers [42]), the proposed sensors are contactless and therefore do not suffer from aging effects caused by friction.It should be noted that not only may the performance of microwave sensors be subjected to changing ambient conditions, but that of sensors is based on other sensing principles (e.g., optical sensors [43]).

Conclusion
In conclusion, a novel type of microwave sensors, recently proposed by the authors and based on the symmetry properties of resonator-loaded transmission lines, has been Figure 15: Schematic of the proposed system for measuring angular velocities in time domain, including the sensing line, circulator and envelope detector (a), and output waveform for a rotating speed of 50 cycles per second (b).From [33], reprinted with permission.reviewed.The sensing principle is based on the disruption of symmetry caused by a certain variable, such as position, angle, or permittivity of a dielectric load.The asymmetry produces a notch in the transmission coefficient, whose depth depends on the level of asymmetry (which in turn determines the net coupling between the line and the resonator).Therefore, the proposed structures are useful for sensing purposes.Two different examples of sensors have been discussed: a linear position/alignment sensor and an angular alignment/displacement/velocity sensor.The reported results of sensor characterization reveal that the sensors exhibit a reasonable sensitivity, linearity, and dynamic range.Moreover, the proposed sensors are robust against changes in environmental conditions and particularly in alignment measurements since geometrical symmetry is not influenced by such changes.

Figure 1 :Figure 2 :
Figure 1: Topology of the first reported metamaterial transmission line based on a CPW loaded with pairs of shunt strips and SRRs (a) and frequency response (b), where the band pass functionality can be appreciated.

Figure 3 :Figure 4 :
Figure 3: CPW loaded with a single SRR: (a) aligned symmetry planes; (b) misaligned symmetry planes.The cross and dot stand for the direction of the magnetic field, which is generated by the CPW, parallel to the SRR axis.

Figure 6 :
Figure 6: Scheme indicating the primitive shifting operations and the resulting transmission coefficient  21 .A notch is indicative of an SRR excitation.A linear displacement in the and -orientation is indicated as Δ and Δ, respectively, relative to the aligned position (i.e., Δ = Δ = 0).From [27], reprinted with permission.

Figure 8 :Figure 9 :
Figure 8: Photograph of the proposed device for the aligned position; (a) top and (b) bottom face.From [27], reprinted with permission.

Figure 10 :
Figure 10: Rectangular-shaped electric-LC (ELC) resonator.The electric and magnetic walls at the fundamental resonance, as well as a sketch of the distribution of charges and currents, are indicated.

Figure 11 :Figure 12 :
Figure 11: CPW symmetrically loaded with an ELC resonator etched in the back side of the substrate.The orientation between the CPW and the resonator is determined by the rotation angle ; the line axis is perfectly aligned with the resonator electric wall for  = 0 ∘ (a) and with the resonator magnetic wall for  = 90 ∘ (b).CPW dimensions are  = 0.78 mm and  = 2 mm, corresponding to a 50 Ω line.ELC dimensions are  1 = 4 mm,  2 =  3 =  1 =  = 0.2 mm, and  2 =  3 = 10 mm.The substrate is Rogers RO3010 with ℎ = 1.27 mm and   = 11.2.