Planar Microwave Sensors

For example, optical sensors exhibit very high sensitivity and selectivity for the detection of many types of biological analytes, such as toxins, drugs, antibodies, proteins, viruses, etc.

In order to enhance the sensitivity of the sensor to temperature or humidity, functional materials exhibiting a strong dependence of the permittivity with those variables can be used. Examples of such materials are polyvinyl alcohol (PVA), with a dielectric constant very sensitive to humidity, or polyamide, a material that exhibits a temperature dependent dielectric constant. This aspect will be further considered in Sect. 2.1.4.

Obviously, there are several commercial techniques for the diagnosis of cancer, e.g., magnetic resonance imaging (MRI), computerized tomography (CT), positron emission tomography (PET), or ultrasounds, among others, but these techniques are, in general, very expensive, and, in some cases, annoying for the patients.

Nevertheless, other binary classification schemes of planar microwave sensors are also included in Sect. 1.

By sensor imbalance, we mean potential differences between the sensors constituting the differential sensor pair, typically caused by fabrication related tolerances. Such imbalances might generate a non-negligible output (differential) signal, despite the fact that the input differential signal is null. Thus, the accuracy in the manufacturing process is critically important in differential-mode sensors.

For broadband characterization of materials, non-resonant sensors should be used. However, it should be clarified that artificial lines, such as slow-wave, CRLH, or EIW transmission lines, inherently exhibit a limited transmission band. Therefore, such artificial lines are not useful to retrieve the dielectric characteristics of materials over broad bands.

The presence of the MUT in contact or in proximity to the sensing line modifies the characteristic impedance and the complex propagation constant of the line, which in turn affects the reflection and transmission coefficient of such line.

Note that the output dynamic range is determined by the input dynamic range and by the sensor sensitivity, or variation of the resonance frequency of the sensing resonator with the dielectric constant of the MUT.

At laboratory level, a signal generator or a VNA is typically used for the generation of the interrogation signal of the sensor.

By semi-infinite we mean a MUT of sufficient thickness and transverse dimensions to guarantee that the electromagnetic field generated by the DB-DGS does not reach the boundaries of the MUT. The semi-infinite MUT approximation is not a general requirement for sensing, but a requisite of the analytical method reported in [122].

For DI water, a mechanical holder (acting as a pool or container) was fabricated by means of a 3D printer and attached to the ground plane of the sensing structure (see further details in [122]).

The divider/combiner configuration, similar to the cascaded configuration, prevents from inter-resonator coupling, since the resonant elements are significantly separated. However, in the divider/combiner frequency-splitting sensor, the notches appear, in general, as consequence of an interfering phenomenon. Namely, at the resonance frequency of the resonator of one of the branches, signal propagation through that branch is precluded. However, signal propagation is not necessarily reflected back to the source, since it can be transmitted, or partially transmitted, through the other (parallel) branch. Thus, in general, the notches are not given by the resonance frequencies of the resonators (except for the symmetric case), but by those frequencies where the signals propagating at both branches destructively interfere at the output T-junction. This mode of operation (signal interference) also degrades sensor sensitivity at small perturbations [141]. However, if the line section between the T-junctions and the plane of the resonators is conveniently chosen, a short at the resonance frequency of the resonators when they are loaded with the REF sample is generated at the input and output T-junctions, and under these circumstances, sensitivity degradation is circumvented, as it is demonstrated in [141]. If the sensing resonant elements are CSRRs or SIRs, the line section between the T-junctions and the plane of the resonators should be a half-wavelength [or θ₁ = π, see Fig. 9b]. By contrast, the electrical length of such line sections should be θ₁ = π/2 (i.e., a quarter-wavelength) for SRRs. The difference is explained by the fact that CSRRs and SIRs generate a short at resonance, whereas SRRs open the line when they resonate.

Nevertheless, frequency-splitting sensors based on bandpass structures are also possible [146]. In this case, the resonances manifest as peaks in the frequency response of the sensor.

It is assumed that these sensors do not exploit electromagnetic symmetry properties, contrarily to those of the preceding paragraph.

It should be mentioned that in [174], rather than implementing the complete system sketched in Fig. 19, the envelope functions at each output arm of the splitter for each frequency (f_0,1 = 4.550 GHz, f_0,2 = 5.160 GHz, f_0,3 = 5.885 GHz, and f_0,4 = 6.540 GHz) were inferred independently, as a first proof-of-concept.

Exceptions are certain electromagnetic encoders (quasi-absolute or absolute), which require several harmonic signals for encoder reading, as explained. Nevertheless, a single VCO, managed by a microcontroller, suffices, at least in most cases, for the generation of such signals. This does not represent a significant increase of the cost of the associated electronics.

However, most phase-variation sensors do not exploit the broadband potentiality of non-resonant sensors.

In this prototype, the sensing resonator is cascaded to a single inverter stage, as a means to enhance the sensitivity. The admittance of this inverter was set in [78] to a small value, particularly, Y₁ = 1/150 S (corresponding to a high inverter impedance of Z₁ = 150 Ω) for the reasons that will be later justified in this subsection.

Namely, resonant elements implemented by means of two metallic layers, such as the broadside-coupled split ring resonator (BC-SRR), or the microstrip step-impedance shut stub (SISS) resonator, both exhibiting a broadside capacitance, are excluded in the present analysis.

Note that, for the lossless case,  α = 0 and (22) rewrites as (17).

It has been assumed that the characteristic impedance, Z_s, is a real number, a reasonable approximation, despite the presence of losses, necessary to avoid an excessive complex formulation.

A slot resonator, as the one depicted in Fig. 21, is described by a parallel resonant tank. A step-impedance resonator (SIR) is an example of a semi-lumped resonator that can be described by means of a series resonant tank.

The higher the ratio between the thickness of the substrate and the width of the slots (of the resonant elements or CPW line), the closer the electric field distribution to a mirror image with regard to the plane of the sensing element [121].

MUT losses have direct impact on the magnitude of the notch, or peak, of the frequency response of the sensor.

Nevertheless, it should be clarified that substrate, conductor, and radiation losses might also contribute to the overall losses of the sensing resonant element.

Note that β has been used to designate the phase constant in previous sections. Nevertheless, in this section, β is identified with the resonator transfer function, following the nomenclature of the original source [292].

It has been shown that the magnitude of the transmission coefficient at resonance, or notch depth, in any of the individual (single-ended) sensors of the differential pair strongly depends on the electrolyte content, and this has been attributed to the high sensitivity of the loss tangent with the concentration of electrolytes. A strong variation in the notch depth of the MUT sensor in comparison with the notch depth of the REF sensor (loaded with DI water) is expected to cause an important variation in the cross-mode transmission coefficient (magnitude) in the vicinity of resonance.

Note that the period is given by p = r·θ, where r is the encoder radius. Thus, in compact rotary encoders, i.e., with small radius, good resolution (θ small) necessarily requires a small period.

It has been previously indicated that differential measurements can alleviate the effects of cross-sensitivities against ambient factors. Nevertheless, if the variations of temperature, humidity, or pressure are severe, differential sensing does not provide a definite solution to this issue.

Although not explicitly mentioned, it is assumed that a frequency-variation sensor is under consideration.