This article presents an exhaustive study of the sensitivity in reflective-mode phase-variation sensors based on an open-ended transmission line with a step-impedance discontinuity. Such discontinuity delimits the sensing region (which extends up to the open end of the so-called sensing line), from the transmission line section connected to the input port (design line), which is used to enhance the sensitivity. The theoretical analysis provides the design guidelines to achieve a sensor with high sensitivity compared with the one based on an ordinary (uniform) line with a similar length. In particular, it is shown that for sensitivity optimization, the electrical length of the design line must be set to 90° (or an odd multiple), whereas either a 90° (or an odd multiple) or a 180° (or an even or odd multiple) sensing line can be alternatively used in order to maximize the sensitivity. It is shown that the impedance contrast, defined as the ratio between the characteristic impedances of the design and sensing line, is a key parameter for sensitivity enhancement, and it must be as low or as high as possible for the 90° or 180° sensing lines, respectively. For validation purposes, two prototype devices (one with a 90° and the other one with a 180° sensing line) have been designed and fabricated following the design guidelines. Such devices have been tested by loading the sensing region with several materials with different dielectric constants. Compared with the ordinary line-based sensors, it is found that the maximum sensitivity is enhanced by a factor of 19.7 and 11.4 in the phase-variation sensor based on a 90° and 180° sensing line, respectively. Finally, the sensor concept is generalized to a multisection step-impedance transmission line as a means of further increasing the sensitivity, and a prototype device exhibiting 528.7° maximum sensitivity is implemented.

This paper presents a one-port reflective-mode phase-variation microwave sensor consisting of a coplanar waveguide (CPW) transmission line terminated with a grounded open complementary split ring resonator (OCSRR). The sensor is useful for measuring the dielectric constant of the so-called material under test (MUT), which should be placed in contact with the OCSRR, the sensitive element. The output variable is the phase of the reflection coefficient. Design guidelines for the implementation of highly sensitive sensors are derived in the paper, and validated through simulation and experiment. As compared to other reflective mode phase-variation sensors based on open-ended sensing lines, the designed and fabricated devices exhibit a very small sensitive region by virtue of the use of an electrically small resonant element, the OCSRR. The relevant figure of merit, defined as the ratio between the maximum sensitivity and the size of the sensing area (expressed in terms of the squared wavelength), is as high as FoM = 5643°/λ ² in one of the reported prototypes. Moreover, the paper analyzes the effects of losses. From this study, it is concluded that MUT losses do not significantly affect the output variable, provided losses are small. It is also demonstrated that the sensor is useful to estimate the loss tangent of the considered MUT samples.

Reflective-mode step-impedance transmission line based sensors for dielectric characterization of solids or liquids have been recently proposed. In this paper, in order to further increase the sensitivity, the sensor is implemented in coplanar waveguide (CPW technology), and this constitutes the main novelty of this work. The sensor thus consists of a high-impedance 90º (or low-impedance 180º) open-ended sensing line cascaded to a low-impedance 90º (or high-impedance 90º) line. The output variable is the phase of the reflection coefficient, which depends on the dielectric constant of the material under test (MUT), the input variable. Placing a MUT on top of the sensing line causes a variation in the effective dielectric constant of the line, thereby modifying the phase of such line. This in turn produces a multiplicative effect on the phase of the reflection coefficient, by virtue of the step-impedance discontinuity. The main advantage of the CPW-based sensor, over other similar sensors based on microstrip technology, is the stronger dependence of the phase velocity of the sensing line with the dielectric constant of the MUT, resulting in sensitivities as high as  45.48º in one of the designed sensors. The sensor is useful for dielectric characterization of solids and liquids, and for the measurement of variables related to changes in the dielectric constant of the MUT (defect detection, material composition, etc.).

Highly sensitive permittivity sensors operating in reflection and exploiting phase variation are presented in this article. The sensors are one-port structures implemented by means of a pair of coupled lines, the sensitive region, with an appropriate termination. In particular, it is demonstrated that by either short-circuiting the crossed port to the input port of the device (opening the remaining two ports), or opening the crossed port to the input port (terminating the other two ports with a short-circuit), the sensitivity can be driven to very high values, controlled by the coupling factor. For that purpose, the electrical length of the pair of coupled lines must be set to 90 $^{\circ}$ when such lines are loaded with the reference (REF) material. Thus, the sensitivity is optimized for dielectric constants (the input variable) in the vicinity of the dielectric constant of the REF material, where the indicated phase condition is fulfilled. The output variable is the phase of the reflection coefficient, an easily measurable quantity. For validation purposes, three prototype sensors are designed and fabricated. The achieved sensitivities in two of the fabricated sensors are as high as 659.6 $^{\circ}$ and 736.0 $^{\circ}$ , with figures of merit (FoMs), or ratio between the maximum sensitivity and the area of the sensing region expressed in terms of the squared-wavelength, of FoM $=$ 9401 $^{\circ}$ / $\lambda^2$ and 12 690 $^{\circ}$ / $\lambda$ , respectively, i.e., very competitive values. Moreover, the indicated high sensitivities and FoMs have been achieved without the need to add further circuit stages to the sensing region, contrarily to other highly sensitive phase-variation sensors, where sensitivity optimization is achieved at the expense of an increase in the overall sensor size.

A phase-variation microwave sensor operating in transmission and implemented by means of a high-impedance half-wavelength sensing line is reported in this paper. The sensor is useful for dielectric constant measurements and dielectric characterization of materials. By forcing the electrical length of the sensing line to be a half-wavelength when it is loaded with the so-called reference (REF) material, perfect matching is obtained regardless of the characteristic impedance of the line. This fact can be used to enhance the sensitivity for small perturbations, by merely increasing the characteristic impedance of the sensing line. An exhaustive analysis that supports such conclusion is reported in the paper. Then, two prototype sensors are designed and fabricated for validation purposes. As compared to the ordinary phase-variation permittivity sensor implemented by means of a matched ( 50-Ω) line with identical length, the sensitivity for small perturbations in the proposed sensor is 2.1 times larger. Further advantages of these sensors are low-cost, small size, implementation in planar technology, and very simple design and fabrication, derived from the fact that the sensing region is a half-wavelength transmission line.

This paper presents a single-frequency reflective-mode phase-variation microwave sensor devoted to the dielectric characterization of materials. The device is implemented in coplanar waveguide (CPW) technology and consists of two parts: (i) the sensing region, a step-impedance resonator (SIR) as termination of a CPW transmission line, and (ii) the design region, a cascade of high/low impedance quarter-wavelength inverters, used to boost up the sensitivity. By placing the so-called material under test (MUT) on top of the sensing region, the capacitance of the SIR is altered due to the effects of the dielectric constant of the MUT. This modifies the phase of the reflection coefficient seen from the input port, the output variable. From a circuit analysis, it is demonstrated that the sensitivity for small perturbations in the vicinity of the dielectric constant of a reference (REF) material can be optimized by setting the operation frequency of the sensor to the resonance frequency of the SIR loaded with such REF material. The maximum sensitivity in one of the reported sensors is as high as 66.5°, and the main figure of merit, defined as the ratio between the maximum sensitivity and the area of the sensing region expressed in terms of the squared guided wavelength, is $\text {FoM} = 3643^{\circ }/\lambda ^{2}$ . Such figure of merit represents a significant improvement as compared to the one of the equivalent sensor implemented by means of an open-ended quarter-wavelength sensing line. Such equivalence between the semi-lumped element (i.e., SIR-based) sensor and the fully distributed counterpart is also analyzed in the paper.