Received September 21, 2020, accepted October 8, 2020, date of publication October 14, 2020, date of current version October 28, 2020. Digital Object Identifier 10.1109/ACCESS.2020.3031032 A Reflective-Mode Phase-Variation Displacement Sensor JONATHAN MUÑOZ-ENANO 1 , (Graduate Student Member, IEEE), PARIS VÉLEZ 1 , (Member, IEEE), LIJUAN SU1 , MARTA GIL-BARBA 2 , (Member, IEEE), AND FERRAN MARTÍN 1 , (Fellow, IEEE) 1 GEMMA/CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain 2 Departamento Ingeniería Audiovisual y Comunicaciones, Universidad Politécnica de Madrid, 28031 Madrid, Spain Corresponding author: Jonathan Muñoz-Enano (jonatan.munoz@uab.cat) This work was supported in part by the MINECO-Spain under Project TEC2016-75650-R and Project PID2019-103904RB-I00, in part by the Generalitat de Catalunya under Project 2017SGR-1159, in part by the Institució Catalana de Recerca i Estudis Avançats (who awarded Ferran Martín), and in part by the FEDER funds. The work of Jonathan Muñoz-Enano was supported by the Secreteraria d’Universitats i Recerca (Gen. Cat.) and European Social Fund for the FI grant. The work of Paris Vélez was supported by the Juan de la Cierva Program under Project IJCI-2017-31339. ABSTRACT In this paper, a displacement sensor based on an open-ended step-impedance transmission line is reported. The sensor operates in reflection, and the output variable is the phase of the reflection coefficient. The static part of the sensor is the step-impedance transmission line, where the open-ended line section is the sensitive part (sensing line). The movable part is a dielectric slab, e.g., an uncladded microwave substrate. When such slab, located on top of the sensing line, is in relative motion to the line, in the direction of the line axis, the portion of the sensing line covered by the slab varies, and this results in a change in the phase of the reflection coefficient of the line. The step impedance discontinuity contributes to optimize the sensor sensitivity, the key parameter. A detailed analysis providing the design guidelines is carried out and used to design a prototype displacement sensor. The characterization of the fabricated device points out the potential of the approach to implement highly sensitive displacement sensors. The sensor is a one-port device and operates at a single frequency. INDEX TERMS Displacement sensor, microstrip, microwave sensor, phase-variation sensor, step-impedance transmission line. I. INTRODUCTION Single-frequency sensors constitute a good alternative to There are several strategies for the measurement of linear and frequency variation sensors in order to reduce sensor costs. angular displacements using microwaves. One of such strat- Among them, substantial investigation has been devoted to egy exploits frequency variation, where, typically, the relative the so-called coupling modulation sensors [7]–[15]. Such motion between the static and the movable part of the sensor sensors belong to the category of symmetry-based sensors, perturbs the resonance frequency (the output variable) of a and consist of a transmission line symmetrically loaded with a planar resonant element [1]–[6]. One of the main limitations symmetric resonator, in relative motion to the line. By choos- of frequency variation sensors (as such sensors are usually ing the line and the resonant element with symmetry planes of referred to) is the requirement of a wideband signal for mea- different electromagnetic sort, i.e., one being a magnetic wall suring purposes. The spectrum of such signal must cover, and the other one an electric wall, line-to-resonator coupling at least, the output dynamic range. Thus, the generation of is prevented, and (roughly) total transmission at the resonance such signals may represent a penalty (in terms of the cost of frequency of the movable resonator is expected. However, the associated electronics) for sensor implementation in a real by disrupting symmetry by means of a linear displacement scenario. or rotation, the coupling between the line and the resonator is activated, thereby reducing the magnitude of the transmission coefficient [5], [16], [17]. Since the intensity of coupling The associate editor coordinating the review of this manuscript and depends on the level of asymmetry (intimately related to the approving it for publication was Flavia Grassi . relative displacement between the line and the resonator), This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020 189565 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor the approach can be used for displacement sensing. In these a single-frequency reflective-mode phase-variation sensor sensors, the output variable is typically the magnitude of devoted to the measurement of linear displacements between the transmission coefficient [7], [8]. However, by injecting the static part, an open-ended (i.e., one-port) step-impedance a harmonic signal to the line, the displacement correlates transmission line, and the movable part, a dielectric slab to the magnitude of the envelope function of the amplitude (other reflective-mode sensors, mainly devoted to material modulated (AM) signal generated at the output port of the characterization, have been recently reported [33]–[36]). Sen- line [11], [12], [15]. sor sensitivity, i.e., the variation of the phase of the reflection It should be mentioned that there are other angular and coefficient with the linear displacement, is high, by virtue linear displacement and velocity sensors, based on pulses, of the step-impedance discontinuity. Moreover, sensor func- which exploit coupling modulation, as well. In these sensors, tionality is based on a simple one-port (phase) measurement, designated as electromagnetic encoders [18]–[22], the static and sensor fabrication is very simple, as far as the main part is also a transmission line, whereas the movable part is a elements, the static and the movable parts, are simply an chain (linear or circular) of metallic or dielectric inclusions open-ended step-impedance microstrip line and a dielectric (typically, although not necessarily, resonators). When the slab, respectively. chain is in motion, in close proximity to the static line, Other approaches for sensing angular displacements have the transmission coefficient of the line at the operating fre- been reported (e.g., sensors based on circularly polar- quency is periodically modulated by the chain inclusions, ized antennas [37], magnetic microrods [38],[39] signal- with the result of a periodic envelope function, with pulses, interference transversal filtering sections [40], etc.), however, at the output port. From the cumulative number of pulses and the complexity of these systems is by far superior to the one the time lapse between adjacent pulses, the linear, or angular, of the phase variation sensors reported in this paper. displacement and velocity can be inferred [18], [19]. Paper organization is as follows. In Section II, the structure, Despite the fact that coupling modulation sensors operate the working principle, and a detailed analysis of the pro- at a single frequency, their robustness against noise is lim- posed sensor (useful for design purposes), are reported. Using ited [17]. Nevertheless, the functionality of electromagnetic the resulting design guidelines of such analysis, a prototype encoders as a low-cost alternative to optical encoders has sensor has been designed and fabricated. The designed and been demonstrated [21], [23], [24]. An additional advantage fabricated prototype are presented in Section III, also devoted of electromagnetic encoders over their optical counterparts is to the experimental validation of the sensor. A discussion on the possibility to operate in environments subjected to harsh sensitivity enhancement is reported in Section IV. A com- and hostile conditions (i.e., with dirtiness, grease, pollution, parative analysis with other planar microwave displacement etc.). Concerning coupling modulation sensors based on sym- sensors is included in Section V. Finally, the main conclusions metry disruption (and exploiting typically a single sensing of the work are highlighted in Section VI. resonator), besides noise, an additional potential limitation concerns resonator detuning, which may limit the output II. SENSOR STRUCTURE, WORKING PRINCIPLE AND dynamic range and sensitivity. ANALYSIS To alleviate the previous drawbacks of single-frequency The proposed phase-variation displacement sensor consists coupling modulation sensors, phase variation sensors have of two parts: a static part and a movable part. The static part been reported [25]–[29] (phase measurements are preferred is an open-ended step-impedance transmission line, where over amplitude measurements in terms of noise). Phase vari- the open-ended section is the sensitive part (Fig. 1). The ation sensors have been applied to the dielectric character- movable part is a dielectric slab in relative motion to the ization of solid and liquids [25]–[27]. In such application, static part. Specifically, the sensor is devoted to the mea- the working principle is the variation of the effective dielec- surement of linear displacement of the slab in the direction tric constant of a sensing line loaded with the material under of the line axis, and this can be achieved by measuring test (MUT), which in turn modifies the phase of the line. The the phase of the reflection coefficient of the step-impedance measurement of linear or angular displacements exploiting open-ended line. The working principle is the variation of phase variation has also been demonstrated [28], [29]. For the phase of the sensing line experienced when the dielectric instance, in [28], the proposed sensor, based on a transmis- slab moves in the axial direction. This modifies the phase of sion line loaded with a rotating complementary split ring the reflection coefficient seen from the input port, the input resonator (CSRR), takes advantage of the asymmetry of the variable. sensor geometry and measures the angle of rotation in terms Indeed, the effective dielectric constant of the sensing line of the change in the relative phase of the reflection coef- is different (larger) in the region covered by the slab. There- ficients. A similar approach was presented in [29], where fore, we can consider the sensing line as formed by two sec- the difference in the phase of the reflection coefficients of tions with variable length, i.e., the uncovered and the covered a slotline loaded with a rotatable SRR is the output variable section (see Fig. 2). Let us designate by l the total length of (nevertheless, most SRR and CSRR based sensors have been the sensing line and by ld and la the lengths of the covered applied to dielectric characterization [30]–[32]). In [28], [29], and uncovered regions, respectively (so that l = ld + la ). two-port measurement are required. In this paper, we report The phase constant and the characteristic impedance of the 189566 VOLUME 8, 2020 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor The sensitivity, S, given by the derivative of φρin,a with ld , can be expressed as 2 D·P−N ·Q S= · (6) N 2 D2  1+ D where N and D are the numerator and the denominator, respectively, of the argument of the arctan in (5), and P and Q are FIGURE 1. Sketch in perspective view of the proposed phase-variation Za Zd βd Za2 βa displacement sensor. P=− + (7) sin2 (β d ld ) cos2 (β a (l − ld )) βa cot (β d ld ) βd tan (β a (l −l d ))   Q = −Z 0 Zd + (8) cos2 (β a (l −ld )) sin2 (β d ld ) The sensitivity in the limit when ld approaches l (or x = 0) is found to be (9), as shown at the bottom of the next page In order to obtain the optimum line length, l, for sensitivity optimization, the derivative of (9) with l is obtained. After a straightforward (but tedious) calculation, the following expression results (10), as shown at the bottom of the next page. The zeros of (10), where the sensitivity, Sl , is either a maximum or a minimum, are obtained for those values of line FIGURE 2. Detail (top view) of the proposed phase-variation displacement sensor and relevant parameters. length satisfying βd l = n · π or βd l = (2n + 1)·π/2, (with n = 1, 2, 3 . . . ). By introducing these values of βd l in (9), the corresponding sensitivities are found to be: sensing line are also different in the covered and uncovered βa βd   regions. Let us call these phase constants βa and βd , and Sl = 2Z0 − (11a) Za Zd the impedances Za and Zd , where the sub-indexes a and d are used to distinguish whether the line is uncovered (air) or for βd l = n · π, and covered (dielectric). 2  Sl = Za β a − Zd β d (11b) The impedance, Zin,d , seen from the plane separating the Z0 covered and uncovered line sections, and looking at the open for βd l = (2n + 1)·π/2. end (Fig. 2), can be expressed as Let us now calculate the second derivative of (10) evaluated Zin,d = −jZd cot (β d ld ) (1) at βd l = n · π and βd l = (2n + 1)·π/2 in order to determine if the sensitivity is either a maximum or a minimum at these This impedance is the load of the uncovered line section, with phase points. The results are: input impedance given by d 2 Sl 4Z0 βd2 n o = (Z a Zd − Zd Z 20 Za−1 )βa + (Z02 − Zd2 )βd  jZa Za tan (β a (l − l d )) − Zd cot (β d ld ) dl 2 3 Zin,a = (2) Zd Za + Zd cot (β d ld ) tan (β a (l − l d )) (12a) Note that (2) has been expressed in terms of the input dis- for βd l = n · π, and placement variable, ld . Let us first consider the sensor as formed only by the d 2 Sl 4Zd βd2 n 2 −1 2 2 o = − (Z Z a d − Z Z Z d 0 a )βa +(Z0 − Zd d)β sensing line, and let us infer the conditions for sensitivity opti- dl 2 Z03 mization by considering the phase of the reflection coefficient (12b) as the output variable. The reflection coefficient is given by for βd l = (2n + 1)·π/2. Inspection of (12a) and (12b) Zin,a − Z0 ρ in,a = (3) reveals that the second derivative at the considered phase Zin,a + Z0 points exhibits different sign. Consequently, either (11a) is a where Z0 is the reference impedance of the port. Introduc- maximum, (11b) being a minimum, or vice versa. In order to ing (2) in (3), the following result is obtained (4), as shown identify the maximum and the minimum, the sign of the term at the bottom of the next page and the phase of the reflection in brackets in (12) should be obtained. By dividing such term coefficient is by Zd , and rearranging the terms, one obtains the following  Za (Zd cot (β d ld ) − Za tan (β a (l − l d ))  positive result, i.e., φρin,a = 2arctan 2 βd βa   Z0 (Za +Zd tan (β a (l − l d )) cot (β d ld )) Z0 − + Za β a − Zd β d > 0 (13) (5) Zd Za VOLUME 8, 2020 189567 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor Expression (13) is positive since Zd < Za , βd > βa , and the metallic layer. For the covered line, the effective dielectric Za βa − Zd βd = 0 (see Appendix). According to this, (12a) constant is given by is positive and therefore (11a) is a minimum. However, since εr + εr,d εr − εr,d the sensitivity is negative, the absolute value of the sensitivity, εeff ,d = + F (17) 2 2 the relevant parameter, exhibits a maximum for βd l = n · π, provided the thickness hd of the dielectric slab extends over and a minimum for βd l = (2n + 1)·π/2 (indeed, the sen- the region of influence of the electromagnetic field generated sitivity is zero for this phase condition, as demonstrated in by the line (i.e., the slab can be considered to be semi-infinite Appendix). in the normal-to-sensor direction). In (17), the geometry fac- Apparently, in view of expression (11a), sensitivity tor F is also given by (16), and the value is identical to the increases by decreasing the characteristic impedance of the one of the uncovered line section, and εr,d is the dielectric uncovered part of the sensing line, Za , and consequently constant of the slab. Zd (as far as both impedances appear in the denominator Concerning the characteristic impedance of the covered in the corresponding expressions). However, reducing the line section, Zd , assuming that t  h, it can be approximated line impedance means enhancing the width of the line. This, by [41] in turn, tends to approach the impedance of the covered line −1 η0   to the one of the uncovered line, as well as the corresponding Ws Ws Zd = √ +1.393 + 0.667 ln +1.444 phase constants, and this seems to go against sensitivity εeff ,d h h optimization, according to (11a). (18a) To determine whether Za (or Zd ) should be high or low, it is convenient to carry out a numerical analysis of expres- for Ws /h ≥ 1, where η0 = 120π  is the characteristic sion (11a), where impedance of vacuum, or by ω√ η0   8h Ws βa = εeff ,a (14) Zd = √ ln + (18b) c 2π εeff ,d Ws 4h and a similar expression applies to βd , with the exception of for Ws /h < 1. For Za , expressions (18) also apply, but εeff ,d the subindex a, which must be replaced with the subindex d. must be replaced with εeff ,a . In (14), c is the speed of light in vacuum, εeff ,a (εeff ,d ) is the With expressions (14)-(18), the sensitivity (9) as a function effective dielectric constant of the uncovered (covered) line, of l (or βd l) can be numerically calculated, and particularly and ω is the angular frequency. For the uncovered line, the the maximum value (corresponding to a phase of βd l = effective dielectric constant is [41] n · π) can be inferred. Figure 3 depicts the dependence of the εr + 1 εr − 1 sensitivity Sl with βd l for different values of the characteristic εeff ,a = + F (15) impedance of the uncovered and covered line sections. For 2 2 that purpose, we have set the substrate thickness to a fixed where F is a geometry factor given by value, h = 1.524 mm, and we have varied the width of h −1/2 the line, thereby modifying the characteristic impedances.   F = 1 + 12 (16a) According to Fig. 3, the maximum sensitivity (for βd l = n·π) Ws increases by decreasing the impedance Za , or Zd . for Ws /h ≥ 1, or by According to the previous words, the strategy for sensitiv-  h −1/2   Ws 2  ity optimization in the sensor merely consisting of the sensing F = 1 + 12 + 0.04 1 − (16b) line is clear. The phase of the covered line should be set to Ws h βd l = n · π, and the characteristic impedance, Zd , or Za , for Ws /h < 1, where Ws and h correspond to the strip width must be small, as compared to the reference impedance of and the substrate thickness, respectively. The validity of (16) the ports. It is also necessary to use a movable slab with is subjected to the condition t  h, where t is the thickness of a relatively high dielectric constant, since this generates an −Z0 (Za + Zd tan (β a (l − l d )) cot (β d ld )) + jZa (Za tan (β a (l − l d )) − Zd cot (β d ld )) ρ in,a = (4) +Z0 (Za + Zd tan (β a (l − l d )) cot (β d ld )) + jZa (Za tan (β a (l − l d )) − Zd cot (β d ld )) 2 −Zd Z0 βd + Za Z0 βa sin2 (β d l) + Z0 Z 2d Za−1 βa cos2 (β d l)  Sl = (9) Z02 sin2 (β d l) + Zd2 cos2 (β d l) 4Zd Z0 βd sin (β d l) cos (β d l) (Z a Zd − Zd Z 20 Za−1 )βa + (Z02 − Zd2 )βd  dSl = 2 (10) dl  2 2 Z sin (β l) + Z 2 cos2 (β l) 0 d d d 189568 VOLUME 8, 2020 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor FIGURE 3. Sensitivity Sl as a function of βd l for different values of the characteristic impedance of the sensing line. appreciable difference between the characteristic impedances FIGURE 4. Photograph of the fabricated sensors, Sensor A (a) and B (b). and phase constants of the uncovered and covered line Dimensions are given in mm. sections. Let us now analyze the sensor based on the step-impedance According to the previous paragraph, for the step- open-ended line of Fig. 2. The presence of the line section impedance based sensor with βd l = n · π and φ1 = π/2, (design line) with impedance Z1 and electrical length φ1 = the sensitivity is given by β1 l1 (β1 and l1 being the phase constant and the line length, Z 2 βa βd   respectively) contributes to sensitivity enhancement, pro- Sl = 2 1 − (24) vided the line parameters are adequately chosen. In particular, Z0 Za Zd let us consider that the electrical length of this line at the and by choosing the impedances according to Z1 > Z0 > Za design frequency is φ1 = 90◦ . The impedance seen from (or Zd ), with a high impedance contrast (i.e., Z1 /Za  1), the input port, Zin , is thus the sensitivity can be significantly optimized. Z12 Zin = (19) III. SENSOR DESIGN, FABRICATION AND VALIDATION Zin,a The design, fabrication and validation of two prototype dis- and the reflection coefficient is placement sensors are reported in this section. The differ- Z12 /Zin,a − Z0 ence concerns the characteristic impedances (covered and ρ= (20) uncovered) of the 180◦ sensing lines. In one prototype sensor, Z12 /Zin,a + Z0 Sensor A, Zd = 97.27  and Za = 150 , whereas Let us now designate by χin,a the reactance of the sensing line, in the prototype identified as Sensor B, Zd = 19.46  i.e., Zin,a = jχin,a . The reflection coefficient can be expressed and Za = 25 . In both sensors, the cascaded 90◦ line as exhibits a high characteristic impedance of Z1 = 150  (the Z12 /jχin,a − Z0 Z12 − jχin,a Z0 reference impedance of the port being Z0 = 50 ). The ρ= = (21) operating frequency of the sensors is set to f0 = 2 GHz. Z12 /jχin,a + Z0 Z12 + jχin,a Z0 The sensors are implemented in the Rogers RO4003C sub- and the phase of the reflection coefficient is thus strate with dielectric constant εr = 3.55 and thickness h = 1.524 mm. The movable dielectric slab is an uncladded ! χin,a φρ = 2arctan − 2 (22) piece of the Rogers RO3010 substrate with dielectric constant Z1 /Z0 εr,d = 10.2 and thickness hd = 3.81 mm (with such dielec- From (3), the phase of the reflection coefficient seen from the tric slab, the above indicated values of Zd in both sensors sensing line can be expressed as result). The photographs of the sensors are depicted in Fig. 4 χin,a   φρin,a = 2arctan − (23) (dimensions are indicated in the figure). Sensor fabrication Z0 has been carried out by means of the LPKF H100 drilling By comparing (22) and (23), it can be concluded that the sen- machine. For sensor validation, the Agilent N5221A vector sitivity analysis carried out by considering only the sensing network analyzer has been used to obtain the phase of the line can be applied to the sensor composed by the sensing line reflection coefficient. Slab displacement over the sensing line plus the quarter-wavelength (φ1 = 90◦ ) transmission line. has been carried out by means of the linear stepper motor It suffices to replace Z0 with Z12 /Z0 in (11), provided (23) is (model THORLABS LTS300/M), available in our laboratory. identical to (22) with this change of variable. The reference (REF) position is the one corresponding to the VOLUME 8, 2020 189569 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor and length of the involved microstrip line sections, provided the substrate parameters and characteristic impedances are known. Nevertheless, dimension fine-tuning has been carried out with Agilent Momentum. IV. DISCUSSION According to (24), the sensitivity, a key parameter in any sen- sor, is mainly dictated by the impedance contrasts of the sens- ing line and the 90◦ line cascaded to it (both with regard to the reference impedance of the port). Depending on the required sensitivity, the necessary impedance contrasts may not be achievable. The reason is that very high line impedances require extremely narrow lines (not implementable if the FIGURE 5. Photograph of the experimental setup for sensor validation. line width is below the limits imposed by the technology in use). Conversely, very wide lines are necessary to achieve extremely low line impedances. However, an excessive line width should be avoided in order to prevent from parasitic effects related to the step discontinuity or the appearance of transverse resonances. There is, however, an alternative approach to enhance the sensitivity, yet keeping the impedance contrasts at relatively small values. The idea is to cascade further 90◦ lines, with alternating characteristic impedances, to the sensing line. Let us consider that N 90◦ -lines are cascaded to the sensing line, and let us call Zi the characteristic impedance of line section i, with i = 1, 2, 3 . . . N . The input impedance can be expressed as (−1)N YN n 2·(−1)i+N o Zin,N = Zin,a · Zi (25) FIGURE 6. Dependence of the phase of the reflection coefficient with the i=1 slab displacement, and sensitivity, for sensors A (a) and B (b). For the measured data, error bars, corresponding to the standard deviation or, using Zin,a = jχin,a divided by the square root of the number of measurements that make up YN n 2·(−1)i+N o (−1)N the mean (3 measurement points in our case), are depicted. Zin,N = j (−1)N χin,a · Zi (26) i=1 where 5 is the product operator. The reflection coefficient is slab with its edge located in the step discontinuity (i.e., la = 0, thus or ld = l, or x = 0). The picture of the experimental setup is (−1)N Q 2·(−1)i+N n o shown in Fig. 5. j (−1)N · χin,a · N i=1 Zi − Z0 Fig. 6 shows the variation of the phase of the reflection ρ= (27) (−1)N Q 2·(−1)i+N n o coefficient in reference to the phase corresponding to the j (−1)N · χin,a · N i=1 Zi + Z0 REF position, as a function of the slab displacement, la , for For N odd, the phase of the reflection coefficient is both sensors. The figure includes the measured data points,   the phase inferred from the HFSS simulator, and the results χin,a predicted by the theory (expression 22). The figure depicts φρ = 2arctan − Q (28)   2·(−1)i+N n o  N also the sensitivity, inferred by simple derivation of the i=1 Zi /Z0 experimental data points. The maximum sensitivity is found to be 35.14 ◦ /mm and 95.24 ◦ /mm for sensors A and B, whereas for N even the phase is found to be   respectively. Such maximum sensitivity is inferred when the slab is in the REF position, and should be coherent with χin,a φρ = 2arctan − (29)   QN n 2·(−1)i+N o  the value predicted by expression (24). Evaluation of this Z0 / i=1 Zi expression for both sensors gives |Sl | = 36.44 ◦ /mm and |Sl | = 97.67 ◦ /mm for sensors A and B, respectively. These Thus, four situations arise, depending on the parity of N and values coincide with the maximum sensitivities of Fig. 6 to the phase of βd l, i.e., a good approximation. Therefore, these simple calculations • For the sensing line satisfying βd l = n · π and N odd, validate the analysis of the previous section. It should be men- the sensitivity is tioned that for the generation of the layout of the proposed QN n 2·(−1)i+N o  i=1 Zi βa βd  sensor, the Linecalc tool of the Keysight ADS commercial Sl = 2 − (30a) software has been used. This software provides the width Z0 Za Zd 189570 VOLUME 8, 2020 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor • For βd l = n · π and N even, the sensitivity is βa βd   Z0 Sl = 2 Q n − (30b) 2·(−1)i+N o N Za Zd i=1 Zi • For βd l = (2n + 1) · π/2 and N odd, the sensitivity is Z0 o Za β a − Zd β d  Sl = 2 Q n (30c) N 2·(−1)i+N i=1 Zi • For βd l = (2n + 1) · π/2 and N even, the sensitivity is QN n 2·(−1)i+N o i=1 Zi Za β a − Zd β d (30d)  Sl = 2 Z0 FIGURE 7. Dependence of the phase of the reflection coefficient with the Nevertheless, for βd l = (2n + 1) · π/2, the sensitivity is slab displacement, and sensitivity, for sensor C (described in the text). null regardless of the parity of N , as far as Za βa − Zd βd = 0, as demonstrated in Appendix. Thus, for sensitivity opti- at the expense of a reduced input dynamic range, as visible mization, the phase of the sensing line should be set to in the quasi-saturation effect of Figs. 6 and 7. However, βd l = n · π, the characteristic impedance of this line must the results of Figs. 6 and 7 and the analysis of this section be low, and the impedances of the subsequent cascaded lines demonstrate that the sensitivity for small displacements can must be alternately high and low. By this means, there is a be enhanced at wish by merely adding 90◦ line sections with multiplicative effect, and the sensitivity can be substantially alternating high and low impedance. Thus, these sensors are enhanced without the need of implementing the lines with indicated in applications where small linear displacements extreme impedances. need to be measured. To demonstrate the sensitivity enhancement capability of One potential application of these sensors may be the the sensor by adding further 90◦ stages, we have simulated the accurate measurement of liquid levels. Although this specific sensor B of the previous section (Fig. 4b) by cascading a low application is left for future investigation and it is out of the impedance (Z2 = 25 ) 90◦ line section to it (let us designate scope of this paper, it is convenient to analyze the effects of this sensor, with N = 2, as Sensor C). Like in Fig. 6, the dielectric constant of the movable slab on the sensor sen- we have simulated the variation of the phase of the reflection sitivity. In particular, since the dielectric constant of liquids coefficient in reference to the phase corresponding to the REF at microwave frequencies is high, it is convenient to simulate position, as a function of the slab displacement, la . The results one of the sensors (for example, Sensor B, with N = 1) by are depicted in Fig. 7. This figure includes also the sensitivity, considering a high dielectric constant slab. A high dielectric which exhibits the maximum value for the REF position. The constant slab increases the impedance contrast and the phase maximum sensitivity inferred from simulation (312.97 ◦ /mm) constant contrast between the covered and uncovered sections is somehow smaller than the value predicted by the theory, of the sensing line. Therefore, according to expression (24), given by expression (30b), i.e., 390.83 ◦ /mm. This relatively it is expected that the sensitivity increase with the dielectric small discrepancy is because with such very high sensibility constant of the movable slab. This aspect is demonstrated it is very difficult to accurately infer the sensitivity from the in Fig. 8, where the simulation of Sensor B by considering derivative of the phase data points. Nevertheless, it is clear slabs of high (εr,d = 30) and low (εr,d = 2) dielectric that the sensitivity is substantially enhanced by adding the constant are considered. It should be mentioned, however, low impedance 90◦ line section to sensor B, resulting in a that the sensor B has been redesigned in each case, to account highly sensitive Sensor C. for the variation of the physical length of the sensing line, It should be emphasized that the sensitivity analysis carried necessary to achieve the required phase of 180◦ (thereby out in this paper refers to Sl , the sensitivity in the limit of small optimizing the maximum sensitivity) when a semi-infinite displacements with regard to the REF position (with x = 0). slab of the indicated dielectric constants covers it. Thus, This sensitivity is maximized if the sensor is designed accord- the width of the sensing lines are Ws = 9.1 mm and the ing to the given design guidelines. Nevertheless, the sensitiv- lengths for εr,d = 30 and for εr,d = 2 are l = 24.77 mm ity decreases as the displacement increases, as it can be appre- and l = 41.75 mm, respectively. In view of Fig. 8, it is ciated in Figs. 6 and 7, where the sensitivity S as a function of confirmed that the maximum sensitivity increases with the the displacement can be observed. According to these figures, dielectric constant of the movable slab, as expected (the ver- it is clear that the proposed sensors are especially useful for tical scale in Fig. 8 is identical to the one of Fig. 6 to ease the the measurement of small displacements in the vicinity of the comparison). REF position, where the phase of the reflection coefficient, Naturally, increasing the thickness of the slabs enhances the output variable, experiences a stronger variation with the also the maximum sensitivity due to identical reasons (further displacement of the slab. Sensitivity enhancement is achieved contrast of the phase constant and characteristic impedance VOLUME 8, 2020 189571 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor TABLE 1. Comparison of various planar microwave linear displacement sensors. FIGURE 8. Dependence of the phase of the reflection coefficient with the slab displacement, and sensitivity, for modified sensor B, with the movable slab of the indicated dielectric constants. between the covered and uncovered sensing line sections). However, in this paper, the considered thickness of the slabs quency variation sensors [1], [2], [5], [6], the system is able (3.81 mm) is sufficient to consider them semi-infinite in the to discern frequency variations of 10 MHz (an optimistic vertical direction (so that the electromagnetic field generated value), thereby providing the input resolution values given by the line does not reach the slab/air interface). That is, in the table. For the coupling modulation sensors, the input further enhancing this thickness does not modify the sensi- resolution has been inferred by considering that 3 dB in the tivity (as it has been verified by independent simulations, not output variable (a transmission coefficient) can be discerned. shown). For the sensors proposed in this work, it is assumed that To end this section, let us mention that sensor sensitivity phase variations of 5◦ can be resolved with any reasonable can also be enhanced by increasing the operating frequency. instrument. According to it, and taking into account the maxi- This is apparent in view of expressions (11), (24) and (30), mum sensitivities given in Table 1, the indicated displacement since the phase constants of the covered and uncovered line resolutions are obtained. These resolutions are competitive, are proportional to the operating frequency. The value con- as consequence of the high sensitivity, especially for sensor sidered in the present paper (f0 = 2 GHz) obeys a tradeoff C. It should be mentioned that for the sensors based on between sensor size (smaller as higher the frequency), sensi- cumulative pulse counting [21], [22], based on chains of tivity, and ease of measurement. inclusions (metallic strips in [21] and dielectric strips in [22]), the resolution is dictated by the period of the inclusions’ V. COMPARISON WITH OTHER LINEAR DISPLACEMENT chain. Such period is relatively high, thereby providing poor SENSORS resolution as compared to the other sensors reported in the Comparing the proposed reflective-mode phase-variation lin- table. However, the sensors in [21], [22] are devoted to the ear displacement sensors with other planar microwave dis- measurement of high range displacements (typically dozens placement sensors is not easy. The reason is that in most of mm, or even more), contrary to the other sensors in Table 1 microwave sensors devoted to the measurement of spatial (with input linear dynamic ranges of few mm or even less). variables, the output variable is typically a resonance fre- For this reason, the sensor resolutions reported in [21], [22] quency, a magnitude (of either a transmission or a reflection (in the millimeter range) are considered to be competitive, coefficient), a voltage amplitude, or a cumulative number of as well. pulses, rather than a phase. Exceptions are the phase-variation Concerning the input dynamic range with linear response sensors reported in [28], [29], but such sensors are devoted to of the sensors reported in this paper, it is apparent that such the measurement of angular, rather than linear, displacements range is degraded by increasing the sensitivity. However, and velocities. a high sensitivity is typically required in applications where Table 1 shows a comparison of various linear displacement small displacements should be detected. If the measuring sensors reported in the recent literature. It can be appreci- displacement range needs to be expanded, it should be conve- ated that in the coupling modulation sensors [8], [9], [13], nient to reduce the maximum sensitivity in order to improve pulse-counting sensors [21], [22], as well as in the sensors the sensor linearity. reported in this work (sensors A, B and C), the required signal for sensing is a single-tone (harmonic) signal, this VI. CONCLUSION representing a clear advantage over the frequency-variation In conclusion, a microwave sensor devoted to the measure- sensors [1], [2], [5], [6], as discussed before. Concerning ment of small displacements has been reported in this paper. sensor resolution, it has been considered that for the fre- The sensor is composed of a static part, an open-ended 189572 VOLUME 8, 2020 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor step-impedance microstrip line, and a movable part, a dielec- Consequently, Za βa −Zd βd = 0, and the sensitivity for βd l = tric slab. The sensor operates in reflection, and the output (2n + 1)·π/2, given by (11b), is Sl = 0. variable is the phase of the reflection coefficient, which varies as the dielectric slab moves along the open-ended (sensing) REFERENCES line on top of it. It has been demonstrated that for sensitivity [1] C. Mandel, B. Kubina, M. Schüßler, and R. Jakoby, ‘‘Passive chipless optimization, the electrical length of the open-ended sensing wireless sensor for two-dimensional displacement measurement,’’ in Proc. 41st Eur. Microw. 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Martin, ‘‘Microwave dielectric constant appears in the numerator in the phase con- encoders for chipless RFID and angular velocity sensors based on S-shaped split ring resonators,’’ IEEE Sensors J., vol. 17, no. 15, pp. 4805–4813, stant, and it appears in the denominator in the characteristic Aug. 2017. impedance, the product Za βa or Zd βd does not depend on the [20] J. Mata-Contreras, C. Herrojo, and F. Martin, ‘‘Detecting the rotation material on top of the sensing line. Indeed, in both cases the direction in contactless angular velocity sensors implemented with rotors loaded with multiple chains of resonators,’’ IEEE Sensors J., vol. 18, no. 17, following result is obtained pp. 7055–7065, Sep. 2018. [21] C. Herrojo, F. Paredes, and F. Martin, ‘‘Double-stub loaded microstrip Zω line reader for very high data density microwave encoders,’’ IEEE Trans. βa Za = βd Zd = (A.2) Microw. Theory Techn., vol. 67, no. 9, pp. 3527–3536, Sep. 2019. c VOLUME 8, 2020 189573 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor [22] C. Herrojo, F. Paredes, J. Bonache, and F. Martin, ‘‘3-D-Printed high data- JONATHAN MUÑOZ-ENANO (Graduate Stu- density electromagnetic encoders based on permittivity contrast for motion dent Member, IEEE) was born in Mollet del Vallès, control and chipless-RFID,’’ IEEE Trans. Microw. Theory Techn., vol. 68, Barcelona, Spain, in 1994. He received the bach- no. 5, pp. 1839–1850, May 2020. elor’s degree in electronic telecommunications [23] C. Herrojo, M. Moras, F. Paredes, A. Nunez, J. Mata-Contreras, E. Ramon, engineering and the master’s degree in telecommu- and F. Martin, ‘‘Time-domain-signature chipless RFID tags: Near-field nications engineering from the Autonomous Uni- chipless-RFID systems with high data capacity,’’ IEEE Microw. Mag., versity of Barcelona (UAB), in 2016 and 2018, vol. 20, no. 12, pp. 87–101, Dec. 2019. respectively. He is currently working with UAB [24] F. Martin, C. Herrojo, J. Mata-Contreras, and F. Paredes, Time-Domain in the elaboration of his Ph.D. degree, which is Signature Barcodes for Chipless-RFID and Sensing Applications. Cham, Switzerland: Springer, 2020. focused on the development of microwave sensors [25] F. Ferrández-Pastor, J. García-Chamizo, and M. Nieto-Hidalgo, ‘‘Electro- based on metamaterials concepts for the dielectric characterization of mate- magnetic differential measuring method: Application in microstrip sensors rials and biosensors. developing,’’ Sensors, vol. 17, no. 7, p. 1650, Jul. 2017. [26] J. Munoz-Enano, P. Velez, M. Gil Barba, and F. Martin, ‘‘An analytical PARIS VÉLEZ (Member, IEEE) was born in method to implement high-sensitivity transmission line differential sensors Barcelona, Spain, in 1982. He received the degree for dielectric constant measurements,’’ IEEE Sensors J., vol. 20, no. 1, in telecommunications engineering, specializing pp. 178–184, Jan. 2020. in electronics, the Electronics Engineering degree, [27] J. Munoz-Enano, P. Velez, M. Gil Barba, J. Mata-Contreras, and and the Ph.D. degree in electrical engineering F. Martin, ‘‘Differential-mode to common-mode conversion detector based from the Universitat Autònoma de Barcelona, on rat-race hybrid couplers: Analysis and application to differential sensors Barcelona, in 2008, 2010, and 2014, respec- and comparators,’’ IEEE Trans. Microw. Theory Techn., vol. 68, no. 4, tively. His Ph.D. thesis concerned common mode pp. 1312–1325, Apr. 2020. suppression differential microwave circuits based [28] A. K. Jha, A. Lamecki, M. Mrozowski, and M. Bozzi, ‘‘A highly sensi- on metamaterial concepts and semi-lumped res- tive planar microwave sensor for detecting direction and angle of rota- onators. During the Ph.D., he was awarded with a pre-doctoral teaching tion,’’ IEEE Trans. Microw. Theory Techn., vol. 68, no. 4, pp. 1598–1609, Apr. 2020. and research fellowship by the Spanish Government from 2011 to 2014. [29] A. K. Horestani, Z. Shaterian, and F. Martin, ‘‘Rotation sensor based on the From 2015 to 2017, he was involved in the subjects related to metamaterials cross-polarized excitation of split ring resonators (SRRs),’’ IEEE Sensors sensors for fluidics detection and characterization at LAAS-CNRS through J., vol. 20, no. 17, pp. 9706–9714, Sep. 2020. a TECNIOSpring fellowship cofounded by the Marie Curie program. His [30] A. M. Albishi, M. K. E. Badawe, V. Nayyeri, and O. M. Ramahi, ‘‘Enhanc- current research interests include the miniaturization of passive circuits ing the sensitivity of dielectric sensors with multiple coupled com- RF/microwave and sensors-based metamaterials through Juan de la Cierva plementary split-ring resonators,’’ IEEE Trans. Microw. Theory Techn., fellowship. He is a Reviewer for the IEEE TRANSACTIONS ON MICROWAVE vol. 68, no. 10, pp. 4340–4347, Oct. 2020, doi: 10.1109/TMTT.2020. THEORY AND TECHNIQUES and for other journals. 3002996. [31] M. Abdolrazzaghi, M. Daneshmand, and A. K. Iyer, ‘‘Strongly enhanced LIJUAN SU was born in Qianjiang, Hubei, China, sensitivity in planar microwave sensors based on metamaterial coupling,’’ in 1983. She received the B.S. degree in com- IEEE Trans. Microw. Theory Techn., vol. 66, no. 4, pp. 1843–1855, munication engineering and the M.S. degree in Apr. 2018. [32] A. Javed, A. Arif, M. Zubair, M. Qasim Mehmood, and K. Riaz, ‘‘A low- circuits and systems from the Wuhan Univer- cost multiple complementary split-ring resonator-based microwave sensor sity of Technology, Wuhan, China, in 2005 and for contactless dielectric characterization of liquids,’’ IEEE Sensors J., 2013, respectively, and the Ph.D. degree in elec- vol. 20, no. 19, pp. 11326–11334, Oct. 2020. tronic engineering from the Universitat Autonoma [33] A. Ebrahimi, J. Scott, and K. Ghorbani, ‘‘Transmission lines terminated de Barcelona, Barcelona, Spain, in 2017. From with LC resonators for differential permittivity sensing,’’ IEEE Microw. November 2017 to December 2019, she worked as Wireless Compon. Lett., vol. 28, no. 12, pp. 1149–1151, Dec. 2018. a Postdoctoral Researcher with the Flexible Elec- [34] A. Ebrahimi, J. Scott, and K. Ghorbani, ‘‘Microwave reflective biosensor tronics Research Center, Huazhong University of Science and Technology, for glucose level detection in aqueous solutions,’’ Sens. Actuators A, Phys., Wuhan. She is currently a Postdoctoral Researcher with CIMITEC, Uni- vol. 301, Jan. 2020, Art. no. 111662. versitat Autònoma de Barcelona. Her current research interests include the [35] J. Muñoz-Enano, P. Vélez, M. Gil, and F. Martín, ‘‘Microfluidic development of novel microwave sensors with improved performance for reflective-mode differential sensor based on open split ring resonators biosensors, dielectric characterization of solids and liquids, defect detection, (OSRRs),’’ Int. J. Microw. Wireless Technol., vol. 12, no. 7, pp. 588–597, and industrial processes. Sep. 2020. [36] J. Munoz-Enano, P. Velez, L. Su, M. Gil, P. Casacuberta, and F. Mart, ‘‘On the sensitivity of reflective-mode phase-variation sensors based on MARTA GIL-BARBA (Member, IEEE) was born open-ended stepped-impedance transmission lines: Theoretical analysis in Valdepeñas, Ciudad Real, Spain, in 1981. She and experimental validation,’’ IEEE Trans. Microw. Theory Techn., early received the degree in physics from the Univer- access, Sep. 25, 2020, doi: 10.1109/TMTT.2020.3023728. sidad de Granada, Spain, in 2005, and the Ph.D. [37] V. Sipal, A. Z. Narbudowicz, and M. J. Ammann, ‘‘Contactless mea- degree in electronic engineering from the Univer- surement of angular velocity using circularly polarized antennas,’’ IEEE sitat Autònoma de Barcelona, Barcelona, Spain, Sensors J., vol. 15, no. 6, pp. 3459–3466, Jun. 2015. in 2009. She studied one year with the Friedrich [38] A. H. Karami, F. K. Horestani, M. Kolahdouz, and A. K. Horestani, Schiller Universität Jena, Jena, Germany. During ‘‘Rotation sensor based on magnetic microrods,’’ IEEE Sensors J., vol. 18, her Ph.D. Thesis, she was holder of a META- no. 1, pp. 77–82, Jan. 2018. MORPHOSE NoE Grant and a National Research [39] A. H. Karami, F. Karami Horestani, M. Kolahdouz, A. K. Horestani, and Fellowship from the FPU Program of the Education and Science Spanish F. Martín, ‘‘2D rotary sensor based on magnetic composite of micro- Ministry. As a Postdoctoral Researcher, she was awarded with a Juan de rods,’’ J. Mater. Sci., Mater. Electron., vol. 31, no. 1, pp. 167–174, la Cierva fellowship working with the Universidad de Castilla-La Mancha. Jan. 2020. She was a Postdoctoral Researcher with the Institut für Mikrowellentechnik [40] C.-H. Chio, R. Gomez-Garcia, L. Yang, K.-W. Tam, W.-W. Choi, and S.-K. Ho, ‘‘An angular-displacement microwave sensor using an unequal- und Photonik, Technische Universität Darmstadt, and with the Carlos III length-Bi-path transversal filtering section,’’ IEEE Sensors J., vol. 20, University of Madrid. She is currently an Assistant Professor with the no. 2, pp. 715–722, Jan. 2020. Universidad Politécnica de Madrid. She has worked in metamaterials, piezo- [41] D. M. Pozar, Microwave Engineering, 4th ed. Hoboken, NJ, USA: Wiley, electric MEMS, and microwave passive devices. Her current interest includes 2011. metamaterials sensors for fluidic detection. 189574 VOLUME 8, 2020 J. Muñoz-Enano et al.: Reflective-Mode Phase-Variation Displacement Sensor FERRAN MARTÍN (Fellow, IEEE) was born in he is a coauthor of the book on Metamaterials Metamaterials with Negative Barakaldo, Vizcaya, Spain, in 1965. He received Parameters: Theory, Design, and Microwave Applications (John Wiley & the B.S. degree in physics from the Universitat Sons Inc.), author of the book Artificial Transmission Lines for RF and Autònoma de Barcelona (UAB), in 1988, and the Microwave Applications (John Wiley & Sons Inc.), co-editor of the book Ph.D. degree in 1992. Balanced Microwave Filters (Wiley/IEEE Press), and coauthor of the book From 1994 to 2006, he was an Associate Time-Domain Signature Barcodes for Chipless-RFID and Sensing Appli- Professor in Electronics with the Departament cations (Springer). He has generated 21 Ph.D. students, has filed several d’Enginyeria Electrònica, Universitat Autònoma patents on metamaterials and has headed several Development Contracts. de Barcelona, where he has been a Full Profes- His research interests include microwave sensors and RFID systems, with sor of Electronics, since 2007. In recent years, special emphasis on the development of high-data capacity chipless-RFID he has been involved in different research activities including modeling and tags. simulation of electron devices for high-frequency applications, millimeter Dr. Martín is a Fellow of the IET. He is a member of the IEEE wave and THz generation systems, and the application of electromagnetic Microwave Theory and Techniques Society (IEEE MTT-S). He is a Reviewer bandgaps to microwave and millimeter wave circuits. He is currently very of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and IEEE active in the field of metamaterials and their application to the miniaturiza- MICROWAVE AND WIRELESS COMPONENTS LETTERS, and among many other jour- tion and optimization of microwave circuits and antennas. He is also the nals. He serves as a member of the Editorial Board of IET Microwaves, Head of the Microwave Engineering, Metamaterials and Antennas Group Antennas, and Propagation, International Journal of RF and Microwave (GEMMA Group), UAB, and the Director of CIMITEC, a research Center Computer-Aided Engineering, and Sensors. He is also a member of the Tech- on Metamaterials supported by TECNIO (Generalitat de Catalunya). He has nical Committees of the European Microwave Conference (EuMC) and Inter- organized several international events related to metamaterials and related national Congress on Advanced Electromagnetic Materials in Microwaves topics, including Workshops at the IEEE International Microwave Sympo- and Optics (Metamaterials). Among his distinctions, he has received the sium in 2005 and 2007, European Microwave Conference in 2009, 2015, 2006 Duran Farell Prize for Technological Research, he holds the Parc de and 2017, and the Fifth International Congress on Advanced Electromagnetic Recerca UAB −− Santander Technology Transfer Chair. He was a recipient Materials in Microwaves and Optics (Metamaterials 2011), where he acted as of three ICREA ACADEMIA awards (calls 2008, 2013, and 2018). He has the Chair of the Local Organizing Committee. He has authored or coauthored acted as a Guest Editor of six Special Issues on metamaterials and sensors in more than 600 technical conference, letter, journal articles and book chapters, five International Journals. VOLUME 8, 2020 189575