sensors Article 3D-Printed All-Dielectric Electromagnetic Encoders with Synchronous Reading for Measuring Displacements and Velocities Cristian Herrojo * , Ferran Paredes and Ferran Martín CIMITEC, Department of Electronic Engineering, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain; ferran.paredes@uab.cat (F.P.); ferran.martin@uab.cat (F.M.) * Correspondence: cristian.herrojo@uab.cat  Received: 1 July 2020; Accepted: 25 August 2020; Published: 27 August 2020  Abstract: In this paper, 3D-printed electromagnetic (or microwave) encoders with synchronous reading based on permittivity contrast, and devoted to the measurement of displacements and velocities, are reported for the first time. The considered encoders are based on two chains of linearly shaped apertures made on a 3D-printed high-permittivity dielectric material. One such aperture chain contains the identification (ID) code, whereas the other chain provides the clock signal. Synchronous reading is necessary in order to determine the absolute position if the velocity between the encoder and the sensitive part of the reader is not constant. Such absolute position can be determined as long as the whole encoder is encoded with the so-called de Bruijn sequence. For encoder reading, a splitter/combiner structure with each branch loaded with a series gap and a slot resonator (each one tuned to a different frequency) is considered. Such a structure is able to detect the presence of the apertures when the encoder is displaced, at short distance, over the slots. Thus, by injecting two harmonic signals, conveniently tuned, at the input port of the splitter/combiner structure, two amplitude modulated (AM) signals are generated by tag motion at the output port of the sensitive part of the reader. One of the AM envelope functions provides the absolute position, whereas the other one provides the clock signal and the velocity of the encoder. These synchronous 3D-printed all-dielectric encoders based on permittivity contrast are a good alternative to microwave encoders based on metallic inclusions in those applications where low cost as well as major robustness against mechanical wearing and aging effects are the main concerns. Keywords: microwave sensors; motion control; 3D printing 1. Introduction Optical encoders are widely used in many applications such as the automotive industry, elevators, robotics, and conveyor belts, among others, in order to accurately measure linear or angular displacements and velocities [1–3]. Usually, such optical encoders are based on a chain (or more generally, a grid) of apertures in a metallic plate (a disc in rotary encoders), which moves with regard to the reader, essentially constituted by a light source and an optical detector. The displacement and/or velocity information of the encoder is determined from the optical pulses received in the detector, as the chain of apertures of the metallic plate is displaced (linearly or angularly) across the optical path between the source and the detector. Typically, optical encoders exhibit very good position resolution. Nevertheless, the reliability of optical encoders is reduced in harsh environments, e.g., with pollution, grease, dirtiness, etc. Electromagnetic (or microwave) encoders can be a good alternative to optical encoders, since microwaves are more tolerant to the effects of pollution than optical signals. Moreover, microwave Sensors 2020, 20, 4837; doi:10.3390/s20174837 www.mdpi.com/journal/sensors Sensors 2020, 20, 4837 2 of 13 encoders represent a low-cost solution in motion control applications. In recent years, many different microwave sensors for measuring angular or linear displacements and velocities have been reported. In [4–10], the microwave sensors are based on a transmission line loaded with a resonant element, which is etched in a different substrate and positioned in close proximity to the transmission line. Typically, the rotation angle or linear displacement of the resonant element with regard to the transmission line is determined from a change in the frequency response of the whole structure (bandwidth, quality factor, resonance frequency, etc.). The main drawback of these approaches is the limited dynamic range. In [11–15], microwave encoders based on a linear or angular chain of metallic inclusions implemented on a dielectric substrate were reported. For encoder reading, a passive structure fed by a harmonic signal, able to detect the presence or absence of such inclusions (located at predefined and equidistant positions on the considered substrate), was designed. The main drawback of this approach is the limited robustness against mechanical wearing (e.g., due to friction) and aging effects. To alleviate this problem, all-dielectric microwave encoders based on permittivity contrast were reported in [16,17]. In such encoders, the metallic inclusions were replaced with apertures or dielectric inclusions made on the considered substrate, and the sensitive part of the reader was designed in order to detect the presence/absence of apertures (or dielectric inclusions). In order to reduce the cost of these all-dielectric encoders, the functionality of 3D-printed microwave encoders was demonstrated in [17]. It is important to mention that, in both types of microwave encoder (either based on metallic inclusions or based on apertures), the position and velocity of the encoder were extracted by considering a complete chain of inclusions (i.e., with all the inclusions present at their predefined positions). The position is determined by counting pulses, which are generated at the output port of the sensitive part of the reader by encoder motion, whereas the velocity is inferred from the time interval between adjacent pulses (provided that the period of the inclusions’ chain is well known). Nevertheless, note that, with this approach (regardless of the considered inclusions), it is not possible to determine the absolute position of the encoder, since such a position is determined from the cumulative number of pulses. Therefore, if the system suffers a reset, the encoder should be driven to a reference position. To solve the previously cited limitation, a new approach for microwave encoders was reported in [18–21]. Specifically, the encoders are based on two metallic inclusion chains. One chain contains a certain identification (ID) code (where the presence and absence of an inclusion in a specific position of the encoder is interpreted as a “1” or “0” logic state, respectively), and another one (with all metallic inclusions present) is used as a clock, in order to properly read the position chain. Moreover, the clock chain provides the instantaneous velocity (or even the acceleration) of the encoder. It is important to highlight that this approach can also be applied to chipless RFID systems based on near-field coupling and sequential bit reading, in order to synchronously read the ID code if the relative velocity of the encoder with regard to the sensitive part of the reader is not constant [22–32]. This paper contributes to the state of the art of electromagnetic encoders with synchronous reading (as compared to encoders based on metallic inclusions) in two main aspects: (i) reduced cost due to the fact that the proposed encoders of this work are fabricated with low-cost 3D printing materials and (ii) very high robustness against exposure to harsh environments. For instance, the encoders do not deteriorate when they are in contact with liquid or water. It is important to mention that, to this end, a specific reader has been designed and fabricated. The paper is organized as follows. The working principle, as well as the design of the low-cost 3D-printed all-dielectric encoders based on permittivity contrast with synchronous reading, is presented in Section 2. Experimental validation is reported in Section 3, where the functionality of the encoders as displacement/velocity sensors is demonstrated. Finally, the main conclusions are highlighted in Section 4. 2. Reader and Encoder Design The considered encoders are based on dielectric inclusions, dedicating one part to the ID code and the other part to the clock signal. This is indeed equivalent to considering a pair of parallel inclusion Sensors 2020, 20, 4837 3 of 13 chains, one devoted to the ID code and the other one to the clock signal (the strategy adopted in [21]). Naturally, in the ID chain, encoding is achieved by the presence (“1” logic state) or absence (“0” logic) state of functional inclusions. By contrast, all the inclusions are present (and they are functional) in the clock chain. In this paper, chains of linear apertures in a 3D-printed material, orthogonally oriented to the chain axis and closely spaced, constitute an optimum strategy for resolution and data density optimization. These encoders were first reported in a recent paper by the authors (without synchronous reading capability) [17]. In [17], the sensitive part of the reader was a microstrip line loaded with a series gap and a transversally oriented slot resonator etched in the ground plane, beneath the gap. It was demonstrated in [33,34] that the resonance frequency of slot resonators is very sensitive to the dielectric constant of the surrounding medium. This explains the use of a linear slot resonator (with dimensions similar to those of the linear apertures of the encoder) as the key element for reader implementation. The series gap merely introduces a pole in the frequency response, convenient to achieve a significant excursion of the transmission coefficient at the operating frequency, fc , i.e., the frequency of the interrogation signal. Such frequency was tuned to the pole frequency of the bare slot resonator in [17], which roughly coincides with the resonance frequency of the resonator covered with the considered encoder substrate [17]. In [17], a single harmonic interrogation signal was needed in order to detect the presence of the apertures (and thus determine the ID code) by encoder motion. In brief, the working principle is as follows: an amplitude modulated (AM) signal is generated at the output port of the reader line as a consequence of encoder motion, by virtue of the different transmission coefficient at fc that results when an aperture is perfectly aligned with the slot resonator. Hence, the envelope function of this AM signal exhibits peaks corresponding to the encoder apertures [17], and the ID code can be inferred by means of an envelope detector. However, since the encoder of this work contains two independent chains, further system complexity is needed. Particularly, two slot resonators tuned to different frequencies must be considered for synchronous encoder reading. One such resonator must be placed beneath the ID code chain and the other beneath the clock chain. Obviously, two independent harmonic signals are also necessary in order to obtain the clock signal and the ID code. A sketch of the conceived system is depicted in Figure 1, where a splitter/combiner configuration with each branch loaded with a series gap and a transverse slot resonator is considered. According to this sketch, a microcontroller ensures that a voltage-controlled oscillator (VCO) alternately injects both interrogation signals to the input port of the splitter/combiner. Then, in order to separately obtain the clock signal and the ID code, a switch as well as an envelope detector (one for each signal) are added to the output port of the splitter/combiner, as can be appreciated in Figure 1. Since the clock chain apertures and the ID chain apertures (if present) are located at the same axial position, it follows that the clock signal provides the time instants necessary to read the ID code from the corresponding envelope function. The design of the splitter/combiner is important since its relevant dimensions must be adequately chosen for correct system functionality. Concerning the slot resonators, the one in the upper branch has been designed so that it resonates at f 0u = 4.229 GHz, whereas the fundamental resonance of the slot resonator of the lower branch is f 0l = 3.155 GHz. The gap apertures are identical in both branches, and such dimensions have been tuned in order to obtain the poles of the corresponding (isolated) branches close to the resonance frequencies of the slots. The width of the lines in both branches corresponds to a characteristic impedance of Zu = Zl = 50 Ω (where the sub-indexes identify the upper and lower branch). Finally, the lengths of the transmission line sections at both sides of the series gaps have been selected so that the open circuit at the resonance frequency of the slot resonators is transformed to a short-to-ground at the Y junction at the corresponding frequencies. This is achieved if the electrical length of the transmission line sections is close to 90◦ or an odd multiple of such electrical length. In order to determine the specific value of the electrical length for each branch, the circuit model of the splitter/combiner is needed. It is depicted in Figure 2, where Cu (Cl ) and Lu (Ll ) account A sketch of the conceived system is depicted in Figure 1, where a splitter/combiner configuration with each branch loaded with a series gap and a transverse slot resonator is considered. According to this sketch, a microcontroller ensures that a voltage-controlled oscillator (VCO) alternately injects both interrogation signals to the input port of the splitter/combiner. Then, in order to separately obtain the clock signal and the ID code, a switch as well as an envelope detector (one for each signal) Sensors 2020, 20, 4837 4 of 13 are added to the output port of the splitter/combiner, as can be appreciated in Figure 1. Since the clock chain apertures and the ID chain apertures (if present) are located at the same axial position, it for the2020, follows Sensors capacitance that and inductance, the PEER 20, x FOR clock respectively, signal provides REVIEW the timeof the upper necessary instants (lower) slottoresonator. read the The ID upper (lower) code from the 4 of 15 series gap is accounted for corresponding envelope function. by means of the series, C gu (C gl ), and shunt, C su (Csl ), capacitances [17]. The design of the splitter/combiner is important since its relevant dimensions must be adequately chosen for correct Sensitive systempartfunctionality. of the Microcontroller Concerning the slot resonators, the one in the 1 1 0 0 reader upper branch has been designed so that it resonates at f0u = 4.229 GHz, whereas the fundamental resonance of the slot VCO resonator of the lower branch is f0l = 3.155 GHz. The gap apertures are identical Vout dimensions have been tuned in order to obtain E.D. V in both branches, and such in the poles of the corresponding (isolated) branches close to the resonance frequencies of the slots. 1 1The 1 1width of the lines in both branches corresponds to a characteristic impedance Switch of Zu = Zl = 50 Ω (where the sub- Bottom indexes identify the upper and lower branch). Finally, the lengths of the transmission E.D. line sections at both sides of the series gaps have been selected so that the open circuit at the resonance frequency of Clock chain the slot resonators is transformed to a short-to-ground at the Y junction at the corresponding (apertures εr =1) frequencies. This Topis achieved if the electrical length ofPthe transmission line sections is close to 90˚ or an odd multiple of such electrical length. In order to determine the specific value of the electrical ID code chain Encoder εhigh length for each branch, the circuit model (apertures εr =1) Clock chainsplitter/combiner is needed. It is depicted in Figure 2, of the where Cu (Cl) and Lu (Ll) account for the capacitance and inductance, respectively, of the upper (lower) slot resonator. Figure The Figure1.1.Sketch Sketchupper showing (lower) showing series gap theworking the working is accounted principle principle ofofthe for by reader/encoder theproposed proposed means of the series, reader/encoder systemC system (Cglon based based gu ),onand shunt, Csu (Csl), capacitances permittivity permittivity contrastwith contrast with[17]. synchronous synchronous reading. reading. Zu, θu Cu Zu, θu Cgu Csu Lu Csu Pin Pout Zl, θl Cl Zl, θl Cgl Csl Ll Csl Figure Figure 2. 2. Circuit Circuit model model of of the the considered considered splitter/combiner splitter/combiner structure. structure. The The condition condition to to translate translate the the open open circuit circuit at the corresponding corresponding slot slot resonance resonance frequency frequency of of a branch to the Y junction junction of of the thesplitter/combiner splitter/combinerisistotoforce forcethatthatYY11 = ∞ 11 = ∞ for this branch (Y11 being the this branch (Y 11 being first element of of the the admittance admittancematrix).matrix).This Thisensures ensuresaatransmission transmissionzero zeroatatthethe resonance resonance frequency frequency of of each each slotslot resonator resonator (i.e., (i.e., two transmission two transmission zeros),zeros), regardless regardless of the loading of the loading of the of the other slotother slot resonator. resonator. For simplification For simplification purposes, let purposes, let usby us designate designate YRu (YRlby) andYRuY(Y ) and SuRl(Y YSuadmittances Sl ) the (YSl) the admittances of of the series the andseries shuntand shunt branches, branches, respectively, of the Π circuits respectively, of the cascaded Π circuitsbetween cascadedthe between the transmission transmission line sections line of the upper (lower) branch. From ABCD matrix to Y matrix conversion, it is found that Y11 = D/B [35]. sections of the upper (lower) branch. From ABCD matrix to Y matrix conversion, it is found that Y 11 =Thus, D/B for [35].each Thus, for each splitter/combiner splitter/combiner branch,matrix branch, the ABCD the ABCD is firstmatrix obtained.is first Forobtained. the upperFor the upper branch, the B branch, the B and and D elements ofDthis elements matrix of arethis matrix found are found to be to be (𝒄𝒐𝒔 𝒖 )𝟐 2 𝟐 𝒀𝟐 2  𝒀  (cos θu )− 𝒁𝒖 (𝒔𝒊𝒏 )𝟐 2 𝟐𝒀𝑺𝒖 + Y𝑺𝒖Su + 𝟐𝒋 𝟏 + Y𝑺𝒖  𝑩 =  Su 𝒁𝒖 𝒔𝒊𝒏 𝒖 𝒄𝒐𝒔 𝒖  𝒖 Bu = 𝒀𝑹𝒖 2 − Zu (sin θu ) 2YSu +𝒀𝑹𝒖  + 2j 1 + 𝒀𝑹𝒖 𝒖 Zu sin θu cos θu (1) (1) YRu YRu YRu 𝒀𝑺𝒖 𝒀𝒖 𝒔𝒊𝒏 𝒖 𝒄𝒐𝒔 𝒖  𝑫𝒖 = 𝟏 + 𝒀 (𝒄𝒐𝒔 𝒖 )𝟐 − (𝒔𝒊𝒏 𝒖 )𝟐 + 𝒋  2   YSu 2 𝑹𝒖 2 Yu sin θu cos θu  𝒀𝑹𝒖 YSu {(cos θu ) − (sin θu ) } + j Zu sin θu cos θu (2)  Du = 1+ 𝒀𝟐 + j2YSu + (2) YRu 𝑺𝒖YRu Y  + 𝒋 𝟐𝒀𝑺𝒖 + 𝒁𝒖 𝒔𝒊𝒏 𝒖 𝒄𝒐𝒔 𝒖 (𝟐) Ru 𝒀𝑹𝒖 with Yu = 1/Zu. Note that, although the characteristic impedances of the transmission line sections of both branches are identical (i.e., Zu = Zl = 50 Ω, as indicated above), the analysis is carried out by relaxing this requirement, namely by considering arbitrary impedances. In Equations (1) and (2), θu Sensors 2020, 20, 4837 5 of 13 with Yu = 1/Zu . Note that, although the characteristic impedances of the transmission line sections of both branches are identical (i.e., Zu = Zl = 50 Ω, as indicated above), the analysis is carried out by relaxing this requirement, namely by considering arbitrary impedances. In Equations (1) and (2), θu is the electrical length of the line sections at both sides of the series gap for the upper branch. Similar expressions to Equations (1) and (2) are obtained for the lower branch by simply replacing the sub-index u with the sub-index l. Using Equations (1) and (2), Y11,u (Y11,l ) can be evaluated as indicated above. In the limit when ω → ω0u (ω → ω0l ), with ω0u = 2πf 0u (and ω0l = 2πf 0l ), the admittance of the series branch of the lumped element circuit is an open circuit, i.e., YRu → 0 (YRl → 0), and the first diagonal element of the admittance matrix can be expressed as Yu sin θu cos θu + jω0u Csu {(cos θu )2 − (sin θu )2 − ω0u Csu Zu sin θu cos θu } Y11,u ω = (3) 0,u (cos θu − ω0u Csu Zu sin θu )2 where YSu = j ω Csu has been used. An equivalent expression results for the lower branch. According to (3), Y11,u = ∞ if the denominator of Equation (3) is null, that is cot θu = ω0u Csu Zu (4) and, obviously, Y11,l = ∞ if the electrical length of the transmission line sections of the lower branch satisfies cot θl = ω0l Csl Zl (5) Inspection of Equations (4) and (5) indicates that, if the fringing capacitance of the series gaps, Csu (Csl ) is null, the electrical lengths must satisfy θu (θl ) = (2n + 1) π/2, where n = 0, 1, 2, 3,..., as expected. Thus, the effect of the fringing capacitance (inevitable, in practice, but small) is a slight modification, as compared to the ideal case (90◦ or an odd multiple) of the electrical length necessary to translate the open circuit (present at the central position) to a short circuit at the Y junction. By choosing the electrical lengths according to Equations (4) and (5), there are two transmission zeros in the bare structure which are not consequences of an interfering phenomenon but are determined by the dimensions of the bare slot resonators. By this means, it is guaranteed that both chains of apertures modify only the corresponding transmission zero (i.e., the resonance frequency of the slot aligned with the corresponding chain) when the encoder is in motion, but they do not have any effect on the other transmission zero. This condition is necessary for system functionality. The specific electrical lengths for the upper and lower transmission line sections have been set to θu = 87.7◦ and θl = 88.3◦ , respectively, as these values are coherent with Equations (4) and (5). To evaluate Equations (4) and (5), we have first inferred the fringing capacitances through the parameter extraction procedure described in [36] and already used in [17]. The extracted element parameters are Csu = Csl = 30.2 fF. The resonance frequency of each slot resonator is directly given by the first transmission zero of the isolated branch. The layout of the designed splitter/combiner structure and relevant dimensions are depicted in Figure 3. It is important to mention that half-wavelength transmission lines have been added to the upper and lower transmission line sections (θu and θl ) in order to be able to implement the splitter/combiner (for electromagnetic and circuit simulation comparison, such half-wavelength transmission line sections have been also added to the circuit model presented in Figure 2). The lossless frequency response of this structure, including the circuit and electromagnetic simulation, is depicted in Figure 4a. Such simulations have been inferred by means of the Keysight ADS software package (Keysight, Santa Rosa, CA, USA), which includes a circuit simulator and an electromagnetic solver (Keysight Momentum). The agreement is very good, thereby pointing out the validity of the model. Moreover, in Figure 4b, it is depicted the current distribution of the sensitive part of the reader at the fundamental resonance of the slot resonator of the upper and lower branch, f 0l = 3.155 GHz and f 0u = 4.229 GHz, in order to demonstrate that, at these frequencies, the current is maximal at the input Sensors 2020, 20, 4837 6 of 13 port (input impedance is zero). The structure has been fabricated by means of the LPKF H100 drilling machine (LPKF Laser & Electronics, Garbsen, Germany) in the Rogers RO4003C substrate (Rogers Corporation, Chandler, AZ, USA) with dielectric constant εr = 3.55, thickness h = 1.52 mm, and loss tangent tanδ = 0.0021. The measured response of the sensitive part of the reader has been obtained by means of the Sensors 2020, 20,Agilent 5221A x FOR PEER vector network analyzer (Keysight, Santa Rosa, CA, U.S.A.) and compared REVIEW 6 of 15 with the electromagnetic simulation (including losses). The results, which are depicted in Figure 5, materialthat, indicate (the by oneloading of the encoders), only one ofthetheresonance frequency slot resonators shifts,ofwith by means the result ofdielectric the considered a modification materialin the corresponding (the transmission one of the encoders), zero, but frequency the resonance leaving unaltered the other shifts, with transmission the result zero. This can of a modification be in the appreciated bytransmission corresponding inspection of thebut zero, measured leaving responses unaltered theinferred other by alternatelyzero. transmission loading Thisthe canslot be resonators. Such appreciated dielectricofmaterial by inspection is the RS the measured Pro MT-Copper. responses inferred by Inalternately [17], the measured dielectric loading the constant slot resonators. and loss Such tangent dielectric of this material material is the RS(inferred by meansInof[17], Pro MT-Copper. the resonant the measuredcavitydielectric Agilent 85072A, constant(Keysight, and loss Santa Rosa, tangent CA,material of this USA) were foundby (inferred tomeans be εr = 7.6 andresonant of the tanδ = 0.015, cavityrespectively. As will Agilent 85072A, be shownSanta (Keysight, next, the permittivity Rosa, CA, USA) were contrast found to be εrthe between = 7.6 and tanδ =material considered (host substrate) 0.015, respectively. andbeair As will (apertures) shown next, the is enough to achieve permittivity contrastsignificant between thevariation of thematerial considered transmission coefficientand (host substrate) at the air interrogation signals (f (apertures) is enough tocl and fcu).significant variation of the transmission coefficient at the interrogation signals (fcl and fcu ). achieve Clock chain P wsu lu W lsu Pin Pout wsl lA … lsl ll slots etched in the ground plane wA Sensitive part of the reader Encoder ID code chain Figure 3.3. Layout Figure Layoutofofthe thedesigned designedsplitter/combiner structure splitter/combiner loaded structure withwith loaded a pair of slots a pair and series of slots gaps. and series SensorsDimensions 2020, 20, gaps. x FOR (in PEER Dimensions mm)(inare W =are REVIEW mm) = 24.1, W l=su3.40, 3.40, su = 0.20, lsu =w24.1, = 32.5, wsu =lsl0.20, sl = 0.20, lsl =w32.5, = 33.6, wsl =lu0.20, = 44.7, lu =ll33.6, A = 62.6, ll =l44.7, lA 7= of 15 w A =w 62.6, 0.40, A = 0.40, = 3.40. and pand p = 3.40. 0 200 -10 100 S11 (dB) φ11 (°) -20 0 -100 -30 EM sim. Circuit sim. -200 0 200 -10 100 S21 (dB) φ21 (°) -20 0 -100 -30 -200 2 3 4 5 2 3 4 5 Frequency (GHz) (a) Figure 4. Cont. -10 100 S21 (dB) φ21 (°) -20 0 -100 -30 -200 2 3 4 5 2 3 4 5 Sensors 2020, 20, 4837 Frequency (GHz) 7 of 13 (a) (b) Figure 4. (a) (a) Frequency Frequency response response of of the the sensitive sensitive part part ofof the the bare bare reader reader inferred inferred from lossless electromagnetic electromagnetic simulation simulationand andcircuit circuitsimulation simulationofofFigure Figure 2. 2. TheTheextracted extractedelement elementparameters parametersare C su = are su = fF, C30.2 30.2Cgu gu =pF, fF,=C0.06 CupF, 0.06 Cu = = 0.40 pF, 0.40Lu pF, = 3.58 = 3.58 Lu nH, Csl nH, = 30.2 =C CslfF, gl = fF, 30.2 0.13 =C CglpF, l = 1.26 0.13 pF, C pF, l =and 1.26L l = pF, 2.02 Ll =Such and nH. 2.02 simulations have been have nH. Such simulations inferred beenbyinferred means ofbythe Keysight means of the ADS software; Keysight ADS (b)software; Current distribution of the sensitive (b) Current distribution of thepart of the part sensitive reader at the of the fundamental reader resonanceresonance at the fundamental frequency of the slot frequency of Sensors 2020, 20, x FOR PEER REVIEW 8 of 15 the slot resonator resonator of theand of the upper upper andbranch. lower lower branch. Figure Electromagneticsimulation Figure 5. Electromagnetic simulation(including (includinglosses) losses)and and measured measured frequency frequency responses responses of the of the (a) (a) barebare reader, reader, (b)(b) reader reader with with the the longerslot longer slotloaded loadedwith withthe theRSRSMT-Copper MT-Copperon on top top of of it, and (c) reader with with the the shorter shorter slot slot loaded loaded with with RS RS MT-Copper MT-Copper on on top top of of it. it. The simulation has been inferred by means of the Keysight ADS software means of the Keysight ADS software 3. Experimental Validation 3. Experimental Validation We have fabricated a 16-bit encoder by means of the Ultimaker 3 Extended 3D printer (Ultimaker, We have fabricated a 16-bit encoder by means of the Ultimaker 3 Extended 3D printer Utrecht, The Netherlands) with the dielectric material indicated before. This 3D printer provides (Ultimaker, Utrecht, Netherlands) with the dielectric material indicated before. This 3D printer enough resolution for our purposes. Concretely, the maximum resolution of this 3D printer in the x, y, provides enough resolution for our purposes. Concretely, the maximum resolution of this 3D printer and z directions is 12.5 µm, 12.5 µm, and 2.5 µm, respectively [37]. On the other hand, the sensitive in the x, y, and z directions is 12.5 μm, 12.5 μm, and 2.5 μm, respectively [37]. On the other hand, the part of the reader has been implemented by means of the milling machine LPKF-100 (LPKF Laser sensitive part of the reader has been implemented by means of the milling machine LPKF-100 (LPKF & Electronics, Garbsen, Germany) on the substrate RO4003C (with dimensions, dielectric constant, Laser & Electronics, Garbsen, Germany) on the substrate RO4003C (with dimensions, dielectric and loss tangent also mentioned before). The photograph of the 16-bit encoder and the sensitive constant, and loss tangent also mentioned before). The photograph of the 16-bit encoder and the part of the reader are depicted in Figure 6. The encoder has been codified with a de Bruijn sequence, sensitive part of the reader are depicted in Figure 6. The encoder has been codified with a de Bruijn which guarantees that, for a given sequence of length k, any n-bit sub-code appears only once [38]. sequence, which guarantees that, for a given sequence of length k, any n-bit sub-code appears only once [38]. Thus, the absolute position of the encoder can be univocally identified by reading a bit of the ID code chain and the previous n-1 bits (in our case, n = 4). Sensors 2020, 20, 4837 8 of 13 Thus, the absolute position of the encoder can be univocally identified by reading a bit of the ID code chain and the previous n-1 bits (in our case, n = 4). Sensors 2020, 20, x FOR PEER REVIEW 9 of 15 Figure 6. Photographs of the fabricated (a) sensitive part of the reader and (b) 3D-printed 16-bit encoder Figure codified6.with Photographs a de Bruijnofsequence. the fabricated (a) sensitive part of the reader and (b) 3D-printed 16-bit encoder codified with a de Bruijn sequence. The photograph of the experimental set-up is shown in Figure 7. As aforementioned, it is necessary The photograph to generate of the experimental two interrogation signals (tunedset-up is shown to fcu and in Figure 7. Asread fcl ) to synchronously aforementioned, the ID code ofitthe is necessary to generate two interrogation signals (tuned to f and encoder. It is important to mention that, as a proof of concept demonstrator, such interrogation cu f cl) to synchronously read the ID code signals of have the encoder. been injectedIt is important independently to mention that, as part to the sensitive a proof of the of reader conceptbydemonstrator, means of a vector such interrogation network analyzer signals have Agilent (model been injected N5221A, independently Keysight, Santa to the sensitive Rosa, CA, USA). part ofFor thevisualizing reader by means the ID of a vector network analyzer (model Agilent N5221A, Keysight, code of the encoder, an oscilloscope (model Agilent MSO-X-3104A, Keysight, Santa Rosa, CA, USA) Santa Rosa, CA, USA.). For visualizing has been used. the IDThe codeenvelope of the encoder, function an ofoscilloscope (model Agilent the AM modulated signal MSO-X-3104A, generated byKeysight, tag motion Santaat Rosa, CA, USA.) has been used. The envelope function of the AM the output port of the sensitive part of the reader has been extracted by means of an envelope modulated signal generated by tag motion detector,atwhich the output port of of is comprised thea sensitive Schottky part diode of(model the reader Avago hasHSMS- been extracted 2860, Broadcom by means of an Limited, envelope San Jose, CA, detector, USA)whichand theisN2795A comprised of probe active a Schottky (withdiode capacitance(modelC Avago = 1 pF and HSMS- 2860, Broadcom resistance R = 1 MΩ, Limited, San Jose, CA, USA.) and the N2795A active probe (with Keysight, Santa Rosa, CA, USA). Moreover, it should be noted that a circulator (model ATM capacitance C = 1 pF and resistance ATc4-8, R = 1 MΩ, Keysight, Santa Rosa, CA, USA.). Moreover, it L3Harris Narda-MITEQ, Hauppauge, NY, USA), acting as isolator, has been added between should be noted that a circulator (modelthe ATM ATc4-8, sensitive part ofL3Harris the readerNarda-MITEQ, and the envelope Hauppauge, detectorNY, in orderUSA.), actingreflections to avoid as isolator,from has the been added Schottky between the sensitive diode. Finally, part ofdisplacement the relative the reader and the envelope between detector the sensitive in order part of thetoreader avoidand reflections from the encoder the has Schottky been achieveddiode.by Finally, meansthe of relative a linear displacement displacement system between(model the sensitive part of theApplied STM 23Q-3AN, reader and Motion the encoder has been achieved by means of a linear displacement system Products Inc., Watsonville, CA, USA). Such a system allows us to control the vertical distance (air gap) (model STM 23Q-3AN, Applied Motion betweenProducts the sensitive Inc., part Watsonville, of the readerCA, USA). and the Such a system encoder, allows usand the velocity, to control even the the vertical distance acceleration of the (air gap) Considering encoder. between thethis sensitive setup forpart of the reader experimental and the validation, theencoder, measuredthe clockvelocity, signal and andIDeven codethe of acceleration of the encoder. Considering this setup for experimental the fabricated 16-bit encoder has been inferred, as depicted in Figure 8. Such measured responses have validation, the measured clock signal and ID by been obtained code of the fabricated displacing the encoder 16-bit overencoder has been the sensitive part inferred, of the reader as depicted in Figure with a constant 8. Such velocity of measured 10 mm/s. Note responses that thehave clockbeen signalobtained perfectly bydetermines displacingthe thetime encoder intervalsoverfor thesynchronously sensitive partreadingof the reader with asequence the de Bruijn constant velocity of 10 mm/s. in the encoder Note that as chain (revealed thepeaks clockinsignal perfectlyfunction). the envelope determines the time Hence, the intervals for synchronously absolute position of the encoder reading can bethe de Bruijn sequence determined. Moreover,inthe themeasured encoder chain relative (revealed velocity as peaks between in thethe envelope encoder and function). the sensitive Hence, part of thethe absolute reader has position of the encoder been found to be 10.17 can be determined. mm/s (from the time Moreover, interval the measured relative velocity between the encoder and the between adjacent peaks of the clock signal), which is in good agreement with the nominal sensitive part of the reader hasvalue been found to beNote (10 mm/s). 10.17that mm/s the(from the timedirection displacement interval between cannot beadjacent detectedpeaks with of theapproach. this clock signal), which is Nevertheless, in good agreement with the nominal value (10 mm/s). Note that such information might be extracted (by software) from the linear displacement stepper motor used the displacement direction cannot in be detected with the experimental set-up. this approach. Nevertheless, such information might be extracted (by software) from the linear displacement stepper motor used in the experimental set-up. Sensors 2020, 20, 4837 9 of 13 Sensors 2020, 20, x FOR PEER REVIEW 10 of 15 Sensors 2020, 20, x FOR PEER REVIEW 11 of 15 Figure Photograph 7. 7. Figure of of Photograph thethe experimental setup. experimental setup. T = 0.334 s ID code Clock 0.4 Vo (V) 0.2 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 0.0 4 5 6 7 8 9 Time (s) Figure Figure8.8.Measured Measuredenvelope envelopefunctions functions(ID (IDcode codeand andclock clocksignals) signals)ofofthe the16-bit 16-bitencoder encoderwith withthe the indicated indicatedcode. code. Asindicated As indicatedin in the the introduction, introduction, the the encoder encoder position, position, or or displacement, displacement,from fromaa well-known well-known reference position can be determined from the cumulative number of reference position can be determined from the cumulative number of pulses (peaks in the envelope pulses (peaks in the envelope function) of the function) theclock clocksignal, provided signal, provided thatthat the chain period the chain (p) is well period (p) isknown. For validation well known. purposes, For validation we have fabricated a 3D-printed 16-bit encoder with all the apertures purposes, we have fabricated a 3D-printed 16-bit encoder with all the apertures present in the present in the ID code chain. ID The photograph code and measured chain. The photograph andenvelope measured function envelope(ID code and clock function (ID codesignal) andofclock the fabricated signal) of16-bit the encoder, by fabricated considering 16-bit encoder,(i)by constant velocity considering (i) and (ii) constant constant velocityacceleration of the encoder and (ii) constant acceleration with of regard the to the sensitive part of the reader, are depicted in Figure 9. With this result, encoder with regard to the sensitive part of the reader, are depicted in Figure 9. With this result, it isit is demonstrated that, by counting pulses, demonstrated that, byit counting is possible to infer pulses, the it is position possible toof the the infer encoder. position Moreover, the ID code of the encoder. can be Moreover, properly the ID codeobtained can be regardless properlyofobtained the instantaneous regardless velocity of theofinstantaneous the encoder. Nevertheless, velocity of the this encoder. approach presents two main Nevertheless, drawbacks: this approach (i) it is two presents not possible to determine main drawbacks: theisabsolute (i) it position not possible of the encoder, to determine the and (ii) aposition absolute reference position of the is needed encoder, and (ii)inaorder to drive reference the encoder position is needed to in such position order to drive if the the system encoderis torestarted for anyif reason. such position the system Conversely, is restartedby for encoding the IDConversely, any reason. code chain by of the encoder encoding thewith a de chain ID code Bruijn ofsequence, the encoder n bits onlywith of Bruijn a de such IDsequence, code chain onlymust be of n bits synchronous such ID code read after chain a system must reset, in order be synchronous readto determine after a system again theinabsolute reset, order toposition determine of the againencoder. the absolute position of the encoder. Sensors 2020, 20, 4837 10 of 13 Sensors 2020, 20, x FOR PEER REVIEW 12 of 15 (a) ID code Clock 0.2 T = 0.330 s (v = 10.3 mm/s) 0.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Vo (V) 0.0 (b) T1 = 0.502 s (v1 = 6.77 mm/s) T2 = 0.410 s (v2 = 8.29 mm/s) T3 = 0.645 s (v3 = 5.27 mm/s) 0.2 0.1 0.0 7 8 9 10 11 12 13 14 Time (s) Figure9.9. Photograph Figure Photograph and and measured measured envelope envelopefunctions functions(ID (IDcode codeand andclock clocksignals) signals)of ofthe the3D-printed 3D-printed 16-bit 16-bitencoder encoderwith allall with thethe apertures present apertures at their present positions, at their inferred positions, by considering inferred encoder encoder by considering motion with (a) constant velocity and with (b) constant acceleration. motion with (a) constant velocity and with (b) constant acceleration. The The number number of of bits bits (or (or pulses) pulses) per per unit unit length length (a (a figure figure ofofmerit) merit) achieved achieved with with the the proposed proposed reader/encoder structure with synchronous reading is as high as 3.11 reader/encoder structure with synchronous reading is as high as 3.11 bit/cm. As compared bit/cm. As compared to other tolinear other displacement/velocity sensors based on microwave encoders with synchronous linear displacement/velocity sensors based on microwave encoders with synchronous reading, such reading, such value is very valuecompetitive. For instance, is very competitive. Forin [21], thein instance, achieved [21], the number achieved of bits per unit number length of bits perwas unit2.29 bit/cm length (to2.29 was the best of our knowledge, the highest value obtained so far). Nevertheless, the microwave bit/cm (to the best of our knowledge, the highest value obtained so far). Nevertheless, the microwave encoders of [21] are based on encoders ofmetallic [21] areinclusions based onimplemented on the considered metallic inclusions implemented substrate. on theSuch encoderssubstrate. considered exhibit limited Such robustness against mechanical wearing and aging effects, as compared encoders exhibit limited robustness against mechanical wearing and aging effects, as compared to all-dielectric microwave to encoders based all-dielectric on permittivity microwave encoderscontrast. basedMoreover, as demonstrated on permittivity in [17], the contrast. Moreover, ascost of the considered demonstrated in [17], 3D-printed materials the cost of the is smaller considered than the 3D-printed one corresponding materials is smaller than to commercial microwaveto the one corresponding substrates commercial or even to that of microwave encoders based on printed metallic inclusions (where microwave substrates or even to that of microwave encoders based on printed metallic inclusions commercial conductive inks are commercial (where used). conductive inks are used). An Animportant importantaspect aspectin inthese theseencoder encodersystems systemsisisthe theeffect effectof ofthe thevariation variationin inthe theair airgap gap(vertical (vertical distance between the encoder and the sensitive part of the reader), which can be distance between the encoder and the sensitive part of the reader), which can be caused by vibrations caused by vibrations in the system. in the This system. aspect This waswas aspect studied in [17], studied which in [17], revealed which that,that, revealed by considering an airan by considering gap airof 0.075 gap mm, of 0.075 itmm, wasitpossible to obtain a significant variation in the magnitude of the transmission was possible to obtain a significant variation in the magnitude of the transmission coefficient coefficient at the carrier frequency signal. Such variation is reduced as the air gap increases. Concretely, at the carrier frequency signal. Such variation is reduced as the air gap increases. Concretely, for air for air gaps greater than 0.1 gaps greater thanmm,0.1 the mm, reader is almost the reader insensitive is almost to thetopresence insensitive of theofencoder. the presence Therefore, the encoder. in a Therefore, real scenario, the guiding system must ensure a vertical distance of the order in a real scenario, the guiding system must ensure a vertical distance of the order of 0.1 mm between of 0.1 mm between the encoder the encoderand and the sensitive part part the sensitive of theofreader. the reader. 4. Conclusions 4. Conclusions All-dielectric 3D-printed electromagnetic encoders based on permittivity contrast with All-dielectric 3D-printed electromagnetic encoders based on permittivity contrast with synchronous reading, useful for measuring displacements and velocities, have been reported for the synchronous reading, useful for measuring displacements and velocities, have been reported for the first time. The encoders are based on linearly shaped apertures made on a 3D-printed material which first time. The encoders are based on linearly shaped apertures made on a 3D-printed material which exhibits high permittivity. The sensitive part of the reader is a splitter/combiner structure, where each exhibits high permittivity. The sensitive part of the reader is a splitter/combiner structure, where each branch has been loaded with a series gap and a slot resonator. Such a structure is able to detect the branch has been loaded with a series gap and a slot resonator. Such a structure is able to detect the presence of the apertures, provided that they are at a short distance. Thus, by feeding the sensitive part of the reader with two interrogation signals properly tuned, two AM modulated signals are Sensors 2020, 20, 4837 11 of 13 presence of the apertures, provided that they are at a short distance. Thus, by feeding the sensitive part of the reader with two interrogation signals properly tuned, two AM modulated signals are alternately generated at the output port of the structure by encoder motion. The envelope function of one such signal contains the ID code providing the absolute position of the encoder, whereas the velocity, or even the acceleration, is given by the other envelope function (acting as a clock signal for synchronous reading). The number of bits per unit length has been significantly increased as compared with other microwave encoders available in the literature. Moreover, the reported all-dielectric encoders exhibit the following advantages as compared to microwave encoders based on metallic inclusions: (i) reduced cost and (ii) major robustness against mechanical wearing and aging effects. Author Contributions: C.H. and F.P. carried out the experiments shown in the paper as well as the analysis of the data. C.H. and F.M. wrote the paper. 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Flye Sainte-Marie on the Counting of Circular Arrangements of 2n Zeros and Ones That Show Each N-Letter Word Exactly Once; Technological University Eindhoven: Eindhoven, The Netherlands, 1975. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).