sensors Article Strategies to Enhance the Data Density in Synchronous Electromagnetic Encoders Ferran Paredes * , Amirhossein Karami-Horestani and Ferran Martín CIMITEC, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain; amirhossein.karami@uab.cat (A.K.-H.); ferran.martin@uab.cat (F.M.) * Correspondence: ferran.paredes@uab.cat Abstract: In this paper, we report two different strategies to enhance the data density in electro- magnetic encoders with synchronous reading. One approach uses a periodic chain of rectangular metallic patches (clock chain) that determines the encoder velocity, and dictates the instants of time for retrieving the bits of the identification (ID) code. However, contrary to previous electromagnetic encoders, the ID is inferred at both the rising and the falling edges of the clock signal generated by the clock chain. Moreover, the bits of information are not given by the presence or absence of metallic patches at their predefined positions in the so-called ID code chain. With this novel encoding system, a bit state corresponding to a certain instant of time is identical to the previous bit state, unless there is a change in the envelope function of the ID code signal, determined by the additional non-periodic ID code chain. The other encoding strategy utilizes a single chain of C-shaped resonators, and encoding is achieved by considering four different resonator dimensions, corresponding to four states and, hence, to two bits per resonator of the chain. Thus, with these two strategies, the data density is twice the one achievable in previously reported synchronous electromagnetic encoders. Keywords: electromagnetic encoders; motion sensors; chipless RFID Citation: Paredes, F.; Karami-Horestani, A.; Martín, F. Strategies to Enhance the Data 1. Introduction Density in Synchronous Electromagnetic encoders constitute an interesting alternative to optical encoders [1–3] Electromagnetic Encoders. Sensors in many applications devoted to motion control. The most well-known optical encoders 2022, 22, 4356. https://doi.org/ are those designated as rotary, consisting of an opaque disc (for example, made of metal) 10.3390/s22124356 with an array of apertures. The system uses an optical source (that generates an optical Academic Editor: Daniel Ramos beam) and a detector (e.g., a photodiode). When any of the apertures of the encoder lie in Received: 13 May 2022 the optical path between the source and the detector, the latter detects an optical signal in Accepted: 7 June 2022 the form of a pulse. For the determination of the angular velocity, a circular periodic chain Published: 8 June 2022 of apertures distributed along the rotor perimeter suffices. The time lapse between two adjacent pulses determines the angular velocity, provided the angular distance between Publisher’s Note: MDPI stays neutral consecutive apertures (or period) is well known. The position can be inferred from the with regard to jurisdictional claims in cumulative number of pulses retrieved in the detector from a reference position. This is published maps and institutional affil- how the so-called incremental encoders work. Nevertheless, in the event of a system reset, iations. incremental encoders cannot provide the angular position. For that purpose, absolute encoders are needed. In such encoders, each position is determined by a unique identi- fication (ID) code, and, for that reason, knowing the previous stages of encoder motion Copyright: © 2022 by the authors. is irrelevant. In optical rotary encoders, the angle resolution is dictated by the number of Licensee MDPI, Basel, Switzerland. pulses per revolution (PPR), a figure of merit, and there are commercially available devices This article is an open access article with thousands of PPR. However, despite such a very good figure of merit achievable with distributed under the terms and optical encoders, and the possibility to implement both incremental- and absolute-type conditions of the Creative Commons encoders, optical signals are affected by dirtiness, grease, or pollution, encountered in Attribution (CC BY) license (https:// many industrial scenarios where encoders operate. Thus, optical encoders offer a limited creativecommons.org/licenses/by/ robustness against hostile surroundings, often present in operational environments. By con- 4.0/). trast, microwave signals are more tolerant to pollution and dirtiness. Thus, the microwave Sensors 2022, 22, 4356. https://doi.org/10.3390/s22124356 https://www.mdpi.com/journal/sensors operational environments. By contrast, microwave signals are more tolerant to p and dirtiness. Thus, the microwave counterparts of optical encoders were report years ago in order to alleviate the indicated limitative aspect [4–11]. Such encod Sensors 2022, 22, 4356 designated as electromagnetic, or microwave, encoders. Their working principle 2 of 16 to the one of optical encoders, the main difference being the fact that, rather tha signals, electromagnetic encoders use microwaves for the determination of the position and counterparts velocity of optical (either encoders linear were or angular). reported a few years ago in order to alleviate the The indicated first reported limitative electromagnetic aspect [4–11]. Such encoders encoders wereasrotary-type were designated andorimplem electromagnetic, etching a circular chain of metallic resonators in the periphery of the rotor, a disc microwave, encoders. Their working principle is similar to the one of optical encoders, the main difference being the fact that, rather than optical signals, electromagnetic encoders a dielectric use microwaves material [4,5]. In theofelectromagnetic for the determination the encoder position rotary encoder(either and velocity of [5], a figure of linear orPPR = 1200 was demonstrated, and the encoder was equipped with an ad angular). (concentric) non-periodic The first reported chain in electromagnetic order were encoders to determine rotary-typetheanddirection implemented of motion, by c or counterclockwise. These electromagnetic rotary encoders were increment etching a circular chain of metallic resonators in the periphery of the rotor, a disc made of a dielectric material [4,5]. In the electromagnetic rotary encoder of [5], a figure of merit working principle was described in [4] (see Figure 1). In brief, a transmission lin of PPR = 1200 was demonstrated, and the encoder was equipped with an additional with a pair (concentric) of resonators non-periodic identical chain in to those the order to determine of the encoder, direction but oppositely of motion, clockwise or orient stator, namely,These counterclockwise. the static part of the electromagnetic system, rotary encoders able toincremental. were provide the motion Their workingvariables pair of resonators of the encoder chain crosses the pair of resonators of principle was described in [4] (see Figure 1). In brief, a transmission line loaded with a the st pair of resonators identical to those of the encoder, but oppositely oriented, is the stator, coupling between these elements significantly alters the transmission coefficie namely, the static part of the system, able to provide the motion variables. When a pair of line. Thus, resonators byencoder of the feedingchainthe crosses transmission the pair line of the stator of resonators with athe of the stator, harmonic coupling signal a frequency between where significantly these elements the transmission alters the coefficient transmission experiences a significant coefficient of the line. Thus, excu byencoder motion, feeding the it is expected transmission line of the that statoranwithamplitude a harmonicmodulated signal tuned to(AM) signal is gen a frequency the output port of the line. The envelope function of such AM signal should where the transmission coefficient experiences a significant excursion by encoder motion, it e is expected that an amplitude modulated (AM) signal is generated at the output port of the many peaks (or dips) as resonators in the encoder chain (an AM detector su line. The envelope function of such AM signal should exhibit as many peaks (or dips) as retrieve in resonators the theenvelope function). encoder chain (an AM detector suffices to retrieve the envelope function). Z0 Envelope Detector Vi @ f0 Figure Figure 1. Sketch 1. Sketch showing showing the working the working principle principle of an electromagnetic of an electromagnetic rotarybased rotary encoder system encoder syst onon a rotor with a circular chain of split-ring resonators (SRRs). a rotor with a circular chain of split-ring resonators (SRRs). Linear electromagnetic encoders based on an identical principle were also reported in severalLinear electromagnetic papers [6–11]. Indeed, such encoders encoders can based on an be applied notidentical principle only to the were also measurement ofinlinear several motionpapers [6–11].andIndeed, (displacement velocity),such but alsoencoders can be applied to the implementation of a kindnot only ofmeasurement of linear motion (displacement and velocity), but also to the implem time-domain chipless radiofrequency identification (chipless RFID) systems, based on near-field coupling (with the sensitive part of the reader, i.e., a transmission-line-based of a kind of time-domain chipless radiofrequency identification (chipless RFID) structure) and sequential bit reading [12–18]. In this latter application, not all the resonators, based on near-field or, more generally, the tagcoupling inclusions,(with the sensitive are present at the periodicpartpositions of the ofreader, i.e., a trans the encoder line-based chain. By this structure) and sequential means, the encoder, bit reading or tag, is provided with[12–18]. In code, a certain ID this latter where applicatio the the resonators, or, more generally, the tag inclusions, are present at the periodic logic state ‘1’ or ‘0’ depends on whether a resonator is present or absent, respectively, at p its predefined position. A clear advantage of these time-domain near-field chipless RFID of the encoder chain. By this means, the encoder, or tag, is provided with a certain systems, as compared to other chipless RFID systems based on time-domain reflectometry where the logic state ‘1’ or ‘0’ depends on whether a resonator is present o Sensors 2022, 22, 4356 3 of 16 (TDR) [19–28], or as compared to other frequency-domain [29–47] or hybrid [48–61] chipless RFID systems, is the fact that the number of bits is only limited by tag size. Moreover, the tags are read sequentially, and a simple harmonic signal suffices for tag reading (by contrast, in frequency-domain and hybrid chipless RFID systems, wideband signals for tag reading are needed). Rigorously speaking, in their functionality as motion sensors, linear or rotary elec- tromagnetic encoders able to provide the absolute position have not been reported so far. The main limitation concerns the fact that providing an ID code identifying the different positions, given by the ratio between the encoder length (in linear encoders), L, and the encoder period, p, may represent an excessive number of bits. For example, to unequivo- cally determine the different positions in a linear encoder with L = 1 m, and p = 1 mm, the number of required bits, N, must satisfy. L N ≥ log2 (1) p i.e., in the considered example, the minimum number of bits is N = 10. However, it is not possible to consider an encoder implementation with 10 parallel chains of inclusions (i.e., with as many chains as required number of bits). The solution was reported in [8] and referred to as a quasi-absolute electromagnetic encoder. In the present paper, one objective is to briefly review the working principle of quasi- absolute electromagnetic encoders based on synchronous reading, and provide a prototype example (this is the subject of Section 2). Then, in Section 3, two different strategies to enhance the data density in electromagnetic encoders with synchronous reading are discussed and validated by means of two prototype examples. This is the main motivation of this paper, as far as these new encoders with enhanced data density represent a clear advance as compared to previous synchronous electromagnetic encoders, mainly reported in [8–11]. 2. Quasi-Absolute Electromagnetic Encoders A quasi-absolute electromagnetic encoder is a system where the encoder is able to provide the velocity and the absolute position (by contrast, in incremental encoders, the cumulative number of pulses from a reference position gives the encoder location). However, after a system reset, the quasi-absolute encoder must move several periods in order to be able to provide the encoder position. Such number of periods is given by the number of bits, N, that are necessary to univocally determine all the different positions of the encoder and given by expression (1). Thus, because the absolute position cannot be immediately determined after a system reset, such encoders have been designated as quasi-absolute encoders. The whole encoder must be codified following the so-called De Bruijn sequence [62], where any subset of N consecutive bits does not repeat along the length of the encoder. By this means, it is guaranteed that all the different encoder positions are identified by a different (and unique) ID code. In the first quasi-absolute electromagnetic encoders reported in the literature, the clock signal, which provides the encoder velocity, determines the instants of time for reading a unique bit of the ID code. The encoder is based on two parallel chains, the clock chain and the ID code chain. The clock chain is periodic, i.e., all the considered inclusions are present at their predefined positions. By contrast, in the ID code chain, only those inclusions corresponding to the logic state ‘10 are present (i.e., the ID code chain is non-periodic). Various realizations of quasi-absolute electromagnetic encoders have been recently reported [8,10,11]. In this paper, we report the one presented in [11], in order to compare it with the implementations based on strategies that double the number of bits per clock pulse, to be discussed in the next section, and representing the relevant contribution of the present paper. Figure 2 depicts the photograph of the quasi-absolute encoder of [11], implemented in a rubber elevator belt. The clock and ID chains are based on rectangular patch inclusions. Such inclusions can be detected by means of a transmission (microstrip) line loaded with a Figure 2 depicts the photograph of the quasi-absolute encoder of [11], implemented in a rubber elevator belt. The clock and ID chains are based on rectangular patch Sensors 2022, 22, 4356 inclusions. Such inclusions can be detected by means of a transmission (microstrip)4 line of 16 loaded with a complementary split-ring resonator (CSRR) [63], etched in the ground plane, beneath the line. The reason is that the presence of a metal patch in close proximity to the CSRR modifies complementary split-ring theresonator frequency response (CSRR) (transmission [63], etched coefficient) in the ground plane, of the line. beneath the Particularly, line. The reason theisresonance frequency that the presence of ashifts metalup. Therefore, patch by injecting in close proximity a harmonic to the CSRR modifiessignal tuned to the resonance the frequency frequency ofcoefficient) response (transmission the bare CSRR, a significant of the line. Particularly,excursion of the the resonance transmission frequency shifts coefficient at that frequency up. Therefore, is expected by injecting a harmonicwhensignala metal patchtocrosses tuned the area the resonance of influenceofofthe frequency the bare CSRR. Consequently, CSRR, a significantan amplitude-modulated excursion of the transmission (AM) signal generated coefficient at by encoder motion is expected. For the periodic clock chain, the envelope function of this that frequency is expected when a metal patch crosses the area of influence of the CSRR. AM signal should Consequently, an be periodic. However, in(AM) amplitude-modulated the considered signal generatedencoderby reader, encoder alsomotion depicted is in Figure 2,For expected. three thedifferent periodic CSRRs can bethe clock chain, appreciated in the ground envelope function of thisplane. One ofshould AM signal these CSRRs, the one be periodic. designated However, in the as considered CSRRp, is devoted encoder toreader, detecting the also inclusions depicted of the ID in Figure code 2, three chain, another one (CSRRc) is used to detect the inclusions of the clock chain, and, finally, different CSRRs can be appreciated in the ground plane. One of these CSRRs, the one it can be appreciated that there is a third resonant element (CSRRd) that lies in the path of designated as CSRR p , is devoted to detecting the inclusions of the ID code chain, another oneclock the (CSRR c ) is but chain, used not tocentered detect the inclusions beneath of the the line. Thisclock latterchain, CSRRdand,is usedfinally, it can be to generate a appreciated that there is a third resonant redundant clock signal with lag or lead as compared to the element (CSRR ) that lies in the path d original one. By this means, of the clock it chain, is but not possible centered beneath to determine the line. the direction This latter of motion. CSRRd isthree Obviously, used harmonic to generatesignals a redundant tuned clock signal with lag or lead as compared to the original one. to the resonance frequency of the three CSRRs are needed. In order to retrieve the three By this means, it is possible to determine envelope the direction functions in a realof motion. system, oneObviously, option is tothreefeedharmonic the line bysignals meanstuned of theto the three resonance frequency of the three CSRRs are needed. In order harmonic signals using a combiner, and then separate the AM signals at the output port to retrieve the three envelope functions by means of in aa triplexer. real system, one option an By connecting is to feed thedetector envelope line by to means each of of the the three output harmonic ports of signals using a combiner, and then separate the AM signals at the output port by means of the triplexer, the three envelope functions can be inferred. An alternative is to use a a triplexer. By connecting an envelope detector to each of the output ports of the triplexer, voltage-controlled oscillator (VCO) managed by a microcontroller, in order to provide the the three envelope functions can be inferred. An alternative is to use a voltage-controlled three harmonic signals consecutively during different periods of time (the solution oscillator (VCO) managed by a microcontroller, in order to provide the three harmonic adopted in [11]). The microcontroller separates also the three envelope functions signals consecutively during different periods of time (the solution adopted in [11]). The corresponding to the clock, redundant and ID code signals (see further details in [11]). microcontroller separates also the three envelope functions corresponding to the clock, redundant and ID code signals (see further details in [11]). (a) (b) (c) Figure 2. Photograph of the quasi-absolute electromagnetic encoder implemented on a rubber Figure 2. Photograph of the quasi-absolute electromagnetic encoder implemented on a rubber elevator belt (a) and photograph of the top (b) and bottom (c) views of the reader. The dimensions elevator belt (a) and photograph of the top (b) and bottom (c) views of the reader. The dimensions of of the encoder are: d1 = 11.5 mm; d2 = 15.9 mm, w = 3 mm, s = 1 mm and g = 1.9 mm. The chain period the is encoder p =4 are: dthat mm. Note 1 = 11.5 L/p =mm; d2 = 15.9 48; thus, N = mm, 6. Thew reader s = 1 mm = 3 mm,(stator) wasand g = 1.9 mm. fabricated The on the chainRO4003C Rogers period is p = 4 mm.with substrate that L/p h= =48; Notethickness 0.81 mm, thus, N=dielectric constant 6. The reader εr = 3.38, (stator) and loss factor was fabricated on the Rogers tanδ RO4003C = 0.0027. The dimensions substrate with of the stator hare: thickness transmission = 0.81 line widths mm, dielectric w1εr= =6.4 constant mmand 3.38, w2 factor andloss = 1.9 mm; tanδ CSRR widths = 0.0027. The w r = 2.9 mm (for dimensions thestator of the threeare: resonators); resonator transmission lengthswl1c ==l6.4 line widths d = 10.5 mmmm w2 =lp1.9 andand = 14.5 mm; mm; CSRRringwidths splits swd r==0.4 mms(for 2.9mm, c = 1.6 themm, and three sp = 6.2 mm; resonators); CSRR slot resonator widthlcc = lengths = 0.5 ld =mm. 10.5 The mmsub-index c, d,mm; and lp = 14.5 and ring p in the splitsvariables sd = 0.4corresponding mm, sc = 1.6 mm, to resonator’s length and sp = 6.2 mm;and ringslot CSRR splits are used width tomm. c = 0.5 differentiate the CSRRs. The sub-index c, d, and p in the variables corresponding to resonator’s length and ring splits are used to differentiate the CSRRs. In order to demonstrate the functionality of the encoder, it was displaced at a velocity of v = 40 mm/s in [11] by means of a dedicated experimental setup based on a linear In order to demonstrate the functionality of the encoder, it was displaced at a v of v = 40 mm/s in [11] by means of a dedicated experimental setup based on displacement system (model Thorlabs LTS300/M (Thorlabs Inc., Newton, NJ, USA Sensors 2022, 22, 4356 air gap, or separation between the stator and encoder, was set to 1 mm. 16 HMC 5 ofThe VCO (Analog Devices, Norwood, MA, USA) was used for the harmonic signal gen The control voltage of this component was managed by means of the ATm microcontroller displacement system (Atmel (modelCorporation, Thorlabs LTS300/M San(Thorlabs Jose, CA, USA) Inc., (Arduino Newton, development NJ, USA)). The air pla gap, or separation between the stator and encoder, was set to 1 mm. The HMC391LP4 VCO whereas the considered envelope detector was the ADL5511 model (further det (Analog Devices, Norwood, MA, USA) was used for the harmonic signal generation. The given in [11]). Figure control voltage of this 3 shows component wasthe threebyenvelope managed means of thefunctions, ATmega328after being retrieved microcontroller microcontroller. (Atmel Corporation, The Sanclock andUSA) Jose, CA, the ID code signals (Arduino exhibit development good synchronism, platform), whereas the whe direction signal is delayed with regard to the clock signal, thus indicating considered envelope detector was the ADL5511 model (further details are given that the e in [11]). Figure 3 shows the three envelope functions, after being retrieved by the microcontroller. moves upwards (in reference to Figure 2c). The separation between peaks is 100 ms The clock and the ID code signals exhibit good synchronism, whereas the direction signal corresponds is delayed with to an encoder regard velocity to the clock of 40 signal, thus mm/s, that indicating sincethethe period encoder movesof the metallic inc upwards (resolution) p = 4 2c). (in reference toisFigure mm.The Note also that separation the peaks between peaks isin100 thems, IDwhich code corresponds signal perfectly c with the presence of rectangular patches in the position chain (see(resolution) to an encoder velocity of 40 mm/s, since the period of the metallic inclusions Figure 2). Let u that is p =the 4 mm.maximum Note also velocity of these that the peaks in thesynchronous ID code signalencoder perfectly systems is determined correlate with the presence of rectangular patches in the position chain (see Figure 2). Let us clarify that the sampling period of the microcontroller, as discussed in [11]. In the systems of [ maximum velocity of these synchronous encoder systems is determined by the sampling maximum period of the velocity was estimated microcontroller, as discussedtoin be [11].roughly 100 mm/s. In the systems of [11], Nevertheless, the maximum with microcontrollers velocity was estimated theto sampling be roughly 100period mm/s.can be reduced Nevertheless, withto a few certain µs, and encoder ve microcontrollers in the range of several meters per second can thus be measured. the range of the sampling period can be reduced to a few µs, and encoder velocities in several meters per second can thus be measured. Figure Figure 3.3.Measured Measured envelope envelope function function for the for the clock, clock,and direction, direction, and position position signals signals corresponding to corres the quasi-absolute encoder system of Figure 2. Reprinted with permission from [11]. to the quasi-absolute encoder system of Figure 2. Reprinted with permission from [11]. 3. Enhancing the Data Density 3. Enhancing thetwo In this section, Data Density different strategies to enhance the data density per unit length in In this section, quasi-absolute two different electromagnetic encoders strategies are reported.to enhance With the data the both approaches, density densityper of unit le bits per unit length is doubled, which means that, after a system reset, the necessary number quasi-absolute of periods that theelectromagnetic encoders encoder should displace are in order to reported. provide the With both absolute approaches, position is half the of thebits perofunit number length periods in theiselectromagnetic doubled, which means encoder that, reported after in the a system previous reset, section. Let the ne number of periods us next discuss that the both strategies encoder should displace in order to provide the a separately. position is half the number of periods in the electromagnetic encoder reported 3.1. Encoder Reading by Rising/Falling Edges of the Clock Signal previous section. Let us next discuss both strategies separately. In the quasi-absolute encoder of the previous section, the ‘0’ and ‘1’ logic states are given by the absence and presence, respectively, of metallic inclusions (rectangular metallic 3.1. Encoder patches) at theReading by positions predefined Rising/Falling in the IDEdges code of the Clock chain. In thatSignal system, the clock signal In the dictates theinstants quasi-absolute encoder of time where the bitsofofthe the previous encoder (ID section, the must code chain) ‘0’ and ‘1’ logic st be read. given by the absence and presence, respectively, of metallic inclusions (rect metallic patches) at the predefined positions in the ID code chain. In that system, th signal dictates the instants of time where the bits of the encoder (ID code chain) m read. Typically, these instants of time are the rising edges of the digital clock sig novel encoding strategy, useful to increase the data capacity using the same encode is illustrated in Figure 4 [64]. Compared to the strategy of the encoder of Figure 2 Sensors 2022, 22, 4356 this novel approach, the rising and the falling edges of the digital clock6 signal of 16 dict instants of time for synchronously reading the bits of the encoder. This means th sampling rate of the ID code signal increases by a factor of two, as compared Typically, these instants of time are the rising edges of the digital clock signal. A novel conventional encoding strategy, encoder, usefulwhere the the to increase bitsdata of the ID code capacity using chain are retrieved the same encoder area, at the is rising ofillustrated the clock in Figure 4 [64]. Compared to the strategy of the encoder of Figure 2, with this is enh signal. With this strategy, the data density per unit length approximately novel approach, the byrising a factor and the offalling two edges (2N-1).of theAn important digital feature clock signal dictate of the this instantsnovel en scheme is that the bit state corresponding to a certain instant of time is identical of time for synchronously reading the bits of the encoder. This means that the sampling rate of the ID code signal increases by a factor of two, as compared to the conventional previous bit state, unless there is a change in the envelope function of the ID code encoder, where the bits of the ID code chain are retrieved at the rising edges of the clock This means signal. thatstrategy, With this encoding is not the data basedper density onunit thelength absence or presence is enhanced of functional approximately by incl ata their factor predefined of two (2N-1).positions An important (thefeature procedure of this of theencoding novel encoderschemeof Section is that2). theBybitcontras this stateencoding correspondingscheme, in the to a certain rising instant andisfalling of time identicaledges of the clock to the previous signal, bit state, unlessthe new identical to the previous one, if the envelope function of the ID code chain do there is a change in the envelope function of the ID code signal. This means that encoding is not based on the absence or presence of functional inclusions at their predefined positions change, and the (the procedure new of the bit switches encoder of Sectionprovided the envelope 2). By contrast, function with this encoding experiences scheme, in the a var Thus, risingthe andencoders exhibit falling edges of theID code clock chains, signal, where, the new bit israther than identical to all-identical the previous one, metallic p atif the predefined positions, envelope function of thethey ID code arechain made, does not in change, general, andoftheunequal patches, wit new bit switches dependent on the number of consecutive ‘1’ in the ID code chain. To clarify provided the envelope function experiences a variation. Thus, the encoders exhibit ID code this chains, where, rather than all-identical metallic patches at predefined positions, they are note that the first ‘1’ of the ID code chain should correspond to the presence of m made, in general, of unequal patches, with size dependent on the number of consecutive ‘1’ that chain in the ID code (i.e., theTo chain. envelope clarify thisfunction up) aspect, note thatforthethe firstreading ‘1’ of theedge ID code (either rising or fall chain should the clock chain. correspond to the presence of metal in that chain (i.e., the envelope function up) for the reading edge (either rising or falling) of the clock chain. Rising edge Rising edge Falling edge Clock chain ID code chain Clock signal ID code signal Decoding code 1 1 1 1 1 0 1 0 1 0 1 (a) (b) Figure Figure 4. Schemeofof 4. Scheme thethe encoding encoding system system based based on the on the rising (a)rising (a) and rising/falling and rising/falling (b) edge o (b) edge of the clock signal. Reprinted with permission from [64]. clock signal. Reprinted with permission from [64]. For validation of this approach, a reader (stator) similar to the one of the system in For2 validation Section was fabricated of(see thisFigure approach, a reader 5). The main (stator) difference similar is that to the in this new oneonly reader, of the sys Section 2 was two CSRRs arefabricated (see Figure present, namely, 5). The the encoder doesmain difference not have is thattoindetermine the possibility this new reade two CSRRs are present, namely, the encoder does not have the possibility the motion direction. The encoders are based on two chains of inclusions, the clock chain, to dete identical to the one of the encoder in Figure 2a (although the dimensions are somehow the motion direction. The encoders are based on two chains of inclusions, the clock different), and the ID code chain. Figure 5 also depicts two 19-bit specific encoders. identical to the one To determine withof the encoder precision in Figure the frequency of the 2a (although interrogation the dimensions signals, the frequencyare som different), response ofand the IDwithout the reader, code chain. Figure rectangular 5 alsopatches metallic depictsontwo top of19-bit it, wasspecific encoders measured. The results (not shown) indicate that the notches appear at fc = 3.90 GHz and fp = 4.15 GHz, and these should be the frequencies of the ID code and clock signals, respectively. The experimental setup for characterization of this new encoder system uses also a linear displacement system identical to the one used for the characterization of the encoder system in Section 2. By considering a nominal air gap of 0.5 mm, the measured envelope signals (ID code and clock) of the two 19-bit encoders have been found to be those depicted in Figure 6. Such signals perfectly correlate with the encoders of Figure 5. Note that the sampling rate, as indicated, is twice the one of the system in Section 2; therefore, the data density is twice the one of that system. Thus, the number of periods of the encoder that are Sensors 2022, 22, 4356 7 of 16 Sensors 2022, 22, x FOR PEER REVIEW 7 of 17 necessary to retrieve the encoder position after a system reset is reduced to half the value of the system based on the encoding scheme reported in Section 2. (a) (b) TOP BOTTOM (c) (d) Figure Figure5.5.Layout Layout ofof thethe reader reader(stator) (a)(a) (stator) andandspecific encoder specific (b),(b), encoder andand photograph photograph of the of reader (c) the reader and two specific encoders (d). Dimensions (in mm) are: w = 1.90, wr = 3.30, lp = 9.35, lc = 9.90, dp = 8.15, (c) and two specific encoders (d). Dimensions (in mm) are: w = 1.90, wr = 3.30, lp = 9.35, lc = 9.90, dc = 8.70, wp = 2.00, s = 2.00, and g = 2.00. The considered substrate for the reader is the Rogers dp = 8.15, dc = 8.70, wp = 2.00, s = 2.00, and g = 2.00. The considered substrate for the reader is Sensors 2022, 22, x FOR PEER REVIEW RO4003C with relative permittivity εr = 3.55, thickness h = 0.81 mm, and loss tangent tanδ = 0.0021. 8 o the Rogers RO4003C with relative permittivity εr = 3.55, thickness h = 0.81 mm, and loss tangent For the encoders, the substrate is the same as the one used in the reader, but with thickness h = 0.204 tanδReprinted mm. = 0.0021. with For the encoders,from permission the [64]. substrate is the same as the one used in the reader, but with thickness h = 0.204 mm. Reprinted with permission from [64]. To determine with precision the frequency of the interrogation signals, the frequency fP =3.90 GHz fC =4.15 GHz response 1.0of the reader, without rectangular metallic patches on top of it, was measured. tw The results (not shown) indicate that the notches appear at fc = 3.90 GHz and fp = 4.15 GHz, and these should be the frequencies of the ID code and clock signals, respectively. The experimental setup for characterization of this new encoder system uses also a linear 0.5 displacement system identical to the one used for the characterization of the encoder system in Section 2. By considering a nominal air gap of 0.5 mm, the measured envelope signals (ID code and 1 0 1clock) 0 1 0of1 the 0 1 two 0 1 19-bit 0 1 0 encoders 1 0 1 0 1have been found to be those 0.0 Vo (v) depicted in Figure 6. Such signals perfectly correlate with the encoders of Figure 5. Note 1.0 that the sampling rate, as indicated, is twice the one of the system in Section 2; therefore, the data density is twice the one of that system. Thus, the number of periods of the encoder that are necessary to retrieve the encoder position after a system reset is reduced to half 0.5of the system based on the encoding scheme reported in Section 2. the value 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0.0 0 1 2 3 4 5 Time (s) Figure 6. Measured Figure 6. Measuredenvelope envelope signals signals (ID code (ID code and of and clock) clock) of the the 19-bit 19-bit tags tags 5ofwith of Figure Figure the 5 with indicated codes.Reprinted indicated codes. Reprinted with with permission permission from [64]. from [64]. 3.2. Hybrid Time-/Frequency-Domain System According to this encoding strategy, the proposed system is a hybrid ti /frequency-domain encoder system [65]. The encoders consist of a single chain of Sensors 2022, 22, 4356 8 of 16 3.2. Hybrid Time-/Frequency-Domain System According to this encoding strategy, the proposed system is a hybrid time-/frequency- domain encoder system [65]. The encoders consist of a single chain of C-shaped resonators etched in a dielectric substrate. The bits of the encoder are read sequentially through the near field, similar to the previous encoder systems, in a time-division multiplexing scheme. However, there is a fundamental difference between the system to be discussed in this subsection and those analyzed before in this paper. That is, in the present system, there is always a C-shaped resonator in the predefined (periodic) positions of the chain. Thus, an additional chain to provide synchronism (clock chain) is not necessary. Thus, encoding is not achieved by the presence or absence of inclusions (C-shaped resonators), but through the size of such resonators. Four different sizes are considered, corresponding to four different states and, consequently, to two bits per resonant element of the chain. Because the size of the resonator correlates with its resonance frequency, it follows that bit encoding is achieved by frequency. For this reason, this system is designated as a hybrid time-/frequency-domain encoder system. The information is encoded in frequency, but it is read sequentially in time domain. However, contrary to the system in Section 2, in the present system, each reading (detection of the size of the C-shaped resonator) provides two bits of information rather than one. Thus, with this system, the data density is twice the one of those systems based on presence/absence of inclusion at the predefined positions in the encoder chain. The sensitive part of the reader (stator) is a transmission line with a series gap, whereas the tag is a chain of C-shaped resonators, as indicated. Figure 7 depicts the layout of the reader (sensitive part), as well as the one of a specific tag made of four C-shaped resonators (i.e., an 8-bit tag), all exhibiting different size. The symmetry plane of the C-shaped resonators is an electric wall at the first (fundamental) resonance, and a magnetic wall at the second resonance frequency. Thus, by displacing the tag across the line, the coupling between the resonator and the line arises at the second resonance frequency, rather than at the fundamental one, when one of the resonant elements crosses the line axis. The reason is that the quasi-microstrip mode of the line is an even mode, unable to drive the odd mode resonance of the C-shaped resonators. Due to the presence of the gap, the structure exhibits a bandpass behavior in the vicinity of the second resonance frequency of Sensors 2022, 22, x FOR PEER REVIEW the C-shaped resonator on top of the line. Thus, by feeding the gap-loaded line with four harmonic signals tuned to the second resonance frequency of each resonator, the ID code can be retrieved. (a) (b) l1 l2 L1 L2 l3 G l4 s U Figure Figure 7.7.Topology Topology of(a) of the the (a) reader reader (sensitive (sensitive part) and part) and (b) 8-bit (or(b) 8-bit (orencoder. 4-resonator) 4-resonator) encoder. For each harmonic signal, tag displacement on top of the reader generates an amplitude- For each harmonic signal, tag displacement on top of the reader gener modulated (AM) signal. The amplitude of the envelope function should be negligible unless amplitude-modulated a C-shaped resonator tuned(AM) (secondsignal. Theto amplitude resonance) the frequencyof the harmonic of that envelope function signal is sh negligible unless a C-shaped resonator tuned (second resonance) to the frequency harmonic signal is on top of the line. Thus, by recording the envelope function f harmonic signal, the ID code can be obtained. An input combiner can be used to f reader line with the four harmonic signals, and an output multiplexer can be used Sensors 2022, 22, 4356 9 of 16 on top of the line. Thus, by recording the envelope function for each harmonic signal, the ID code can be obtained. An input combiner can be used to feed the reader line with the four harmonic signals, and an output multiplexer can be used for the separation of the different AM signals. In this case, four envelope detectors are needed. Thus, a preferred option should consider a voltage-controlled oscillator (VCO) managed by a microcontroller, so that the frequency of the single injected signal varies periodically between the four required values (second resonance frequencies of the C-shaped resonators). The AM signals are separated at the output port also by means of the microcontroller; thus, the four envelope functions can be inferred. With this approach, a single envelope detector is needed. The line of the reader was implemented in the Rogers RO4003C substrate with dielectric constant εr = 3.55, thickness h = 0.81 mm, and loss factor tanδ = 0.0022. The width of the line is w = 0.40 mm, gap separation is set to G = 1 mm, and the total line length from port to port is L = 50 mm. The gap is not in the middle of the microstrip line, as it is shown in Figure 7, where L1 = 22 mm and L2 = 27 mm. The tags were implemented in the Rogers RO4003C substrate with dielectric constant εr = 3.55, thickness h = 0.81 mm, and loss factor tanδ = 0.0022. The strip width of the C-shaped resonators is 0.25 mm, whereas the length varies from resonator to resonator. Indeed, only the length of the external arms varies, i.e., it is l4 = 16 mm, l3 = 20 mm, l2 = 24 mm, and l1 = 28 mm from the smallest to the largest resonator. The length of the central strip of the C-shaped resonators is U = 3 mm in all cases, and the separation between adjacent resonators is S = 5 mm, corresponding to a period of 8 mm. The (second) resonance frequencies of these resonators are f 0,1 = 3.70 GHz, f 0,2 = 4.25 GHz, f 0,3 = 5.00 GHz, and f 0,4 = 5.80 GHz. Before the characterization of this type of encoders, we carried out a set of simulations, consisting of obtaining the transmission coefficient as a function of the displacement for a tag based on four resonators, each with different dimensions. This simulation, carried out by means of the ANSYS HFSS commercial software, was obtained four times, each one by considering the (second) resonance of each resonator (the results are depicted in Figure 8). In all the simulations, the air gap was set to 0.5 mm, and the displacement step was set to 1 mm which is several times smaller than the chain period. With this displacement step, the accuracy in the response is good enough to conclude that the capacity of discrimination of the proposed system is very reasonable. In particular, it can be appreciated that when a certain resonator is on top of the line, at the frequency of this resonator, the transmission is high, whereas at the other frequencies, it decreases significantly, and this occurs for the four C-shaped resonators. Namely, the excursion (or window) between the high and low levels of transmission is important, a necessary condition for the discrimination and functionality of the system. Thus, these results indicate that the functionality of this encoding near-field chipless RFID system can potentially be achieved. For experimental validation, the reader and the encoder depicted in Figure 7 were fabricated. The photograph of the fabricated reader and tag are shown in Figure 9. For tag reading, we displaced the tag over the reader by means of a linear displacement system previously indicated with a velocity of 10 mm/s (the air gap was set to 0.5 mm). The four envelope functions recorded for each frequency, when the tag is displaced across the line axis of the reader, are depicted in Figure 10. With these results, the proof-of-concept of the proposed system is experimentally validated, since each resonator is perfectly identified. Note that for each carrier frequency, a different peak in the envelope function arises, indicative of the fact that the tag is made of four different resonators. To further demonstrate the functionality of this system, we fabricated additional encoders. For example, an encoder where all the C-shaped resonators are identical, and corresponding to the largest one, is depicted in Figure 11, where the envelope functions are also shown. It can be observed that the responses perfectly correlate with the encoder of the inset. Sensors 2022, 22, x FOR PEER REVIEW 10 Sensors 2022, 22, 4356 indicate that the functionality of this encoding near-field chipless RFID 10 of 16 system potentially be achieved. Figure 8. Simulation of the transmission coefficient for the resonance frequencies of the fo shaped resonators of the encoder, as a function of the encoder displacement. The considered en is depicted in Figure 7. Reprinted with permission from [65]. For experimental validation, the reader and the encoder depicted in Figure 7 fabricated. The photograph of the fabricated reader and tag are shown in Figure 9. Fo reading, we displaced the tag over the reader by means of a linear displacement sy previously indicated with a velocity of 10 mm/s (the air gap was set to 0.5 mm). The envelope functions recorded for each frequency, when the tag is displaced across th axis of the reader, are depicted in Figure 10. With these results, the proof-of-concept o proposed Figure system is of 8. Simulation experimentally the transmission validated, since each resonator is perfectly ident Figure 8. Simulation of the transmission coefficient coefficient for the for the resonance resonance frequencies of thefrequencies four C-shapedof the fo Note that for shaped resonators resonators each carrier of the of the encoder, asencoder, frequency, a functionasofa the a function encoder different peak ofdisplacement. in the the encoder displacement. envelope The consideredThe function considered encoder is ena indicative is depicted depicted ofFigure in in Figurethe fact thatwith thepermission 7. Reprinted 7. Reprinted tag with is made from of[65].four permission fromdifferent [65]. resonators. For experimental validation, the reader and the encoder depicted in Figure 7 fabricated. The photograph of the fabricated reader and tag are shown in Figure 9. Fo reading, we displaced the tag over the reader by means of a linear displacement sy previously indicated with a velocity of 10 mm/s (the air gap was set to 0.5 mm). The envelope functions recorded for each frequency, when the tag is displaced across the axis of the reader, are depicted in Figure 10. With these results, the proof-of-concept o proposed system is experimentally validated, since each resonator is perfectly ident Note that for each carrier frequency, a different peak in the envelope function a indicative of the fact that the tag is made of four different resonators. Sensors 2022, 22, x FOR PEER REVIEW 11 Figure Figure 9. 9. Photograph Photograph offabricated of the the fabricated reader reader and and encoder. encoder. Reprinted Reprinted withfrom with permission permission [65]. from [ Figure 9. Photograph of the fabricated reader and encoder. Reprinted with permission from [ Figure10.10.Envelope Figure Envelope functions functions forfour for the thefrequencies four frequencies corresponding corresponding to the to the (second) (second)ofresonanc resonances thefour the fourC-shaped C-shaped resonators, resonators, fortagthe for the tag depicted depicted in Figurein9.Figure 9. Reprinted Reprinted with from with permission permission [65]. from To further demonstrate the functionality of this system, we fabricated additi encoders. For example, an encoder where all the C-shaped resonators are identical, corresponding to the largest one, is depicted in Figure 11, where the envelope funct are also shown. It can be observed that the responses perfectly correlate with the enc encoders. For example, an encoder where all the C-shaped resonators are identical To further demonstrate the functionality of this system, we fabricated additi corresponding to the largest one, is depicted in Figure 11, where the envelope func encoders. For example, an encoder where all the C-shaped resonators are identical, are also shown. It can be observed that the responses perfectly correlate with the enc corresponding to the largest one, is depicted in Figure 11, where the envelope funct of the inset. Sensors 2022, 22, 4356 are also shown. It can be observed that the responses perfectly correlate with 11 of 16the enco of the inset. Figure 11. Envelope functions for the four frequencies corresponding to the (second) resonan the four C-shaped resonators, for the tag depicted in the inset. Reprinted with permission from Figure 11.Envelope Figure 11. Envelope functions functions forfour for the thefrequencies four frequencies corresponding corresponding to the to the (second) (second)ofresonanc resonances the fourC-shaped the four C-shaped resonators, resonators, fortag for the thedepicted tag depicted in the in the inset. inset. Reprinted Reprinted with permission with permission from [65]. from Figure 12 depicts a different combination of resonators and the correspon envelope Figure functions 12 depicts awhere, again, different there isofa resonators combination perfect correlation between theen- and the corresponding peaks an Figure 12 depicts a different combination of resonators and the correspond resonant velope elements. functions where, again, there is a perfect correlation between the peaks and the envelope functions where, again, there is a perfect correlation between the peaks and resonant elements. resonant elements. Figure 12. Envelope functions for the four frequencies corresponding to the (second) resonances of the four C-shaped resonators, for the tag depicted in the inset. We have also fabricated encoders with reduced period, particularly by reducing the distance between adjacent C-shaped resonators. Thus, Figure 13 depicts a 6 mm period encoder where the four resonators are different, and the corresponding envelope functions. Note that the envelope function responses are similar to those of Figure 10, where identical resonators are considered. However, in Figure 13, the time interval between the first and the last pulse is smaller by virtue of the smaller period in the structure of Figure 13 (the displacement velocity of the encoder is identical in all the cases). Finally, let us mention that it is possible to program the encoders. That is, by fabricating the encoders with all the resonators identical and corresponding to the largest one, it is possible to generate the desired code by simply cutting the convenient resonators. For example, it can be observed in Figure 14 an encoder where three of the C-shaped resonators are cut By this means, four different resonances are generated, as can be seen in the envelope functions, equivalent to an encoder exhibiting four different resonators. Note, however, that the bit combination is different to that of Figure 13, since the order of the resonators in the encoder is also different. encoder where the four resonators are different, and the corresponding enve functions. Note that the envelope function responses are similar to those of Figure where identical resonators are considered. However, in Figure 13, the time inte between the first and the last pulse is smaller by virtue of the smaller period in Sensors 2022, 22, 4356 12 of 16 structure of Figure 13 (the displacement velocity of the encoder is identical in all the ca Figure 13. Envelope functions for the four frequencies corresponding to the (second) resonance the four C-shaped resonators, for the tag depicted in the inset. Finally, let us mention that it is possible to program the encoders. That is, fabricating the encoders with all the resonators identical and corresponding to the larg one, it is possible to generate the desired code by simply cutting the convenient resonato For example, it can be observed in Figure 14 an encoder where three of the C-shap resonators are cut By this means, four different resonances are generated, as can be s in the envelope functions, equivalent to an encoder exhibiting four different resonato Note, however, that the bit combination is different to that of Figure 13, since the orde the resonators Figure Figure in functions 13. Envelope 13. Envelopethefunctions encoder for theisfour also for the different. frequencies four corresponding to the (second) resonances of frequencies corresponding to the (second) resonanc the four C-shaped resonators, for the tag depicted in the inset. the four C-shaped resonators, for the tag depicted in the inset. Finally, let us mention that it is possible to program the encoders. That is fabricating the encoders with all the resonators identical and lcorresponding 3 to the lar one, it is possible to generate the desired code by simply cutting the convenient resona For example, it can be observed in Figure 14 an encoder where l1 three of the C-sha resonators are cut By this means, four different resonances are generated, as can be in the envelope functions, equivalent to an encoder exhibitingl4 four different resona Note, however, that the bit combination is different to that of Figure 13, since the orde the resonators in the encoder is also different. l2 l3 Figure Figure 14. Envelopefunctions 14. Envelope functionsfor for the four the four frequencies frequencies corresponding corresponding to theresonances to the (second) (second) of resonance the four C-shaped resonators, for the indicated encoder, with cuts in certain resonators. the four C-shaped resonators, for the indicated encoder, with cuts in certain l 1 resonators. The lengths The leng ofofthe the resonators, after resonators, after practicing practicing the cuts, the cuts, correspond correspond to thosetolengths thoseshown lengths in shown in Figure 7b. Figure 7b. 4. Discussion l4 The quasi-absolute electromagnetic encoders reported in this paper cannot compete against the absolute optical encoders in terms of resolution. However, lelectromagnetic 2 encoders use microwave signals, more robust against the effects of pollution, grease, or dirtiness encountered in many industrial scenarios. Let us also mention that there are many displacement and proximity sensors based on the Hall effect [66–72]. Although these systems generally exhibit very good resolutions, they are based on magnets, thereby representing solutions with higher cost, at least compared to the systems reported in this FigureMagnetic paper. 14. Envelope functions encoders have for alsothe four been frequencies reported corresponding [73,74]. Such encoderstoare thealso (second) robustresonanc the four C-shaped resonators, for the indicated encoder, with cuts in certain resonators. against hostile environments, but such sensors are relatively complex since they need The len of the resonators, after practicing the cuts, correspond to those lengths shown in Figure 7b. inductive coils. Concerning other displacement, proximity, and velocity sensors based on microwave signals, there are many implementations in the available literature. For example, there are sensors that exploit coupling modulation [75–79], whereas other sensors are based on frequency variation [80]. In such sensors, a resonant (movable) element is displaced over a transmission line structure (typically, the resonator in motion is displaced in a plane parallel to the one of the line, but there are also realizations, where the resonator displaces Sensors 2022, 22, 4356 13 of 16 vertically [79,81]). Although these sensors are relatively simple, their input dynamic range is usually very limited, since it is of the order of the size of the resonant elements. By contrast, in linear electromagnetic encoders, such dynamic range is potentially unlimited. Thus, electromagnetic encoders can find applications as sensing elements in various scenarios involving motion control of industrial systems, such as conveyor belts, servomechanisms, or elevators, among others. It is also worth mentioning that there are alternatives to the electromagnetic rotary encoders, based on the use of a single resonant element [82–84]. Generally, such angular displacement and velocity sensors use a circular resonator axial to the rotor. The main disadvantage as compared to the rotary electromagnetic encoders is the fact that they cannot provide the instantaneous velocity, but rather the average velocity per cycle. 5. Conclusions In summary, two different strategies to enhance the data density in electromagnetic encoders were reported. Such strategies are very different, but both share the fact that the data density is twice the one of conventional encoders. In one case, the data density is improved by retrieving the ID code in both the rising and falling edges of the clock signal. Namely, this system requires a clock signal in order to synchronously read the ID code. By contrast, in the second approach, such a clock signal is not required, as far as an inclusion is always present at the predefined positions of the encoder chain. In this second approach, the data density is improved because each resonant element of the encoder chain provides two bits of information, as far as four different resonator sizes are considered. Both strategies have been experimentally validated by considering various encoders with different ID codes. The reported approaches are of interest for the implementation of quasi-absolute electromagnetic encoders. Thanks to the improved data density, the displacement of the encoder necessary to retrieve the absolute position after a system reset can be reduced. Author Contributions: Conceptualization, F.P. and A.K.-H.; simulations, F.P. and A.K.-H.; experi- mental validation, F.P. and A.K.-H.; writing—original draft preparation, F.M.; writing—review and editing, F.P., A.K.-H. and F.M.; supervision, F.M.; funding acquisition, F.M. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the projects: grant PID2019-103904RB-I00 funded by MCIN/AEI 10.13039/501100011033, grant RTC-2017-6303-7 funded by MCIN/AEI 10.13039/501100011033 and ERDF European Union, grant PDC2021-121085-I00 funded by MCIN/AEI 10.13039/501100011033 and European Union Next Generation EU/PRTR, grant 2017SGR-1159 funded by the AGAUR Research Agency, Catalonia Government, and the grant funded by Institució Catalana de Recerca i Estudis Avançats (who awarded Ferran Martín). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Petriu, E.M. Reconsidering natural binary encoding for absolute position measurement application. IEEE Trans. Instrum. Meas. 1989, 38, 1014–1016. [CrossRef] 2. Ueda, T.; Kohsaka, F.; Iino, T.; Kazami, K.; Nakayama, H. Optical absolute encoder using spatial filter. 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