3D-Printed Quasi-Absolute Electromagnetic Encoders for Chipless-RFID and Motion Control Applications

: This paper presents electromagnetic encoders useful for chipless-RFID and motion control applications. The encoders consist in a pair of linear chains of rectangular apertures implemented by means of 3D printing. One of these chains is periodic and acts as a clock, whereas the other chain contains an identiﬁcation (ID) code. With these two aperture chains, the ID code can be synchronously read, so that the relative velocity between the tag and the reader is irrelevant. Additionally, it is shown in the paper that by properly designing the reader, it is possible to determine the motion direction. The sensitive part of the reader is a microstrip line loaded with three complementary split ring resonators (CSRRs) etched in the ground plane and fed by three harmonic signals. By encoder motion, the characteristics of the local medium surrounding the CSRRs are modiﬁed, and the harmonic signals are amplitude modulated (AM) at the output port of the line, thereby providing the clock signal (which gives the encoder velocity), the ID code (providing also the quasi-absolute position) and the direction of motion. A fabricated prototype encoder is characterized by reading it with a dedicated reader.


Introduction
Optical encoders [1][2][3][4] are the most genuine and widespread technology for motion control applications. As the encoder moves across an optical beam generated by an optical source, typically a laser diode, a chain of apertures made on a (typically) metallic substrate are detected. When an aperture crosses the optical beam, the encoder is transparent and an optical detector, placed on the other side of the encoder, can record the optical beam in the form of a pulse. Thus, as many pulses as apertures are detected by the optical reader. Obviously, the encoders can be implemented with several chains of apertures, which can be codified, and therefore can be used to determine the absolute position of the encoder [5,6]. These absolute encoder systems are able to provide the position regardless of the previous motion stages of the encoder, contrary to the so-called incremental-type encoders, where the position is determined from the cumulative number of pulses (i.e., through pulse counting).
Electromagnetic encoders [7][8][9][10][11][12][13][14][15][16] are an alternative to optical encoders. Both systems exhibit a similar working principle, but the optical signals are replaced by microwave signals. In electromagnetic systems, the encoders can be made of chains of apertures, or also chains of inclusions (metallic or dielectric). However, these encoders should not be confused with the so-called magnetic encoders, based on magnets or inductive elements [17][18][19][20][21][22][23][24]. The first reported electromagnetic encoders were implemented by etching circular chains of metallic inclusions (planar resonators) in the periphery of a dielectric disc [25] (these encoders indeed appeared as an evolution of previous angular displacement sensors based on coupling modulation between a microstrip line and a single circular chain. In applications of the encoders as chipless-RFID tags, the ID code can be arbitrary. The clock chain gives the instants of time to read the ID code from the ID code chain. By contrast, as position sensor able to determine the quasi-absolute position, the ID code should not be arbitrary. It should be selected according to the De Bruijn sequence [73]. Let us explain the reason next. Let us consider that the total length of the encoder is L. The number of different discrete positions that must be codified in order to determine the relative position of the encoder with regard to the reader is thus L/p. Therefore, the number of bits necessary to unequivocally differentiating the discrete positions of the encoder should satisfy N ≥ log 2 (L/p) (1) Implementing as many aperture chains as number of bits N is not a realistic solution because it represents a penalty in terms of encoder size. However, if the ID code of the complete (single) position chain follows the De Bruijn sequence, any sub-set of N sequential bits is unique (it is different to any other). Therefore, the bit corresponding to a certain position, plus the N-1 bits of the previous positions univocally determine the position. However, it is necessary to know the direction of motion, and, moreover, after a system reset, the encoder must be displaced N positions before an absolute position can be determined. For this main reason, the designation of these encoders should be quasi-absolute, rather than absolute.
The photograph of the fabricated 16-bit encoder is depicted in Figure 1. The encoder was 3D-printed by means of the Ultimaker 3 Extended 3D printer, using dielectric Polylactic Acid (PLA) as filament. Prior to the implementation of the encoder, and in order to obtain the dielectric constant of the PLA by means of a Keysight 85072A 10-GHz Split Cylinder Resonator, a square-shape slab sample (the dimensions are provided by the split cylinder resonator) was printed. The measured dielectric constant of this dielectric PLA is ε r = 3, although this value can slightly suffer variations depending on the PLA properties [74,75]. contrast, as position sensor able to determine the quasi-absolute position, the ID code should not be arbitrary. It should be selected according to the De Bruijn sequence [73]. Let us explain the reason next.
Let us consider that the total length of the encoder is L. The number of different discrete positions that must be codified in order to determine the relative position of the encoder with regard to the reader is thus L/p. Therefore, the number of bits necessary to unequivocally differentiating the discrete positions of the encoder should satisfy Implementing as many aperture chains as number of bits N is not a realistic solution because it represents a penalty in terms of encoder size. However, if the ID code of the complete (single) position chain follows the De Bruijn sequence, any sub-set of N sequential bits is unique (it is different to any other). Therefore, the bit corresponding to a certain position, plus the N-1 bits of the previous positions univocally determine the position. However, it is necessary to know the direction of motion, and, moreover, after a system reset, the encoder must be displaced N positions before an absolute position can be determined. For this main reason, the designation of these encoders should be quasi-absolute, rather than absolute.
The photograph of the fabricated 16-bit encoder is depicted in Figure 1. The encoder was 3D-printed by means of the Ultimaker 3 Extended 3D printer, using dielectric Polylactic Acid (PLA) as filament. Prior to the implementation of the encoder, and in order to obtain the dielectric constant of the PLA by means of a Keysight 85072A 10-GHz Split Cylinder Resonator, a square-shape slab sample (the dimensions are provided by the split cylinder resonator) was printed. The measured dielectric constant of this dielectric PLA is εr = 3, although this value can slightly suffer variations depending on the PLA properties [74,75].
After having measured the dielectric constant, the encoder was fabricated using the following printer parameters: nozzle size 0.44 mm, printing temperature 200 °C, build plate (or bed plate) temperature 60 °C, printing speed 70 mm/s and infill density 100%. The (rectangular) apertures of both chains, if present, are located at identical positions, as indicated before. The dimensions of the encoder were optimized, according to electromagnetic simulations, as it will be later shown. It is also important to emphasize that other dielectric substrates, even flexible [76], could be used as encoders, but in this case, we took advantage of the high versatility and faster fabrication process of 3D printing, previously demonstrated in the RFID devices [77][78][79].  After having measured the dielectric constant, the encoder was fabricated using the following printer parameters: nozzle size 0.44 mm, printing temperature 200 • C, build plate (or bed plate) temperature 60 • C, printing speed 70 mm/s and infill density 100%. The (rectangular) apertures of both chains, if present, are located at identical positions, as indicated before. The dimensions of the encoder were optimized, according to electromagnetic simulations, as it will be later shown. It is also important to emphasize that other dielectric substrates, even flexible [76], could be used as encoders, but in this case, we took advantage of the high versatility and faster fabrication process of 3D printing, previously demonstrated in the RFID devices [77][78][79].
Concerning the sensitive part of the reader, it consists of a microstrip line loaded with three complementary split ring resonators (CSRRs) etched in the ground plane, as Figure 2  illustrates. It has been demonstrated that CSRR-loaded lines are efficient permittivity sensors, based on the variation experienced by the resonance frequency when a certain material under test (MUT) is placed on top of the resonator [80][81][82][83][84][85]. Indeed, the reported encoders exhibit a significant permittivity contrast between the apertures (with ε r = 1) and the substrate (PLA with ε r = 3). Consequently, it is expected that, by encoder motion, the presence of PLA on top of the sensitive part of the reader (i.e., the absence of the apertures) shifts down the resonance frequency of the resonant elements. Note that if the quality factor of the CSRRs is significant, the excursion experienced by the transmission coefficient at the frequency of resonance of the CSRR covered by the substrate should be high, a necessary condition to ensure the functionality and robustness of the system. Concerning the sensitive part of the reader, it consists of a microstrip line loaded with three complementary split ring resonators (CSRRs) etched in the ground plane, as Figure  2 illustrates. It has been demonstrated that CSRR-loaded lines are efficient permittivity sensors, based on the variation experienced by the resonance frequency when a certain material under test (MUT) is placed on top of the resonator [80][81][82][83][84][85]. Indeed, the reported encoders exhibit a significant permittivity contrast between the apertures (with εr = 1) and the substrate (PLA with εr = 3). Consequently, it is expected that, by encoder motion, the presence of PLA on top of the sensitive part of the reader (i.e., the absence of the apertures) shifts down the resonance frequency of the resonant elements. Note that if the quality factor of the CSRRs is significant, the excursion experienced by the transmission coefficient at the frequency of resonance of the CSRR covered by the substrate should be high, a necessary condition to ensure the functionality and robustness of the system. Note that the presence of three CSRRs obeys the fact that, in order to obtain the encoder velocity (and clock signal), the quasi-absolute position, and the motion direction, three signals are needed. The three CSRRs are tuned to different frequencies, and can be labeled by sub-indexes, in order to differentiate between the position resonator, CSRRp, the clock resonator CSRRc, and the motion direction resonator CSRRd.
The electromagnetic simulation of the bare reader is shown in Figure 3, where the three notches corresponding to the frequencies coherently designated as fp = 4.030 GHz, fc = 4.300 GHz and fd = 4.570 GHz can be seen. These notches (or dips) reflect the injected signals at the frequencies of interest. This situation corresponds to the encoder apertures, which can be assigned the logic state "1". However, as previously mentioned, the presence of PLA at certain distance on top of the sensitive part of the reader shifts down the whole frequency response. Thus, instead of having a notch or dip at the frequencies of interest, the presence of this dielectric substrate allows the signal to be transmitted (equivalent to the logic state "0"), as can be observed in the graph of Figure 3. Note that the presence of three CSRRs obeys the fact that, in order to obtain the encoder velocity (and clock signal), the quasi-absolute position, and the motion direction, three signals are needed. The three CSRRs are tuned to different frequencies, and can be labeled by sub-indexes, in order to differentiate between the position resonator, CSRR p , the clock resonator CSRR c , and the motion direction resonator CSRR d .
The electromagnetic simulation of the bare reader is shown in Figure 3, where the three notches corresponding to the frequencies coherently designated as f p = 4.030 GHz, f c = 4.300 GHz and f d = 4.570 GHz can be seen. These notches (or dips) reflect the injected signals at the frequencies of interest. This situation corresponds to the encoder apertures, which can be assigned the logic state "1". However, as previously mentioned, the presence of PLA at certain distance on top of the sensitive part of the reader shifts down the whole frequency response. Thus, instead of having a notch or dip at the frequencies of interest, the presence of this dielectric substrate allows the signal to be transmitted (equivalent to the logic state "0"), as can be observed in the graph of Figure 3. Electronics 2021, 10, x FOR PEER REVIEW 5 of 11 The three harmonic signals necessary for reading purposes are tuned to frequencies fp, fc and fd, as depicted in Figure 4. Such three harmonic signals can be injected simultaneously to the input port of the microstrip line by means of a combiner, and the corresponding AM signals, with different carrier frequencies, separated at the output port by means of a triplexer. Then, the envelope function, containing the relevant information, can be inferred by means of an envelope detector connected to each output port of the triplexer, as done in several reported prototypes of electromagnetic encoders [11,18].
According to the explained working principle, it is clear that the position chain will generate as many dips as apertures in the chain. The instants of time to infer the ID code of that chain are given by the dips generated in the channel corresponding to the clock chain. Also, from the time lapse between adjacent dips in the envelope function generated by the clock chain, the velocity is inferred, provided the period, p, is well known. The system provides the instantaneous velocity, as far as such velocity does not significantly change during time intervals corresponding to the lapse between adjacent dips in the envelope function. Thus, it is also possible to measure the instantaneous acceleration. For the determination of the motion direction, it is not necessary an additional chain. The clock/velocity chain is useful for that purpose, provided the CSRRd is conveniently located with regard to the CSRRc. Particularly, the CSRRd and the CSRRc are located as indicated in Figure 2, so that the apertures of the clock chain first cross one resonator and, immediately, the other one. Thus, from the lead or lag between the corresponding envelope functions, the motion direction can be inferred.  The three harmonic signals necessary for reading purposes are tuned to frequencies f p , f c and f d , as depicted in Figure 4. Such three harmonic signals can be injected simultaneously to the input port of the microstrip line by means of a combiner, and the corresponding AM signals, with different carrier frequencies, separated at the output port by means of a triplexer. Then, the envelope function, containing the relevant information, can be inferred by means of an envelope detector connected to each output port of the triplexer, as done in several reported prototypes of electromagnetic encoders [11,18]. The three harmonic signals necessary for reading purposes are tuned to frequencies fp, fc and fd, as depicted in Figure 4. Such three harmonic signals can be injected simultaneously to the input port of the microstrip line by means of a combiner, and the corresponding AM signals, with different carrier frequencies, separated at the output port by means of a triplexer. Then, the envelope function, containing the relevant information, can be inferred by means of an envelope detector connected to each output port of the triplexer, as done in several reported prototypes of electromagnetic encoders [11,18].
According to the explained working principle, it is clear that the position chain will generate as many dips as apertures in the chain. The instants of time to infer the ID code of that chain are given by the dips generated in the channel corresponding to the clock chain. Also, from the time lapse between adjacent dips in the envelope function generated by the clock chain, the velocity is inferred, provided the period, p, is well known. The system provides the instantaneous velocity, as far as such velocity does not significantly change during time intervals corresponding to the lapse between adjacent dips in the envelope function. Thus, it is also possible to measure the instantaneous acceleration. For the determination of the motion direction, it is not necessary an additional chain. The clock/velocity chain is useful for that purpose, provided the CSRRd is conveniently located with regard to the CSRRc. Particularly, the CSRRd and the CSRRc are located as indicated in Figure 2, so that the apertures of the clock chain first cross one resonator and, immediately, the other one. Thus, from the lead or lag between the corresponding envelope functions, the motion direction can be inferred.  According to the explained working principle, it is clear that the position chain will generate as many dips as apertures in the chain. The instants of time to infer the ID code of that chain are given by the dips generated in the channel corresponding to the clock chain. Also, from the time lapse between adjacent dips in the envelope function generated by the clock chain, the velocity is inferred, provided the period, p, is well known. The system provides the instantaneous velocity, as far as such velocity does not significantly change during time intervals corresponding to the lapse between adjacent dips in the envelope function. Thus, it is also possible to measure the instantaneous acceleration. For the determination of the motion direction, it is not necessary an additional chain. The clock/velocity chain is useful for that purpose, provided the CSRR d is conveniently located with regard to the CSRR c . Particularly, the CSRR d and the CSRR c are located as indicated in Figure 2, so that the apertures of the clock chain first cross one resonator and, immediately, the other one. Thus, from the lead or lag between the corresponding envelope functions, the motion direction can be inferred.

Results
The sensitive part of the reader was measured by means of a vector network analyzer (model Agilent N5221A). The behavior of this prototype without any dielectric in the proximity (bare reader) is shown in Figure 3, and it was in good agreement with the electromagnetic simulation. Later, a dielectric PLA slab was placed on top of the reader, and it was moved upwards, thus modifying the air gap, until the behavior was the expected one. The air gap was set to 0.2 mm. This value differs from the nominal air gap considered in the EM simulation (of 0.5 mm). One reason to explain this effect is the EM software, which considers that the substrates are infinite, thereby slightly modifying the effective dielectric constant. Another possible cause can be attributed to the variation of the dielectric constant of the PLA, as explained before, due to fabrication tolerances. In any case, it is important to bear in mind that the higher the air gap, the lower is the dynamic range at the operation frequencies, that is to say that the lower is the difference between the two logic states. On the other hand, if the air gap is reduced, the dynamic range can be improved but, due to the fact that the frequency behavior is shifted down, the frequency notches can affect the vicinity frequency responses (overlap).
In order to read the encoder of Figure 1 with the reader of Figure 2, using the arrangement of Figure 4, the setup depicted in Figure 5 was used. The displacement of the encoder over the reader was achieved by means of a linear displacement system (model STM 23Q-3AN). It is necessary to generate three harmonic signals (tuned to f p = 4.030 GHz, f c = 4.300 GHz and f d = 4.570 GHz) to synchronous reading the ID code of the encoder, as well as to determine the encoder direction. However, as a proof of concept, instead of injecting simultaneously three signals generated by means of VCOs, the abovementioned vector network analyzer was used to independently generate such signals. As mentioned before, at the output port of the sensitive part of the reader, the signal was AM modulated by the encoder motion. Thus, a Schottky diode (model Avago HSMS-2860) was used to obtain the envelop function. Since the diode input impedance was different from the output impedance of the sensitive part of the reader, a circulator (model ATM ATc4-8) was added between these devices to prevent undesired reflections. Finally, an oscilloscope (model Agilent MSO-X-3104A) connected to the diode, through the N2795A active probe (with capacitance C = 1 pF and resistance R = 1 MΩ), was used for visualizing the envelope functions (ID code and clock signals).

Results
The sensitive part of the reader was measured by means of a vector network analyzer (model Agilent N5221A). The behavior of this prototype without any dielectric in the proximity (bare reader) is shown in Figure 3, and it was in good agreement with the electromagnetic simulation. Later, a dielectric PLA slab was placed on top of the reader, and it was moved upwards, thus modifying the air gap, until the behavior was the expected one. The air gap was set to 0.2 mm. This value differs from the nominal air gap considered in the EM simulation (of 0.5 mm). One reason to explain this effect is the EM software, which considers that the substrates are infinite, thereby slightly modifying the effective dielectric constant. Another possible cause can be attributed to the variation of the dielectric constant of the PLA, as explained before, due to fabrication tolerances. In any case, it is important to bear in mind that the higher the air gap, the lower is the dynamic range at the operation frequencies, that is to say that the lower is the difference between the two logic states. On the other hand, if the air gap is reduced, the dynamic range can be improved but, due to the fact that the frequency behavior is shifted down, the frequency notches can affect the vicinity frequency responses (overlap).
In order to read the encoder of Figure 1 with the reader of Figure 2, using the arrangement of Figure 4, the setup depicted in Figure 5 was used. The displacement of the encoder over the reader was achieved by means of a linear displacement system (model STM 23Q-3AN). It is necessary to generate three harmonic signals (tuned to fp = 4.030 GHz, fc = 4.300 GHz and fd = 4.570 GHz) to synchronous reading the ID code of the encoder, as well as to determine the encoder direction. However, as a proof of concept, instead of injecting simultaneously three signals generated by means of VCOs, the abovementioned vector network analyzer was used to independently generate such signals. As mentioned before, at the output port of the sensitive part of the reader, the signal was AM modulated by the encoder motion. Thus, a Schottky diode (model Avago HSMS-2860) was used to obtain the envelop function. Since the diode input impedance was different from the output impedance of the sensitive part of the reader, a circulator (model ATM  was added between these devices to prevent undesired reflections. Finally, an oscilloscope (model Agilent MSO-X-3104A) connected to the diode, through the N2795A active probe (with capacitance C = 1 pF and resistance R = 1 MΩ), was used for visualizing the envelope functions (ID code and clock signals).    Figure 6, obtained by displacing the encoder at constant velocity of v = 10 mm/s. As it can be seen, the ID code was correctly read, and the clock signals were shifted, as consequence of the different positions of the resonators CSRR c and CSRR d in the reader. According to these results, the clock chain first crossed the CSRR c and then the CSRR d . Thus, the direction of motion was determined.
According to these results, the clock chain first crossed the CSRRc and then the CSRRd. Thus, the direction of motion was determined.
This was the first electromagnetic encoder able to provide the ID code synchronously, and able to discriminate the direction of motion, implemented without metallic inclusions. As compared to the encoder reported in [67], the proposed encoder is very robust against friction (eventually caused by unexpected contact between the encoder and the reader, as consequence, e.g., of vibrations), since the inclusions are simple apertures. Thus, these 3D-printed encoders may be of interest as quasi-absolute encoders in motion control applications. Nevertheless, the reported prototype demonstrated that by opening apertures in a 3D-printed material, it was possible to generate an encoder containing an identifying ID code. Thus, with the results of this work, the possibility of generating an identifying tag embedded in a certain fabricated (3D-printed) material or consumer product during fabrication was possible.

Conclusions
In this paper, electromagnetic encoders with synchronous reading and motion direction detection capability have been presented. The encoder is implemented by means of chains of apertures made in a host substrate, which can be any dielectric material, even flexible, with a dielectric constant significantly different than the one of vacuum. In this work, 3D-printing techniques were employed due to their versatility and good performance already demonstrated with the implementation of other RFID devices. For that purpose, a prototype 3D-printed electromagnetic encoder with 16 bits has been fabricated in dielectric PLA filament. On the other hand, the sensitive part of the reader detects the presence of the apertures by virtue of the permittivity contrast with the host substrate material (PLA), since the sensitive part of the reader is, indeed, a permittivity sensor. In the reported encoders, the relevant information relative to the ID code, encoder velocity (and acceleration, if encoder motion is non-uniform), and motion direction is contained in the envelope functions of the AM modulated signals generated at the output ports of the corresponding channels. The measured envelope functions are indicative of the functionality of the proposed reader/encoder system. Such systems, based on all-dielectric 3D- This was the first electromagnetic encoder able to provide the ID code synchronously, and able to discriminate the direction of motion, implemented without metallic inclusions. As compared to the encoder reported in [67], the proposed encoder is very robust against friction (eventually caused by unexpected contact between the encoder and the reader, as consequence, e.g., of vibrations), since the inclusions are simple apertures. Thus, these 3D-printed encoders may be of interest as quasi-absolute encoders in motion control applications. Nevertheless, the reported prototype demonstrated that by opening apertures in a 3D-printed material, it was possible to generate an encoder containing an identifying ID code. Thus, with the results of this work, the possibility of generating an identifying tag embedded in a certain fabricated (3D-printed) material or consumer product during fabrication was possible.

Conclusions
In this paper, electromagnetic encoders with synchronous reading and motion direction detection capability have been presented. The encoder is implemented by means of chains of apertures made in a host substrate, which can be any dielectric material, even flexible, with a dielectric constant significantly different than the one of vacuum. In this work, 3D-printing techniques were employed due to their versatility and good performance already demonstrated with the implementation of other RFID devices. For that purpose, a prototype 3D-printed electromagnetic encoder with 16 bits has been fabricated in dielectric PLA filament. On the other hand, the sensitive part of the reader detects the presence of the apertures by virtue of the permittivity contrast with the host substrate material (PLA), since the sensitive part of the reader is, indeed, a permittivity sensor. In the reported encoders, the relevant information relative to the ID code, encoder velocity (and acceleration, if encoder motion is non-uniform), and motion direction is contained in the envelope functions of the AM modulated signals generated at the output ports of the corresponding channels. The measured envelope functions are indicative of the functionality of the proposed reader/encoder system. Such systems, based on all-dielectric 3D-printed encoders, can find applications in motion control (where robustness against mechanical friction is a key aspect), chipless-RFID tags (where the encoder can be embedded in the product during 3D-printing fabrication), and other potential applications in industrial scenarios.

Conflicts of Interest:
The authors declare no conflict of interest.