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A Differential Monolithically Integrated Inductive Linear Displacement Measurement Microsystem Matija Podhraški 1, * and Janez Trontelj 2 1 2

*

Letrika Lab d.o.o., Polje 15, Šempeter pri Gorici 5290, Slovenia Laboratory of Microelectronics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, Ljubljana 1000, Slovenia; [email protected] Correspondence: [email protected]; Tel.: +386-1-4768-727

Academic Editor: Vittorio M. N. Passaro Received: 20 January 2016; Accepted: 11 March 2016; Published: 17 March 2016

Abstract: An inductive linear displacement measurement microsystem realized as a monolithic Application-Specific Integrated Circuit (ASIC) is presented. The system comprises integrated microtransformers as sensing elements, and analog front-end electronics for signal processing and demodulation, both jointly fabricated in a conventional commercially available four-metal 350-nm CMOS process. The key novelty of the presented system is its full integration, straightforward fabrication, and ease of application, requiring no external light or magnetic field source. Such systems therefore have the possibility of substituting certain conventional position encoder types. The microtransformers are excited by an AC signal in MHz range. The displacement information is modulated into the AC signal by a metal grating scale placed over the microsystem, employing a differential measurement principle. Homodyne mixing is used for the demodulation of the scale displacement information, returned by the ASIC as a DC signal in two quadrature channels allowing the determination of linear position of the target scale. The microsystem design, simulations, and characterization are presented. Various system operating conditions such as frequency, phase, target scale material and distance have been experimentally evaluated. The best results have been achieved at 4 MHz, demonstrating a linear resolution of 20 µm with steel and copper scale, having respective sensitivities of 0.71 V/mm and 0.99 V/mm. Keywords: inductive sensor; eddy-current sensor; displacement measurement; position measurement; analog front-end; CMOS; ASIC; microtransformer; microcoil

1. Introduction Various types of position encoders are used in position sensing applications, most of them based on optical, inductive and magnetic sensing elements [1]. The latter rely on the effect of the Lorentz force onto the charge carriers (e.g., Hall and magnetoresistive sensors). Among these, Hall sensors are more common, since they can be fabricated using a conventional microelectronic process, allowing for a cost-efficient monolithic combination of the Hall elements and the analog sensor front-end [2] on the same silicon die, representing an Application-Specific Integrated Circuit (ASIC). Furthermore, digital signal processing circuitry can also be added to integrated sensor systems, thus creating a cost-efficient mixed signal sensor system [3]. Optical position encoders can also be integrated in a similar manner [4]. Magnetic position sensors operate by measuring the variations in spatially variable magnetic field strength. Magnetic position sensors suffer from variable offset, temperature drift, hysteresis and low immunity to noise [5]. As they require an external source of magnetic field for their operation, e.g., a magnetized scale, the availability, cost and environmental concerns about the production of rare-earth magnetic materials, may also present additional issues [6]. Since integrated optical position encoders Sensors 2016, 16, 384; doi:10.3390/s16030384

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comprise photodiodes, meaning that CMOS process modifications are required for their fabrication, the complexity and cost of optical microsensor systems are increased. Moreover, an external light source (e.g., a LED) is required [1] (p. 308). Dirt, omnipresent in industrial environments, also presents a strong issue with optical encoders [7]. However, due to their high resolution in 1 nm range [8], they are indispensable in high-precision applications. Due to the presented disadvantages, further research of innovative integrated position encoder types is persistently encouraged by the industry, which is continuously in pursuit of dependable, accurate and inexpensive position encoders, realized in the form of an ASIC. In this paper, we present a monolithic implementation of an inductive linear incremental encoder, fabricated in using a conventional inexpensive microtechnologic process (350 nm 4-metal CMOS) without any post-processing modifications, representing a significant improvement over previously reported solutions [9–13] which use additional processing steps for the microinductor fabrication. We believe such inductive monolithic microsystems have the potential of substituting or supplementing conventional position encoder technologies, such as optical or Hall sensor devices. The paper first explains the operation of the device, and presents the construction of the sensor element—an integrated microtransformer—along with its model circuit. Then, results of FEM and system-level simulations of the sensing elements’ performance with different target scales are presented, as well as the design of the measurement channel electronics supported with Cadence simulations. Finally, results of the microsystem prototype evaluation are provided with an outlook for the future work. 1.1. Integrated Inductive Displacement Sensors Inductive position sensing is commonly found in large-scale devices in industrial applications, e.g., in rotary or linear variable differential transformers (RVDT/LVDT) with the position information coded in the amplitude and the phase of the output signal [14]. Integrated versions of similar devices are also reported, however with a non-monolithically integrated primary winding [10,11]. The inductive sensor output can also be observed in the frequency domain: the location of the target object can affect the inductance of a coil wired into an oscillator circuit. Integrated versions of such proximity sensors have been reported, with the coil deposited onto the surface of the silicon die during post-processing fabrication steps [12] or placed by the ASIC realized on an adjoining PCB [9]. Eddy current sensors, which are also inductive devices, commonly comprise a dual-coil structure, where the second coil voltage, induced by the current flowing through the first coil, is reduced in the presence of a conductive object due to the energy dissipation through the flow of eddy currents within the object ([1], p. 290). A dual-coil structure for eddy-current crack detection, deposited on glass substrate and employing a permalloy core, is reported by Sadler and Ahn [13]. Weiwen et al. reported non-integrated eddy current displacement sensors that use small planar differential coils wired into oscillatory circuits which communicate the displacement of a grating scale in frequency and phase domains [15]. Following recent developments, eddy current sensors can also be used for nanometer range measurements and have allegedly yet to reach their physical limits [16]. Wang et al. [17] reported of a very stable, sub-nanometer resolution displacement sensor system based on measuring the change of the inductance and resistance of a coil caused by eddy currents induced in a conductive target. Tseng and Xie [18] demonstrated a inductive system for sensing the vertical displacement of a micromirror. The system relies on adjacent transmitter and receiver coils, fabricated by the deposition of metal layers on glass substrate, operating in resonance. The two coils are coupled by the micromirror, with its displacement affecting the induced voltage of the receiver coil. The best reported resolution is 20 nm at 130 µm range. ASICs functioning as front-ends for the conditioning and the processing of the output signals of (macroscopic) inductive sensor elements are also being researched. For example, a system comprising two ASIC frontends for an inductive proximity sensor with a frequency output is reported in [19]. An

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ASIC prototype for synchronous demodulation of inductive sensor output signals is reported in [20,21] front-end eddy current sensors employing amplifiers reported by by Rahal andfor Demosthenous. A ratiometric synchronoustransimpedance detection front-end for eddy is current sensors Nabavi et al. [22,23], stating that this is the most power efficient method for interfacing eddy current employing transimpedance amplifiers is reported by Nabavi et al. [22,23], stating that this is the most position sensors. power efficient method for interfacing eddy current position sensors. Thepresented presenteddesign designalso alsoemploys employsa asynchronous synchronousdetection detectiondemodulation demodulationmethod, method,combining combining The the demodulation electronics with inductive sensing elements in a monolithic ASIC, which outputsaa the demodulation electronics with inductive sensing elements in a monolithic ASIC, which outputs voltagesignal signal directly related to the target displacement. target is periodically and can voltage directly related to the target displacement. The The target is periodically gratedgrated and can have have unlimited length, as the microsystem is essentially a prototype of an incremental linear encoder unlimited length, as the microsystem is essentially a prototype of an incremental linear encoder device. device. the presented device constitutes a bridge between larger inductive sensors and Thus, theThus, presented device constitutes a bridge between larger inductive sensors and conventional conventional integrated position used in incremental encoders (e.g., sensors). Hall or optical sensors). integrated position sensors used insensors incremental encoders (e.g., Hall or optical 1.2. 1.2.Sensor SensorElement ElementOperation Operation The inin thethe discussed microsystem employs a concept of operation similar to Thesensor sensorelement elementused used discussed microsystem employs a concept of operation similar ato LVDT, as well as to an eddy current sensor. It is based on an integrated microtransformer pair, as a LVDT, as well as to an eddy current sensor. It is based on an integrated microtransformer pair, presented in Figure 1a,b.1a,b. The The primary current Iexc induces the the secondary voltages Uind1 and Uind2 . . as presented in Figure primary current Iexc induces secondary voltages Uind1 and Uind2

(a)

(b)

(c)

Figure 1. (a) The basic operation of the presented microsystem, consisting of two integrated Figure 1. (a) The basic operation of the presented microsystem, consisting of two integrated microtransformers anda amovable movableconductive conductiveand/or and/or ferromagnetic ferromagnetic target targetaffecting affectingthe thevoltage voltage microtransformers and induction between between primary primary and andsecondary secondary windings; windings; (b) (b) The The schematic schematic representation representation ofof a a induction microtransformer pair; (c) The quadrature output signals are generated by movinga agrating grating microtransformer pair; (c) The quadrature output signals are generated by moving measurement scale over the microtransformer pairs. Sinusoidal signal shape is assumed. measurement scale over the microtransformer pairs. Sinusoidal signal shape is assumed.

The primary and the secondary winding of a microtransformer are inductively coupled by a The primary and the secondary winding of a microtransformer are inductively coupled by a movable conductive and/or ferromagnetic target positioned over the microtransformer. The movable conductive and/or ferromagnetic target positioned over the microtransformer. The amplitude amplitude and phase of the secondary voltage deviate with the movement of the target. If a and phase of the secondary voltage deviate with the movement of the target. If a ferromagnetic target ferromagnetic target is used, the induced secondary voltage is increased when the target is is used, the induced secondary voltage is increased when the target is positioned over it due to flux positioned over it due to flux concentration properties of the target. For a conductive concentration properties of the target. For a conductive (non-ferromagnetic) target, the operation (non-ferromagnetic) target, the operation is reverse [11]: when a microtransformer is completely is reverse [11]: when a microtransformer is completely covered with metal, its secondary voltage is covered with metal, its secondary voltage is reduced due to energy dissipation in the conductive reduced due to energy dissipation in the conductive target through the mechanism of eddy currents. If target through the mechanism of eddy currents. If a conductive ferromagnetic target (i.e., a conductive ferromagnetic target (i.e., transformer steel) is used, the eddy current dissipation, which transformer steel) is used, the eddy current dissipation, which increases with frequency, overcomes increases with frequency, overcomes the ferromagnetic effect at a specific margin frequency [11,17]. At the ferromagnetic effect at a specific margin frequency [11,17]. At this frequency, which was found this frequency, which was found using FEM simulations to be typically in the range between 1–10 MHz using FEM simulations to be typically in the range between 1–10 MHz and is strongly dependent on and is strongly dependent on the material conductivity and permeability [24], the effects of eddy the material conductivity and permeability [24], the effects of eddy currents and the magnetic currents and the magnetic reluctance of the ferromagnetic material, may cancel each other, resulting in reluctance of the ferromagnetic material, may cancel each other, resulting in a very low sensitivity of a very low sensitivity of microtransformers operating around that frequency [17]. microtransformers operating around that frequency [17]. If the target is made periodic, i.e., to consist of exchanging full and void areas with an equal width, If the target is made periodic, i.e., to consist of exchanging full and void areas with an equal and is moved over a microtransformer pair, incremental outputs are obtained, as illustrated using an width, and is moved over a microtransformer pair, incremental outputs are obtained, as illustrated example of a ferromagnetic scale in Figure 1c. Conductive scales can also be used. The areas should using an example of a ferromagnetic scale in Figure 1c. Conductive scales can also be used. The areas always cover a single microtransformer to maximize the effect of the target on the secondary voltage. should always cover a single microtransformer to maximize the effect of the target on the secondary When the full half-period of the ferromagnetic scale is positioned centrally over the first voltage. microtransformer, the coupling between the primary and the secondary winding is strongest for When the full half-period of the ferromagnetic scale is positioned centrally over the first microtransformer, the coupling between the primary and the secondary winding is strongest for this microtransformer. Conversely, the coupling is weakest for the third microtransformer as the void

half-period is positioned over it. In this situation, the voltage difference of the microtransformer pair is maximal. In the same position, the second and fourth microtransformer have equal outputs as they are set to cover equal areas of full and void half-periods. Therefore, their differential signal is Sensors The 2016, 16, 384 4 of 20 zero. outputs change periodically if the target moves, returning the sine and the cosine differential quadrature signals given by the equations in Figure 1c. Again, the signals would be inverted for a conductive non-ferromagnetic scale. this microtransformer. Conversely, the coupling is weakest for the third microtransformer as the void Incremental position encoders (e.g., those based on optical [4] and Hall Effect [25] devices) half-period is positioned over it. In this situation, the voltage difference of the microtransformer pair is generally utilize quadrature signals. If they have a sinusoidal shape, the arctangent of their maximal. In the same position, the second and fourth microtransformer have equal outputs as they amplitude ratio: are set to cover equal areas of full and void half-periods. Therefore, their differential signal is zero. 2π The outputs change periodically if the target moves, sinreturning the sine and the cosine differential = arctan quadrature signals given by the equations in Figure 1c. Again, the signals would be inverted for (1) a 2π cos conductive non-ferromagnetic scale. Incremental position encoders (e.g., those based on optical [4] and Hall Effect [25] devices) returns a periodically linear positon x over a half of a scale period P [25]. generally utilize quadrature signals. If they have a sinusoidal shape, the arctangent of their The implementation of the integrated differential transformer as presented in Figure 1 differs amplitude ratio: from the previously known designs [10,11] in the¨fact 2π that˛it is completely fabricated in a CMOS xand a counter-phase connection of the sin process, and in that it utilizes a single excitation coil ˚ P ‹ (1) x “ arctan ‚ [14] (p. 85). The presented structure, ˝ secondary windings, which are both features of a generic2πLVDT cos x employing two primary windings and an amplifier forP the subtraction of the secondary signals, introduces more symmetry the IC layout, thus the undesirable common mode voltage returns a periodically linearinto positon x over a half ofreducing a scale period P [25]. in the differential signal.ofThis common mode voltage can be due to noise,inelectromagnetic The implementation the integrated differential transformer as presented Figure 1 differs interference (EMI) and, most importantly, the capacitive coupling between the primary and from the previously known designs [10,11] in the fact that it is completely fabricated in a CMOS secondary winding. process, and in that it utilizes a single excitation coil and a counter-phase connection of the secondary windings, which are both features of a generic LVDT [14] (p. 85). The presented structure, employing 2. Microsystem Designand andan Simulation two primary windings amplifier for the subtraction of the secondary signals, introduces more symmetry into the IC layout, thus the undesirable common voltage differential The design of the prototypereducing microsystem with a piece of amode target scale in is the presented in signal. 2a. This mode voltage be due tothe noise, electromagnetic along interference (EMI) front-end and, most Figure It common consists of a silicon diecan comprising microtransformers with analog importantly, capacitive coupling between the primary and secondary winding. electronics forthe signal conditioning and processing. The external dimensions of the primary and the

secondary microcoil of the microtransformer are 750 by 495 µm and 576 by 321 µm, respectively, 2. Microsystem Design and Simulation with the scale period P of 1 mm. The center-to-center distance of two adjacent microtransformers equals P/2, i.e., 500 As the microsystem is intended to find finalscale application in an incremental The design of µm. the prototype microsystem with a piece of aits target is presented in Figure 2a. linear encoder, it is desired that its outputs have a round period, facilitating the interpolation and the It consists of a silicon die comprising the microtransformers along with analog front-end electronics evaluation of the signal. Furthermore, the external period size and consecutively the and microtransformer for signal conditioning and processing. The dimensions of the primary the secondary dimensions also directed by the ASIC. microcoil ofwere the microtransformer arelimited 750 by silicon 495 µmarea andfor 576prototyping by 321 µm, the respectively, with the scale TheP of number microtransformers can be increased to improve the output signal by period 1 mm.of The center-to-center distance of two adjacent microtransformers equalslevel P/2, i.e., summing the output voltages of coils with the same position inside a distinct scale period. The 500 µm. As the microsystem is intended to find its final application in an incremental linear encoder, it summation scheme for the discussed prototype comprising and fourthe microtransformers is desired that its outputs have a roundsensor period,system facilitating the interpolation evaluation of the per channel is presented in Figure Asconsecutively presented inthe Figure 2a, the sensordimensions is comprised of two signal. Furthermore, the period size2b. and microtransformer were also channels shifted for a quarter of the scale period, thus yielding quadrature output signals. directed by the limited silicon area for prototyping the ASIC.

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Figure Figure 2. 2. (a) (a) A A block block representation representation of of the the presented presented microsystem microsystem with with aa metal metal scale scale of of period period and and quadrature output signals; (b) The summation scheme of the presented microsystem comprising quadrature output signals; (b) The summation scheme of the presented microsystem comprising four four microcoils per channel. microcoils per channel.

The number of microtransformers can be increased to improve the output signal level by summing the output voltages of coils with the same position inside a distinct scale period. The summation

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scheme for the discussed sensor system prototype comprising four microtransformers per channel is presented in Figure 2b. As presented in Figure 2a, the sensor is comprised of two channels shifted for 2016,of 16,the 384scale period, thus yielding quadrature output signals. 5 of 20 aSensors quarter 2.1. Microtransformer Design and Its Model Circuit A 3D model of the the microtransformer microtransformer isispresented presentedin inFigure Figures and 4b. Both the primary and 3a3a and Figure 4b. Both the primary the winding comprise 45 windings in threeinmetal per layer) with the bridging andsecondary the secondary winding comprise 45 windings threelayers metal(15 layers (15 per layer) with the interconnections realized in the fourth metal layer. A standard nm microtechnologic process is bridging interconnections realized in the fourth metal layer. A 350 standard 350 nm microtechnologic used. The winding width is 1.5 µm and spacing traces the is 0.2 µm. is The process is used. Thetrace winding trace width is 1.5the µm and thebetween spacingthe between traces 0.2structure µm. The of the layered presented in Figure 3b. Only one winding is shown with two structure of thewinding layerediswinding is presented in Figure 3b. Only one(primary) winding (primary) is shown turns per layer clearly principle. current The flowcurrent direction is indicated arrows. with two turnsto per layerillustrate to clearlythe illustrate theThe principle. flow direction with is indicated The winding with winding the samewith structure is placed concentrically the middle of withsecondary arrows. The secondary the same structure is placed in concentrically inthe theprimary middle winding. The inter-winding capacitance iscapacitance reduced byisplacing windings inwindings different of the primary winding. The inter-winding reducedneighboring by placing neighboring heights. This is believed an approximate 60% reduction ofreduction the inter-winding capacitance in different heights. This to is bring believed to bring an approximate 60% of the inter-winding (simulated FEM asusing the ratio between of two parallel rectangular conductors with capacitanceusing (simulated FEM as the the ratiocapacitance between the capacitance of two parallel rectangular trace dimensions, placed in the same placed and in another metaland layer).The tracemetal widthlayer).The was chosen according conductors with trace dimensions, in the same in another trace width to process recommended maximum current per maximum metal tracecurrent width (1 to was chosenspecification according toofprocess specification of recommended permA/µm), metal trace allow nominal excitation current of 1excitation mA. The trace wasofwidened to 1.5 µmwas as awidened safety measure to widththe (1 mA/µm), to allow the nominal current 1 mA. The trace to 1.5 µm prevent the heating theprevent ASIC, which would of affect operation the electronics. rectangular as a safety measureofto the heating the the ASIC, whichofwould affect theAoperation of coil the shape was selected to maximize the silicon space utilization. number mainly The directed electronics. A rectangular coil shape was selected to maximizeThe theturn silicon space was utilization. turn by the target primarydirected resistance of 5 primary kΩ: the excitation limit is limited to number was mainly by range the target resistance voltage range ofamplitude 5 kΩ: the excitation voltage 5amplitude V, which gives current of 1 mAgives at that resistance. This voltage limit is equal to the ASIC limit aisnominal limited to 5 V, which a nominal current of 1 mA at that resistance. This supply and has followed due to theand requirements of the IC due ESDtoprotection structures. voltage voltage limit is equal to to thebeASIC supply voltage has to be followed the requirements of The turn count also governs the windings’ inductance and their coupling factor k,inductance which is maximized the IC ESD protection structures. The turn count also governs the windings’ and their by positioning windings concentrically. coupling factorthe k, which is maximized by positioning the windings concentrically.

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Figure 3. 3. (a) single microtransformer microtransformer introduced introduced into into the the parasitic parasitic extraction extraction Figure (a) The The 3D 3D model model of of aa single software; (b) (b)The Thewinding winding structure used in microtransformers. the microtransformers. thicknesses andcoding color software; structure used in the LayerLayer thicknesses and color coding are given in Figure 4a; (c) The model circuit of a single microtransformer. The components’ are given in Figure 4a; (c) The model circuit of a single microtransformer. The components’ values are valuesinare given given Table 1. in Table 1.

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Figure 4. (a) Thicknesses (d) of metal layers used for the microtransformer construction; (b) A three-dimensional representation of the microtransformer windings. The same layer coloring is used in both figures.

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Figure 3. (a) The 3D model of a single microtransformer introduced into the parasitic extraction software; (b) The winding structure used in the microtransformers. Layer thicknesses and color Sensors 2016, 16, 384 coding are given in Figure 4a; (c) The model circuit of a single microtransformer. The components’6 of 20 values are given in Table 1.

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(b)

Figure (a) Thicknesses Thicknesses(d)(d)of of metal layers for microtransformer the microtransformer construction; Figure 4.4. (a) metal layers usedused for the construction; (b) A (b) A three-dimensional representation of the microtransformer windings. The same layer is three-dimensional representation of the microtransformer windings. The same layer coloringcoloring is used in used in both figures. both figures. Table 1. The components’ values for the model circuit presented in Figure 3c. Components Value

R1 , R2

R3 , R4

L1 , L2

L3 , L4

C1

C2

C3

k1 , k2

2657 Ω

1816 Ω

1.16 µH

658 nH

3.55 pF

3.4 fF

2.39 pF

0.429

A model circuit of a single microtransformer (without the target) is presented in Figure 3c. Connection Terminals 1 and 2 are used for the introduction of the primary (excitation) current into the system. The induced voltage is measured at Terminal 3 of the microtransformer. Terminal 4 is used for the reference potential connection, i.e., the DC bias voltage for the amplifier. ANSYS Electronic Desktop (Q3D Extractor) software package was used to determine the model circuit parameters. A GDS file, including the metal layers from the IC layout database, was imported into the software. The model circuit extraction process is not extensively time- and memory-consuming: it took approximately 45 min on 16 cores of a Xeon E5-2680 processor, requiring less than 2 GB of RAM. The extraction results are given in Table 1. The model circuit component values indicate high winding resistances (e.g., 5314 Ω for the primary). This is due to the small cross-sectional area of the trace and the large number of windings. The total primary load resistance of all eight microtransformers (wired in parallel in the IC) is therefore 664 Ω. The capacitances are relatively large, causing a significant capacitive coupling between the primary and the secondary winding. However, this effect is effectively mitigated by the symmetry of the coils forming a pair and the differential operation of the sensor: since the capacitively transferred signal is equal for all microtransformers, it is effectively subtracted out of the differential signal. Also, the ASIC substrate ground must be well-defined to suppress the coupling between the windings through the substrate. The simulated transfer function of the microtransformer is presented in Figure 5. Its bandwidth (over 100 MHz) does not limit the system operation, which is instead limited by the analog front-end electronics to approximately 10 MHz. High winding resistances result in strongly damped resonant circuits formed by the microtransformers’ inductances and parasitic capacitances. The approximate quality factor Q of the primary winding is 0.30 with a resonant frequency of 111 MHz. For the secondary winding, the quality is 0.42 and the resonant frequency is 183 MHz. These resonances are difficult to discern from Figure 5 due to strong resistive damping. The use of such in-chip high-resistance and high-inductance microcoils with thin conductor widths in the resonance is limited due to their low Q and high resonant frequency. Therefore, the

The capacitances are relatively large, causing a significant capacitive coupling between the primary and the secondary winding. However, this effect is effectively mitigated by the symmetry of the coils forming a pair and the differential operation of the sensor: since the capacitively transferred signal is equal for all microtransformers, it is effectively subtracted out of the differential signal. Also, the ASIC substrate ground must be well-defined to suppress the coupling between the Sensors 2016, 16, 384 7 of 20 windings through the substrate. The simulated transfer function of the microtransformer is presented in Figure 5. Its bandwidth presented microsystem inductive found (over 100 MHz) does notrelies limit on thenon-resonant system operation, whichcoupling. is insteadWe limited bythe themicrotransformer analog front-end parameters satisfactory for the electronics to approximately 10task. MHz.

5.384 The voltage voltage transfer transfer function functionof ofthe themicrotransformer microtransformerasaspresented presentedininFigure Figure The circuit SensorsFigure 2016, 16, Figure 5. The 3. 3. The circuit is7 of 20 1 with an AC source of unity magnitude, and the output is measured in is excited into node excited into thethe node V1 V with an AC source of unity magnitude, and the output is measured in node

presented relies ongrounded. non-resonant inductive coupling. We found the microtransformer 3. Nodes V2 and V4 are node Vmicrosystem V 3 . Nodes V 2 and V 4 are grounded. parameters satisfactory for the task. High winding resistances result intostrongly damped resonant circuits formed by and the However it would be interesting investigate the CMOS-technology feasibility However it would be interesting to investigate the CMOS-technology feasibility and performance microtransformers’ inductances and parasitic The quality factorinductor Q of the performance of microtransformers using widercapacitances. traces, similar to approximate the displacement-sensing of microtransformers using wider traces, similar to the displacement-sensing inductor reported in [18] primary winding is 0.30 with a resonant MHz. For thefactor secondary the reported in [18] with a significantly largerfrequency size (2 byof2111 mm), a quality of 14 winding, and a lower with a significantly larger size (2 by 2 mm), a quality factor of 14 and a lower resonance frequency quality is 0.42 and the resonant frequency is 183 MHz. These resonances are difficult to discern from resonance frequency (9.4 MHz). (9.4 MHz). Figure 5 due to strong resistive damping. The use ofofofsuch in-chip high-resistance and high-inductance microcoils with thin conductor 2.2. the Effect 2.2. Simulations Simulations theTarget Target Effect widths in the resonance is limited due to their low Q and high resonant frequency. Therefore, the The The microtransformer microtransformer transfer transfer function function presented presented in in Figure Figure 5, 5, indicates indicates an an output output magnitude magnitude range of approximately 1–10 mV in the frequency range of 1–10 MHz if 1 V excitation is used. range of approximately 1–10 mV in the frequency range of 1–10 MHz if 1 V excitation is used. However, However, a full 3-D simulation to be out to determine the modulation of a full 3-D simulation needs to beneeds carried outcarried to determine the modulation parametersparameters of the output the output signal if a target scale is moved over the microtransformers. COMSOL Multiphysics FEM signal if a target scale is moved over the microtransformers. COMSOL Multiphysics FEM simulation simulation software has for been software has been used theused task.for the task. The performance of a microtransformer has been evaluated forfor a The performance of a microtransformerpair pair(as (aspresented presentedininFigure Figure1a) 1a) has been evaluated copper scale fabricated as a printed circuit board (PCB), and a laser-cut ferromagnetic scale, made a copper scale fabricated as a printed circuit board (PCB), and a laser-cut ferromagnetic scale, made from transformersteel steel(Acroni (Acroni M330-35A [26]). The simulated scalesdesigned were designed to from transformer M330-35A [26]). The simulated target target scales were to represent represent the actual scales used for the microsystem characterization, presented in Figure 6. the actual scales used for the microsystem characterization, presented in Figure 6.

Figure 6. 6. Measurement Measurementscales scalesused usedfor forthe thesimulation simulationand andthe thecharacterization characterizationof ofthe themicrosystem. microsystem. Figure 1—transformer steel laser cut scale with 0.35 mm thickness; 2—PCB scale with 35 µm copper 1—transformer steel laser cut scale with 0.35 mm thickness; 2—PCB scale with 35 µmthickness. copper Full and void of the scaleofare wide, resulting a scale period of 1period mm. of 1 mm. thickness. Full parts and void parts theeach scale0.5 aremm each 0.5 mm wide,in resulting in a scale 7 S/m, 7 S/m, In 1010 while thethe conductivity of In the thesimulator, simulator,the theconductivity conductivityofofcopper copperwas wasset settoto5.9 5.9× ˆ while conductivity 6 S/m 6 steel was set to 2.2 × 10 according to [27] (p. 14/3). The relative magnetic permeability of the of steel was set to 2.2 ˆ 10 S/m according to [27] (p. 14/3). The relative magnetic permeability of steel waswas set to value of 10 according to to [28], since the steel setatogeneric a generic value of 10 according [28], sincewe wehave havebeen beenunable unabletotoobtain obtain exact exact electromagnetic properties for the used scale material. The microtransformer was modeled as a planar rectangular spiral coil. A 3-D image of the simulated structure is presented in Figure 7.

Figure 6. Measurement scales used for the simulation and the characterization of the microsystem. 1—transformer steel laser cut scale with 0.35 mm thickness; 2—PCB scale with 35 µm copper thickness. Full and void parts of the scale are each 0.5 mm wide, resulting in a scale period of 1 mm.

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the conductivity of copper was set to 5.9 × 107 S/m, while the conductivity of 8 of 20 steel was set to 2.2 × 106 S/m according to [27] (p. 14/3). The relative magnetic permeability of the steel was set to a generic value of 10 according to [28], since we have been unable to obtain exact electromagnetic used scale material. The The microtransformer was modeled as a planar electromagnetic properties propertiesfor forthethe used scale material. microtransformer was modeled as a rectangular spiral coil. A 3-D image of the simulated structure is presented in Figure 7. planar rectangular spiral coil. A 3-D image of the simulated structure is presented in Figure 7.

Figure 7. microtransformer pairpair geometry withwith a scale period P of 1Pmm a dand = 0.35 Figure 7. The Thesimulated simulated microtransformer geometry a scale period of and 1 mm a thick target scale, representing the ferromagnetic scale type.scale The type. direction the scaleof movement dmm = 0.35 mm thick target scale, representing the ferromagnetic Theofdirection the scale is indicatedisby an arrow. are given inare µm. movement indicated byDimensions an arrow. Dimensions given in µm.

Since the cross-section of the microtransformer aluminum conductors (0.64 by 1.5 µm) is small in comparison to the dimensions of the target and to the skin depth of aluminum (37 µm at 5 MHz [29], p. 315), which assures an uniform current distribution in the conductor cross-section), the conductors can be modeled as current-carrying lines, significantly reducing the complexity of the FEM mesh. Despite this simplification, a displacement sweep with the target position calculated in 30 steps of a 1 mm displacement range still takes several hours for a single frequency, requiring more than 30 GB of RAM in a workstation using 16 cores of an Intel Xeon E5-2680 processor. Due to the complexity of the simulation we have chosen to simulate only a single pair of microtransformers instead of two prototyped pairs. The primary current amplitude was set to 1 mA, which approximately corresponds to the excitation voltage amplitude of 5 V at 5 kΩ primary winding resistance. The simulation was carried out in the complex domain. The vertical distance between the target and the microtransformers was 200 µm. The secondary induced voltage can be determined using line integration of the vector magnetic potential A over a closed loop L of the secondary winding ([29], p. 192 and 197): ¿˝ Uind “ ´2π f

A ¨ dl

(2)

L

For each microtransformer, an array of complex induced voltages is returned, corresponding to the swept scale positions. Amplitudes and phase angles of the two microtransformer output signals (Uind1 , Uind2 ) for two target materials and two operating frequencies (1 and 4 MHz) are presented in Figure 8a. The amplitude of the differential signal (Udi f f = Uind1 ´ Uind2 ) are also shown. Note that the simulated signals’ phases do not exhibit a 90˝ inductive shift, since the secondary signals originate in line current, which does not have an inductive character. The described inverse operation for the ferromagnetic and the conductive target scale is clearly visible in Figure 8a: magnitudes of displacement-dependent induced voltages |Uind1,2 | for the copper scale are always lower due to an increased eddy-current induced energy caused by larger copper conductivity. Furthermore, the maxima and the minima of voltages |Uind1,2 | oppose each other for the two materials. At 1 MHz excitation frequency, the ferromagnetic effect manifested in steel overcomes the eddy-current effect in copper, resulting in greater modulation (larger |Udi f f |). At 4 MHz, the modulation approximately

The primary current amplitude was set to 1 mA, which approximately corresponds to the excitation voltage amplitude of 5 V at 5 kΩ primary winding resistance. The simulation was carried out in the complex domain. The vertical distance between the target and the microtransformers was 200 µm. The secondary induced voltage can be determined using line integration of the vector magnetic potential A over a closed loop L of the secondary winding ([29], p. 192 and 197): Sensors 2016, 16, 384 9 of 20 (2) = −2π ⋅ equalizes, indicating the increasing prominence of the eddy-current effects with rising frequency. As the phase modulation (arg (Uind1,2 )) array is related to the eddy current losses, its characteristics are notto For each microtransformer, an of complex induced voltages is returned, corresponding opposite forscale the two materials. It can be seen how the shape thetwo differential signal (converted to the the swept positions. Amplitudes and phase angles ofof the microtransformer output signals time domain in Figure 8b) is much more sinusoidal in comparison to the direct transformer outputs’ (Uind1, Uind2) for two target materials and two operating frequencies (1 and 4 MHz) are presented in amplitudes Figure 8a. |Uind1,2 |, indicating the importance of the differential operation of such sensors.

|Uind1,2| [V]

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Figure8.8.(a)(a) Simulated displacement dependence the amplitude andofphase of the secondary Figure Simulated displacement dependence of theofamplitude and phase the secondary induced induced signals U ind1, Uind2 (shown in dotted lines), and the differential signal Udiff; (b) The signals Uind1 , Uind2 (shown in dotted lines), and the differential signal Udi f f ; (b) The time-domain time-domain differential udiff for steel and scaleisatshown. 4 MHz A is percent shown. A percent THD differential signal udi f f forsignal the steel andthe copper scalecopper at 4 MHz THD value of diffmix at their corresponding phases of the mixing value of thesynchronously demodulated utheir thesynchronously demodulated signals udisignals at corresponding phases of the mixing signal f f mix ϕmix given is alsoin given in the legend. φsignal is also the legend. mix

The secondary voltages are then subtracted and transformed from the complex domain into a time-domain signal udi f f , shown in Figure 8b. The actual simulated results ranging between 0–1000 µm are duplicated, resulting in 0–2000 µm range, to better illustrate the signals’ shape. For the purpose of the analysis of the demodulation principle, an arbitrary frequency fc of this signal can be chosen, in this case 1000-times higher than the frequency of the scale movement. During the operation of an actual device, this ratio can be much higher; however the usage of a lower ratio does not affect the illustration of the principle. 2.2.1. Signal Demodulation The synchronous demodulation method (also: coherent detection) is based on mixing (i.e., multiplying) the modulated signal with a sinusoidal signal of the same carrier frequency fc and

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phase φmix . The resulting signal is composed of an AC signal with 2fc frequency and a DC component in a linear correlation with the modulation of the signal and the mixing signal phase φmix [30] (p. 96). To suppress the AC component of the signal Udi f f , a low-pass filter (LPF) is employed. A fourth-order Butterworth LPF with the 3dB frequency margin of 1% fc was used, resulting in the demodulated signal udi f f mix . The shape of this signal depends on different material and geometric properties of each scale. The result of the coherent demodulation is also strongly dependent on φmix , as demonstrated in Figure 8b. Therefore, an optimal mixing signal phase φmix can be determined for each target configuration to maximize the output signal amplitude, as will be demonstrated in Section 3 when discussing the microsystem characterization. To establish the linear position using the arctangent of quadrature signals (Equation (1)), a sinusoidal shape of the position-dependent output signal is required. As its figure of merit, the total harmonic distortion (THD) [31] (p. 83) for the first five harmonics of the demodulated signal has been calculated, which is also stated next to the corresponding phases φmix in Figure 8b. 2.2.2. Scale Tilting Another issue worth addressing is the tilting of the scale over the sensor, which is inevitable at a sensor operating in an actual application. The tilting was analyzed using the same methodology and the same simulation setup as presented in Section 2.2. The target scale was rotated for an angle of 3˝ in three dimensions, as depicted in Figure 9a. The simulation was carried out with a copper scale at ˝ 4 MHz and16,φ384 Sensors 2016, 10 of 20 mix = 0 ; its results are shown in Figure 9b. −4

x 10

X; 4.18% Y; 11.00% Z; 4.41% None; 4.20%

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diffmix

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Figure 9. (a) (a) The Thesimulated simulatedscale scale rotation shown the sensor with the microcoils; Figure 9. rotation (3˝ (3°) ) axesaxes shown overover the sensor with the microcoils; (b) the diffmix signal). Signal THDs (b) the target rotation simulation results (the demodulated and filtered u target rotation simulation results (the demodulated and filtered udi f f mix signal). Signal THDs are given are given in the legend. in the legend.

Their outputs are not complementary any more, resulting in increased offset and distortion of The simulation results show that the rotation of the target scale in x and z axis does not significantly the differential signal, which is also reflected in the THD increase. For other two (x and z) axes, the affect the output differential signal udi f f mix , as the results virtually align with the situation without effect of the tilt is almost equal for both microtransformers in a pair, so it is still compensated by the tilting (None). However, a notable deviation occurs when the target is tilted longitudinally (y axis): subtraction of their output signals. each microtransformer in the pair has a different target coupling characteristics due to the different height of Design the scale over each microtransformer. 2.3. ASIC and Simulation Their outputs are not complementary any more, resulting in increased offset and distortion of We have already introduced synchronous demodulation for(x the the differential signal, which is also the reflected in the THD increase. Formethod other two and differential z) axes, the microtransformer signal. This section describes the actual measurement channel realized effect of the tilt is almost equal for both microtransformers in a pair, so it is still compensated in by the the prototype ASIC, depicted schematically in Figure 10. Cadence Virtuoso Analog Design Environment subtraction of their output signals. software (Spectre Simulator) was used as the main tool in the analog front-end design process.

are given in the legend.

Their outputs are not complementary any more, resulting in increased offset and distortion of the differential signal, which is also reflected in the THD increase. For other two (x and z) axes, the effect2016, of the Sensors 16, tilt 384 is almost equal for both microtransformers in a pair, so it is still compensated11by of the 20 subtraction of their output signals. 2.3. 2.3.ASIC ASICDesign Designand andSimulation Simulation We We have have already already introduced introduced the the synchronous synchronous demodulation demodulation method method for for the the differential differential microtransformer signal. This section describes the actual measurement channel realized microtransformer signal. actual measurement channel realized in in the the prototype prototypeASIC, ASIC,depicted depictedschematically schematicallyin inFigure Figure10. 10.Cadence CadenceVirtuoso VirtuosoAnalog AnalogDesign DesignEnvironment Environment software software(Spectre (SpectreSimulator) Simulator)was wasused usedas asthe themain maintool toolininthe theanalog analogfront-end front-enddesign designprocess. process.

Figure 10. The measurement channel for a single chain of microtransformers, as realized in the Figure 10. The measurement channel for a single chain of microtransformers, as realized in the prototype ASIC. For the described synchronous demodulation method, fmix equals fexc. The DC biasing prototype ASIC. For the described synchronous demodulation method, fmix equals fexc . The DC biasing voltage of the IC Ubias is set to 2.5 V, i.e., to the half of supply voltage (5 V). voltage of the IC Ubias is set to 2.5 V, i.e., to the half of supply voltage (5 V).

As previously explained, two differential transformers are wired serially to increase the signal As previously explained, two transformers are wired serially increase due the signal level. Fully differential design is differential used for signal amplification, mixing, andtofiltering, to the level. Fully differential design is used for signal amplification, mixing, and filtering, due to the symmetric nature of the problem (subtracting the signals of two identical microtransformers), symmetric the problem (subtracting signals of two as identical microtransformers), improved improved nature noise of immunity and common the mode rejection well as simpler DC biasing ([32], noise immunity common mode rejection wellstages. as simpler biasing ([32], p. 100–102). The p. 100–102). Theand amplification is realized in as three DueDC to different requirements of each amplification is realized in three stages. Due to different requirements of each particular stage, three particular stage, three different operational amplifiers had to be designed. The first wideband different amplifiers to be designed. Thedue firsttowideband amplifier in the chain employs amplifieroperational in the chain employshad a telescopic topology its required high frequency range ([32], ap.telescopic duea tosimulated its required frequencygain rangeof([32], p. 297–299), featuring aproduct simulated 297–299),topology featuring DChigh closed-loop 6 and a gain-bandwidth of DC closed-loop gain of 6 and a gain-bandwidth product MHz The withlevel twoofserially connected 72 MHz with two serially connected microtransformers atof the72input. the output signal microtransformers at the the amplitude input. Theof level the output can be controlled by the of can be controlled by the of mixing signal.signal A single-balanced Gilbert cell amplitude mixer is used the mixing signal. A single-balanced Gilbert cell mixer is used ([33], p. 418). The second-stage DC gain is 15. This amplifier employs a simpler Miller topology ([32], p. 296). The second-stage amplifier also functions as a LPF for the suppression of the excitation frequency fexc : its 3dB corner frequency is designed to be 325 kHz. This relatively high corner frequency allows for an optional operation of the system with heterodyne mixing ([30], p. 128), if the frequency fmix is set to a value different from fexc , resulting in a mixer output signal with a frequency of fout = |fexc ´ fmix | (another component with a frequency of fexc + fmix is suppressed by the LPF). The third-stage amplifier subtracts the signals of the positive and negative signal path, amplifies this difference with a gain of 100, and serves as the output buffer. The results of the IC simulation are presented in Figure 11a. The circuit presented in Section 2.1 has been used to model the differential transformers. The scale modulation (with a frequency fscale ) was introduced into the model by sinusoidally varying the value of inductor coupling coefficient k, resulting in a symmetric amplitude-only modulation. For this purpose, the model circuit was rewritten into a high-level analog behavioral model description language Verilog-A [34], which allows for the dynamic variation of the model parameters. The modulation was configured to approximate the performance of the FEM-simulated copper scale at 4 MHz when the secondary windings had no load connected. An agreement has been found when the coupling coefficient function was set to: k “ 0.43 ` p0.43 ¨ 0.02q sin p2π f scale tq

(3)

Verilog-A [34], which allows for the dynamic variation of the model parameters. The modulation was configured to approximate the performance of the FEM-simulated copper scale at 4 MHz when the secondary windings had no load connected. An agreement has been found when the coupling coefficient function was set to: = 0.43 + (0.43 ⋅ 0.02) sin(2π

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)

12 of (3) 20

uind1, uind2 [V]

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Figure11. 11.(a) (a)Results ResultsofofCadence Cadencesimulations simulationsofofthe themeasurement measurementchannel channelatat4 4MHz MHzoperation operation Figure mix is swept between 0°–90°; (b) The frequency. In the bottom figure, the mixing signal phase ϕ ˝ ˝ frequency. In the bottom figure, the mixing signal phase φmix is swept between 0 –90 ; (b)layout The of theofintegrated circuit, comprising two identical The fabricated fabricatedASIC ASIC layout the integrated circuit, comprising two identicalquadrature quadraturechannels; channels; (c) (c) The prototype,mounted mountedonona atest testPCB. PCB. prototype,

When the amplifier is connected to the microtransformer, the coil output signals are reduced When the amplifier is connected to the microtransformer, the coil output signals are reduced due due to the impedance of the amplifier feedback connected to their output. The effect of this loading to the impedance of the amplifier feedback connected to their output. The effect of this loading is visible in the middle chart in Figure 11a, showing the unloaded differential signal in blue color, and the loaded differential signal in green. The top chart also shows the unloaded (green and blue) and loaded (light green and red) positive and negative coil output signals. Since the microtransformer and the first-stage amplifier introduce respective 90˝ and 180˝ (low-frequency values) phase shifts, with the actual simulated total phase shift being 243˝ at 4 MHz due to poles in the transfer characteristic, this value is added to the simulated mixing signal phase φmix , assuring the mixing and demodulated signal coherency at φmix = 0˝ . The excitation voltage uexc and mixing voltage umix amplitudes are set to the same values used later in the characterization of the IC, i.e., 2.5 V and 0.25 V respectively. The bottom graph in Figure 11a indicates that the amplitude maximum of the output signal Uout occurs when φmix = 0˝ . Since the phase modulation is not modeled, the mixing signal and the signal being demodulated are in-phase at zero φmix , resulting in maximal amplitude. Such simulations that neglect the phase modulation of the target have been used primarily to adjust the gain of the amplifier chain. The layout of the microsystem is depicted in Figure 11b. The silicon footprint of the analog front-end is relatively small in comparison to the area of the microtransformers. The fabricated ASIC prototype on a mounting PCB is presented in Figure 11c. The ASIC silicon die dimensions are 2500 by 2200 µm, at a 300 µm wafer thickness. As the bonding wires are thin (several 10 µm), they can easily

they can easily bend or tear in case of a contact with scale, which is highly possible. Therefore they must be protected. A protective epoxy coating is used for their encapsulation. 3. Measurement Results 12384 presents SensorsFigure 2016, 16,

the laboratory setup for the microsystem characterization. The scale, fixed to 13 of 20 a support fork, is moved over the microsystem by a computer-controlled three-axis motorized manipulator. The ASIC excitation and mixing signals are generated by a function generator. The bend or tear in case of a contact with scale, which is highly possible. Therefore they must be protected. signal is sampled by a DAQ computer interface. A personal computer (not shown) uses MATLAB A protective epoxy coating is used for their encapsulation. scripts to control the manipulator, the function generator, the DAQ interface, and to process the acquired signals. Results 3. Measurement The scale was placed to such vertical position that it barely made contact with the coating Figure presents the laboratory 200–250 setup forµm thethick, microsystem Thedistance scale, fixed surface. The12 coating is approximately meaningcharacterization. that the IC-to-scale also to a support fork, is moved over the microsystem by a computer-controlled three-axis had such value. Unfortunately the coating thickness could not be accurately determined motorized due to the manipulator.of The excitation mixing by suitable a function generator. The signal unevenness theASIC coating (as it isand applied bysignals hand)are andgenerated the lack of accurate measurement is sampled by a DAQ computer interface. A personal computer (not shown) uses MATLAB scripts to devices. The effect of coating unevenness can be estimated by the scale tilting simulation results control theinmanipulator, provided Section 2.2.2.the function generator, the DAQ interface, and to process the acquired signals.

Figure 12. The microsystem characterization setup. 1—three-axis motorized manipulator; Figure 12. The microsystem characterization setup. 1—three-axis motorized manipulator; 2—16-bit 2—16-bit data acquisition interface (DAQ) NI USB-6251; 3—function generator Agilent 33500B; data acquisition interface (DAQ) NI USB-6251; 3—function generator Agilent 33500B; 4—DC power 4—DC power supply; 5—main PCB board, providing the DC bias voltages for the ASIC, and supply; 5—main PCB board, providing the DC bias voltages for the ASIC, and connection terminals; connection terminals; 6—measurement scale support (the scales (not shown, scale types presented in 6—measurement scale support (the scales (not shown, scale types presented in Figure 6) are positioned Figure are supported positionedbyover the ASIC, byboard the (Figure forks); 11c). 7—the sensor PCB board over the6)ASIC, the forks); 7—thesupported sensor PCB (Figure 11c).

The scale was placed to such vertical position that it barely made contact with the coating surface. The coating is approximately 200–250 µm thick, meaning that the IC-to-scale distance also had such value. Unfortunately the coating thickness could not be accurately determined due to the unevenness of the coating (as it is applied by hand) and the lack of suitable accurate measurement devices. The effect of coating unevenness can be estimated by the scale tilting simulation results provided in Section 2.2.2. All presented measurements have been carried out with an RC filter at the IC output with a corner frequency of 100 Hz to remove the remaining AC component. Sinusoidal signals with 2.5 V and 250 mV amplitude were used as the excitation and the mixing signal respectively. 3.1. Optimal Operating Frequency and Phase In the first measurement, the frequency of the excitation signal fexc (equaling the frequency of the mixing signal fmix ) and the phase of the mixing signal φmix were swept in the range between 1–4 MHz (0.5 MHz steps) and 0˝ –90˝ (10˝ steps) to determine the optimal operating conditions of the microsystem for both scale types. The excitation signal phase was 0˝ . The peak-to-peak IC output voltage of the first measurement channel (U pp1 ) was chosen as a figure of merit. Since the IC output voltage is DC, in this context peak-to-peak voltage means the difference between the maximum and the minimum output voltage over the scale linear displacement range of 2 mm. The positioning step was 50 µm. The results are presented in Figure 13.

(0.5 MHz steps) and 0°–90° (10° steps) to determine the optimal operating conditions of the (0.5 MHz steps) and 0°–90° (10° steps) to determine the optimal operating conditions of the microsystem for both scale types. The excitation signal phase was 0°. The peak-to-peak IC output microsystem for both scale types. The excitation signal phase was 0°. The peak-to-peak IC output voltage of the first measurement channel (Upp1) was chosen as a figure of merit. voltage of the first measurement channel (Upp1) was chosen as a figure of merit. Since the IC output voltage is DC, in this context peak-to-peak voltage means the difference Since the IC output voltage is DC, in this context peak-to-peak voltage means the difference between the maximum and the minimum output voltage over the scale linear displacement range of between Sensors 2016, 16,the 384maximum and the minimum output voltage over the scale linear displacement range 14 ofof20 2 mm. The positioning step was 50 µ m. The results are presented in Figure 13. 2 mm. The positioning step was 50 µm. The results are presented in Figure 13.

Figure 13. Determining the optimal operating frequency fexc and the mixing signal phase ϕmix of the Figure 13. 13. Determining thethe optimal operating frequency phase ϕφmix the Figure Determining optimal operating frequencyf fexc and and the the mixing mixing signal signal phase mixofofthe microsystem for each of the scales. The color represents theexc Upp1 voltage. The images are interpolated. microsystem each of the scales. The color representsthe theUU pp1 voltage. microsystem for for each of the scales. The color represents voltage. The Theimages imagesare areinterpolated. interpolated. pp1

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Figure 14 demonstrates the agreement of the simulated (using the method described in Figure 14 demonstrates the agreement the simulated (using the described method described in Figure 14and demonstrates the of simulated (using the method in Section Section 2.2 Figure 8b) the andagreement measured of dependence of the output signal Upp1 amplitude on ϕmix.2.2 Section 2.2 and Figure 8b) and measured dependence of the output signal Upp1 amplitude on ϕmix. Similarly as before, the totaldependence phase shift of ofthe theoutput microtransformers and the first-stage amplifier as and Figure 8b) and measured signal Upp1 amplitude on φmix . Similarly Similarly as before, the total phase shift of the microtransformers and the first-stage amplifier (263°the at 1total MHz, 243° shift at 4 MHz) to be added toand the simulated coil output signals before, phase of theneeds microtransformers the first-stage amplifier (263˝toatcorrespond 1 MHz, 243˝ (263° at 1 MHz, 243° at 4 MHz) needs to be added to the simulated coil output signals to correspond the measurements. at 4toMHz) needs to be added to the simulated coil output signals to correspond to the measurements. to the measurements. Copper

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Figure 14. dependence The dependence mix on the Upp1 microsystem voltage Figure 14. The of φmix onofof the ϕUϕ microsystem voltage at 1 output and 4 MHz. Lines pp1 Figure 14. The dependence mix on the Uoutput pp1 microsystem output voltage at 1 and 4 MHz. Lines denote simulated values, while the measured points are marked by circles and denote simulated values, while the measured points are marked by circles and diamonds. All amplitude at 1 and 4 MHz. Lines denote simulated values, while the measured points are marked by circles and diamonds. All amplitude values are normalized. (a) Results for copper scale; (b) Results for values are normalized. (a) Results for are copper scale; (b) (a) Results for steel scale. scale; (b) Results for diamonds. All amplitude values normalized. Results for copper steel scale. steel scale.

Then, the (i.e., providing providingthe themaximal maximaloutput output amplitude) Then, theexperimentally experimentallydetermined determined optimal optimal (i.e., amplitude) ˝ ˝ Then, the experimentally determined optimal (i.e., providing the maximal output amplitude) frequency and phase forfor both scales (4 MHz; 80 80° andand 40 40° forfor copper andand steel scale, respectively), were frequency and phase both scales (4 MHz; copper steel scale, respectively), frequency andmore phaseprecise for both scales (4 MHz; 80°sweeps and 40° for acopper and steel respectively), used to carry out with positioning stepscale, of 20 µm, were used to carry out more target precisedisplacement target displacement sweeps with a positioning step of presented 20 µ m, were used to carry out more precise displacement with a positioning step (channels of 20 µm, 1 in Figure 15. Periodically grated scalestarget (see Figure 6) give sweeps periodic quadrature outputs and 2). The starting position was arbitrary for both scales and the measurement is incremental: the displacement is always zero at the starting position. Since the voltages of both channels are not in the same range, they need to be normalized between 1 and ´1 before the calculation of the arctangent of their ratio: ˜ arctan

U pp2 U pp1

¸ (4)

which should ideally be periodically linear over a half of the scale period (P/2=0.5 mm). After scaling and unwrapping, i.e., removing jumps, the arctangent should present a linear function Xatan (x) of the displacement x [25], as shown in Figure 15. In the bottom chart, the nonlinearity error E of the arctangent function is shown, defined as the difference of the measured displacement Xatan and the reference linear position Xre f : E pxq “ Xatan pxq ´ Xre f pxq (5)

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presented in Figure 15. Periodically grated scales (see Figure 6) give periodic quadrature outputs 1 and 2). The starting position was arbitrary for both scales and the measurement is Sensors(channels 2016, 16, 384 15 of 20 incremental: the displacement is always zero at the starting position. mix

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Figure 15. The results of the microsystem linear displacement characterization at optimal excitation Figure 15. The results of the microsystem linear displacement characterization at optimal excitation frequency and mixing signal phase for each scale type. Results for two scale period lengths are frequency and mixing signal phase for each scale type. Results for two scale period lengths are shown. shown. The unwrapped arctangent function for the normalized sensor outputs is also shown, along The unwrapped arctangent function for the normalized sensor outputs is also shown, along with errors with errors relative to the reference linear position. (a) Results for copper scale; (b) Results for relative to the reference linear position. (a) Results for copper scale; (b) Results for steel scale. steel scale.

Since theanalog voltages of both channels in the same range, they need to be normalized Commonly, quadrature signalsare (Unot pp1 and U pp2 in this case) of any incremental encoder between 1 and −1 before the calculation of the arctangent of their ratio: [35,36]. To return the discrete type are driven into an interpolator device (typically also an ASIC)

position information, interpolators employ advanced mixed signal processing methods for amplitude arctan (4) (e.g., automated/programmable gain control), offset, and phase correction of the signal nonidealities, which can be for example by scale tilting. presented microsystem is already fabricated which should ideally becaused periodically linear over a As halfthe of the scale period (P/2=0.5 mm). After scaling as anand ASIC, there also exists a potential for a same-chip implementation of an interpolator, resulting in unwrapping, i.e., removing jumps, the arctangent should present a linear function Xatan(x) of the further improved xcost-efficiency functionality. displacement [25], as shownand in Figure 15. In the bottom chart, the nonlinearity error E of the arctangent function shown, defined as the difference of the(Equation measured displacement Xatanofand The sensitivity of is the discussed microsystem, defined 6) as the ratio thethe output reference linear Xref∆U : pp = max(U pp ) ´ min(U pp ) and the scale period P: voltage change overposition a period ( „ ) − ( ) (5) ∆U pp V S “(Upp1 and Upp2 in this case) of any incremental encoder Commonly, analog quadrature signals P mm ( )=

(6)

type are driven into an interpolator device (typically also an ASIC) [35,36]. To return the discrete

position information, interpolators advanced shape, mixed vertical signal processing methods foras the depends on many variables, namely theemploy target material, displacement, as well amplitude (e.g., automated/programmable gain control), offset, and phase correction of the signal ASIC input signals’ parameters: shape, amplitude and frequency of the excitation and the mixing signal, and also the phase shift between the excitation and mixing signal. Sensitivities for the optimal setup with the parameters as given in this section (results in Figure 15), are presented in Table 2. Maximal and RMS values of nonlinearity error E (Equation (5)) are also given for both scales.

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Table 2. The comparison of the sensitivities S and errors E for the both targets for results given in Figure 15. Target „  V S (Ch. 1) „ mm  V S (Ch. 2) mm max (E) [µm] rms (E) [µm]

Copper

Steel

0.99

0.57

0.71

0.44

18.79 6.89

33.05 11.32

3.2. Target Vertical Displacement The same optimal frequency and phase have also been used for the measurement of the dependence between the target vertical displacement and output signal U pp amplitude in a scale period, given in Figure 16. The characterization was carried out in the vertical displacement range between 0 and 0.5 mm in 50 µm steps. The horizontal step was also 50 µm. The vertical displacement is measured from the top of the IC epoxy coating with the approximate thickness of 200–250 µm (see Figure 11b). To establish the effective vertical displacement between the top surface of the IC and the target, the measured vertical displacement displayed in Figure 16c must be added to the coating thickness. It can be seen that the vertical displacement of the target has a significant effect on the target sensitivity, reducing it for an approximate factor of three when the target is raised for 200 µm. As the arctangent method is used for linear position determination, only the ratio of the quadrature signals is important, which remains constant regardless of vertical displacement once the quadrature channels are normalized (commonly done in the interpolator). The usable vertical range of operation is limited by theSensors required signal-to-noise ratio of the given application. 2016, 16, x 16 of 20

(a)

(b)

Figure 16. The results of the microsystem vertical target displacement sweep for both scale types;

Figure 16. The results of the microsystem vertical target displacement sweep for both scale types; (a) the measured IC output voltages for both channels at all vertical target positions; (b) The relation (a) the measured IC output voltages for both channels at all vertical target positions; (b) The relation of of the measured Vpp voltages from (a) to the vertical target displacement. The linear starting position the measured Vpp voltages from (a) to the vertical target displacement. The linear starting position was was arbitrary for both scales. arbitrary for both scales.

4. Discussion

For aSimulation microtransformer comprising concentric coils covered a target,sensing monotonic diminishing and measurement results of an inductive linear with displacement microsystem of thehave target coupling effect magnitude on its secondary voltage is expected if the target been presented. The main purpose of the simulations has been the dimensioning of the gainisofbeing vertically displaced. This is confirmed by the measurement data shape, in Figure 16b withsuccessful. the exception the analog front-end circuits and the prediction of the output signal which proved The output signals’ mean value shouldcurves be closeattolow Ubiasvertical = 2.5 V according to theory simulations. of a visible flatness of the characteristic displacements at and the steel scale. This We attribute the exhibited DC offset to the asymmetries in the positive and negative signal path,point can be explained by the flexibility of the steel scale due to its thinness (0.35 mm). The contact caused by on-chip element mismatch and fabrication tolerances, which manifest strongly due to the between the sensor and the target might have been set slightly too low, causing upwards bending high gain of the system. The differences in the offset voltages and sensitivities between the channels of the scale in its center, therefore raising it marginally above the IC coating surface, with the bend are also significant. They can be attributed to the mispositioning of the target scale (e.g., its tilting leveling in the next height step, placing the scale closer to the IC. Due to its rigidness, this did not relatively to the ASIC, as suggested by the simulation results in Section 2.2.2.). This could be caused by the unevenness of the top coating. Within-die CMOS process parameter variations [32] due to the large distance between the front-end electronics for each channel are another possible reason. In future ASIC improvements, the described offsets and differences can be alleviated by implementing trimming structures into the analog front-end. Ideas for offset compensation and transimpedance amplifier utilization to improve the performance of similar sensor designs are also suggested in [22].

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occur with the thicker copper scale. Another possible explanation is provided by Tseng and Xie [18], who have studied a conductive micromirror plate placed over a transmitting and a receiving microcoil positioned in line. The maximum effect of the plate on the inter-coil inductive coupling occurred at a certain vertical distance between the coils and the plate. It is possible that a similar effect also manifests here between primary and secondary windings of different microtransformers, resulting in distorted characteristics at small vertical displacements. 4. Discussion Simulation and measurement results of an inductive linear displacement sensing microsystem have been presented. The main purpose of the simulations has been the dimensioning of the gain of the analog front-end circuits and the prediction of the output signal shape, which proved successful. The output signals’ mean value should be close to Ubias = 2.5 V according to theory and simulations. We attribute the exhibited DC offset to the asymmetries in the positive and negative signal path, caused by on-chip element mismatch and fabrication tolerances, which manifest strongly due to the high gain of the system. The differences in the offset voltages and sensitivities between the channels are also significant. They can be attributed to the mispositioning of the target scale (e.g., its tilting relatively to the ASIC, as suggested by the simulation results in Section 2.2.2.). This could be caused by the unevenness of the top coating. Within-die CMOS process parameter variations [32] due to the large distance between the front-end electronics for each channel are another possible reason. In future ASIC improvements, the described offsets and differences can be alleviated by implementing trimming structures into the analog front-end. Ideas for offset compensation and transimpedance amplifier utilization to improve the performance of similar sensor designs are also suggested in [22]. With the microsystem input stimulation equalized between Cadence simulations and the measurement setup, the output signal amplitudes have been comparable. A measurement able to assess a more exact agreement between the simulated and measured output voltages is demanding to design from a mechanical point of view, since the IC-to-scale distance and parallelism would have to be very precisely controlled, as indicated by the strong dependence between the vertical displacement of the target and IC output voltage (Figure 16c). The FEM simulation results have predicted approximately equal sensitivity of the signal for the steel and copper scale at 4 MHz. This does not agree with measurements, which display significantly better sensitivity for the copper scale. We attribute this difference to the imprecise material properties of steel used in the FEM simulation due to lack of material data. The measured inferior performance of the steel scale agrees with literature [17]. The simulations have predicted smaller distortion for the steel scale which should reflect in better linearity. This does not agree with measurements displaying a greater nonlinearity error for the steel scale (11.32 µm RMS vs. 6.89 µm RMS for copper). Beside lower signal levels due to the lower sensitivity, the reason for the inferior linearity of the steel scale may also be in its imprecise manufacturing due to laser cutting tolerances (beam width 40 µm), possibly making the scale half-periods asymmetric. The system exhibits a resolution of at least 20 µm using both transformer steel and copper target scales, as indicated by the monotonicity of arctangent waveforms (Figure 15). We were unable to assess the performance at smaller displacement steps due to the step resolution limitation of mechanical manipulator used for the characterization. However, the simulated and the measured results for the optimal mixing phase angle φmix are in good agreement for both materials, except for the steel scale at 4 MHz, which exhibits a 10˝ –20˝ deviation of the amplitude maximum. This can again be attributed to the inexact steel material properties used in the simulation. Theoretical Resolution Limit The theoretical resolution limit of the discussed microsystem is set by the thermal noise of the sensor (i.e., the secondary microtransformer winding) and the desired bandwidth, dictated by the maximum target movement speed. If, for example, the target having a period of 1 mm moves with

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1 m/s, an analog front-end bandwidth (after mixer) of 1 kHz is required. As the secondary resistance of a single microtransformer is approximately 4 kΩ, totaling in 16 kΩ of sensor output resistance (four coils per channel are used), this returns 0.51 µVrms thermal input noise at 20 ˝ C [32] (p. 210). At 4 MHz excitation frequency, the simulated input sensitivity (directly at the microtransformer output) at copper target (at 1 mA primary current; Figure 8b) is in the range of 1 mV/mm. Therefore, the resolution limit in the described situation is 0.51 µm at 1 kHz bandwidth (1.6 µm at 10 kHz). Lower movement speed specifications, allowing for stronger low-pass filtering, would reduce the required bandwidth, resulting in an improvement of the noise performance. The resolution can also be improved by raising the excitation signal frequency or magnitude. 5. Conclusions 5.1. Summary We have presented the operational background and the design flow for a monolithic linear displacement measurement microsystem based on integrated microtransformers and synchronous demodulation. The system is intended to be used in a linear incremental encoder. In the design process, we have relied on FEM modeling, parasitic extraction, system-level mathematical and behavioral modeling, as well as CMOS circuit-level simulation of the microsystem. A prototype ASIC, fabricated using a low-cost 4-metal conventional 350 nm CMOS process, was described, followed by the prototype characterization. A considerable agreement between the simulation results and the measurements was demonstrated, confirming the appropriateness of the presented design methodology for the use in the design process of miniaturized inductive sensor systems. The key novelty and advantage of the prototyped microsystem is its monolithic integration; sensor elements and analog front-end are jointly fabricated on a single silicon die using a non-modified cost-efficient CMOS process. This assures ease and repeatability of the fabrication of such microsystems, as well as their easy implementation in target encoder applications. By employing inductive technology, the need for an external light or magnetic field source as required by conventional optical or magnetic position encoders, is eliminated. The prototype demonstrates a resolution of at least 20 µm using both steel and copper measurement scales. The best performance (sensitivity of 0.99 V/mm and RMS nonlinearity error of 6.89 µm) was achieved at 4 MHz operating frequency with a scale fabricated as a conventional PCB with 35 µm copper plating. The system directly outputs two standard DC quadrature outputs, which can be interpolated using a standard arctangent method to obtain a linear position signal. 5.2. Outlook To the best of our knowledge, there are no other comprehensive reports of such devices (integrated incremental displacement measurement system operating with microtransformers thoroughly fabricated in CMOS technology), in the available literature, so a direct comparison is difficult to make. This work should therefore be regarded as a proof of concept and feasibility of such device, as well as a presentation of suitable design and modeling methodology. Based on reports presenting many small scale, yet non-integrated eddy-current displacement sensors with submicrometer resolutions (e.g., [18]—20 nm, [17]—0.5 nm, [9]—120 nm), we believe that with further improvements focusing on the processing electronics, such integrated design will allow to approach its resolution limit of few µm, set by the resistance of the microtransformer secondary winding and the desired movement speed. This will make the system comparable to conventional inductive [37] and magnetic incremental encoders [38], both types reaching resolutions close to 1 µm. As the system is able to operate with non-ferromagnetic scales, it does not suffer from hysteresis, which presents another disadvantage of magnetic systems [5,38]. The main goal of the proposed system is not to achieve extreme measurement resolutions provided by optical encoders (down to 1 nm [8]), but to find its use in applications requiring high cost efficiency,

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which is enabled by monolithic CMOS fabrication. The presented work can also serve as a basis and encouragement for further research in the field. We plan to continue our work on integrated inductive microsystems, in which the design methodology introduced in this article will be of key importance. Acknowledgments: The authors thank to Daniele Bertocchi and Boštjan Fink for preparing the layout of prototype integrated circuits. This work has been supported in part by Slovenian Research Agency and RLS d.o.o. Author Contributions: M.P. designed the microstructures and integrated circuits, carried out the analysis and simulations, and prepared the manuscript. J.T. supported the preparation of the manuscript and contributed to the microsystem design process. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations FEM IC CMOS ASIC ESD PCB THD GDS LPF RMS

Finite Element Method Integrated Circuit Complementary Metal Oxide Semiconductor Application Specific Integrated Circuit Electrostatic Discharge Printed Circuit Board Total Harmonic Distortion Graphic Database System (an industry standard file format for IC layout database exchange) Low-Pass Filter Root Mean Square

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