A Capacitive 3-Axis MEMS Accelerometer for Medipost: a Portable System Dedicated to Monitoring Imbalance Disorders

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Article A Capacitive 3-Axis MEMS Accelerometer for Medipost: A Portable System Dedicated to Monitoring Imbalance Disorders

Michał Szermer * , Piotr Zaj ˛ac,Piotr Amrozik, Cezary Maj, Mariusz Jankowski, Grzegorz Jabło ´nski , Rafał Kiełbik, Jacek Nazdrowicz, Małgorzata Napieralska and Bartosz Sakowicz

Department of Microelectronics and Computer Science, Lodz University of Technology, 93-005 Lodz, Poland; [email protected] (P.Z.); [email protected] (P.A.); [email protected] (C.M.); [email protected] (M.J.); [email protected] (G.J.); [email protected] (R.K.); [email protected] (J.N.); [email protected] (M.N.); [email protected] (B.S.) * Correspondence: [email protected]; Tel.: +48-42-631-2722

Abstract: The constant development and miniaturization of MEMS sensors invariably provides new possibilities for their use in health-related and medical applications. The application of MEMS devices in posturographic systems allows faster diagnosis and significantly facilitates the work of medical staff. MEMS accelerometers constitute a vital part of such systems, particularly those intended for monitoring patients with imbalance disorders. The correct design of such sensors is crucial for gathering data about patient movement and ensuring the good overall performance of the entire system. This paper presents the design and measurements of a three-axis accelerometer Citation: Szermer, M.; Zaj ˛ac,P.; dedicated for use in a device which tracks patient movement. Its main focus is the characterization Amrozik, P.; Maj, C.; Jankowski, M.; Jabłoński,G.; Kiełbik, R.; of the sensor, comparing different designs and evaluating the impact of the packaging and readout Nazdrowicz, J.; Napieralska, M.; circuit integration on sensor operation. Extensive testing and measurements confirm that the designed Sakowicz, B. A Capacitive 3-Axis accelerometer works correctly and allows identifying the best design in terms of sensitivity/stability. MEMS Accelerometer for Medipost: Moreover, the response of the proposed sensor as a function of the applied acceleration demonstrates A Portable System Dedicated to very good linearity only if the readout circuit is integrated in the same package as the MEMS sensor. Monitoring Imbalance Disorders. Sensors 2021, 21, 3564. https:// Keywords: MEMS accelerometer; ASIC readout circuit; portable system; imbalance disorders doi.org/10.3390/s21103564

Academic Editor: Daniel Arvidsson 1. Introduction Received: 16 April 2021 Research into microelectromechanical systems (MEMS) is one of the most dynamically Accepted: 20 May 2021 Published: 20 May 2021 developing branches in microelectronics [1–4]. The devices can be found almost every- where, from smartphones and the internet-of-things to clothes and many other applications.

Publisher’s Note: MDPI stays neutral Most importantly, MEMS accelerometers are used in GPS-aided navigation systems [5–7], with regard to jurisdictional claims in and military [8], automotive [9], aerospace [10] and medical devices [11–14]. Thanks to published maps and institutional afﬁl- their miniature size they can also be easily used in healthcare applications. For example, iations. two devices, SwayStar [15] and VertiGuard [16], can be used to monitor the gaits of patients by examining their movement. We propose a similar system developed in cooperation with the Medical University of Lodz [17,18] for patients with imbalance disorders. Medipost is a small, compact device which can be easily mounted on the back of the patient’s belt. It is supplied by a Li-Ion battery and can be used at home. Medipost communicates via Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Bluetooth with a smartphone [19], on which any received data is preliminarily processed This article is an open access article by a dedicated application. Next, the data is transmitted to a PC located in a medical centre, distributed under the terms and where the patient’s movement can be monitored by a doctor and the proper treatment conditions of the Creative Commons administered. Apart from monitoring movement, the system can also prevent serious Attribution (CC BY) license (https:// injury by triggering a warning when the patient is about to fall. creativecommons.org/licenses/by/ On its basic level, Medipost uses MEMS inertial sensors and dedicated integrated 4.0/). readout circuits for measuring the acceleration and angular velocity of certain parts of

Sensors 2021, 21, 3564. https://doi.org/10.3390/s21103564 https://www.mdpi.com/journal/sensors Sensors 2021, 21, x FOR PEER REVIEW 2 of 16

Sensors 2021, 21, 3564 2 of 16 On its basic level, Medipost uses MEMS inertial sensors and dedicated integrated readout circuits for measuring the acceleration and angular velocity of certain parts of the patient’s body, which allows precise evaluation of their movement and potential move- the patient’s body, which allows precise evaluation of their movement and potential ment-related health issues. movement-related health issues. However, the correct operation of the entire system requires the proper design of an However, the correct operation of the entire system requires the proper design of accelerationan acceleration sensor. sensor. Therefore, Therefore, in this in paper this paperwe present we present and characterize and characterize a custom a customaccel- erometeraccelerometer designed designed specifically speciﬁcally for the Medipost for the Medipost device. The device. paper The is organized paper is organized as follows: as Sectionfollows: 2 presents Section2 thepresents operation the operation principle principleand the design and the of design the 3-axis of the accelerometer; 3-axis accelerome- Sec- tionter; 3 Section describes3 describes the simulations, the simulations, as well asas well the measurement as the measurement results results of the ofsensor; the sensor; and Sectionand Section 4 presents4 presents our Conclusions. our Conclusions.

2.2. MEMS MEMS Accelerometer Accelerometer Design Design and and Manufacturing Manufacturing 2.1.2.1. Capacitive Capacitive Accelerometer Accelerometer Operation Operation Principle Principle and and Design Design WeWe designed designed a a3-axis 3-axis accelerometer, accelerometer, consis consistingting of threethree independentindependentcapacitive capacitive single- sin- gle-axisaxis accelerometers, accelerometers, which which operates operates by measuring by measuring changes changes in capacitance in capacitance caused caused by applied by appliedacceleration. acceleration. The accelerometer The accelerometer itself consists itself ofconsists a seismic of massa seismic hanging mass on hanging springs overon springsa substrate over a [20 substrate]. Combs [20]. are Combs attached are to attach the mass,ed to formingthe mass, a forming movable a partmovable of the part sensor. of theThe sensor. same numberThe same of number parallel of combs parallel is in combs turn connected is in turn to connected a frame which to a frame forms which a ﬁxed formspart ofa thefixed sensor, part thusof the forming sensor, two thus capacitors forming with two movablecapacitors and with ﬁxed movable plates on and both fixed sides platesof the on seismic both sides mass. of The the concept seismic ofmass. a single-axis The concept accelerometer of a single-axis is shown accelerometer in Figure1. is In shownthe sensor in Figure described 1. In the in this sensor paper, described two accelerometers in this paper, have two beenaccelerometers designed according have been to designedthis principle: according one to operating this principle: in the one X-axis oper andating another in the in X-axis the Y-axis. and another in the Y-axis.

Anchor

Fixed Spring Fingers

Seismic Mass

d-x Ctop Ctop d-x

Fixed Fixed Comb Comb

d+x Cbottom Cbottom d+x

Spring Movable Fingers Anchor

FigureFigure 1. 1.TheThe operation operation principle principle of the of thecapacitive capacitive accele accelerometerrometer acting acting in the in X the and X andY axes Y axes(not to (not scale).to scale).

AsAs shown shown in in Figure Figure 1,1, the design consists ofof twotwo capacitors:capacitors: CCtop andand C bottombottom. .When When accelerated,accelerated, the the mass mass moves, andand oneone of of the th capacitancese capacitances increases increases while while the otherthe other decreases de- creasesdue to due the to displacement the displacement of the of ﬁngers. the finger Thes. difference The difference between between these these capacitances capacitances can be canmeasured, be measured, thus the thus magnitude the magnitude of acceleration of acce canleration be derived. can be Thederived. value The of the value capacitances of the capacitancesCtop and Cbottom Ctop andafter C accelerationbottom after acceleration is applied is is applied given by: is given by:

11 11 𝐶C =𝜀𝑛𝑆= εnS ,, C 𝐶==𝜀𝑛𝑆εnS (1)(1) top 𝑑−𝑥d − x bottom d𝑑+𝑥+ x

where S is the surface of a single finger, d is the distance between fingers, x is the displacement caused by acceleration, n is the number of fingers which form a single capacitor plate and ε is the electrical permittivity of the material between the fingers.

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where S is the surface of a single finger, d is the distance between fingers, x is the displacement caused by acceleration, n is the number of fingers which form a single capacitor plate and ε is the electrical permittivity of the material between the fingers. As the principle of operation of such a sensor is well described in literature [21], we have only presented the most important equations necessary to understand the accelerometer’s behaviour; these are given in Appendix A of this paper. Although we have also designed a Z-axis accelerometer, it has to be emphasized that it has a slightly different design to the X- and Y-axis accelerometers described above [22]. left right Sensors 2021, 21, 3564While it is also constructed with two combs, which form C and C capacitors (Figure 3 of 16 2), the design of the seismic mass is asymmetric to obtain a capacitance change upon acceleration. In this design, the mass with movable fingers rotates in the XZ plane, which is presented in Figure 2. Two types ofAs fingers the principle are used of in operation this desi ofgn: such normal a sensor fingers, is well as describedfixed combs, in literature and [21], we thinned fingershave (with only reduced presented height), the most as mova importantble combs. equations When necessary acceleration to understand is applied, the accelerom- only one capacitanceeter’s behaviour; changes thesesignificantly, are given because in Appendix its correspondingA of this paper. comb moves out from the overlappingAlthough area, wethus have allowing also designed the direction a Z-axis of the accelerometer, applied acceleration it has to be to emphasized be that determined. However,it has a slightly the disadvantage different design of such to the an X-approach and Y-axis is that accelerometers it demonstrates described only above [22]. half the sensitivityWhile with it is respect also constructed to X- and Y-axis with twoaccelerometers. combs, which This form asymmetric Cleft and comb- Cright capacitors drive design (Figurewas necessary2), the designbecause of it theis impossible seismic mass to create is asymmetric an electric to connection obtain a capacitanceon the change substrate: theupon chosen acceleration. technology In does this design,not allow the the mass deposition with movable of a metal ﬁngers layer rotates on the in the XZ plane, substrate in awhich cavity. is presented in Figure2.

Fixed Movable Fixed Combs Combs Combs

C C Frame left right Frame

Seismic Mass

FigureFigure 2. The2. The operation operation principle principle of of the the capacitive capacitive accelerometer accelerometer in thein the Z axisZ axis (rotation (rotation not not to scale).to scale). Two types of fingers are used in this design: normal fingers, as fixed combs, and thinned The finalfingers version (with of the reduced 3-axis accelerometer height), as movable is composed combs. of Whentwo accelerometers acceleration is based applied, only one on a standardcapacitance comb-drive changes design significantly, (Figure 3a) becauseand one its accelerometer corresponding based comb on moves an asym- out from the over- metric comb-drivelapping design area, (Figure thus allowing 3b). The thefirst direction two allow of the the acceleration applied acceleration to be measured to be determined. in the X and However,Y axes and the the disadvantage third in the ofZ ax suchis. Additionally, an approach isas that the itfirst demonstrates manufacturing only half the sen- run of the devicesitivity was with a trial, respect it was to decided X- andY-axis to test accelerometers. two different designs This asymmetric for X- and Y-axis comb-drive design accelerometers.was The necessary X-axis device because was it ismade impossible 1.5 times to larger create than an electric the Y-axis connection one: conse- on the substrate: quently, it hasthe noticeably chosen technology higher sensitivity does not but allow at the the cost deposition of a longer of aresponse metal layer time. on the substrate in a cavity. The final version of the 3-axis accelerometer is composed of two accelerometers based on a standard comb-drive design (Figure3a) and one accelerometer based on an asymmetric comb-drive design (Figure3b). The first two allow the acceleration to be measured in the X and Y axes and the third in the Z axis. Additionally, as the first manufacturing run of the device was a trial, it was decided to test two different designs for X- and Y- Sensors 2021, 21, x FOR PEER REVIEW 4 of 16 axis accelerometers. The X-axis device was made 1.5 times larger than the Y-axis one: consequently, it has noticeably higher sensitivity but at the cost of a longer response time.

(a) (b) Figure 3. Models of the designed accelerometers: (a) X-axis accelerometer; (b) Z-axis accelerometer. Figure 3. Models of the designed accelerometers: (a) X-axis accelerometer; (b) Z-axis accelerometer. 2.2. Dedicated Readout Circuit Design The presented accelerometer requires ReadOut Integrated Circuit (ROIC) [23,24] in order to process signals from the sensor. We designed three different independent structures for each axis with quite small sensitivities (e.g., 0.31 fF/g for Z axis) and differential outputs. Therefore, we designed three independent readout channels optimized for each structure. This approach has the following advantages: • Each structure of the MEMS sensor can have its own dedicated readout circuit whose parameters are tailored to this particular structure. • It allows us to align the bonding pads of the readout circuit with the pads of the sensor. It equalizes the bonding wire lengths and creates a regular, symmetrical connection structure between both dies, minimizing the influence of parasitics. • Each of the three readout channels is digitally configurable, i.e., the parameters of the channel, such as: gain, reference voltages, mismatch compensation, switching frequency, etc., can be easily adapted to application requirements. The ROIC converts the signal from the MEMS sensor (capacitance difference) into voltage to amplify it and to digitize it using an integrated analog-to-digital converter (ADC). It operates in a differential mode and uses switched-capacitor circuits. The digitized signal can be sent via SPI interface to a separate microcontroller, which can then transmit the data wirelessly using Wi-Fi or Bluetooth. More detailed information on the designed ROIC has been given previously [20].

2.3. Manufacturing of the Accelerometer The sensor was designed and manufactured in XFAB MEMS 3D capacitive technology [25]. Its layout and photography are presented in Figures 4 and 5, respectively. Three independent sensors are used, one for each axis. This approach to the design is simpler in comparison to one with a single seismic mass for all axes. It also reduces the cross-axis sensitivity. Moreover, it allows each structure to be optimized individually. One of the disadvantages is the larger size of the accelerometer. The designs of our X-axis and Y-axis sensors follow the classic approach used in capacitive parallel-plate MEMS accelerometers (Figure 6). Meanwhile, the Z-axis sensor has a slightly different design; please refer to [22] for details. Since the sensor structure is differential, special consideration is taken to ensure that the lengths of all signal paths are the same to minimize the impact of parasitic

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2.2. Dedicated Readout Circuit Design The presented accelerometer requires ReadOut Integrated Circuit (ROIC) [23,24] in order to process signals from the sensor. We designed three different independent structures for each axis with quite small sensitivities (e.g., 0.31 fF/g for Z axis) and differential outputs. Therefore, we designed three independent readout channels optimized for each structure. This approach has the following advantages: • Each structure of the MEMS sensor can have its own dedicated readout circuit whose parameters are tailored to this particular structure. • It allows us to align the bonding pads of the readout circuit with the pads of the sensor. It equalizes the bonding wire lengths and creates a regular, symmetrical connection structure between both dies, minimizing the inﬂuence of parasitics. • Each of the three readout channels is digitally conﬁgurable, i.e., the parameters of the channel, such as: gain, reference voltages, mismatch compensation, switching frequency, etc., can be easily adapted to application requirements. The ROIC converts the signal from the MEMS sensor (capacitance difference) into Sensors 2021, 21, x FOR PEER REVIEW 5 of 16 voltage to amplify it and to digitize it using an integrated analog-to-digital converter (ADC). It operates in a differential mode and uses switched-capacitor circuits. The digitized signal can be sent via SPI interface to a separate microcontroller, which can then transmit the data wirelesslycapacitances using on Wi-Fithe sensor or Bluetooth. output. In More addition detailed, all informationstructures are on integrated the designed in an ROIC enclosed has beenpackage given to previouslyprotect them [20 from]. mechanical damage or external interference. Although both the sensor and the ROIC were integrated in the same package to en- 2.3.sure Manufacturing the best performance, of the Accelerometer both were also manufactured in their own separate packages to allowThe sensorthem to was be designed studied separately and manufactured (Figure in 7). XFAB In addition, MEMS 3D we capacitive also receivedtechnology an unpack- [25]. Itsaged layout version and photographyof the sensor are chip presented (a naked in die) Figures to allow4 and 5measurements, respectively. Three to be independentconducted on sensorsa probe are station. used, one for each axis. This approach to the design is simpler in comparison to one with aAll single variants seismic of the mass accelerometer for all axes. Itpackaging also reduces are thegiven cross-axis in Figure sensitivity. 7: the naked Moreover, die with it allowsMEMS each sensor structure only to(bottom), be optimized the MEMS individually. sensor-only One of thestructure disadvantages in a QFN-100 is the larger package size of(right), the accelerometer. and the MEMS The sensor designs bonded of our X-axiswith th ande corresponding Y-axis sensors followreadout the circuit classic in approach the same usedQFN-100 in capacitive enclosure parallel-plate (left). Figure MEMS 8 depicts accelerometers a close-up (Figure view6 ).of Meanwhile,the naked sensor the Z-axis dies. sensor has aThe slightly present different study design; focuses please mostly refer on tothe [22 MEMS] for details. device. Since The main the sensor goal of structure the paper is differential,is not only specialto characterize consideration the designed is taken toaccele ensurerometer, that the but lengths also to of verify all signal the pathsimpact are of theparasitic same tocapacitances minimize the induced impact ofby parasitic the pads capacitances and packaging on the on sensor sens output.or performance. In addition, It allshould structures be emphasized are integrated that in the an enclosedmeasured package capacitances to protect arethem very fromsmall mechanical and output damage signals orcan external be quite interference. easily disrupted by large parasitics.

FigureFigure 4. 4.3-axis 3-axis MEMS MEMS accelerometer accelerometer layout. layout. (right (right) X-axis) X-axis accelerometer, accelerometer, (centre (centre) Y-axis) Y-axis accelerome- accel- erometer, (left) Z-axis accelerometer. ter, (left) Z-axis accelerometer.

Figure 5. 3-axis MEMS accelerometer photography. (right) X-axis accelerometer, (centre) Y-axis accelerometer, (left) Z-axis accelerometer.

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capacitances on the sensor output. In addition, all structures are integrated in an enclosed package to protect them from mechanical damage or external interference. Although both the sensor and the ROIC were integrated in the same package to ensure the best performance, both were also manufactured in their own separate packages to allow them to be studied separately (Figure 7). In addition, we also received an unpack- aged version of the sensor chip (a naked die) to allow measurements to be conducted on a probe station. All variants of the accelerometer packaging are given in Figure 7: the naked die with MEMS sensor only (bottom), the MEMS sensor-only structure in a QFN-100 package (right), and the MEMS sensor bonded with the corresponding readout circuit in the same QFN-100 enclosure (left). Figure 8 depicts a close-up view of the naked sensor dies. The present study focuses mostly on the MEMS device. The main goal of the paper is not only to characterize the designed accelerometer, but also to verify the impact of parasitic capacitances induced by the pads and packaging on sensor performance. It should be emphasized that the measured capacitances are very small and output signals can be quite easily disrupted by large parasitics.

Sensors 2021, 21, 3564 5 of 16 Figure 4. 3-axis MEMS accelerometer layout. (right) X-axis accelerometer, (centre) Y-axis accelerometer, (left) Z-axis accelerometer.

Sensors 2021, 21, x FOR PEER REVIEWFigureFigure 5. 3-axis3-axis MEMS MEMS accelero accelerometermeter photography. photography. (right (right) X-axis) X-axis accelerometer, accelerometer, (centre (centre) Y-axis) Y-axis6 of 16 accelerometer, (left) Z-axis accelerometer. accelerometer, (left) Z-axis accelerometer.

FigureFigure 6. 6.X-axis X-axis accelerometer accelerometer photography. photography.

Although both the sensor and the ROIC were integrated in the same package to ensure the best performance, both were also manufactured in their own separate packages to allow them to be studied separately (Figure7). In addition, we also received an unpack- aged version of the sensor chip (a naked die) to allow measurements to be conducted on a probe station. All variants of the accelerometer packaging are given in Figure7: the naked die with MEMS sensor only (bottom), the MEMS sensor-only structure in a QFN-100 package (right), and the MEMS sensor bonded with the corresponding readout circuit in the same QFN-100 enclosure (left). Figure8 depicts a close-up view of the naked sensor dies. The present study focuses mostly on the MEMS device. The main goal of the paper is not only to characterize the designed accelerometer, but also to verify the impact of parasitic capacitances induced by the pads and packaging on sensor performance. It should be emphasized that the measured capacitances are very small and output signals can be quite easily disrupted by large parasitics.

Figure 7. All variants of the MEMS structure packaging: naked die with MEMS sensor only (bottom), MEMS sensor-only structure in a QFN-100 package (right) and the MEMS sensor bonded with the ROIC in the same QFN-100 enclosure (left).

Figure 8. Close-up views of the naked sensor dies.

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Figure 6. X-axis accelerometer photography. Figure 6. X-axis accelerometer photography.

FigureFigure 7. 7.All All variants variants of of the the MEMS MEMS structure structure packaging: packaging: naked naked die die with with MEMS MEMS sensor sensor only only (bottom (bot-), MEMSFiguretom), MEMS sensor-only7. All variantssensor-only structure of the struct MEMS inure a QFN-100 instructure a QFN-100 packagepackag packageing: (right naked (right) and die) and the with the MEMS MEMS MEMS sensor sensor sensor bonded only bonded (bot- with thetomwith ROIC), the MEMS ROIC in the sensor-only in same the QFN-100same struct QFN-100 enclosureure in enclosure a QFN-100 (left). (left package). (right) and the MEMS sensor bonded with the ROIC in the same QFN-100 enclosure (left).

Figure 8. Close-up views of the naked sensor dies.

FigureFigure 8.8. Close-upClose-up viewsviews ofof thethe nakednaked sensorsensor dies.dies.

3. Simulation Results and Measurements The MEMS accelerometers were designed in Coventor MEMS+ software [26]. The software uses fundamental MEMS-speciﬁc building blocks (combs, anchors, etc.) which are

combined to create a complete design. The simulations of such models are up to 100 times faster than those performed in Finite Element Analysis tools, according to the Coventor MEMS+ developer [27]. Additionally, the Coventor model of the device can be easily exported to Cadence Virtuoso software [28], in which it can be simulated together with the corresponding readout circuit. Table1 lists the sensitivities and ﬁrst eigenfrequencies found for each sensor. In Figure9, the frequency response of the sensor is presented. As expected, the most sensitive structure (X-axis accelerometer) has the lowest eigenfrequency (Equation (A2) in AppendixA). Sensors 2021, 21, 3564 7 of 16

Table 1. List of parameters of the X-, Y- and Z-axis sensors.

Max. Measurable/min. Detectable Resolution at Operating Resonance Frequency Sensitivity Accelerometer Type (Ideal, i.e., no Noise) Acceleration Bandwidth (10 Hz) [kHz] [fF/g] [mg] [mg] X axis 6.043 13.15 ±2.85/5.57 12.8 Y axis 16.321 0.85 ±2.94/5.74 140 Z axis 6.484 0.31 ±4.03/7.87 –

FigureFigure 9.9. FrequencyFrequency responseresponse ofof thethe accelerometer.accelerometer.

3.1. Accelerometer Capacitance Measurements Using Impedance Analyzer In order to characterize the device, static measurements were performed using Summit Sensors 2021, 21, x FOR PEER REVIEW11000/12000 Probe Station (Cascade Microtech, Beaverton, OR, USA). The naked8 die of 16

was placed in the probe station and probes were placed on chip’s pads (see Figure 10). A Keysight E4990A Impedance Analyzer was then used to measure the capacitance of each accelerometer. The obtained results are shown in Table2, which also provides simulated Y-axis 1.446 1.449 values obtained from Coventor MEMS+ for comparison purposes. Good agreement was Z-axis 1.445 1.397 observed between measurements and simulation results.

(a) (b)

FigureFigure 10. The 10. The measurements measurements of the of naked the naked die performed die performed on the on probe the probe station. station. General General view viewof the of device the device on the on probe the probe station (a). Zoomstation of the (a ).probes Zoom placed of the on probes the chip’s placed pads on the (b). chip’s pads (b).

As it is impossible to apply the acceleration to the device placed in the probe station, another method had to be used to measure the responses of the accelerometers to applied loads. The seismic mass was displaced by applying a voltage to one of the capacitances; the induced electrostatic force causes a capacitance change, similar to that obtained by acceleration [29]. The measurement setup is shown in Figure 11. A DC voltage was applied across one capacitance Ctop while the second capacitance Cbottom was measured using the impedance analyser. Following this, the roles of Ctop and Cbotttom were swapped and the measurements were repeated. It was found that the results of such reversed measurements were almost identical to the original ones. 1 DC Power Supply IT6302 Top DC Source

Ctop

Hc High Mass Hp

Cbottom

Lp MEMS Accelerometer Low Bottom

Lc Gnd E4990A Impedance Analyzer Impedance

Figure 11. Measurement setup for the electrostatic actuation of the MEMS accelerometer.

This method allows the capacitances to be measured as a function of the applied DC voltage in the X- and Y-axis accelerometers. This approach is not viable in the case of the Z-axis accelerometer due to its design. The measurements and simulations performed in Coventor MEMS+ and Cadence are compared in Figure 12. In the larger structure (X-axis sensor), a pull-in effect can be observed when a voltage of around 4.7 V is applied between the plates. It was verified that this effect is reversible and does not damage the sensor. In the case of the Y-axis sensor

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Y-axis 1.446 1.449 Z-axis 1.445 1.397

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Table 2. Measurement and simulation results of the nominal capacitance of the X-, Y- and Z-axis accelerometer.

C [pF] Accelerometer 0 Simulations Measurements (a) X-axis 3.070(b) 2.933 Y-axis 1.446 1.449 Figure 10. The measurements of the naked die performed on the probe station. General view of the device on the probe station (a). Z-axis 1.445 1.397 Zoom of the probes placed on the chip’s pads (b).

AsAs it is impossible to to apply apply the the acceleration acceleration to to the the device device placed placed in the in theprobe probe station, station,another another method method had to had be used to be to used measure to measure the responses the responses of the accelerometers of the accelerometers to applied to appliedloads. The loads. seismic The seismicmass was mass displaced was displaced by appl byying applying a voltage a voltage to one toof onethe ofcapacitances; the capacitances;the induced the induced electrostatic electrostatic force forcecauses causes a capacitance a capacitance change, change, similar similar to that to that obtained obtained by byacceleration acceleration [29]. [29 ]. TheThe measurementmeasurement setupsetup isis shownshown inin FigureFigure 11 11.. AA DCDC voltagevoltage waswas appliedapplied acrossacross oneone capacitancecapacitance CCtoptop while thethe secondsecond capacitancecapacitance C Cbottombottom waswas measured using thethe impedanceimpedance analyser.analyser. FollowingFollowing this, this, the the roles roles of of C Ctoptopand and C Cbotttombotttom werewere swapped and the measurementsmeasurements werewere repeated.repeated. ItIt waswas foundfound thatthat thethe resultsresults ofof suchsuch reversedreversed measurementsmeasurements werewere almostalmost identicalidentical toto thethe originaloriginal ones.ones.

DC Power Supply IT6302 Top DC Source

Ctop

Hc High Mass Hp

Cbottom

Lp MEMS Accelerometer Low Bottom

Lc Gnd E4990A Impedance Analyzer Impedance

FigureFigure 11.11. MeasurementMeasurement setupsetup forfor thethe electrostaticelectrostatic actuationactuation ofof thethe MEMSMEMS accelerometer.accelerometer.

ThisThis methodmethod allowsallows thethe capacitancescapacitances toto bebe measuredmeasured asas aa functionfunction ofof thethe appliedapplied DCDC voltagevoltage inin the X- and and YY-axis-axis accelerometers. accelerometers. This This approach approach is isnot not viable viable in inthe the case case of the of theZ-axisZ-axis accelerometer accelerometer due due to its to design. its design. TheThe measurements and and simulations simulations performed performed in in Coventor Coventor MEMS+ MEMS+ and and Cadence Cadence are arecompared compared in Figure in Figure 12. 12In. the In thelarger larger structure structure (X-axis (X-axis sensor), sensor), a pull-in a pull-in effect effect can can be ob- be observedserved when when a avoltage voltage of of around around 4.7 4.7 V V is is appl appliedied between between the plates. It was veriﬁedverified thatthat thisthis effecteffect isis reversiblereversible andand doesdoes notnot damagedamage thethe sensor.sensor. InIn thethe casecase ofof thethe Y-axisY-axis sensorsensor (Figure 12b) the pull-in effect is not observed in the range of applied voltage, because the structure is more rigid. The measurements correlate very well with the simulations.

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Sensors 2021, 21, 3564 9 of 16 (Figure 12b) the pull-in effect is not observed in the range of applied voltage, because the structure is more rigid. The measurements correlate very well with the simulations.

(a) (b) (a) (b) Figure 12. TheFigure value 12 of. The C valuase of a C functionbottom as ofa function applied voltage:of applied (a )voltage X-axis: accelerometer; (a) X-axis accelerometer; (b) Y-axis accelerometer. (b) Y-axis Figure 12. The value ofbottom Cbottom as a function of applied voltage: (a) X-axis accelerometer; (b) Y-axis accelerometer. accelerometer. 3.2. Accelerometer Capacitance Measurements with External Readout Circuit 3.2. Accelerometer Capacitance Measurements with External Readout Circuit TheThe sensitivity sensitivity of of the the MEMS MEMS device device is isaround around 13.15 13.15 fF/g fF/g in the in X-axis the X-axis and andaround around 0.85 fF/g0.85 for fF/g thefor Y-axis. the Y-axis. Measuring Measuring such small such capacitance small capacitance changes changes using a usingKeysight a Keysight E4990A impedanceE4990A impedance analyser can analyser be a challenge can be a challengedue to its limited due to resolution. its limited resolution.Therefore, an Therefore, external readoutan external circuit readout (ERC) circuit was designed (ERC) was and designed built. It and uses built. the Itstandard uses the approach standard approachof applying of aapplying differential a differential sinusoidal sinusoidal signal to signalthe top to and the topbottom and electrodes bottom electrodes of the capacitive of the capacitive sensor andsensor reading and reading the output the output signal signal at the at middle the middle node node (Figure (Figure 13). 13 The). The middle middle node node signal signal is convertedis converted to tothe the voltage voltage V1, V1, whose whose amplitude amplitude should should be be proportional proportional to to the the capacitance capacitance changechange Δ∆C, using aa transimpedancetransimpedance amplifier.amplifier. High High impedance impedance is is ensured ensured at at the the output output of ofthe the transimpedance transimpedance amplifier amplifier using using a voltage a voltage follower. follower. Subsequently, Subsequently, a 47× a 47×gain gain is applied is ap- pliedby the by inverting the inverting amplifier. amplifier. Note that Note the that output the signaloutput is signal a high-frequency is a high-frequency signal; therefore, signal; therefore,in the final in step, the final these step, high these frequencies high freq areuencies removed are removed using an activeusing an peak active detector. peak de- As tector.a result, As the a result, amplitude the amplitude of the output of voltagethe output V3 isvoltage proportional V3 is proportional to ∆C and can to beΔC measured and can beusing measured an oscilloscope. using an oscilloscope.

FigureFigure 13. 13. OperatingOperating principle principle of of the the design designeded external external readout circuit.

The choice of the appropriate voltage Vac and the frequency f depends on the param- The choice of the appropriate voltage Vac and the frequency f depends on the parameters of the measured MEMS device. In our case, it was determined that the use of Vac eters of the measured MEMS device. In our case, it was determined that the use of Vac between 1–3 volts and the frequency between 200–500 kHz produces the best results. between 1–3 volts and the frequency between 200–500 kHz produces the best results. The ERC was used with the probe station (using a similar setup as in Section 3.1). The ERC was used with the probe station (using a similar setup as in Section 3.1). Two complementary input signals were applied by a signal generator. Its outputs were Two complementary input signals were applied by a signal generator. Its outputs were synchronized to provide two sinusoids with the same amplitude and frequency but inverted phases. The signals were applied through probes to the top and bottom MEMS electrodes. The output was read by the probe from the middle electrode and used as an input to the ERC

2 Sensors 2021, 21, x FOR PEER REVIEW 10 of 16

synchronized to provide two sinusoids with the same amplitude and frequency but in- Sensors 2021, 21, 3564 10 of 16 verted phases. The signals were applied through probes to the top and bottom MEMS electrodes. The output was read by the probe from the middle electrode and used as an input to the ERC circuit. To obtain a capacitance change, a variable DC offset voltage was appliedcircuit. together To obtain with a capacitance the input change,signals, generating a variable DC an offsetelectrostatic voltage force was between applied togetherthe accelerometer’swith the input plates. signals, generating an electrostatic force between the accelerometer’s plates. TheThe initial initial measurements measurements were were performed performed on on the the probe probe station station for for the the naked naked die. die. FollowingFollowing this, this, another another set set of ofmeasurements measurements based based on onthe thesame same method method was wasrun for run the for packagedthe packaged chip, chip, with with the probes the probes placed placed on onthe the external external pins pins of ofthe the chip. chip. Finally, Finally, the the same same measurementsmeasurements were were repeated repeated once once more, more, this this time time with with the theMEMS MEMS sensor sensor mounted mounted on the on PCBthe PCBand probes and probes injected injected into the into PCB the PCBpads. pads. FigureFigure 14 14 shows shows the the obtained obtained dependence dependence of the of the amplitude amplitude of the of theoutput output voltage voltage V2 asV2 a function as a function of the of applied the applied voltage voltage offset. offset.Several Several interesting interesting conclusions conclusions can be drawn can be bydrawn analysing by analysing these results. these For results. voltages For voltages below 1.5 below V, the 1.5 output V, the signal output was signal mostly was mostlynoise; however,noise; however, a clear sinusoid a clear sinusoidwas visible was at visiblethe ERC at output the ERC after output exceeding after 1.5 exceeding V. The simi- 1.5 V. larityThe similaritybetween the between curves the for curves the naked for the and naked packaged and packageddie indicates die indicatesthat adding that the adding chip packagethe chip (inserting package (insertinggold wires gold and wires chip pins and chipto the pins signal to the path) signal does path) not produce does not any produce no- ticeableany noticeable difference difference in the results. in the results.Thus, one Thus, may one assume may assumethat even that if evensome ifparasitic some parasitic pack- agepackage capacitances capacitances are added, are added, they are they equal are on equal both on signal both lines signal and lines therefore and therefore do not doinflu- not enceinﬂuence the difference the difference in capacitance. in capacitance. On the On contrary, the contrary, reading reading the sensor the sensor output output from fromthe PCBthe PCBpads padsproduces produces very verydifferent different results: results: for example, for example, for the for highest the highest voltage voltage of 4 V, of the 4 V, measuredthe measured output output voltage voltage amplitude amplitude was about was about 20% lower 20% lower than thanthe one the obtained one obtained for the for nakedthe naked die. die.The Thereason reason is that is that the theoutput output amplitude amplitude depends depends on on the the difference difference between between C and C . Consequently, when the PCB pads and connections introduced additional Ctoptop and Cbottombottom. Consequently, when the PCB pads and connections introduced additional parasitic capacitances in parallel to those two capacitances, the difference between Ctop parasitic capacitances in parallel to those two capacitances, the difference between Ctop and C decreased, causing an error in the readout. and Cbottombottom decreased, causing an error in the readout.

450 400 350 300 250 [mV]

out 200

V Naked 150 die 100 Packaged die 50 Packaged die on PCB 0 0 0.5 1 1.5 2 2.5 3 3.5 4 offset [V]

FigureFigure 14. 14. ComparisonComparison of of results results for for three three sets sets of of me measurementsasurements (for the naked die, for the packagedpack- ageddie anddie and forthe for packagedthe packaged die mounteddie mounted on the onPCB). the PCB). 3.3. Gravitional Acceleration Measurements 3.3. Gravitional Acceleration Measurements As a ﬁnal test, the MEMS chip on the PCB was mounted on a movable lever to study As a final test, the MEMS chip on the PCB was mounted on a movable lever to study the response of the sensor to gravitational acceleration. As in previous measurements, the response of the sensor to gravitational acceleration. As in previous measurements, an an ERC was used to read the voltage output signal proportional to the measured capaci- ERC was used to read the voltage output signal proportional to the measured capacitance tance change. By moving the lever and varying the angle at which the MEMS sensor was change. By moving the lever and varying the angle at which the MEMS sensor was posi- positioned, we were able to determine the dependence of the output voltage on the acceler- tioned, we were able to determine the dependence of the output voltage on the accelera- ation. Four sets of measurements were performed for four different angles (see Figure 15). tion. Four sets of measurements were performed for four different angles (see Figure 15). It can be seen that, especially in the middle of the acceleration range, substantially different It can be seen that, especially in the middle of the acceleration range, substantially differ- values were measured for the same angle (0.5 g) and the dependence is not exactly linear, ent values were measured for the same angle (0.5 g) and the dependence is not exactly as could be expected. However, it should be noted that the measurements were very sus- linear, as could be expected. However, it should be noted that the measurements were ceptible to any external interference. In particular, the signal corresponding to the middle node of the accelerometer was very sensitive to any change in its position with respect to other connections. Even after isolating these connections, the output signal was quite noisy and unstable, which made these measurements challenging. Sensors 2021, 21, x FOR PEER REVIEW 11 of 16

very susceptible to any external interference. In particular, the signal corresponding to the Sensors 2021, 21, 3564 middle node of the accelerometer was very sensitive to any change in its position with11 of 16 respect to other connections. Even after isolating these connections, the output signal was quite noisy and unstable, which made these measurements challenging.

FigureFigureFigure 15. 15.15 The. The measured measuredmeasured output output voltage voltage voltage of theof of the theERC ERC ERC as aas asfunction a afunction function of acceleration.of of acceleration. The measured The measured devicedeviceacceleration was was positioned positioned. The measured at four at four anglesdevice angles (0, was 30, (0, position 60 30, and 60 ed90 and atdegrees). 90four degrees). angles The same(0, The 30, measurements same60 and measurements were re- were peated90 d egreesfour times.). The same measurements were repeated four times. repeated four times.

TheThe results results obtained obtained in in this this section section confirm conﬁrm that, to ensure thethe stabilitystability ofof the the measure- meas- urements,ments, the the readout readout circuit circuit for for capacitive capacitive MEMS MEMS accelerometers accelerometers should should always always be integrated be inte- gratedin the in same the same package package as the as sensor. the sensor. The capacitance The capacitance change change of such of accelerometerssuch accelerometers is very is small,very small, in the rangein the ofrange femtofarads of femtofarads per g, and per therefore g, and therefore the signal the at the signal middle at the node middle of such nodedifferential of such differential sensors is also sensors quite is small also quit ande easily small disruptedand easily by disrupted noise, external by noise, interference, external interference,or the impact or ofthe parasitics. impact of parasitics. ToTo demonstrate demonstrate this, this, the the results results obtained obtained for for the the X-axis X-axis and and Y-axis Y-axis accelerometers accelerometers withwith an an integrated integrated readout readout circuit (ROIC,(ROIC, SectionSection 2.2 2.2)) are are given given in in Figures Figures 16– 16–18.18. The The mea- measurementssurements appear appear to to be be completely completely stable stable and and the the output output has has an an almost almost perfectly perfectly linear lin- eardependence dependence on on the the acceleration. acceleration. The The selected selected tests tests are straightforward,are straightforward, and theirand resultstheir re- are sultseasy are to easy interpret. to interpret. In Figure In 16Figure, ROIC 16, output ROIC wasoutput measured was measured as a function as a function of the tilt of angle. the tiltThe angle. tilting The device tilting used device during used theduring conducted the conducted procedure procedure was calibrated was calibrated both in both degrees in degreesand fractions and fractions of gravitational of gravitational acceleration acceleration (g). The (g). output The output of the of ROIC the ROIC was measuredwas meas- at ured10-degree at 10-degree intervals intervals and the and output the output vs. g fraction vs. g fraction was taken was everytaken 0.05every g. 0.05 To minimize g. To mini- any mizeunwanted any unwanted inﬂuence influence of issues of related issues torelate thed test to the setup, test thesetup, ADC the output ADC output was averaged was av- to eragedproduce to produce individual individual data points data for points each for tested each tilt tested angle tilt and angle g fraction. and g fraction.

700

650

600

550

500

450

ADC readout value ADC readout 400

350

300 0 45 90 135 180 225 270 315 360 Tilt angle [°]

FigureFigure 16. 16. TheThe output output of ofthe the ROIC ROIC as asa function a function of ofthe the tilt tilt angle. angle.

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The presented data were read from the 10-bit ADC built into the ROIC with the MEMSThe Thesensor presented presented at its datainput. data were wereA built-in read read from mismatch thethe 10-bit10-bit compensation ADC ADC built built circuit into into the wasthe ROIC usedROIC with to with theshift MEMSthe the MEMSoutputsensor sensoroffset at its atto input. itsensure input. A built-inthat A built-in zero mismatch accelerati mismatch compensationon compensationproduced circuit an outputcircuit was usedwaslevel used to roughly shift to shift the in output thethe outputmiddleoffset offset of to the ensure to entire ensure that range zero that acceleration(0zero–1023). accelerati For produced theon X-axisproduced an (Figures output an output level16 and roughly level 17) theroughly in ADC the middle in range the of middlecorrespondsthe entire of the range to entire the (0–1023). measurement range (0 For–1023). the range X-axis For of the (Figuresabout X-axis ±2.85 16 (Figures and g, to17 comply) the16 and ADC with 17) range therequirements correspondsADC range of to correspondsthethe methodology measurement to the used measurement range in ofthe about Medipost range±2.85 ofdevice. g, about to comply It ±2.85 can withbeg, observedto requirementscomply that with the ofrequirements theoutput methodology capaci- of thetanceused methodology of in the the MEMS Medipost used sensor in device. the has Medipost a Itquite can regular be device. observed si Itnusoidal can that be the observeddependence output that capacitance on the the output tilt of angle, the capaci- MEMS and tancea clearlysensor of the linear has MEMS a dependence quite sensor regular has on sinusoidala quiteg fraction regular dependence(R2 si= nusoidal0.9996 for on dependence X the axis). tilt angle,Slightly on the and worse tilt a clearlyangle, results and linear in 2 2 aterms clearlydependence of linear linearity ondependenceg (Rfraction2 = 0.9917) (Ron g= werefraction 0.9996 obtained for (R X = axis). 0.9996 forSlightly the for Y-axis X axis). worse accelerometer Slightly results inworse terms (Figure results of linearity 18). in 2 termsThus,(R =ofboth0.9917) linearity the wereMEMS (R2 obtained = sensor0.9917) forand were the the Y-axisobtained correspon accelerometer fording the ROICY-axis (Figure integrated accelerometer 18). Thus, in the both (Figure same the MEMSchip18). Thus,packagesensor both appear and the the MEMS to corresponding work sensor correctly and ROIC andthe maycorrespon integrated be implementedding in the ROIC same inintegrated chip the Medipost package in the appear device. same to chip work packagecorrectly appear and to may work be implementedcorrectly and inmay the be Medipost implemented device. in the Medipost device.

700 700 650 R² = 0.9996 650 R² = 0.9996 600 600 550 550 500 500 450 450

ADC readout value 400

ADC readout value 400 350 350 300 300 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25Acceleration 0 [g] 0.25 0.5 0.75 1 Acceleration [g]

FigureFigure 17. 17. TheThe output output of ofthe the ROIC ROIC of ofthe the X-axis X-axis sensor sensor as asa function a function of ofgravitational gravitational acceleration. acceleration. Figure 17. The output of the ROIC of the X-axis sensor as a function of gravitational acceleration.

515 515 510 510 505 505 500 500 495 495 R² = 0.9917

ADC readout value 490 R² = 0.9917

ADC readout value 490 485 485 480 480 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25Acceleration 0 [g] 0.25 0.5 0.75 1 Acceleration [g]

FigureFigure 18. 18. TheThe output output of ofthe the ROIC ROIC of ofthe the Y-axis Y-axis sensor sensor as asa function a function of ofgravitational gravitational acceleration. acceleration. Figure 18. The output of the ROIC of the Y-axis sensor as a function of gravitational acceleration. 3.4. Comparison of the Three-axis Multiple Sesmic Mass Accelerometers 3.4. Comparison of the Three-axis Multiple Sesmic Mass Accelerometers 3.4. ComparisonTo summarize of the Three-axis our investigations, Multiple Sesmic we compare Mass Accelerometers our design with various accelerometers whoseTo summarize parameters our have investigations, been published we in compare literature our [30 design]. We only with considered various accelerome- sensors with To summarize our investigations, we compare our design with various accelerome- tersthree whose separate parameters one-axis have structures been published and multiple in literature seismic [30]. masses We (threeonly considered seismic masses, sensors one ters whose parameters have been published in literature [30]. We only considered sensors withper three one-axis separate structure). one-axis The structures most important and multiple features seismic of themasses selected (three accelerometers seismic masses, are with three separate one-axis structures and multiple seismic masses (three seismic masses, onecollected per one-axis in Table structure).3. The most important features of the selected accelerometers one per one-axis structure). The most important features of the selected accelerometers are collectedThe range in Table of our 3. accelerometer results from the requirements of its medical application. are collected in Table 3. FollowingThe range the of guidelines our accelerometer from medical results staff, from it was the established requirements that of a rangeits medical of ±2.5 applica- g would The range of our accelerometer results from the requirements of its medical application.be enoughFollowing to adequatelythe guidelines track from the movementmedical staff, of patients. it was established The device that size a is range quite of typical ±2.5 g for tion. Following the guidelines from medical staff, it was established that a range of ±2.5 g wouldthis typebe enough of accelerometer. to adequately The sensitivitytrack the movement (in fF/g) on of the patients. other handThe device is low, assize we is decidedquite would be enough to adequately track the movement of patients. The device size is quite typicalto design for this quite type rigid of accelerometer. structures; this The allowed sensitivity higher (in fF/g) linearity on the and other avoided hand is damaging low, as typical for this type of accelerometer. The sensitivity (in fF/g) on the other hand is low, as

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the sensor in case of excessive accelerations (for example, during a patient’s fall). Still, the sensitivity of the ROIC output (in mV/g) is satisfactory. The obtained linearity is very good; however, we have to emphasize that it was so far only measured in the range of ±1 g (a wider range of measurements is planned for the future).

Table 3. Parameters of three-axis multiple seismic mass accelerometers.

Device Size Range X, Y, Z Sensitivity Nonlinearity Ref. Year [mm × mm] [±g] X, Y, Z X, Y, Z

[31] 1999 4 × 4 1.9 0.4 fF/bit –

25 fF/g [32] 1999 5 × 5 – 25 fF/g – 100 fF/g 6.8 pF/g [33] 2005 7 × 9 1 6.8 pF/g – 2.9 pF/g 105 mV/g 1% [34] 2013 1.57 × 1.73 0.01 ÷ 2 127 mV/g 0.5% 58 mV/g 2.4% 10 0.34% [35] 2015 12 × 7 10 – 0.28% +12, –7 0.41% 0.40% (R2 = 0.9996) 2.85 13.15 fF/g, 701 mV/g for ±1 g range This work 2018 3.95 × 6.55 0.83% (R2 = 0.9917) 2.94 0.85 fF/g, 680 mV/g for ±1 g range 4.03 0.31 fF/g, 496 mV/g –

4. Conclusions This paper presents the design and test results of a 3-axis accelerometer used in a portable system for monitoring imbalance disorders. The device was constructed by combining three independent single-axis accelerometers. As the first manufacturing run was only a trial, with a second, final run being planned, the accelerometers for the X- and Y-axes differed in size to explore the design space. Our findings indicate that the larger structure, i.e., the X-axis, is better suited for the application, as it provides higher sensitivity and its lower bandwidth is acceptable. Initially, we performed an extensive characterization of the MEMS sensor without the ROIC. First, the measurements of the sensor capacitance as a function of applied voltage showed good agreement with software simulations; even the pull-in effect was correctly predicted. Following this, we tested the X-axis accelerometer in three configurations: as a naked die, a packaged die, and as a package mounted on the PCB. It was discovered that adding a package does not introduce any noticeable changes in the sensor output; however, a visible difference in the results was observed for the sensor mounted on the PCB compared to the two previously analysed cases. Thus, it may be concluded that when splitting the system into separate MEMS and ROIC packages, the weak capacitive MEMS sensor signal is affected by the parasitics of PCB connections and pads, causing a significant error in the output value (up to 20% in the analysed case). Our findings indicate that to obtain the best performance, the capacitive accelerometers intended for the MEMS should be designed with an integrated ROIC. This was further proved by testing X-axis and Y-axis accelerometers with the ROIC integrated in the same package: a very stable output and reproducible measurements were obtained, and a very good linearity was observed in the analysed ±1 g range. Sensors 2021, 21, 3564 14 of 16

5. Patents Two relevant patents were granted by The Patent Ofﬁce of the Republic of Poland: • Three-axis acceleration sensor layout in XMB10 MEMS technology (INNOREH MEMS C1), Authors: Szermer, M., Maj, C., Zaj ˛ac,P., Nazdrowicz, J. Application Number: S.0071, Application Date: 03.02.2021 • Readout integrated circuits layout for a three-axis acceleration sensor in CMOS 180 nm technology (INNOREH ASIC C1), Authors: Amrozik, P., Kiełbik, R., Za- j ˛ac,P., Jankowski, M., Jabło´nski,G. Application Number: S.0072, Application Date: 3 February 2021.

Author Contributions: Conceptualization, M.S., P.Z. and P.A.; methodology, M.S., P.Z., P.A., C.M., M.J, G.J., R.K. and J.N.; software, P.A.; validation, M.S., P.Z., P.A. and M.J.; formal analysis, M.S., P.Z., P.A., C.M. and G.J.; investigation, M.S., P.Z., P.A., C.M., M.J., G.J., R.K. and J.N.; resources, P.A.; data curation, P.A.; writing—original draft preparation, M.S. and P.Z.; writing—review and editing, P.A., C.M., M.J., G.J., R.K., J.N. and M.N.; visualization, M.S. and P.Z.; supervision, M.S. and B.S. All authors have read and agreed to the published version of the manuscript. Funding: Results presented in the paper are supported by the project STRATEGMED 2/266299/19NC BR/2016 funded by The National Centre for Research and Development in Poland. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not available. Acknowledgments: The Authors would like to express their gratitude to Aleksander Mielczarek for his help to solve the manifold technical problems during the development of the system. We would also like to thank Edward Lowczowski, BSc. for English correction. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Appendix A The operation principle of the presented accelerometer can be described by the following equation: d2x(t) m + kx(t) = ma (t) (A1) dt2 x where m is the mass of the movable part of the accelerometer, k is a suspension stiffness, x(t) is a position of the seismic mass along the X axis as a function of time and ax(t) is the value of the component of the acceleration vector parallel to the X axis. On the basis of Equation (A1), the eigenfrequencies can be obtained by the following formula: r 1 k f = (A2) 0 2π m The above equations are valid when the sensor operates in a vacuum. The air surround- ing the sensor has an inﬂuence on its movement and it is necessary to add an additional term responsible for damping to the Equation (A1):

d2x(t) dx(t) m + b + kx(t) = ma (t) (A3) dt2 dt x where b is the damping coefﬁcient. According to this equation, we can see that damping force is proportional to the seismic mass velocity. Although this is true if the sensor is located alone in the air (i.e., without the package), this is not the case if it is placed in a small package with very small distance from the frame: the air in the gap compresses or expands during movement, which is a nonlinear phenomenon and has little to do with the most-common viscous damping effects. Sensors 2021, 21, 3564 15 of 16

In the literature, this phenomenon is known as a squeeze-film damping effect [36,37]. This effect has a small influence on the movement of the seismic masses in sensors for the X- and Y-axis, where fingers are used to create the capacitor plates. In these sensors the bandwidth is much wider than in the sensors in the Z-axis, where the damping is much higher. If we add the following components to the Equation (A3):

k b ω2 = and β = (A4) 0 m 2m We obtain the following equations:

d2x(t) b dx(t) k + + x(t) = a (t) (A5) dt2 m dt m x

.. . 2 x + 2βx + ω0 x = ax(t) (A6) 2 where ω0 is a pulsation of undamped vibrations and β is the normalized damping factor. Fourier transformation of Equation (A6) results in the following equation:

2 2 ω x(jω) + j2βωx(jω) + ω0 x(jω) = ax(jω) (A7)

Next, we can calculate the frequency response of the model:

x(jω) 1 T(jω) = = (A8) ( ) 2 2 ax jω ω0 + ω + j2βω It is possible to obtain the amplitude and phase characteristics from Equation (A8) by calculating the modulus and argument of the above expression, respectively. If β < ω0, we receive the resonant curve with the following resonance frequency: q 2 2 ω0 − β f = (A9) r 2π Hence, the natural frequency decreases as damping increases. If the damping is sufﬁciently strong, no resonance will occur at all.

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