Design of Interface Circuits for Capacitive

Sensing Applications

by Fatemeh Aezinia

M.A.Sc., University of Tehran, 2006 B.Sc., University of Tehran, 2003

Thesis Submitted In Partial Fulfillment of the

Requirements for the Degree of

Doctor of Philosophy

in the

School of Mechatronic Systems Engineering

Faculty of Applied Sciences

Fatemeh Aezinia 2014

SIMON FRASER UNIVERSITY Summer 2014

ii

Approval

Name: Fatemeh Aezinia

Degree: Doctor of Philosophy

Title of Thesis: Design of Interface Circuits for Capacitive Sensing Applications

Examining Committee: Chair: Gary Wang Professor

Behraad Bahreyni, P. Eng. Senior Supervisor Assistant Professor

Shawn Stapleton, P. Eng. Supervisor Professor School of Engineering Science

Mehrdad Moallem, P. Eng. Supervisor Professor

Ash Parameswaran, P. Eng. Internal Examiner Professor School of Engineering Science

Kambiz Moez, P. Eng. External Examiner Associate professor, Department of Electrical and Computer Engineering University of Alberta

Date Defended/Approved:

August 08, 2014

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Partial Copyright Licence

iv

Abstract

This thesis focuses on the design of integrated readout circuits for differential

capacitive sensing applications. Such circuits are needed especially for interfacing with

microsensors where capacitive transduction is predominantly used. The result of this

research is the development of common framework for interface circuitries suitable for

different sensing applications. These interface circuits were designed and fabricated in

standard Complementary Metal-Oxide-Semiconductor (CMOS) processes and can be

integrated into the design of various sensing systems. The proposed circuits in this work

are characterized by high dynamic range, low power consumption, and adjustable

sensing range. Such circuits promote easy-to-use user interfaces while having a low

cost.

Three different circuit designs were proposed and form the highlights of this

thesis. The first interface circuit is a novel realization of a synchronous demodulation

technique. The main advantage of the proposed circuit compared to state-of-the-art is

that it has a high sensing dynamic range of 112 and is capable of measuring capacitance as small as30 with a total power consumption of8 .

Low power consumption is one of the most important design criteria for portable

sensing systems besides accuracy and precision. Following this requirement, low power

consumption is the main criterion in the second circuit proposed in this work. This circuit

uses a switch-based capacitance-to-voltage converter that is designed and fabricated in

0.35 CMOS technology. This circuit had a low power consumption of600 . Its simple structure offers area and power advantages over the more complex circuits. In

addition, its ratiometric sensing feature provides an adjustable sensing range which can

be tuned for different applications. This circuit can detect capacitances as small

as230 in 1 range of capacitance.

To reduce the effect of parasitics on the circuit performance and improve the

linearity, the design of the second circuit was enhanced. By using an additional block

and an analog divider, the sensitivity of the circuit to parasitics was significantly reduced.

On the other hand, a time based output allowed for the elimination of the analog buffers.

The fabricated circuit consumed a total power of only720 and was fabricated in

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0.35 CMOS technology. Another advantage of this circuit over the previous designs is that the pulse-width output signal of this circuit can be more easily digitized.

The proposed circuits in this thesis have been tested with different types of

sensors including humidity, motion, and variable MEMS capacitors. For all of them also,

the measurement results are found to be in good agreement with the analytic and

simulation results. These circuits can be used as standalone chips or can be integrated

into the design of larger sensing systems.

Keywords: Interface circuit; capacitive sensors; wide dynamic range; low power consumption

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Dedication

To my mother, father, and my husband for

their endless love and support

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Acknowledgements

I would not have been able to make it to this point without the support of my supervisor

Dr. Behraad Bahreyni. His patience, generous help, and wise suggestions helped me a

lot during my PhD studies. Other than his thoughtful guidance throughout my research

work, he taught me a lot about technical writing and technical presentation skills. I also

thank, Dr. Shawn Stapleton and Dr. Mehrdad Moallem for their helpful comments and

technical suggestions through my proposal defence. I also want to thank my examiners,

Dr. Ash Parameswaran and Dr. Kambiz Moez for accepting to be on my committee

despite their busy schedule and giving thoughtful comments and advice.

I would also like to thank anonymous reviewers of my research papers for their

comments which helped me improve the quality of my works. Thanks to the computing

system staffs at SFU, especially Chao Cheng, and fabrication team at CMC

Microsystems for their helps in computing problem solving and their supports through

the hard time before the deadlines. Further, I thank faculty, staff, and all graduate

students in both School of Engineering Science and Mechatronic Systems Engineering

at SFU. Every one of these people has helped me in my studies. Also thanks to NSERC

Canada, Nokia Corporation, and IMRIS Company which supported part of this work

through Grant.

I would also like to thank all my friends who gave me the energy all the time to work and

all members of IMUTS lab for their supports and encouragements.

Finally, I wish to thank my beloved parents and sisters for their never ending love that

always filled my heart with energy. Last but not least, I thank my love, Mani, for his

emotional support as a husband, his sincere suggestions as a friend, and his technical

advices as a colleague throughout my PhD program.

And I start this thesis in the name of God...

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Table of Contents

Approval .............................................................................................................................ii Partial Copyright Licence .................................................................................................. iii Abstract .............................................................................................................................iv Dedication .........................................................................................................................vi Acknowledgements .......................................................................................................... vii Table of Contents ............................................................................................................ viii List of Tables ..................................................................................................................... x List of Figures....................................................................................................................xi List of Acronyms ............................................................................................................. xvii 

1.  Introduction ............................................................................................................ 1 1.1.  Background .............................................................................................................. 1 1.2.  Motivation ................................................................................................................. 3 1.3.  Organization of the thesis ........................................................................................ 4 

2.  Literature review..................................................................................................... 5 2.1.  Capacitive sensing ................................................................................................... 5 

2.1.1.  Basic configuration of capacitive sensors ..................................................... 5 2.1.2.  Differential capacitive sensing ...................................................................... 8 2.1.3.  Capacitive sensing based on coplanar electrodes ....................................... 8 

2.2.  Applications of capacitive sensing systems ........................................................... 10 2.3.  Interface electronics for capacitive microsensors .................................................. 19 

2.3.1.  Capacitance to voltage converters (C2V) ................................................... 19 2.3.2.  Capacitance to frequency converters (C2F) ............................................... 22 2.3.3.  Capacitance to current converters (C2C) ................................................... 24 2.3.4.  Capacitance to pulse-width converters (C2PW) ......................................... 26 2.3.5.  Capacitive to digital converters (C2D) ........................................................ 26 

2.4.  Synchronous demodulation-based circuits ............................................................ 28 

3.  Differential capacitive sensing circuit with extended dynamic range ............ 31 3.1.  Conventional synchronous demodulator topology ................................................. 32 3.2.  Expanding the dynamic range of circuits based on synchronous

demodulation .......................................................................................................... 43 3.3.  Circuit design ......................................................................................................... 43 3.4.  Simulation results ................................................................................................... 52 3.5.  Experimental results ............................................................................................... 57 

4.  Low power differential capacitance sensing ..................................................... 62 4.1.  Circuit design ......................................................................................................... 63 4.2.  Simulation result ..................................................................................................... 70 4.3.  Experimental Results ............................................................................................. 76 

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5.  Linear, low power, capacitive sensing circuit with insensitivity to parasitics .............................................................................................................. 87 

5.1.  Circuit topology ...................................................................................................... 87 5.2.  Simulation results ................................................................................................... 95 5.3.  Experimental results ............................................................................................. 100 

6.  Conclusions and future work ............................................................................ 107 6.1.  Summary of results .............................................................................................. 107 6.2.  Future works ........................................................................................................ 108 6.3.  Publications .......................................................................................................... 109 

References ................................................................................................................... 111  

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List of Tables

Table 3-1.Circuit characteristics and comparison ........................................................... 60 

Table 4-1. Minimum measurable capacitance ................................................................ 83 

Table 4-2. Interface circuit characteristics and comparison. ........................................... 85 

Table 5-1. Minimum measurable capacitance .............................................................. 104 

Table 5-2. Interface circuit characteristics and comparison. ......................................... 105 

xi

List of Figures

Figure 2.1. Capacitor with two parallel plates. .................................................................. 6 

Figure 2.2. A simple structure of a distance-type capacitive sensor along with the curves showing capacitance and the related impedance value versus the gap displacement. ..................................................................................... 6 

Figure 2.3. A simple structure of two-parallel electrodes with overlapping. ...................... 7 

Figure 2.4. Parallel plate capacitor with guard ring. .......................................................... 7 

Figure 2.5. Two parallel plate capacitor in an area-type sensor. ...................................... 8 

Figure 2.6. A simplified structure of a differential capacitive sensing. ............................... 9 

Figure 2.7. Coplanar-plate capacitive sensing. ................................................................. 9 

Figure 2.8. 2D capacitive position sensing by coplanar electrodes. ................................. 9 

Figure 2.9. A capacitive liquid-level detector. .................................................................. 11 

Figure 2.10. Cross-sectional view of a capacitive proximity sensor. ............................... 11 

Figure 2.11. Lateral (Y-direction) movement in comb structure. ..................................... 13 

Figure 2.12. Transverse (X direction) motion in comb structure. .................................... 13 

Figure 2.13. Cross-sectional view of a finger in a comb structure before on top and after rotation at the bottom. .................................................................... 14 

Figure 2.14. Simplified structure of a capacitive strain sensor and the fabricated device. © [2003] IEEE [65] ............................................................................ 15 

Figure 2.15. Transverse movement in capacitive sensors based on comb structure. ....................................................................................................... 16 

Figure 2.16. The SEM micrograph of a typical torsional accelerometer on left, Close-up of a torsional beam on right © [1998] IEEE [61]. ........................... 16 

Figure 2.17. Schematic of a capacitive humidity sensor, close-up view of the upper, lower electrodes and polyimide column © [2000] IEEE [70]. ............. 17 

Figure 2.18. Schematic of the sensing and reference capacitor made from the two metal layers of the CMOS process. © [2002] IEEE [72]. ........................ 18 

Figure 2.19. Top view of a fully fabricated pressure sensor on left and cross-sectional view on right. © [2011] IEEE [49] ................................................... 18 

xii

Figure 2.20. AC bridge sensing circuit. ........................................................................... 20 

Figure 2.21. Rectifier-based capacitive sensing system including two current sense amplifiers, two diode rectifiers and an instrumentation amplifier. ....... 21 

Figure 2.22. Readout circuit using switched capacitor charge amplification. .................. 22 

Figure 2.23. Basic Colpitt Oscillator Circuit. .................................................................... 23 

Figure 2.24. Capacitance to frequency converter using an oscillator. ............................ 24 

Figure 2.25. Schematic of a capacitance to current converter. ....................................... 25 

Figure 2.26. Schematic block diagram of a readout circuit based on pulse width modulation. .................................................................................................... 26 

Figure 2.27. Basic circuit diagram of a C2D convertor on top, The related signals on bottom. ..................................................................................................... 27 

Figure 2.28. Synchronous demodulation technique. ....................................................... 29 

Figure 2.29. Reference signal and noise before and after passing through a synchronous demodulator in frequency domain. .......................................... 29 

Figure 2.30. Using synchronous demodulation technique in interface circuit based on trans-impedance amplification. ...................................................... 29 

Figure 3.1. Synchronous demodulation circuit diagram. ................................................. 31 

Figure 3.2. The overall view of the designed circuit. ....................................................... 32 

Figure 3.3. Schematic diagram of TIA. ............................................................................ 33 

Figure 3.4. Schematic diagram of a synchronous modulator .......................................... 33 

Figure 3.5. The overall view of the low-pass filter ........................................................... 34 

Figure 3.6. Three coplanar electrodes needed for monitoring hand movements. ........... 36 

Figure 3.7. Electrical field distribution around a conductive object moving on top of three conductive electrodes is illustrated. ................................................. 36 

Figure 3.8. Capacitance between electrodes ‘1’ and ‘2’ as well as the capacitance between electrodes ‘2’ and ‘3’ simulated in ANSYS. ................ 37 

Figure 3.9. Differential capacitance between and simulated in ANSYS........... 38 

Figure 3.10. Planar electrodes needed for monitoring hand movement. ........................ 38 

Figure 3.11. Readout circuit on PCB. .............................................................................. 39 

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Figure 3.12. Measured results of the proposed sensing system when finger moves laterally. ............................................................................................. 40 

Figure 3.13. Measured results of the proposed sensing system when finger moves vertically ............................................................................................. 41 

Figure 3.14. Measurement results when an object moves laterally. ............................... 42 

Figure 3.15. Experimental results when an object moves vertically. ............................... 42 

Figure 3.16. A differential capacitance measurement circuit based on synchronous demodulation of reference signals. Employing feedback (dashed line/box) let us increase the dynamic range of the circuit significantly. ................................................................................................... 44 

Figure 3.17. Schematic view of the closed-loop configuration. ....................................... 45 

Figure 3.18. Schematic view of the triangular-wave generator. ...................................... 45 

Figure 3.19. Schematic view of the synchronous demodulator. ...................................... 46 

Figure 3.20. Schematic view of the low-pass filter. ......................................................... 46 

Figure 3.21. Schematic view of the amplitude controller. ................................................ 47 

Figure 3.22. Bode plot of the loop gain for the designed chip. ........................................ 49 

Figure 3.23. Structure of the folded cascode operational trans-conductance amplifiers in low pass filter. ........................................................................... 51 

Figure 3.24. Comparison of analytical and simulation results for the noise performance of the circuit. ............................................................................. 53 

Figure 3.25. Simulated results show open- and closed-loop performance of the circuit with different sense capacitors. .......................................................... 54 

Figure 3.26. Schematic view of the switch. ..................................................................... 54 

Figure 3.27. Schematic view of the triangular-wave reference signal generator with switch blocks. ......................................................................................... 55 

Figure 3.28. Layout view of the proposed circuit. ............................................................ 56 

Figure 3.29. Simulated reference signals produced by the circuit in open-loop (top) and closed-loop configurations when . ............................... 56 

Figure 3.30. Photograph of the die fabricated in 0.35μm CMOS technology from Austriamicrosystems. .................................................................................... 57 

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Figure 3.31. Photograph of the off-chip circuitry including the trans-impedance amplifier, demodulator, and the low-pass filter. ............................................. 58 

Figure 3.32. The comb-shaped humidity sensor. ............................................................ 58 

Figure 3.33. Measured reference signals generated by the fabricated chip in open-loop and closed-loop configurations. ................................................... 59 

Figure 3.34. Normalized output voltage versus the differential capacitance ( ) corresponding to different humilities as well as the linearized curve. ............................................................................................ 60 

Figure 4.1. Differential capacitive sensing. ..................................................................... 63 

Figure 4.2. Schematic view of the main block on top, switching signals on the bottom. .......................................................................................................... 64 

Figure 4.3. Output buffer circuitry. ................................................................................... 66 

Figure 4.4. The diagram of the oscillator used for switching signal generation. ............. 67 

Figure 4.5. Digital blocks used for generating the controlling signals. ............................ 68 

Figure 4.6. The schematic of the delay unit. ................................................................... 68 

Figure 4.7. Layout view of the proposed circuit. .............................................................. 71 

Figure 4.8. Noise simulation results of the proposed circuit. ........................................... 71 

Figure 4.9. Schematic view of the transistors inside the switch in C-V converter. .......... 72 

Figure 4.10. Schematic view of the buffer ....................................................................... 73 

Figure 4.11. Simulation waveforms showing the effect of clock feedthrough, output voltage which is decreasing step by step and its close-up view. ....... 73 

Figure 4.12. Simulation waveforms of the clock ( and its close-up. ....................... 74 

Figure 4.13. Simulation results of the proposed circuit including output voltage after and before buffering in two different cases: without common-node capacitance on top and with common-node capacitance on the bottom. .................................................................................................... 75 

Figure 4.14. Optical photograph of the fabricated chip. .................................................. 76 

Figure 4.15. Common-centroid symmetrical structure for building the capacitance in clock generator. ......................................................................................... 76 

Figure 4.16. Circuit’s response to sensing capacitors’ variations. .................................. 77 

xv

Figure 4.17. Simplified model of a displacement sensor with three electrodes. ............. 77 

Figure 4.18. Capacitance variations versus time on top, output voltage on the bottom based on measurement. ................................................................... 78 

Figure 4.19. A microscope photo of the MEMS variable capacitor including the thermal actuator and a close-up view of the comb structure. ........................ 79 

Figure 4.20. Total capacitance of the comb-shaped structure versus finger engagements. ............................................................................................... 80 

Figure 4.21. Theoretical values of the surface capacitance with comb-shaped structure versus finger engagements ............................................................ 81 

Figure 4.22. Changes in capacitance of the comb-shaped structure versus displacement based the simulation results. .................................................. 81 

Figure 4.23. Changes capacitance values versus time. .................................................. 82 

Figure 4.24. Changes in output voltage when the distance between two electrodes becomes smaller over time, based on experimental data and simulation results (dotted points). .......................................................... 82 

Figure 4.25. Noise density the circuit measured by signal analyzer. .............................. 83 

Figure 4.26. Measured output voltage versus the ratiometric change in sensing capacitance. .................................................................................................. 85 

Figure 5.1. The main building block of the proposed circuit. ........................................... 88 

Figure 5.2. Simplified schematic view of the two capacitance-to-voltage converters used for cancelling the parasitic effects. ..................................... 89 

Figure 5.3. Simplified schematic view of the voltage divider. .......................................... 90 

Figure 5.4. Simplified schematic view of the circuits for converting voltage division to a pulse-width using both falling and rising ramp signal. ............... 92 

Figure 5.5. Simplified schematic view of a comparator when is negative. ........... 93 Figure 5.6. Simplified schematic view of a comparator when is positive. ............ 94 Figure 5.7. Simplified schematic view of the pulse width for falling ramp. ...................... 94 

Figure 5.8. Simplified schematic view of the pulse width for rising ramp. ....................... 95 

Figure 5.9. Layout view of the proposed circuit. .............................................................. 95 

Figure 5.10. Simplified view of switching unit on left and a comparator when is positive on right. ............................................................................. 96 

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Figure 5.11. Simplified view of a pulse-width generator when is positive. ........... 96 Figure 5.12. Simulation results of the proposed circuit’s response, when

. and . . ................................................................................ 97 Figure 5.13. Simulation results of the proposed circuit’s response when

. and . . ................................................................................ 97 Figure 5.14. Simulation results for pulse-width versus capacitance variations with

parasitic capacitance and with parasitic capacitance. ................ 98 Figure 5.15. Simulation results for output voltage ( ) versus capacitance

variations with parasitic capacitance and with parasitic capacitance. .................................................................................................. 99 

Figure 5.16. Die photograph. .......................................................................................... 99 

Figure 5.17. Difference between two sensing capacitance generates pulse at the output. ......................................................................................................... 100 

Figure 5.18. Measured results for two variable capacitors, while one of the capacitors ( ) is not changed and the other one ( ) is changed as labeled on the graphs. ................................................................................. 101 

Figure 5.19. Experimental results show the readout response and output pulse-width when displacement of microsensor generates different capacitances ( =8). ................................................................................... 102 

Figure 5.20. Effects of parasitic capacitance on ( =1.65). ............................ 103 Figure 5.21. Effects of parasitic capacitance on pulse-width ( ) testing two

variable capacitance ( =1.65). .................................................................. 103 

Figure 5.22. Readout’s behavior in measuring comb-drive capacitive microsensor. ................................................................................................ 105 

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List of Acronyms

AC Alternating current

ADC Analog to digital converter

AMS Austria-Micro-Systems

C2C Capacitive to current

C2D Capacitive to digital

C2F Capacitive to frequency

C2PW Capacitive to pulse width

C2V Capacitive to voltage

DC Direct current

FET Field effect transistor

GPS Global positioning system

IC Integrated circuit

LVS Layout versus schematic

MEMS Micro electro mechanical systems

MOS Metal-oxide-semiconductor

OTA-C Operational Trans-conductance Amplifier with Capacitance

PEVA poly-ethylene vinyl-acetate

PCB Printed Circuit Board

TIA Trans-impedance amplifier

1

1. Introduction

1.1. Background

Developing Metal-oxide-semiconductor (MOS) transistor which is the

fundamental building block of modern electronic devices, and is ubiquitous in modern

electronic systems is one of the greatest achievements of the 20th century [1], [2], [3].

Over the past decades, continuous miniaturization of transistors has led to integrating a

larger number of transistors on a single chip and production of increasingly complicated

systems [4], [5]. Developing ICs in CMOS technologies launched new applications,

including laptops, cellphones, electronic games consoles, and portable audio

player/recorders, among others.

Fabrication technologies developed for IC industries were later employed to build

micromechanical features with moving structures [6], [7]. These miniaturized integrated

devices or systems that combine electrical and mechanical components are called

micro-electromechanical systems (MEMS) [8], [9]. They have been widely manufactured

for different purposes due to their inexpensive batch fabrication, miniaturized

dimensions, and in some cases, compatibility with CMOS processes. Attention in this

area has predominantly been focused on microsensor development. MEMS sensors

typically convert a physical, chemical, or biological signal from surrounding environment

to an electrical signal [10], [11]. The first commercially fabricated microsensor was a

pressure sensor [12], [13].

In recent decades, MEMS sensors have penetrated different areas of daily life

[14], [15]. They are used for example, in automotive industry in airbags and braking

systems for navigation and safety [16], [17], in biomedical industry for implanted

microsystems [18], in cellphones for motion sensors [19], [20], and in workplaces for air

condition monitoring [21]. Micro-sensors can be categorized according to the basic

2

transduction mechanisms they employ, including piezoresistive [22], piezoelectric [23],

capacitive [24], optical [25], etc.

Among different types of microsensors, capacitive sensors are most commonly

used due to the relatively simple structure, high sensitivity, as well as inherently low

temperature sensitivity [26], [27], [28]. These features make them suitable for a wide

variety of sensing and measurement purposes such as proximity detection, linear and

rotary position monitoring, acceleration detection, pressure measurement, and so on.

However, the high impedance nature of a capacitor at low frequencies makes the sensor

susceptible to parasitics and electromagnetic interference, necessitating careful design

of interface electronics [29].

In capacitive sensors, changes in the electric field between the two electrodes of

a capacitor lead to a change in the capacitance value. These variations usually occur by

changing the area or distance between the electrodes ( or ) or the dielectric constant of the material ( ). These changes are related to the variations in the physical or

chemical quantity of interest. The capacitance value is often measured indirectly and

needs to be converted into a form that can be easily processed and in many cases

digitized [30]. This is the role of the interface circuit. As a result, the growth of the market

of capacitive sensors leads to increasing interest in research and development of

suitable interface circuits.

In most applications, capacitance variations for micromachined devices can be

small [31], [32]. Hence, the interface circuit is required to possess a good noise

performance. In many cases, the capacitance value can vary widely, from less than one

up to tens of . Thus, having a wide sensing range is required. In most cases, the interface circuit needs to remain insensitive to parasitic capacitances. Moreover, the

interface circuits should be linear. Since, many of these micro-sensors are employed in

mobile devices; low-power consumptions is also desired so that the sensing system can

operate for a long period of time on a limited amount of energy [33], [34].

3

1.2. Motivation

Generally, the sensing systems consists of sensors, interface circuits, and signal

conditioning blocks that may include a digital signal processing unit, a display and

communication block. These systems are usually developed for particular purposes and

sometimes require several design iterations for new sensing applications. For many

applications, a common framework exists where a common interface circuit can be

employed, letting only sensors and digital signal processing units be customized for

specific applications. Such a generic readout circuit provides a flexible, easy to use, and

low cost solution for various microsensing systems [35]. Therefore, designing a common

readout circuit lowers the design, prototyping, and manufacturing costs of many sensing

systems.

Several companies have offered solutions to address the needs for a common

interface circuit. For example, AD7745 and AD7746 from Analog Devices are

capacitance-to-digital converters designed for floating sensing capacitors and AD7747

for grounded sensing capacitors [36]. They have high resolution response at the cost of

high measurement time (90 / ) which limits their applications. Their power dissipation is on the order of , making them unsuitable for many wireless devices. In addition, the same company offers AD7150 with lower power consumption (300 ) with 1 resolution over 5 full range sensing, while lower resolutions or wider sensing range may be needed in some applications. Hence, one of the drawbacks of this

interface is not having an adjustable sensing range. A disadvantage for all of these

interfaces is their limited tolerance to parasitic capacitances. Also, often their

performance is very sensitive to the current leakage of the capacitive sensor. On the

other hand, designing interface circuits is pursued by many research groups [37], [38],

[39]. Most of these systems were designed for industrial applications, where very low

power consumption is often not the deciding factor. As a consequence, their power

dissipation is unacceptably high for today’s mobile applications.

This study aims to propose multi-purpose readout architectures for capacitive

sensing systems. These interface circuits were designed based on configurable blocks.

The settings of these blocks can be adjusted according to the needs of different

applications, such as dynamic range, sensitivity, minimum measureable capacitance,

4

and insensitivity to parasitics. The developed topologies were tested with several

capacitive sensors at macro and micro scales in applications such as humidity,

proximity, and displacement sensing.

1.3. Organization of the thesis

This thesis has been divided into six chapters. In Chapter 2, an overview of

principle properties of capacitive microsensors and their applications is provided. This is

followed by a discussion of various techniques for designing interface circuits. Recent

works for improving the performance of the capacitive readout circuit are presented in

details. Three circuit architectures are designed, analyzed, and tested which result in

following chapters.

In Chapter 3, a capacitive measurement circuit based on synchronous

demodulation is described. The basic operation of a synchronous demodulation has

been tested by building a prototype on printed-circuit board. It is tailored for hand-

gesture monitoring for consumer electronic devices such as cell phones. In order to

expand the dynamic range of the circuit, a new feedback mechanism is added to the

original circuit. This circuit was designed in 0.35μ CMOS technology and tested with a humidity sensor.

To reduce the power consumption, an interface circuit based on charge transfer

method was employed. The design and analysis of the switch-based capacitive to

voltage converter is presented in Chapter 4. Simulation and experimental evaluations

are also provided. Having a ratiometric capacitive sensing automatically extends the

sensing range in this design. This topology was implemented in 0.35μ CMOS technology and tested for position sensing. To eliminate the dependence of sensing

response on the parasitic capacitance, a new technique is proposed in Chapter 5. In this

design, a capacitance-to-pulse-width converter is built utilizing the main building block

from the preceding design and addition of a voltage-to-pulse-width converter. Both

simulation and experimental evaluations are provided. This circuit was also fabricated in

0.35μ CMOS technology and tested with a position sensor as well as a variable MEMS capacitor. Conclusions for this study and future work are presented in Chapter 6.

5

2. Literature review

2.1. Capacitive sensing

Capacitive microsensor detects the changes of a physical or chemical stimulus

by measuring the displacement or changes in dielectric properties of a material. In

designing the sensing element structure, care should be taken to determine how the

stimulus influences the capacitance value. The basic principles of capacitive sensors will

be reviewed in the following.

2.1.1. Basic configuration of capacitive sensors

A simple configuration of a capacitive sensor is two parallel electrodes with

distance and overlapping area (Figure 2.1). The capacitance value can be obtained from:

(2.1)

where is the permittivity of the vacuum, and is the relative permittivity of the

dielectric in between the two electrodes.

Capacitive sensing based on change in gap

One of the methods used for capacitive sensing is based on changing the plates

separation distance, (Figure 2.2). The capacitance is inversely proportional to the gap between the electrodes. If capacitive impedance is measured, the behaviour is linear.

However, the output is nonlinear if the capacitance is measured directly instead. Hence,

the direct measurement often requires further signal conditioning to compensate for the

reciprocal relationship between the capacitance and its electrodes’ motion. One of the

6

problems with parallel-plate capacitive sensor is its cross-sensitivity to motion along

other axes. This problem can be remedied by fully enclosing one of the electrodes’

edges by the other (Figure 2.3). Having different dimensions ensure that the two plates

are constantly overlapping and, as a result, mitigating errors caused by movement along

the edges.

Another source of nonlinearity in a parallel plate sensor is the fringe fields along

the edges of the two plates. Adding a guard ring to the sensor leads to a homogenous

electric field between them and reduces the effects of this nonlinearity on measurement

[40]. A guard ring is an extra electrode separated by an insulator that encloses the

sensing electrode in the same potential. As illustrated in Figure 2.4, field lines are

distorted at the edges of the guard electrode but remain uniform between sensing

electrodes.

Figure 2.2. A simple structure of a distance-type capacitive sensor along with the curves showing capacitance and the related impedance value versus the gap

displacement.

Figure 2.1. Capacitor with two parallel plates.

Displacement

Impe

danc

e

Cap

acita

nce

Displacement

7

Figure 2.3. A simple structure of two-parallel electrodes with overlapping.

Although, these methods lessen the nonlinear effects in capacitive sensors, the

main drawback of using these sensors with varying gaps is the limit on useful range of

motion. The reciprocal relationship between motion and capacitance as mentioned

earlier limits the sensing range.

Capacitive sensing based on change in area

Another family of capacitive sensors work based on changes in overlap area

between of the electrodes [41]. A transverse motion sensor is shown in Figure 2.5. The

common area of the two plates is changed by the lateral movement of one of the plates

against the other. Since the area and capacitance values are linearly proportional (see

equation. (2.1)), measured capacitance is linearly related to the displacement. Same as

distance-type sensors, area-type sensors are sensitive to spacing and tilt. Some of the

cross-sensitivity errors can be reduced with modifying the electrode geometries [40]. The

accuracy of these types of sensors depends on mechanical accuracy of the electrodes.

Roughness of the electrodes’ surface, deformation, and varying distance between them

can lead to nonlinear effects on these types of measurements.

Figure 2.4. Parallel plate capacitor with guard ring.

8

Capacitive sensing based on change in dielectric properties

Changes in dielectric properties of the medium between the electrodes also vary

the capacitance (see equation (2.1)). A direct relationship between the relative

permittivity of a dielectric and its capacitance value makes these capacitive sensors

suitable for material characterization [42]. They may also be used to determine the

position of the interface between various different types of materials. Humidity

measurement and liquid level detection are well-known applications of this type of

sensing [43]. For example, capacitive humidity sensor is usually composed of a material

whose dielectric constant varies with humidity and a capacitor employing that material as

the dielectric [44].

2.1.2. Differential capacitive sensing

Sensitivity to mechanical displacements can be improved by using an additional

electrode in between of the two plates in both spacing and area variation techniques

(see Figure 2.6). The three-plate sensor offers the well-known advantages of a

differential system, such as rejection of common-mode interference [45]. The detection

circuit measures the difference between two capacitances rather than an absolute value

of one capacitance [46]. Depending on the sensing system, the measured value can be

proportional to or .

2.1.3. Capacitive sensing based on coplanar electrodes

Aside from the simple parallel plate capacitive sensors previously discussed, two

coplanar electrodes may also be used for capacitive sensing (see Figure 2.7). The

fringing field between the two electrodes defines the mutual capacitance between them

[47]. Interference with this fringing field changes the capacitance value. For example,

Figure 2.5. Two parallel plate capacitor in an area-type sensor.

Displacement

Impe

danc

e

9

moving one of the electrodes or changing the effective dielectric material result in

capacitance variations.

The technique of the differential capacitive sensing can be extended to coplanar-

plate capacitive sensors. One simple example of this structure is a 2D capacitive

position sensor, as shown in Figure 2.8, where the dielectric properties of the human

body affect the coupling between adjacent electrodes. Such an arrangement can, for

example, be used for touchless display units.

Figure 2.6. A simplified structure of a differential capacitive sensing.

Figure 2.7. Coplanar-plate capacitive sensing.

Figure 2.8. 2D capacitive position sensing by coplanar electrodes.

10

2.2. Applications of capacitive sensing systems

Capacitive microsensors are used in numerous macro and micro-devices for

sensing different physical/chemical properties such as acceleration [48], pressure [49],

strain [50], position [51], proximity [52], humidity [53], gas concentration [54], etc. An

important advantage of capacitive sensing in such cases is the ease of the mass

production and low cost [43]. Another advantage of using capacitive sensing is that the

power consumption of these sensors is low. This is because ideal capacitors are perfect

insulators at Direct Current (DC) frequencies; i.e., they do not require any DC current

which makes them ideally suited for low-power applications. Their other advantages

include:

Simple structure

Relative insensitivity to temperature

Good resolution, stability, and speed

Compatibility with microfabrication technologies

In this document, micro-scale sensors refer to devices that are batch fabricated

through MEMS micromachining processes in contrast to macro-scale devices that are

made through conventional serial assembly techniques. Some structures of capacitive

sensors in macro-scales can be fabricated and used in micro-scales as well. The main

distinction in that case will be batch fabrication versus serial assembly.

Macro-scale capacitive sensing applications

One benefit of capacitive sensing at macro-scales is that there is no physical

contact between the measuring surfaces, which means that the sensor does not

physically load the mechanical movement. One application of capacitive sensors is

monitoring the liquid level in a container. For this application high resolution sensing is

required that can be provided by capacitive sensing [55]. As shown in Figure 2.9, the

electrode structure consists of a long electrode and one that is divided into insulated

segments. At each time the test electrode is connected to readout circuit and the rest are

11

all connected to ground. Changes in the measured capacitance from one electrode to

another provide information about the level of the liquid inside the tank.

A proximity sensor detects the presence of a nearby object without physical

contact [52], [56]. Proximity measurement constitutes a large number of measurements

made in science and technology. For many practical purposes, it is important to be able

to measure small changes in distance between two parts.

Figure 2.10. Cross-sectional view of a capacitive proximity sensor.

Figure 2.9. A capacitive liquid-level detector.

12

The proximity sensor shown in Figure 2.10 works based on the principle of fringe

capacitance between two electrodes with ring-shaped structure [57]. Bringing an object

close to the fringing field increases the capacitance value. The target object can be

either conductor or non-conductor.

Micro-scale capacitive sensing applications

The typical capacitive sensor arrangements produce small capacitances at

micro-scales. The change in capacitance can be a result of a change in area, gap, or

dielectric properties of the material between the two electrodes as discussed in section

2.1.1. Depending on the application requirements, MEMS designers can employ one of

three mechanisms mentioned in the above to achieve the design objectives. For

example, most pressure sensors operate based on the deflections of a membrane as a

function of pressure. For capacitive pressure sensors, the change in capacitance is a

result of the change in the gap between the membrane and a fixed electrode. For

laterally moving structures, the area of the capacitive elements is limited due to the small

thickness of MEMS structures (typically between 1μm and 100μm). Therefore, the

change in capacitance as the structure moves is often rather small. To increase the

effective area between the electrodes without modifying the microfabrication process,

interdigitated electrodes are commonly used at micro-scales [58]. The interdigitated

electrodes, often referred to as comb structures, increase the overlap area between the

electrodes and can improve the output linearity.

Comb capacitors are used to measure lateral [59], transverse [60], and torsional

[61] displacements. In lateral configuration, two planar fingers move towards each other

as shown in Figure 2.11. When the top electrode moves toward the fixed electrode on

the bottom, the capacitance value between the two electrodes increases. The amount of

the capacitance can be found from:

(2.2)

13

where is the height of fingers, is the distance between the fingers, is the engagement length of fingers, and is the fringing capacitance, and is the

number of fingers.

In transverse configuration, movement occurs sideways (see Figure 2.15) [62]. Moving the top beam along the X-axis changes the mutual capacitance. The amount of

the capacitance is found from:

, (2.3)

Figure 2.11. Lateral (Y-direction) movement in comb structure.

Figure 2.12. Transverse (X direction) motion in comb structure.

14

As illustrated in Figure 2.13, in torsional configuration, one electrode rotates

around one side of the beam. Varying the side overlapping area between the electrodes

changes the mutual capacitance. For small angles, change in the mutual capacitance of

this comb-structure with fingers can be found from [61]:

2 (2.4)

where is the length of rotating finger, is the length of fixed finger, is the distance between the fingers, and is the rotating angle.

The aforementioned comb structures can be used in different applications.

Capacitive strain sensors employ changes in capacitance to measure the displacements

of the beam due to external strain. They are used in advanced industrial applications,

such as torque sensing in rotating shaft, blades, and ball-bearings [63], [64]. They can

also be employed in biomechanical application such as spinal fusion detection [50]. A

lateral comb configuration of a strain sensor with three amplifying beams for improving

the device’s sensitivity is depicted in Figure 2.14 [65]. An external strain causes a

displacement (∆ ) and the lateral movement of the comb-structures in different direction provides differential sensing which has better sensing performance compared to the

single one.

Figure 2.13. Cross-sectional view of a finger in a comb structure before on top and after rotation at the bottom.

15

Transverse comb structures can also be employed for various purposes. For

example, in force sensors, an external force moves one comb electrode respect to

another one and as a result the mutual capacitance between them changes. One unit

cell of a typical capacitive sensor is shown in Figure 2.15. Two fixed structures used in

this unit act as a plate for two separate electrodes of the capacitors. Force causes the

beam movement and results in decreasing one capacitor while increasing the other one.

Higher number of unit cells enhances the sensitivity of the overall sensing system.

Torsional comb structure can be employed in acceleration sensing [66].

Capacitive MEMS accelerometers employ changes in capacitance to measure the

displacements of the proof-mass due to external acceleration [67], [68], [69]. Figure 2.16

shows a capacitive accelerometer working based on torsional motion. The change in

Figure 2.14. Simplified structure of a capacitive strain sensor and the fabricated device. © [2003] IEEE [65]

16

capacitance happens because the overlapping area between comb electrodes varies.

The direct relationship between capacitance and overlapping area enables the design of

sensors with a wide full-scale range since the size of the air gap no longer limits the

movement range of the electrodes.

Figure 2.15. Transverse movement in capacitive sensors based on comb structure.

Figure 2.16. The SEM micrograph of a typical torsional accelerometer on left, Close-up of a torsional beam on right © [1998] IEEE [61].

17

Figure 2.17. Schematic of a capacitive humidity sensor, close-up view of the upper, lower electrodes and polyimide column © [2000] IEEE [70].

The aforementioned capacitive sensors with comb structure work based on

changes in area or gap. In some applications, changes in dielectric properties change

the mutual capacitance between two comb-structure electrodes. Polymer coated

materials are sensitive to humidity as well as the types of chemicals exposed to. Their

transduction mechanism relies on the permittivity changes and swelling of the coating

polymer exposed to humidity and chemical materials [71], [72]. For example, the

polymer named poly-ethylene vinyl-acetate (PEVA) which swells on exposure to

benzene can be used as a dielectric material of capacitive sensing to detect the

concentration of benzene in the air [73]. Thus, capacitive sensors are useful for sensing

the relative humidity and distinguishing the surrounding materials [74], [75].

As shown in Figure 2.17, the humidity sensor consists of a capacitive sensor with

two electrodes which are electrically isolated from each other. The top electrode has a

comb shape and is located in parallel to the bottom one. The dielectric layer consists of

thousands of polyimide columns with relative permittivity sensitive to absorbing water

[70].

Figure 2.18 shows a chemical capacitive sensor consisting of sensing and

reference capacitance; each of them comprises two comb-structure metal layers. When

the sensor is exposed to the target material, absorption from the material to the dielectric

film takes place and results swelling in the polymer and increasing in dielectric

permittivity. The sensitivity can be increased by maximizing the polymer volume in the

region with strong electric field.

18

Figure 2.18. Schematic of the sensing and reference capacitor made from the two metal layers of the CMOS process. © [2002] IEEE [72].

Figure 2.19. Top view of a fully fabricated pressure sensor on left and cross-sectional view on right. © [2011] IEEE [49]

19

In addition to the comb-structure capacitive sensors, two parallel plate capacitive

sensors are still a good choice in sensing large capacitances, especially when the gap

between two plates varies in response to an external force. This method can be used in

MEMS pressure sensors. Figure 2.19 shows top view of a pressure sensor as well as

the cross-sectional view of the capacitive sensing element. It consists of a two parallel

plane electrodes [49]. Increasing the diaphragm size, reducing diaphragm thickness, and

decreasing sensing gap lead higher pressure sensitivity of a capacitive pressure sensor.

In contrary, decreasing the sensing gap results in non-linearity and limited dynamic

range of the sensing system.

2.3. Interface electronics for capacitive microsensors

A signal conditioning circuit to measure the capacitance value is needed to

convert the capacitance change into a voltage [76], frequency [77], pulse-width [78], or

current [79]. Depending on the output signals, different topologies of readout circuits can

be employed [80], [81], [82]. In the following sections, different conversion techniques

are presented with examples. Some state-of-the-art interfaces are introduced to

enhance various design factors in capacitive sensing systems, such as resolution,

dynamic range, power, and linearity.

2.3.1. Capacitance to voltage converters (C2V)

AC bridge

Using an AC bridge is a classic method for measuring changes in a capacitance.

The principal function is similar to the resistive Wheatstone bridge where a balanced

ratio of impedance results a balanced condition as indicated by a voltage detector.

Changes in one of the impedances cause imbalance that is sensed [83]. In an AC

bridge, this detector can be an oscilloscope, voltage amplifier, or any devices capable of

registering small AC voltage levels (see Figure 2.20).

20

Figure 2.20. AC bridge sensing circuit.

Despite its simple structure, a major drawback of this circuit is its sensitivity to

electrical interference between the bridge circuit and external bodies. A potential

problem of this sensing circuit is the stray capacitance between either end of the voltage

detector and ground. These stray capacitances result in current paths to ground, can

affect the bridge balance, and causes nonlinearity of the sensor response.

Rectifying circuits

In this configuration, a reference voltage is processed by a circuit that converts

the capacitors’ value to a voltage. The signal is then rectified and processed by a low-

pass filter to generate a DC value proportional to the amplitude.

Figure 2.21 presents a differential capacitive sensing system using this topology

[84]. Based on the capacitance variation, different current signals are generated. The

generated currents are then fed to TIAs whose outputs are then passed through the

diode rectifiers and filtered. The differential signal is finally fed to the input of an

instrumentation amplifier. The gain control resistor of the instrumentation amplifier

provides the option of dynamic range extension. Moreover, connecting the sensing

electrodes to the virtual ground input node of the instrumentation amplifier reduces the

sensitivity to interferences. However, one limitation of this topology is that the frequency

of the reference signal should be more than 1/ to have a linear relationship between output and sensing capacitance. In addition, having diodes or diode-connected

21

transistors limits the amplitude of the signal before rectifier and decreases the output

swing.

Switched-capacitor amplifying circuits

In switched-capacitor amplifier based readout circuit, switches are used to

transfer the charge accumulated on the sensing capacitor to the output signal. In Figure

2.22, a simplified model of a switched capacitor amplifier is shown. Square-wave signal

has been used for the excitation. In one phase , integrator’s capacitor is discharged and in the following phase , accumulated charges on sensing capacitance will be transferred to the output [85]. In this case, the output voltage is

directly proportional to the differential capacitance ( ) and amplitude of the

excitation voltage ( ):

∝ (2.5)

Figure 2.21. Rectifier-based capacitive sensing system including two current sense amplifiers, two diode rectifiers and an instrumentation amplifier.

22

Figure 2.22. Readout circuit using switched capacitor charge amplification.

The main advantage of the switched-capacitor amplifier based readout circuit is its

temperature insensitivity, as capacitors, when compared to resistors, are relatively

insensitive to the temperature variations. Major drawbacks are the speed limitation and

the need for non-overlapping clock signals. In MOS sampling circuits, channel charge

injection and clock feedthrough of the switches lead to gain error, DC offset, and

nonlinearity [86].

2.3.2. Capacitance to frequency converters (C2F)

Capacitance to frequency converters are simple and often require less power

compared to C2V circuits. The output of these circuits is a quasi-digital quantity

(frequency) and there is no need for an analog to digital converter in the front-end. On

the other hand, the high sensitivity to process parameters of most practical

implementations limits the achievable accuracy.

Linear oscillators

A linear oscillator can be based on an LC-tank where capacitor in the tank is

variable [87]. The output frequency of a Colpitts oscillator shown in Figure 2.23 is

23

proportional to the fixed inductance ( ∝ 1 ⁄ ) [80]. These oscillators have less temperature sensitivity compared to most other types of the oscillator topologies.

Their high power consumption and high frequency limits their applications in typical

capacitive measurement. In addition, its frequency measurement can be very sensitive

to the parasitic capacitances involved in the measurement of sensor and all external

interferences [88].

Figure 2.23. Basic Colpitt Oscillator Circuit.

Nonlinear oscillators

Many topologies exist that operate based nonlinear elements or switches to

produce a signal whose frequency is a function of a particular capacitor value. A

simplified schematic of an example circuit is shown in Figure 2.24. The sensor

capacitance is charged and discharged with constant currents ( ). The output voltage

drives the switch. The comparators convert the triangular voltage on the capacitor

to a square-wave and the multiplexer changes the output level.

24

Figure 2.24. Capacitance to frequency converter using an oscillator.

The comparators have two different threshold voltages ( , ) to set the upper and lower limits of the triangular voltage. However, the effects of temperature and supply

voltage variations on the output frequency are eliminated in this structure [77], [82]. For

this particular design, the output frequency is a function of the charging/discharging

currents, and hence, the circuit’s performance is sensitive to the variation of these

currents. For many nonlinear oscillator circuits (e.g., relaxation type), the output

frequency is a function of passive or active element values, which in general, adversely

affect the stability of the oscillator signal. Nonetheless, these circuits often consume little

power and are widely employed.

2.3.3. Capacitance to current converters (C2C)

A simplified model of this topology is shown in Figure 2.25. In this circuit, switches are

controlled by a clock signal of period equal to ( ). During the discharge phase

( ), and are closed and currents and are the same, thereby forcing to be zero. Differential current amplifier provides a virtual ground at its inputs and ideally

nullifies the effect of the stray capacitances at these nodes [79]. As a result, when these

two switches are open in measurement phase ( ), the input current ( ) will be divided

in two branches according to the ratio of the two capacitors and the output current can

be found by:

25

(2.6)

where and are sensing capacitance, is the input current, and is the output current. These two switches ( , ) are needed to be closed periodically to avoid the saturation of the circuit that might occur because of a linear increase of the voltage at

the sensor common node due to constant input current ( . One of the advantages of

this method is that adding or subtracting current signals are simple. Additionally, current

amplification is possible through using simple current-mirror-like schemes for improved

sensitivity [89]. Thus, capacitance to current converters are adopted to increase speed

and simplify the circuit complexity and enable low-voltage, low-power operation [79],

[84]. On the other hand, this solution is sensitive to the stray capacitance at the common

node electrode which should be smaller than the sensing capacitance for proper

operation. Another drawback is that current leakage in switches can lead to nonlinearity

issues in the signal path and output signal.

Figure 2.25. Schematic of a capacitance to current converter.

26

2.3.4. Capacitance to pulse-width converters (C2PW)

Figure 2.26 shows a topology to produce a pulse-width modulated signal with

pulse duration linearly proportional to a capacitance. In this circuit, sensing capacitance

is charged and discharged by a DC current ( . In charging phase ( is on), the slope

of the triangular-wave signal after block is positive and is compared with a threshold

voltage ( . When this voltage becomes larger than the threshold voltage of the

comparator, the output of the comparator becomes high.

One of the advantages of these types of readout circuit is that a digitized signal is

produced without realizing the analog to digital converter. Hence, the hardware cost can

be reduced. Besides, the output signal is a pulse stream, it can be transmitted over

moderately noisy or nonlinear channels, such as RF or optical links [78], [90].

Furthermore, this signal can be easily read by a microcontroller or converted into an

analog signal using only a low pass filter [78]. One of the drawbacks of these circuits is

that the output frequency could not be higher than hundred kHz frequency band which

limits the dynamic range.

Figure 2.26. Schematic block diagram of a readout circuit based on pulse width modulation.

2.3.5. Capacitive to digital converters (C2D)

In some applications, it is needed to have a digital output. Sigma-delta converters

can be used for these purposes. They usually have high resolution and high accuracy

27

[91], [92]. However, due to the oversampling technique, the main disadvantage of this

readout circuit is its long measurement time. Having a higher clock rate can lead to a

higher measurement bandwidth but at the cost of higher power consumption and

complexity of the circuit. Figure 2.27 presents a basic circuit diagram of a sigma-delta

converter [42]. An amplifier with C in its feedback loop acts as an integrator. It is supposed that the output voltage of the integrator is negative at the beginning of the

measurement. Thus, output of the comparator (D) is zero as shown in Figure 2.27. Both control signals (φ ,φ ) are low when is low. When clock ( ) is high, is charged by

and in the second phase ( is low), the charge ( ) is transferred to . As long as the output of integrator ( / ) is negative, comparator generates zero. When it becomes positive, the charge of is transferred to . So, for times / and for times / will be added to the integrator’s output ( and are number of ones and zeroes in , respectively). the ratio of ones to the total numbers ( ⁄ )) equals to the ratio of ( / ) [42].

Figure 2.27. Basic circuit diagram of a C2D convertor on top, The related signals on bottom.

28

2.4. Synchronous demodulation-based circuits

Synchronous demodulation technique is a good solution in readout circuit design

to reduce noise, increase linearity, and dynamic range. It is a common signal processing

technique to extract weak signals from low-frequency noise and interferences. A

simplified structure of a synchronous demodulator for a capacitance to voltage

conversion is shown in Figure 2.28. It consists of a reference signal generator, an

amplifier, a synchronous demodulator unit, and a low-pass filter. The reference signal is

an AC signal that is typically in the range of 1 to 10 [40]. Different signals can be used for the excitation but square-wave and sinusoidal signals are most commonly

used. Sine wave excitation is suitable for measuring small capacitances with high

accuracy. However, on-chip generation of a sine wave reference signal is difficult.

Square wave oscillators are easy to integrate on a single chip system, but nonlinear

effects may reduce the performance of the circuit [79]. As illustrated in Figure 2.28, the

reference voltage is connected to the sensing capacitance ( ). An amplifier is used to

convert the capacitance value to an amplified AC voltage. After passing through the

synchronous demodulator block, the low-pass filter produces a DC output signal with an

amplitude and phase corresponding to the sensing capacitance value. Moreover, the

low-pass filter limits the bandwidth, and thus, enhances the resolution.

Figure 2.29 illustrates the transformations in frequency domain when a sinusoidal

reference signal passes through the test device and the synchronous demodulator

topology. Synchronous demodulator block operates at the same frequency as the

reference signal generator. After initial amplification and passing through the

synchronous demodulation block, the amplified reference signal with a value

proportional to is moved to low-frequency region. Finally, the low-pass filter limits the noise-bandwidth independently of the reference and input signal frequencies, making

this circuit well-suited for low-noise measurement of small signals.

29

Figure 2.28. Synchronous demodulation technique.

Figure 2.29. Reference signal and noise before and after passing through a synchronous demodulator in frequency domain.

Figure 2.30. Using synchronous demodulation technique in interface circuit based on trans-impedance amplification.

30

Figure 2.30 demonstrates using a synchronous demodulation technique in a

differential capacitive sensing system. In this design, a Trans-Impedance Amplifier (TIA)

is used to convert the differential sensing capacitor to an amplified voltage. The output

voltage of this circuit is directly proportional to the differential capacitors, excitation

frequency ( ), and feedback resistor ( ) of the TIA:

∝ (2.7)

As discussed in details earlier, this circuit architecture is one of the most common

methods for measuring capacitance because of its high accuracy and flexibility.

Measuring capacitance at higher frequencies and using synchronous demodulation

allows for separation of the sensing signal from amplifier offset, 1 ⁄ noise, and other interferences located mainly in the low frequency range. In addition, differential sensing

and using an amplifier with virtual ground input node results low sensitivity to parasitic

capacitance and other environmental interferences. Limiting the bandwidth of the low-

pass filter also provides high dynamic range and high resolution.

31

3. Differential capacitive sensing circuit with extended dynamic range

As mentioned in Chapter 2, differential capacitive sensing is often used to

improve the sensing resolution and reject common-mode interferences. In differential

sensing, the influence of undesired inputs and disturbances (e.g., temperature) is

cancelled largely. Besides the differential sensing method, high performance readout

circuits are needed to improve the efficiency of the sensing process.

Most sensor output signals are in the low-frequency band, where many

interfering signals such as 1⁄ noise, op-amp offset, and main-supply interferences are also located [42], [93]. A good way to separate the sensor signal from the above-

mentioned undesired interfering signals is to modulate the sensor signal to a higher

frequency, so that it can be processed to eliminate 1⁄ noise, offset and main-supply interference [94], [95]. The modulated signal is shown by in Figure 3.1. After demodulation, the signal is converted back to the baseband frequency. A low-pass filter

removes the undesired signals. The demodulation can easily be performed with a mixer

(see Figure 3.1). The amplified input signal is demodulated, while the op-amp input

noise and offset are chopped by the square-wave signal and passing through the low-pass filter.

Figure 3.1. Synchronous demodulation circuit diagram.

32

3.1. Conventional synchronous demodulator topology

A differential interface circuit working based on synchronous demodulation for

capacitive sensing is designed. The block diagram of this circuit is shown in Figure 3.2

[96]. The circuit is composed of three main building blocks: a C2V converter, a

synchronous demodulator, and a low-pass filter for reducing noise bandwidth and

removing the high-frequency harmonics. The output is DC signal in correspondence to

the capacitance changes. The configuration and working principle of these building

blocks is described in detail in following sections.

TIA which plays the role of C2V converter translates the changes in capacitance

to a voltage signal (see Figure 3.3). With sinusoidal waves with opposing polarities

applied to the sense electrodes [96], the output voltage is:

sin 2 cos (3.1)

where and are the two sensing capacitors, is the feedback resistor shown in

Figure 3.3 ( sin ). The demodulator can be made using a differential amplifier and two switches that are controlled by reference signals phase shifted by 90°

or 270° (see Figure 3.4).

Figure 3.2. The overall view of the designed circuit.

33

Figure 3.3. Schematic diagram of TIA.

Figure 3.4. Schematic diagram of a synchronous modulator

34

Figure 3.5. The overall view of the low-pass filter

The upper switch that is controlled by 90-degree phase-shifted signal passes the first

half of the cycle of the output voltage of TIA ( ). The bottom switch that is

controlled by 270-degree phase-shifted signal passes the second half of the cycle of the

output voltage of TIA ( ) which is become inverted by the differential amplifier. As

a result, the out ( ) becomes rectified and can be found by:

|cos | (3.2)

The final block of the interface electronic structure, which follows the

synchronous demodulator, is a Bessel low pass filter to extract the DC component of the

signal (see Figure 3.20). The average value of a periodic function can be calculated from

(3.2) in which is the period of the periodic function and in this design is equal to .

1 2 | | (3.3)

As a result, the output of the filter ( ) which is a DC voltage whose level is

proportional to the amplitude of the rectified sine wave from the previous stage (i.e.,

35

proportional to the difference between the capacitance of the sensing electrodes). The

output voltage ( ) is given by:

2 (3.4)

3.1.1. Using synchronous demodulation for differential capacitive sensing

As an example for potential applications of capacitive detection circuit based on

synchronous demodulation, a circuit for touchless interfaces for mobile devices was

designed and analyzed. In this experiment, three coplanar electrodes were used as a

capacitive displacement sensor and an interface circuit to translate an object’s (e.g.,

user’s finger) movement on top of device display to a voltage signal. An analytical model

presented by Chen et al [81] showed that the capacitance between two parallel coplanar

electrodes in semi-infinite domain is directly proportional to the relative dielectric

constant of the material on top of the surface. Since water has high dielectric constant

( 80), and human body is largely composed of water, finger displacement can change the capacitance significantly.

This sensor detects the displacement of a user’s hand or finger near the device

surface in three-dimensional space. Compared to the sensor with one sensing element,

using these electrodes differentially has lower sensitivity to environmental effects (e.g.,

temperature or humidity variations) [95]. The advantages of using capacitive transducers

for motion monitoring over other methods based on video, sonar, or RF signals are low

power consumption, small size, and low cost of construction [84], [97], [98].

As shown in Figure 3.6, the differential capacitive sensor is composed of three

coplanar electrodes. When the finger represented by a conducting cylinder above the

electrodes moves from side to side, the mutual capacitances between the sense

electrodes and the centre reference electrode change correspondingly. Interfering with

the electric field built between them is basically the reason of changes in the mutual

capacitances. With the aid of another set of three electrodes along the other axis (e.g.,

y-axis), hand movement can be detected in two-dimensional (x-y) space (as discussed

36

Figure 3.6. Three coplanar electrodes needed for monitoring hand movements.

in section 2.1.3). To trace hand movements along the z-axis (i.e., normal to the plane of

electrodes) a single capacitive sensor (i.e., one pair of electrodes located on a plane

perpendicular to z-axis) can be employed. Moving hand too far from the surface (more

than 10 cm for our prototype) decreases the contribution of hand capacitance.

Figure 3.7. Electrical field distribution around a conductive object moving on top of three conductive electrodes is illustrated.

37

Finite element simulations were employed to study the field distribution around

the sensing element. The structure is modeled by three rectangular elements as the

electrodes and one circular element as a human finger. Since our body consists of ions,

it is considered as a conductive material. Thus, both electrodes and finger were defined

as conductors which were surrounded by a body of air around the structures. Selecting

different material and geometry for the elements in sensing structure alters electric field

distributions and mutual capacitance between them (see Figure 3.7).

Variation in mutual capacitance between two electrodes is illustrated in Figure

3.8 when the finger (located at 2 above the surface) is moved from 9 cm to the left to 9 to the right of center electrode. It can be seen that each of these capacitances ( and ) reaches its maximum where finger is located around the middle of that pair of electrodes. The differential capacitance (C ) is also illustrated in Figure 3.9.

Figure 3.8. Capacitance between electrodes ‘1’ and ‘2’ as well as the capacitance between electrodes ‘2’ and ‘3’ simulated in ANSYS.

−9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9100

120

140

160

180

200

Longtitude (cm)

Cap

acita

nce

(fF)

C23

C12

38

Figure 3.9. Differential capacitance between and simulated in ANSYS.

To verify the proposed capacitive sensing and its sensitivity to the capacitance

changes, a prototype including three electrodes on glass in both x and y directions and

readout circuit were designed and implemented on a printed circuit board (PCB) (see

Figure 3.10 and Figure 3.11). This circuit was based on the topology shown in Figure

3.2. Movement of a finger along x-y axis on top of these electrodes changes the

differential capacitance in each direction. To separate the signals for x and y directions

from each other, two different reference frequencies (250 and300 ) were adopted.

Figure 3.10. Planar electrodes needed for monitoring hand movement.

−9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9−40

−30

−20

−10

0

10

20

30

40

Longtitude (cm)

Dif

fere

ntia

l cap

acita

nce

C23

−C

12 (

fF)

39

Figure 3.11. Readout circuit on PCB.

In our measurement, the reference electrode in x and y directions are connected

to 2 sinusoidal signals of 250 and 300 frequencies, respectively. Lateral displacement along x-axis and y-axis change the two output signals displayed by

pink and yellow waveform in Figure 3.12. Also, normal displacement along z-axis

generates voltage changes at the outputs. Depending on the location of the finger (on

top of x-axis electrodes or y-axis electrodes), pink and yellow signals are created which

are shown in Figure 3.13.

Measured responses of the sensing circuit are plotted in Figure 3.14 and Figure

3.15 while moving a finger laterally above the electrodes and vertically between each

pair of electrodes. It can be seen in Figure 3.14 that the output voltage reaches its

maximum when finger is in the middle of each pair of electrodes (i.e., between the

sensing electrode and the middle electrode) and decreases when a finger is taken away

from the sensing electrodes. According to these measured data, finger’s lateral

movement from 9 to 4 which is related to the change of 5 differential capacitive sensing can be detected by this circuit.

40

Figure 3.12. Measured results of the proposed sensing system when finger moves laterally.

41

Figure 3.13. Measured results of the proposed sensing system when finger moves vertically

42

Figure 3.14. Measurement results when an object moves laterally.

Figure 3.15. Experimental results when an object moves vertically.

43

3.2. Expanding the dynamic range of circuits based on synchronous demodulation

Since every sensor has its own requirements for readout, a configurable sensor

interface is crucial for successful implementation. This allows users to reuse a given

circuit topology for several applications and adjust the sensing range and sensitivity for

each particular application [85]. Although the synchronous demodulation topology

provides a good noise performance, its dynamic range is limited especially if the circuit is

realized using IC technologies.

In addition to being able to interface a wider variety of capacitive sensors, a large

dynamic range is required especially when the sensing capacitance changes

nonlinearly. In some cases, the gap between the two electrodes of a capacitive sensor

changes during operation. Since the sensor sensitivity is inversely proportional to the

gap, the measurements will be inherently nonlinear. Other phenomena such as

structural deflections often exacerbate these nonlinearities [99]. It is therefore necessary

that the signals from capacitive microsensors be measured with adjustable sensing

range circuits to capture the wide range of input quantities. Depending on the

microsensor and the application, the capacitance value can change from sub-fF to

hundreds of pF, making design of such circuits challenging [100], [94].

In the next part, we present a circuit topology with adjustable sensing range for

differential capacitive sensors. In this design, differential sensing is also employed to

cancel or reduce the influence of interferences. The reference signals required for this

measurement scheme were produced on-chip. The sensing range was increased using

a novel feedback mechanism that modified the reference signal amplitudes.

3.3. Circuit design

The topology proposed here uses the output signal of the open-loop topology in

Figure 3.16 and, through a feedback network, adjusts the amplitude of the reference

signals, in accordance to the sensed capacitor values. This ensures that the amplifier

remains in its linear region and enhances the linear sensing range of the system.

44

Figure 3.16. A differential capacitance measurement circuit based on synchronous demodulation of reference signals. Employing feedback (dashed line/box)

let us increase the dynamic range of the circuit significantly.

The designed circuit consists of a TIA, a synchronous demodulator, amplitude

controller, and a low pass filter, as shown in Figure 3.16, [101]. Capacitors ∆ and ∆ are differentially driven by reference signals and . These signals are in the form of triangular-wave signals and are produced on chip. As shown in

Figure 3.17, they are generated through charging and discharging of on-chip timing

capacitors, , using two constant current sources with value , which are switched by

a symmetric square control signal, . The current alteration is labeled in this figure

which is zero in open loop case. The control signal, , is produced by an on-chip

relaxation oscillator and is a square wave signal with period 1/