Appendix A

Fabrication and Packaging

Here we describe the microfabrication process developed in the course of this work

for the fabrication of various prototypes reported in this dissertation. The reported

fabrication process, developed based on the previous single-mask die-level process

from [5] and wafer-level DRIE recipe optimization from [135], is a two mask SOI

process with patterned metal wirebonding pads and traces on the front side and

blanket metallization of the wafer backside for packaging and die attachment.

1. Substrate specification.

• SOI wafer details: Typical characteristics of the SOI wafers used in the

process are summarized in Table A.1. The suggested vendor is Thomas

Table A.1: Typical parameters of the SOI wafers.

Parameter, units ValueWafer diameter, mm 100Device layer thickness, µm 50Device layer resistivity, Ω-cm 0.01-0.03Device layer type P/B, (1-0-0)Surface finish type double-sided polishedBuried oxide (BOX) thickness, µm 5Handle layer thickness, µm 500Device layer resistivity, Ω-cm 10 to 100 rangeDevice layer type P/B, (1-0-0)

227

Gentemann, Ultrasil Corporation, (510)-266-3700, ultrasiltg@aol.com,

http://www.ultrasil.com/. Other vendors, especially Silicon Quest Inter-

national (SQI) are strongly discouraged. When ordering the SOI wafers,

make sure their fabrication is done by bonding an oxidized wafer to a sili-

con wafer, NOT by oxide-to-oxide bonding of pairs of two oxidized silicon

wafers.

2. Blanket metallization of the SOI wafer backside (handle layer) for packaging.

• Clean the wafer: Rinse with acetone. Rinse with isopropanol. Rinse

with DI water. Remove surface oxides using a 20 % or less concentrated

HF bath for 30 seconds. Rinse in DI water. Blow-dry with nitrogen.

At this point water should easily bead-up and come off the hydrophobic

surface of the exposed silicon.

• Deposit metal: E-beam evaporate 500 A chromium adhesion layer and

5000 A gold layer. The outer gold layer provides a corrosion-resistant

interface for eutectic bonding and electrical connectivity for the wafer’s

handle layer.

3. Lift-off metallization∗ of the SOI wafer front-side (device layer).

• Clean the wafer: Repeat the cleaning procedure described above. De-

hydrate the wafer using a 90 to 120 nitrogen dehydration oven for at

least 30 minutes.

• Lithography for lift-off: Spin-coat Shipley 1827 on the front side of the

wafer at 2500 RPM; do not use any adhesion promoter! Soft-bake in 90

∗The described lift-off recipe was suggested by Mo Kebaili, Kebaili Corporation,http://www.kebaili.com.

228

oven for 30 minutes. Expose in MA-6 for 25 seconds. Soak in chlorobenzene

for 3-4 min. Nitrogen dry-blow, do not rinse! Develop in MF-319 for 45

seconds. Rinse in DI water, nitrogen dry-blow. The photoresist mask

should be 3 to 4 µm thick, which is sufficient for metal thicknesses below 1

µm. Swelling of the photoresist due to the chlorobenzene exposure ensures

the overhanging profile needed for correct lift-off.

• Deposit metal: E-beam evaporate 500 A chromium adhesion layer and

5000 A gold layer. The gold provides an interface for device wire-bonding.

• Lift-off metal: Soak the wafer for several hours in acetone, Figure A.1.

Rinse with isopropanol and nitrogen blow-dry, Figure A.2.

4. DRIE etching of the SOI wafer device layer.

• Clean the wafer: Repeat the cleaning procedure described above. De-

hydrate the wafer using a 90 to 120 nitrogen dehydration oven for at

least 30 minutes.

• Lithography for DRIE: Program the spinner for 20 seconds at 500 RPM

followed by 40 seconds at 5000 RPM (use moderate acceleration). Spin-

coat adhesion promoter HMDS on on the front side of the wafer. Spin-coat

AZ-4620 photoresist. Soft-bake in 90 oven for 20 minutes. Use MA-6 to

align the device mask to the alignment marks defined in the metal lift-off

step; expose for 30 to 35 seconds. Develop in 4:1 water:AZ-400 (by volume)

solution for several minutes. Rinse in DI water, nitrogen dry-blow. The

photoresist mask should be around 6 µm thick, which is sufficient for at

leat 50 µm deep DRIE. Reduce the second stage of the spinning to 3000

RPM (corresponding to about 10 µm thick photoresist) if a 100 µm DRIE

is needed.

229

• DRIE: Etch the device layer of the SOI wafer in the STS ASE tool using

the “Alex6R1” recipe (first and last step is etch, 13 s etch, 8 s passivation,

manual APC at 70 %). The etch rate of the process is approximately 0.5

µm/min; for 50 µm device thickness use 105 to 110 etching cycles. Do not

overetch the wafers, as this will cause severe undercutting of structures,

possible dry-release, and inability to correctly release the structures in the

HF bath.

• Photoresist removal: Soak the wafer in acetone for 10 minutes. Rinse

with acetone and isopropanol. Nitrogen blow-dry. Use an oxygen plasma

tool to remove the photoresist residue. Set the pressure to 200 mTorr.

Gradually ramp the power up to 200 W. Keep for half an hour or until all

the photoresist residue is removed, Figure A.3.

5. Wafer dicing.

• Prepare for dicing: Spin-coat a thick layer, ≈10 µm, of AZ-4620 pho-

toresist. Soft-bake in 90 oven for 15 minutes.

• Dicing: Ship the prepared wafer for professional dicing and provide a dic-

ing map. The suggested vendor is Jeff Olson, Spectrum Micromechanical,

Inc. 858 395-2264, http://spmmi.com.

• Extracting dies: The diced wafer is typically shipped back attached to

a stretched blue tape circle, Figure A.4. Extract the individual dies by

gently pushing on the backside of the blue tape with tweezers.

• Dies cleaning: Clean the individual dies by soaking for 10 minutes in ace-

tone twice, followed by a isopropanol bath. Shake of the excess isopropanol

from the dies and let them dry on a cleanroom wipe, Figure A.5.

230

6. Wet release of the fabricated devices.

• HF bath: Collect 10-20 dies in a HF-proof perforated basket. Soak the

devices in a 20 % HF solution for approximately 45 minutes (the timing is

design dependent).

• Dies cleaning: Extract the basket from the HF bath. Soak and rinse in

DI water. Soak in warm isopropanol.

• Dies drying: Pick the dies from the warm isopropanol bath, place them

on a cleanroom wipe, let them dry. Figure A.6 shows an SEM micrograph

of a fabricated 50 µm thick gyroscope with 5 µm minimal features and

capacitive gaps.

7. Device packaging and wirebonding.

• Die attachment: Attach individual dies to the ceramic packages using

SEM carbon tape adhesive (fast and recyclable, but not rigid and vacuum

sealing compliant), epoxy (not easily recyclable, medium rigidity, generally

not vacuum sealing compliant), or eutectic preform (rigid, vacuum sealing

compliant) die attachment as discussed in [135]. A good point of contact on

eutectic packaging topics is David Virissimo of Semiconductor Packaging

Materials.

• Wirebonding: Wirebond the devices to provide electrical connectivity

from the package leads, Figure A.7 Use a wedge bonder with 1 mil Al

wire with 1 % Si from Kulicke & Soffa Industries, 1-800-422-5542, cust-

serv@kns.com, http://www.kns.com/. The suggested resource for all other

wirebonding questions, supplies, and services is George Garcia, PG Enter-

prises, Inc., http://www.pgent.net/.

231

• Lid sealing: Seal the package cavity containing a wirebonded MEMS de-

vice using kovar lids with pre-deposited eutectic (“combo lids”) in ambient

or vacuum environment, Figure A.8. Consult [135] for detailed informa-

tion on the eutectic packaging and sealing process. Suggested vendor for

package-level vacuum sealing is Paul Barnes, SST International, 562-803-

3361, pwbarnes@sstinternational.com, http://www.sstinternational.com/.

This completes the fabrication and packaging process. The devices are now ready

for experimental characterization using the extensive available package-level infras-

tructure.

232

Figure A.1: Photograph of a wafer during lift-off.

Figure A.2: Photograph of a wafer after lift-off.

233

Figure A.3: Photograph of a fabricated SOI wafer with approximately 400 individualMEMS devices designed in 3.5 mm dies.

Figure A.4: Photograph of a diced wafer.

234

Figure A.5: Photograph of cleaned dies. Gyroscopes [34, 60, 88] implemented in 3.5mm die size are visible.

Figure A.6: SEM micrograph of a fabricated MEMS gyroscope [112,124]. The lateralcomb electrode fingers are 5 µm wide with 5 µm spacing.

235

Figure A.7: Photograph of a gyroscope [60] die eutectically attached to a J-Leadceramic package and wirebonded.

Figure A.8: Photograph of a eutectically sealed package containing a gyroscope die.

236

Appendix B

Stand-Alone DSP for VersatileMEMS Characterization

This chapter reports a stand-alone signal processing and control unit designed to pro-

vide flexible characterization of MEMS vibratory gyroscopes. The unit consists of a

programmable 32-bit 150 MIPS DSP controller, 16-bit 1 MSPS digital-to-analog and

18-bit analog-to-digital interface circuits, and signal conditioning electronics. The

multi-channel analog-to-digital interface is optimized for detection of small electrical

signals typical for MEMS devices. Digitally controlled conditioning of analog signals

allows for high-resolution differential digitization of a wide range of detection signals.

The digital-to-analog interface circuit produces a wide range of DC and AC voltages

needed for actuation and detection in gyroscopes; a single 5 V supply is used to

power the board. The DSP controller allows easy MATLAB/Simulink programming

and execution-time data exchange. Performance of the board was experimentally

characterized using an anti-phase driven rate gyroscope with multi-degree of freedom

sense mode. Using 16-bit conversion, the measured capacitance-change equivalent res-

olution is 27 aF/√

Hz. Due to its flexible architecture, the unit is easily customizable

for stand-alone and computer controlled operation of a variety of dynamic MEMS.

237

B.1 Introduction

Discrete bench-top instruments such as dynamic signal analyzers and lock-in ampli-

fiers are often used for initial structural and Coriolis characterization of microma-

chined gyroscopes [26, 136]. However, this approach is not practical for stand-alone

field-testing of prototypes and does not allow fast and flexible evaluation of different

actuation, detection and control algorithms. General-purpose Digital Signal Process-

ing (DSP) systems such as dSPACE and National Instruments Compact RIO can

provide a powerful control solution, but have limited portability, are costly and not

optimized to interface capacitive MEMS. Custom made integrated and Printed Cir-

cuit Board (PCB) level electronics are commonly used for stand-alone operation of

gyroscopes [10, 11]; however, change of operational parameters or signal processing

and control algorithms often involves circuit re-design and reassembly with different

electrical components. In this work, we report an easily programmable and computer-

interfaced yet compact signal processing and control platform for capacitive micro-

machined gyroscopes and other dynamic MEMS.

B.2 Electronics Design

The main hardware components of the proposed platform are a programmable DSP

controller, digital-to-analog and analog-to-digital interface circuits equipped with sig-

nal conditioning analog electronics, see Figure B.1. The unit was assembled using off

the shelf components on a single 112 by 87 mm six-layer PCB. Below we discuss design

and implementation of the major circuit blocks and choice of particular components.

The main properties of the unit are summarized in Table B.1.

238

Figure B.1: Block diagram of the main hardware components.

B.2.1 Processor

A highly integrated Texas Instruments TMS320F2812 single-chip DSP controller was

chosen for the board due to its performance/cost efficiency. This DSP has a maxi-

mum internal frequency of 150 MHz (i.e., 6.67 ns cycle time) stabilized by a 30 MHz

external quartz resonator, and is equipped with 128 K x 16 Flash memory, 18 K

x 16 Single-Access RAM (SARAM). A 16-bit bus with independent data and ad-

dress transmission lines interfaces the processor with on-board DACs and ADCs. A

Serial Peripheral Interface (SPI) and discrete glue logic is used to digitally control

potentiometers in the independent analog signal conditioning circuits. The board is

linked to a host computer for execution-time data exchange and adjustment of signal

processing parameters using an external RS-232C transceiver and an internal Serial

Table B.1: Main operational parameters of the DSP board.

Functional Subsystem CharacteristicsDSP controller TI TMS320F2812 32-bit 150 MIPSADC and DAC conversion update rate 100 kHz2 DACs AC carrier channels 10 Vpp, 0.15 mV step2 DACs AC+DC actuation channels ±100 V, 0.8 mV step3 DACs monitor channels 10 Vpp, 0.15 mV step3 differential I-to-V ADCs 1-10 MΩ gain, 18-bit

239

Communication Interface (SCI). Programming of the processor is done using a JTAG

port.

B.2.2 Digital-to-Analog Interface Circuit

The purpose of the digital-to-analog interface circuit is to convert the digital signals

generated by the processor into analog waveforms to control gyroscopes and to provide

connectivity to external measurement equipment. Based on the high-speed 1 MSPS

16-bit digital-to-analog converter (DAC) TI DAC8820, three types of digital-to-analog

interface circuits with different analog signal conditioning were incorporated on the

board.

Two identical but independent actuation channels were designed in order to ac-

commodate gyroscopes with multi-degree of freedom drive modes. Each of the chan-

nels consists of a DAC and an additional circuit, which amplifies the generated analog

signal and adds a digitally controlled DC bias. These control channels are able to

output arbitrary waveform actuation voltages in the range from 0 to ±100 V.

Two additional arbitrary waveform low-voltage (-5 to +5 V) channels each based

on a simple buffer at the DAC output were also designed to provide accurate probing

voltages (carriers) necessary for detection of motion in dynamic microstructures.

A separate group of DAC channels was implemented to enable connectivity of the

DSP board to external measurement equipment, such as dynamic signal analyzers,

for debugging of algorithms and monitoring of experiments in real time. In these

channels, the DACs are followed by high quality four-pole Low-Pass Filters (LPF) to

suppress the sampling rate signal. The output signals range from -5 to +5 V.

240

B.2.3 Analog-to-Digital Interface Circuit

Capacitive sensing of drive and sense mode vibratory motion in gyroscopes is typ-

ically based on measuring the current induced by the relative motion of capacitive

electrodes. To accurately digitize pick-up currents from microgyroscopes, three inde-

pendent channels were designed and implemented each based on a three-stage fully

differential transimpedance amplifier and a high speed 18-bit ADC.

The three amplification stages are based on TI THS4141 high-speed fully differ-

ential amplifiers with 84 dB common mode rejection. The first stage converts the

difference of the input currents into a voltage difference across its two outputs with

a digitally controlled transimpedance gain of 100 - 110 kΩ. The second stage is a

fully differential two-pole anti-aliasing LPF with the -3 dB cutoff frequency of ap-

proximately 50 kHz. The last stage is a variable gain voltage amplifier. The gain is

defined by Digitally Controlled Potentiometers (DCP) AD5290 and can range from

0 to 20 dB. A high-speed ADC TI ADS8482 was used in each detection channel to

convert the analog voltage difference to the digital code with a sampling rate up to 1

MSPS.

B.2.4 Power Handling

A single +5 V stabilized external DC voltage source powers the board. All other

voltage levels necessary for operation are formed on the board by the dedicated power

converters. To power the analog amplifiers, an additional -5 V voltage is generated

onboard. A pair of -100 and +100 V is also generated to power the high-voltage

amplifiers in the control voltage channels. An additional +1.9 V is used to power the

DSP core, and +3.3 V is used for the digital circuits.

241

Figure B.2: A photograph of an assembled controller board with a packaged gyro-scope.

B.3 Experimental Characterization

In this section we report preliminary characterization of both drive and sense mode

functionality of the board with a MEMS gyroscope using electromechanical amplitude

modulation (EAM) detection technique, see, for example, [58]. Figure B.2 shows

a photograph of a fully assembled signal processing unit and highlights its main

components.

B.3.1 Hardware and Software Configuration

The onboard ADCs were configured for 16-bit conversions. A MATLAB-based Graph-

ical User Interface (GUI) was developed for the real-time control of the transimpedance

gains, value of the DC component of the driving voltage, as well as amplitudes and fre-

quencies of the AC driving and carrier voltages. The interface can be easily modified

to control any run-time variables.

242

Figure B.3: SEM of the gyroscope used for the experimental evaluation of the board.

B.3.2 Test Device

An anti-phase driven rate gyroscope with multi-degree of freedom sense mode [60,88]

was used for the experiments. The gyroscope’s drive mode consists of two coupled

frames driven into anti-phase resonance using a common lateral comb drive electrode

in the center of the device. Two separate 2-DOF sense mode resonators are located

inside of the drive mode decoupling frames. The drive mode resonant frequency is

designed to be in-between the 2-DOF sense mode resonant frequencies for robust off-

resonant operation and anti-phase detection of the input angular rate. Figure B.3

shows an SEM of a device fabricated in-house using an SOI process. The gyroscope

was packaged and wire-bonded in a CDIP-24 package and tested in atmospheric pres-

sure (drive-mode quality factor was approximately 300, sense-mode effective quality

factors were approximately 40).

243

B.3.3 Drive-Mode Detection

In order to actuate the anti-phase motion in the drive mode of the gyroscope, a

driving voltage was applied to the central anchored lateral comb electrode. The

drive voltage consisted of a 37.5 V DC bias and an AC component at the 1.568

kHz resonant frequency of the device. Using the real-time computer graphical user

interface, the amplitude of the AC driving component was adjusted to 14.75 V to

achieve the vibration with a nominal 6 µm amplitude. A 5 V AC carrier voltage at

20 kHz frequency was applied to the movable mass of the gyroscope to enable EAM

detection of motion.

Anti-phase motion of the gyroscope’s decoupling frames was detected using drive-

mode parallel plate detection capacitors. The pick-up currents from the anchored

electrodes were amplified using the on-board three-stage differential transimpedance

amplifier and digitized. Figure B.4 shows Power Spectral Density (PSD) of the drive-

mode pick-up signals for the cases of single-sided and fully differential capacitive

detection. The single-sided detection signal contains feed-through of drive and carrier

AC voltages, as well as multiple informational sidebands inherent to parallel plate

detection of sinusoidal motion [58].

Differential detection with independently tuned gains has several practical ad-

vantages. Unwanted parasitic feed-through of the drive AC signal was suppressed by

almost 20 dB. Also, the white noise floor was improved by approximately 10 dB. Most

importantly, the 20 kHz carrier signal was suppressed by more than 30 dB to the level

below the main informational sidebands, thus improving the useable dynamic range.

In the described experiment, the nominal parallel plate sense capacitance of the

gyroscope’s drive mode was 0.22 pF. During the 6 µm amplitude vibration, the main

harmonic of the parallel plate capacitance change had an amplitude of 0.15 pF [58].

244

5 10 15 20 25

−100

−80

−60

−40

−20

0

Frequency, kHz

PS

D, d

BV

rms/

rt−

Hz

32 d

B

single−sided differential

Drive, 1.57 kHz

Carrier

Main EAM Sidebands−45 dBVrms/rt−Hz

Noise Floor −100 dBVrms/rt−Hz

Figure B.4: Experimentally measured PSD of the drive-mode modulated pick-upsignal during 6 µm amplitude vibrations.

For the tested gyroscope, the measured displacement-equivalent resolution was 1.13

nm/√

Hz. By normalizing to the gyroscope’s parameters, capacitance-change equiv-

alent resolution of the board with 16-bit ADC was derived to be 0.027 fF/√

Hz.

B.3.4 Sense-Mode Detection

Preliminary characterization of the Coriolis detection functionality of the board was

also performed using the anti-phase driven gyroscope [60,88]. Actuation of the drive

mode vibration was done as in the previously described experiments; the detection

channels were switched from the drive mode to the two differential sense mode capac-

itors inside one of the decoupling frames. The board was mounted on a rate table,

which was configured to produce sinusoidal rotation of a fixed amplitude and fre-

quency. Two different experiments were performed: 3.6 rotation at 5 Hz frequency,

and 7.2 rotation at 2.5 Hz frequency. In both cases, the amplitude of the applied

245

18.48 18.485 18.49−75

−70

−65

−60

−55

−50

−45

−40

Frequency, kHz

PS

D, d

BV

rms/

rt−

Hz

18 d

eg/s

sin

usoi

d

7.2 deg at 2.5 Hz3.6 deg at 5 Hz

Quadrature, 40 deg/s

5 Hz2.5 Hz

Figure B.5: Experimentally measured PSD of the sense-mode modulated pick-upsignal during sinusoidal rotation.

sinusoidal angular rate was 18 /s.

Figure B.5 shows PSD of the sense-mode pick-up signal around the left informa-

tional sideband. In each experiment, the signal contains two angular rate-modulated

sidebands, and a 40 /s uncompensated quadrature. The demonstrated resolution

is sufficient for scale factor characterization of gyroscopes in various temperature

and pressure conditions; it can be improved by using the built-in 18-bit conversion

capability, performing demodulation of the EAM signal digitally before outputting

analog measurements, increasing the maximum transimpedance gains, and increasing

amplitude and frequency of the carrier AC voltage.

246

Appendix C

Velocity-FeedbackSelf-Resonance with Carrier

This chapter highlights the development of a self-resonant drive-mode loop based on

velocity feedback with Electromechanical Amplitude Modulation (EAM). Drive-mode

of vibratory gyroscopes should be excited at the resonant frequency to provide the

highest amplitude of drive-mode motion for a given amount of driving voltages. Also,

maintaining the resonant phase condition in the drive-mode is beneficial for phase

based suppression of quadrature signals.

C.1 Phase Control and Velocity Feedback

There are two different approaches to resonant closed-loop operation of a microma-

chined oscillator. The first possible approach to resonant excitation relies on a voltage

controlled oscillator (VCO) and phase detection using a PLL or dual-phase demodu-

lation [137]. The second approach, common in micromachined oscillators, is based on

self-resonant motion excited by velocity-feedback closed loop. Simply put, velocity

feedback with sufficiently high gain turns a linear system with positive damping into

a system with negative damping; in practical implementations the system contains

nonlinearities, such as saturation, that prevent the infinite growth of the amplitude of

247

motion. The velocity feedback approach allows to eliminate the external VCO from

the system and guarantees excitation at the resonant frequency. The potential dis-

advantages of the velocity feedback self-resonance approach include the phase noise

in the Coriolis demodulation reference signal as well as the difficulty in accurately

modeling and selecting the feedback gains.

C.2 Velocity Feedback Self-Resonance

The VCO approach with an amplitude control, also known as automatic gain control

(AGC), is discussed in [135]. Here we focus on design of the velocity feedback self-

resonant loop based on electromechanical amplitude modulation. The approach is

demonstrated using an analog circuit assembled on a breadboard using off the shelf

components, Figure C.1. A MATLAB/Simulink model of the velocity feedback loop

with EAM was created and used to provide additional insight into the closed loop

dynamics of the analog circuit velocity feedback circuit, Figure C.2.

C.3 Analog Circuit Design

The overall circuit consists of several different functional blocks. The EAM carrier

voltage is generated on-board using an XR2206 function generator IC and is applied

directly to the device. The carrier generation circuit blocks allow to adjust the signal

frequency and amplitude in from 73 to 84 kHz and from 0.5 to 8 Vrms, respectively.

The carrier block outputs a sinusoidal waveform applied to the micromachined de-

vice, as well as a 90 phase shifted square waveform used as a carrier demodulation

reference.

The drive mode detection is performed using a differential amplification stage

248

Figure C.1: Analog implementation of the self resonant loop with EAM.

Velocity Feedback Self-Resonance

Simulation parameters

– 1 kHz natural freq.– 103 Quality factor

Simulink model: settling time ~50 ms

10/84Figure C.2: Simulink model of the velocity feedback loop.

249

Figure C.3: Differential driving circuit block.

followed by a high pass filter to eliminate the feed-through signal. This signal is then

mixed with the carrier reference and low pass filtered to obtain the motional drive

mode voltage. This signal is then amplified, phase shifted, coupled to a DC voltage

in a differential manner, as illustrated in Figure C.3. The drive block utilizes a simple

RC circuit for AC plus DC coupling and provides low distortion of AC phase (<1

for frequencies above 0.1 kHz). Finally, the differential voltages and applied to the

device closing the loop.

C.4 Experimental Demonstration

The developed circuit for velocity feedback self-resonant drive-mode excitation using

EAM was experimentally demonstrated and characterized using an anti-phase driven

micromachined gyroscope [131] in air. The external DC drive voltage was gradually

ramped up until self-resonant motion was started, Figure C.4. After the transient

process with characteristic start-up time of 300 ms settled, both the detected veloc-

ity and the feedback generated driving signal were sinusoidal waveforms, Figure C.5.

Spectral measurements of the detected steady state drive-mode velocity were per-

250

Self-Resonance: Start-Up

Feedback drive DC+AC

Detected velocity AC

DC is ramped up until self-resonance starts. Time constant is ~300 ms.

Figure C.4: Demonstration of the closed loop self resonance: velocity signal.

formed to analyze the frequency content. As Figure C.6 shows, the self-resonant

motion occurs mostly at the resonant frequency of the mechanical structure. The

measured signal-to-noise ratio was on the order of 50 dB and harmonic distortion

was on the order of 35 dB, demonstrating feasibility of EAM-based velocity feedback

self-resonance.

C.5 Single-Sided and Differential Operation

As mentioned previously, the reported circuit was designed and demonstrated with

both driving and detection signals operated in a differential manner. Differential

operation is an important practical technique for improvement of the signal-to-noise

ratio and dynamic range by the means of common mode parasitics suppression. Fig-

251

Self-Resonance: Signals

DC+AC drive Detected velocity

Figure C.5: Demonstration of the closed loop self resonance: drive.

Self-Resonance: Frequency Spectrum

35 d

B

Figure C.6: Demonstration of the closed loop self resonance: spectrum.

252

0 10 20 30 40 50 60 70 80 90−110

−100

−90

−80

−70

−60

−50

−40

−30

−20

Frequency, kHz

Mag

, dbV

rms

1−DRV, 1−SNS

(a) Single-sided drive, single-sided pick-up.

0 10 20 30 40 50 60 70 80 90−110

−100

−90

−80

−70

−60

−50

−40

−30

−20

Frequency, kHz

Mag

, dbV

rms

1−DRV, 1−SNS2−DRV, 1−SNS

(b) Differential drive, single-sided pick-up.

0 10 20 30 40 50 60 70 80 90−110

−100

−90

−80

−70

−60

−50

−40

−30

−20

Frequency, kHz

Mag

, dbV

rms

1−DRV, 1−SNS2−DRV, 1−SNS2−DRV, 2−SNS

(c) Differential drive, Differential pick-up.

0 10 20 30 40 50 60 70 80 90−110

−100

−90

−80

−70

−60

−50

−40

−30

−20

Frequency, kHz

Mag

, dbV

rms

1−DRV, 1−SNS2−DRV, 1−SNS2−DRV, 2−SNS2−D&2−S, HPF

(d) Differential drive and pick-up, after LPF.

Figure C.7: Comparison of measured frequency spectrums for single-sided and differ-ential actuation and detection.

ure C.7 illustrates the advantages of differential operation with experimental spectral

measurements of the velocity pick-up signal.

253

254

Appendix D

Allan Variance Analysis

This chapter discusses methods of random process analysis using Allan variance.

While this dissertation is primarily concerned with analysis of random noise compo-

nents in the output signal of a vibratory MEMS gyroscopes, most of the discussed

techniques are equally applicable to analysis of any other random signals.

D.1 Allan Variance Analysis Procedure

A basic procedure of the Allan variance (AVAR) analysis of a signal is presented in

Figure D.1. Allan variance analysis consists of computing a signal’s w(t) root Allan

variance (R-AVAR or RAVAR) σ for different integration time constants τ and then

analyzing the characteristic regions and log-log scale slopes of the σ(τ) curve in order

to identify different noise modes, i.e., random components of the signal with different

autocorrelation power laws σ(τ) ∝ τβ.

The first step of the analysis is to acquire a time history w(t), 0 ≤ t ≤ T , of the

signal of interest using an experimental setup with a digital to analog converter (or

a computer simulation of the experiment). The second step is to fix the integration

time constant τ , divide the acquired time history of the signal into K “bins” of

span τ , average each bin to obtain wk =∫ (k+1)τ

kτw(t)dt, and compute the Allan

255

variance defined as one half of the average of the squares of the differences between

the successive averaged values σ2(τ) = 12〈(wk+1 − wk)2〉|k=0...(K−1).

The described sequence of steps yields the estimated value of the root Allan vari-

ance σ(τ) for the chosen integration time constant τ . In order to obtain the whole

σ(τ) curve, the second step is repeated multiple times for a sequence of τ values. Typ-

ically, the integration time constants τ are iterated through the sequence τ = 2n∆T

with n = 0, 1, . . . N , where ∆T is the sampling time of the w(t) time history.

D.2 Random Noise Modes Classification

While an Allan variance curve for a signal contains essentially the same information as

the signal’s power spectral density (PSD), it presents the information in an alternative

and somewhat more convenient way. The power laws of PSD and RAVAR are related

to each other in the following way:

PSD(f) ∝ fα ⇐⇒ σAV AR(τ) ∝ τβ,

where β = −α + 1

2and f = 1/τ.

Figure D.2 presents a classification of main noise components, or modes, based on

their power spectral density and Allan variance power laws. In the following sections

we discuss the three main noise types, i.e, the white, pink or 1/f , and red or 1/f 2

random processes.

256

Time

Val

ue

Sample Noise −− Time History

(a) First step: collect a time history w(t) of the signal ofinterest.

Time

Val

ue

Sample Noise −− Time History

log−log AVAR

(b) Second step: divide the time history w(t) into bins ofspan τ and compute σ(τ). Repeat for different times.

Figure D.1: Explanation of Allan variance analysis procedure using an example ran-dom process with a white noise and a random walk components.

SpectralType

PossibleSources

AssociatedTerms

PSD(f)power law

σ(t)power law

LongerAveraging

White ThermalAngle

RandomWalk

f 0 t -1/2

t 0

t -1/2

Pink ElectronicsNoise

Flicker f -1

Good

Neutral

Red(Brown)

White NoiseAccumulation

Angle RateRandom Walk

f -2 Bad

Figure D.2: Classification of random noise modes as applied to rate gyroscopes.

257

D.3 White Noise

White noise is a random signal, or process, with a constant power spectral density.

While this definition presents a mathematical abstraction not physically possible due

to its infinite total power, it presents a practically convenient and useful model of

random processes with very short characteristic autocorrelation times. For instance,

the random motion of particles due to mechanical thermal noise has a characteris-

tic cutoff frequency of kBT/h which has a value of approximately 6 THz at room

temperature, making an ideal white noise a good approximation for most practical

purposes.

Important characteristic properties of a white noise type random process in time,

frequency, and Allan variance domains are shown in Figure D.3 using a computer sim-

ulated signal. Power spectral density of the white noise is independent of frequency,

i.e. PSD(f) ∝ fα with α = 0. As expected from Equation E.1, the numerically calcu-

lated root Allan variance of the simulated white noise is governed by σAV AR(τ) ∝ τβ

with β = −1/2, which can be identified from the −1/2 slope of the RAVAR plot in

log-log coordinates.

Figure D.4 illustrates effects of time averaging and integration of a white noise

process. Accumulation or integration of a white noise process yield a random walk

type process whose power spectral density is governed by PSD(f) ∝ fα with α = 2

making it 1/f 2, or equivalently, red noise.

D.4 Pink, 1/f Noise

Random processes with 1/f spectral density power law are naturally the next class

of noise to consider. Flicker noise, commonly encountered in electronic circuits, falls

258

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−10

−5

0

5

10

Time, s

Val

ue

White Noise (Gaussian)

−2−1

0

Time, s

√AV

AR

√AVAR

0 0.1 0.2 0.3 0.4 0.55

10

15

20

Frequency, HzP

ow/fr

eq, d

B/H

z

Power Spectral Density

Figure D.3: Properties of white noise in time, frequency, and Allan variance domain.

0 10 20 30 40 50 60 70 80 90 100−50

0

50

100

150

200

250

300

Time, s

Val

ue

Averaging and Integration of White Noise

White

Averaged White

Integrated White

Figure D.4: Time averaging and integration of white noise.

259

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−2

−1

0

1

2

Time, s

Val

uePink "1/f" Noise

−2−1

0

Time, s

√AV

AR

√AVAR

0 0.1 0.2 0.3 0.4 0.5

−20

−10

0

10

20

Frequency, Hz

Pow

/freq

, dB

/Hz

Power Spectral Density

Figure D.5: Properties of pink, 1/f 2 noise in time, frequency, and Allan variancedomain.

into this category. Figure D.5 illustrates time, frequency, and Allan variance domain

properties of 1/f , or pink noise using a computer simulation. A pink noise can be

obtained by low-pass filtering a white noise with a 3 dB per octave filter. Simply

put, pink noise can be differentiated from a white noise process by more visible low

frequency, slow fluctuations. As expected from Equation E.1, RAVAR has essentially

flat profile in the case of pink, or 1/f noise.

D.5 Red, 1/f 2 Noise

The third important type of random noise to consider is red noise characterized by

1/f 2 power spectral density. This type of random process is also often referred to as a

random walk and occurs whenever a white noise is accumulated or integrated. While

not correct from the color spectral parallel, red, or 1/f 2 noise is sometimes referred

260

to as Brown noise, in honor of Robert Brown who first studied Brownian motion.

Figure D.6 illustrates time, frequency, and Allan variance domain properties of

random walk, or 1/f 2, process by numerically integrating a computer simulated signal

white noise signal. An alternative way to simulate a random walk process is to low-

pass filter a white noise signal with a 6 dB per octave filter. Random walk signal

shows low frequency, slow fluctuations more pronounced than in the pink, 1/f case.

Since the power spectral density of a random walk is given by PSD(f) ∝ fα with

α = −2, its root Allan variance profile is governed by σAV AR(τ) ∝ τβ with β = −1/2,

which can be identified by the α = +1/2 slope of the RAVAR in the log-log scale.

Figure D.7 illustrates properties of a random walk signal with respect to time

integration and averaging using a computer simulated signal, both of which are detri-

mental to the uncertainty of the produced measurement.

D.6 Random Noise Modes Identification

In the previous sections, we discussed how the characteristic slopes of the root Allan

variance curve can be used to identify random noises of different categories. However,

the true brilliance of Allan variance analysis comes from its ability to easily decouple,

identify, and quantify noise modes with different autocorrelation power laws from a

single, combined random process. Figure D.8 illustrates this concept with a computer

simulated sum of a white and red, or 1/f 2 noises.

As the example shows, it is not straightforward to identify the presence and pa-

rameters of the white and red noise components in the simulated signal from its time

history or power spectral density. At the same time, RAVAR plot of the signal clearly

shows two different regions on the log-log scale plot: a region with the −1/2 slope

corresponding to the white noise component, and a region with a +1/2 slope corre-

261

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−200

−150

−100

−50

0

50

Time, s

Val

ue

Brown "1/f2" Noise − Integral of White Noise

−20

1

2

Time, s

√AV

AR

√AVAR

0 0.25 0.50

20

40

60

Frequency, Hz

Pow

/freq

, dB

/Hz

Power Spectral Density

WhiteBrown

Figure D.6: Properties of red, 1/f 2 noise in time, frequency, and Allan variancedomain.

0 2 4 6 8 10 12 14 16 18 20−3

−2.5

−2

−1.5

−1

−0.5

0

0.5x 104

Time, s

Val

ue

Averaging and Integration of Brown Noise

BrownAveraged BrownIntegrated Brown

Figure D.7: Time averaging and integration of red, 1/f 2 noise.

262

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−100

0

100

200

Time, s

Val

ue

White Noise + Brown Noise

−20

1

Time, s

√AV

AR

√AVAR

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

Frequency, HzP

ow/fr

eq, d

B/H

z

Power Spectral Density

White

White+Brown

Brown

Figure D.8: Identification of noise modes using Allan variance analysis illustratedusing a computer simulated sum of a white noise and a red noise.

sponding to the random walk component. Parameters of the two noise components

can be numerically identified by fitting the two regions of the RAVAR log-log curve

with y = ax−1/2 and y = bx1/2, respectively.

The analysis also allows to identify the crossover time, or frequency, between the

two noise modes. As illustrated in Figure D.8, low-pass and high-pass filtering of the

combined noise with respect to the identified crossover frequency allows to separate

out the two noise components in the time domain.

D.7 Application to Rate Gyroscopes

Root Allan variance analysis of zero rate output of micromachined Coriolis vibratory

gyroscope typically reveals well pronounced white and red noises, 1/f 2 noise modes

(pink, or 1/f noise component is sometimes obscured by the other two noise modes).

263

Root Allan variance analysis allows to quantify uncertainty or the rate measurement

as a function of the averaging or integration time in intuitive unit of input angular

rate (usually /s or /h).

One of the traditional applications of gyroscopes is, however, angle measurement.

Since most available micromachined gyroscopes fall into the rate measuring category,

their output has to be integrated to obtain the total angle of rotation. As discussed

in the previous sections, time integration shifts the power spectral density power law

of a random process by −2 exponent. This means that a white noise component in

the rate signal becomes a random walk type component in the angle measurement,

which explains why the white noise of a rate gyroscope is often referred to as angle

random walk (ARW), Figure D.2. Similarly, time integration or a random walk

component of a rate gyroscope output results in a angle measurement noise component

with PSD(f) ∝ fα, α = −4 and root Allan variance σ(τ) ∝ τβ with β = +3/2.

This sheds light on one of the reasons why micromachined rate gyroscopes are not

optimal for applications where an angle measurement is needed. A rate integrating

micromachined gyroscope would provide much better performance since the time

integration of the noise could be avoided.

D.8 Mechanical-Thermal Noise

One of the fundamental performance limits in micromachined vibratory gyroscopes

comes from the mechanical-thermal noise. Analytical investigation of mechanical-

thermal noise output is complicated by the fact that the initial white noise input

first passes through the sense-mode dynamics (which shapes the white noise power

spectral density according to its frequency response profile) and then goes through

the amplitude demodulation with the drive-mode reference signal. Theoretical power

264

−1000 −800 −600 −400 −200 0 200 400 600 800 10000

1

2

3

4

5

6

7

Frequency, Hz

Noi

se S

pect

ral D

ensi

ty, [°/h/

√Hz]

Mechanical−Thermal Noise in Mode−Matched MEMS Gyroscopes

linear−log10 scale

√S(ω)=1.5e5√ (KbTω

y/(4Q3A2M) / (ω2+ω

y2/(2Q)2))

Max(√S)=1.5e5√(KbT/(ω

yA2MQ )), FWHP(S)=ω

y/Q

Levered Tuning Fork3×7 mm2×50 µm SOI

2.5 kHz frequency

increasing Q log

10(Q)= 1:0.5:5.5

Figure D.9: Spectral density of mechanical-thermal noise output.

spectral density of mechanical-thermal noise output in Coriolis vibratory microma-

chined gyroscopes is shown in Figure D.9.

Figure D.10 presents a numerical case study of mechanical-thermal noise in MEMS

gyroscopes. A time history of the output obtained using a MATLAB/Simulink model

of a mode-matched Coriolis vibratory gyroscope is shown in Figure D.10(a). Allan

variance curve of the simulated output time history is shown in Figure D.10(b).

Two distinct regions with different slopes can be identified in the Allan variance of

mechanical-thermal noise. At short integration times Allan variance of mechanical-

thermal noise shows a positive slope β due to the low-pass characteristic of the noise

spectral density at long times. At longer integration times, however, the Allan vari-

ance shows a negative slope β due to the fact that the noise spectral density is essen-

tially flat at very slow frequencies. The crossover time between the two regions of the

mechanical-thermal noise Allan variance can be associated with the time constant of

the resonant sense-mode, 1/∆f = Q/f .

265

0 10 20 30 40 50 60 70 80 90 100

−3

−2

−1

0

1

2

3

Time, s

Rat

e S

igna

l and

Rat

e N

oise

, °/

h

Mechanical−Thermal Noise in Mode−Matched MEMS Gyroscopes

Output Rate Signal, °/h RMS(Output Rate Signal), °/h Input Rate Signal, °/h

Levered Tuning Fork3×7 mm2×50 µm SOI

2.5 kHz frequency, Q=103

RMS =1.5e5√(KbT/(4A2MQ2)) = 1 °/h

(a) Time history of the input and output.

10−2

10−1

100

101

102

103

104

10−3

10−2

10−1

100

Cluster Time, s

Roo

t Alla

n V

aria

nce,

°/h

Mechanical−Thermal Noise in Mode−Matched MEMS Gyroscopes

Gyroscope output Sense−mode LPF ARW=1.5e5√(KbT/(ω

yA2MQ ))=0.53 °/h

Sense−mode time constant Q/f=0.4 s

Levered Tuning Fork3×7 mm2×50 µm SOI

2.5 kHz frequency, Q=103

(b) Allan variance of the rate output.

Figure D.10: Mechanical-Thermal noise in Coriolis vibratory rate gyroscopes.

266

Appendix E

Micro Stage for On-ChipElectro-Mechanical Calibration

This chapter highlights the preliminary development of an on-chip electro-mechanical

self-calibration system for micromachined gyroscopes based on an embedded micro

rotary stage. Figure E.1 illustrates the conceptual design of the system and presents

its potential advantages. The overall goal of the proposed system is the continuous,

in-situ elimination of inertial sensor drifts. The proposed system-on-a-chip utilizes

a Micro Rotary Stage (MiRS) to provide a reference input rate signal, electrical

interconnects to provide uninterrupted power and signal coupling with the rotating

platform, and signal processing algorithm for continuous calibration of scale factor

drifts. The ultimate vision is to combine batch fabricated MiRS with embedded

devices, micro-fluidic interconnects system, and drift elimination electronics to enable

autonomous, drift-free rate sensor system. Alternatively, the MiRS system-on-a-chip

can be used as a versatile packaging platform for separately fabricated microsystems.

E.1 Conceptual Design of the System

The novel drift elimination system based on the MiRS may enable a revolutionary re-

duction of drifts by real-time execution of autonomous, in-situ calibration of sensors.

267

Micro Rotary Stage (MiRS) for On-Chip Electro-Mechanical Calibration

Micro Rotary Stages (MiRS) compensates sensor drifts by providing a persistent input reference for continuous recalibration

MiRS for inertial sensors can attain 1000x reduction of scale factor drift

MAIN ACHIEVEMENT:Architecture for system-on-a-chip combining MiRS, inertial sensors, micro-fluidic electrical interconnects system, and signal processing electronics for sensor drift elimination.

HOW IT WORKS: .

KEY INNOVATIONS:• Micro-fluidic electrical interconnects system

with micro-scale carbon electrodes provides uninterrupted transfer of power and signals between the MiRS base and sensor.

• Sensor scale factor is continuously updated using MiRS angular rate reference signal.

• MiRS reference is extremely accurate due to SideBand Ratio (SBR) detection algorithm.

State of the Art (Draper Lab):Precision/ resolution 1 °/hRepeatability 500 °/h

Low repeatability limits potential applications

QU

AN

TIT

AT

IVE

IM

PA

CT

EN

D-O

F-P

RO

JEC

T G

OA

L

ST

AT

US

QU

ON

EW

IN

SIG

HT

S

Stand alone MEMSgyroscope scale factor stability

400ppm

MiRS with embeddedgyroscope scale factor stability

<2ppm

MiRS robustness is enabled by SBR detection with inherent self calibration

Fully integrated MiRS and inertial sensor on a chip with 1000x improved scale factor drift

Figure E.1: Conceptual design and potential advantages of an on-chip electro-mechanical calibration system enabled by an embedded micro rotary stage.

While the MiRS architecture can augment the functionality of various sensors, the

main focus is on the drastic improvement of MEMS gyroscopes drifts. During opera-

tion, the embedded gyroscope is subject to both external input angular rate (DC to

100 Hz frequency range) as well as a persistent, sinusoidal reference generated by the

MiRS at a frequency higher than the gyroscope’s desired bandwidth (on the order of

200 Hz). The gyroscope output will contain signals corresponding to both the exter-

nal rate and the internal reference which can be frequency de-multiplexed into the low

frequency response to the external angular rate, and the higher frequency response to

the MiRS reference. Through continuous measurement of the “Calibration Output”

to the “MiRS Calibration Reference” ratio, the algorithm eliminates scale factor drift

from the final angular rate measurement. The MiRS enabled gyroscope with in-situ

calibration is projected to achieve <2 ppm stability - a 1000 improvement compared

268

to the current state of the art.

In order to implement and demonstrate the proposed system, a number of engi-

neering challenges need to be addressed, including the following:

1. Mechanical crosstalk between a MiRS and the embedded sensor. The MiRS

structural modes should be precisely engineered to yield one low-frequency op-

erational mode, while elevating the higher frequency modes away from the sen-

sor’s sensitive frequencies.

2. Electrical contact quality and reliability. Technology for micro-glassblowing

with pre-deposited metal traces can be developed to produce very smooth micro-

channels. The glass-blown micro-channels may enable an intriguing capability

of conductive liquid (liquid metals or ionic fluids) encapsulation. Elimination of

the dry contact by the fluidic electrical interconnects may allow exceptionally

low friction and wear combined with low resistance electrical contact.

The complete micromachined rate table system-on-a-chip consists of three main

components: a Micro Rotary Stage (MiRS) to provide an input reference rate signal

to the gyroscope, micro-fluidic electrical interconnect system for continuous electri-

cal power and signal coupling with the rotating platform, and the drift elimination

algorithm to perform the autonomous, real-time recalibration. Specific technical ap-

proaches for realizing the mechanical structure of the MiRS are discussed in [135].

Below we review a proposed design of the calibration algorithm.

E.2 Scale Factor Drifts in Rate Gyroscopes

The input-output relationship of a sensor, such as a MEMS gyroscope, can be de-

scribed as Vout(Ωin) = SF [G] × Ωin, where Ωin is the input angular rate, Vout is the

269

SBRDetector

Control

Feedb

ack

||||Calibration Output

Micro-Rotary Stage (MiRS)with embedded MEMS gyroscope

Self-CalibrationAlgorithm

MiRS Calibration Reference

Input RateUncalibrated Output

In-SituCalibratedRateOutput

||||||||

(2)(1)x( / )(3)

(3)

(1)

(2)

LPF

HPF

V (Ù )out in

Total Gyro Output

Ùin

Ùref

Figure E.2: MiRS based in-situ calibration algorithm for real-time drift elimination.

output voltage, and SF [G] is the gyroscope’s scale factor. Generally, the scale factor

value is identified through initial calibration and ideally remains constant through the

lifetime of the sensor. However, a more realistic model that reflects experimentally

observed drifts is given by

SF [G] = SF0[G] + SF∆[G] + SFσ[G], (E.1)

where SF0[G] is the nominal constant value, SF∆[G] is a slowly varying drift com-

ponent responsible for loss of calibration and decreased accuracy, and SFσ[G] is a

stochastic component of the gyroscope’s instantaneous scale factor with standard de-

viation σ. Periodic calibration is needed to eliminate SF∆[G] and minimize the effect

of SFσ[G]. MEMS gyroscope scale factor drifts are extremely challenging to com-

pensate due to complex dynamics of the multi degree of freedom electromechanical

system with multiple drift-prone parameters and extremely small Coriolis-induced

sense-mode displacements.

270

E.3 Proposed Calibration Algorithm

In the proposed rate measurement system, Figure E.2, a self-calibration algorithm is

employed to produce a final, drift-free, voltage output proportional to the external

input angular rate. The idea of the algorithm is to use the continuously measured

ratio between the “Calibration Output” and “MiRS Output Calibration Reference”

to cancel out any drifts of the MEMS gyroscope. More specifically, the input-output

relationship for the proposed rate measurement system can be derived as

Vout(Ωin) = SF [G]× Ωin ×SF [MiRS]× γ0

SF [G]× γ0

= SF [MiRS]× Ωin, (E.2)

where SF [MiRS] is the scale factor of the integrated MiRS and γ0 is the amplitude

of the generated sinusoidal angular rate reference signal. The scale factor of the

proposed system does not depend on the scale factor (and its drift) of the embedded

gyroscope; instead, it is defined only by MiRS scale factor SF [MiRS].

The proposed MiRS is a single degree of freedom system operated in continuous,

large amplitude self-resonant motion. As shown in Figure E.3, these unique char-

acteristics of the MiRS allows the direct application of the SideBand Ratio (SBR)

detection method described in [123, 132]. The SBR detection method constructively

utilizes the inherent nonlinearity of parallel plate capacitive pick-up and is robust to

variations of critical parameters: nominal capacitance, frequency and amplitude of

the probing voltage, and amplifier gain. Robustness of the SBR detection method

untimely translates into extreme stability of the MiRS scale factor and consequently

can provide a 3 order of magnitude improvement to the stability and drift of the

proposed rate system with on-chip autonomous self-calibration.

271

amplitude of motion x0is detected independently of

R, Csn, ωc, and vcwhile also boosting the SNR.

SBR r

)(tCplates)sin()( 0 txtx dω=

)sin( tvV ccdc ω+ Current

SBR r

γ

x0=2r/(r2+1)

Figure E.3: SideBand Ratio (SBR) detection of motion constructively utilizes nonlin-earity of capacitive pick-up to provide the MiRS with superior robustness and scalefactor stability.

272