Self-Noise of the MET Angular Motion Seismic Sensors

Research ArticleSelf-Noise of the MET Angular Motion Seismic Sensors

Egor V Egorov Ivan V Egorov and Vadim M Agafonov

Center for Molecular Electronics Moscow Institute of Physics and Technology 9 Institutskiy Pereulok DolgoprudnyMoscow 141700 Russia

Correspondence should be addressed to Vadim M Agafonov agvadimyandexru

Received 29 October 2014 Revised 5 January 2015 Accepted 5 January 2015

Academic Editor Yanbiao Liao

Copyright copy 2015 Egor V Egorov et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Interest to angular motion seismic sensors is generated by an expectation that direct measurement of the rotations associatedwith seismic signals would allow obtaining more detailed and accurate information from them Due to the seismic signals lowintensity a self-noise of the sensors is one of the most crucial parameters characterizing their performance In seismic applicationsthe molecular-electronic transfer (MET) technology is considered as one of the most promising technologies for the rotationsmeasurements In this researchwe have developed a noisemodel for theMET angular sensorsThe experimental part of the researchwhich fully agrees with theoretical data includes the instrument self-noise measurement in quite locations Based on the modellingwe have revealed the directions of further research to improve the MET angular sensors performance

1 Introduction

Unlike traditional geophones angular motion seismic sen-sors are not sensitive to translational vertical or horizontalmotions and generate an output signal only in presence ofground or structure rotations Interest to angular motionseismic sensors is stimulated by an expectation that directmeasurements of the rotations associated with seismic sig-nals would allow estimating more precisely the responseof the structures to seismic input providing more accuratemeasurement of the seismic field spatial distribution andseparating modes of seismic waves based on their polariza-tion and determine site effect [1ndash3]

For seismic applications the angular motion sensorsshould be capable of a better than 01 120583radsec resolution anddisplay low sensitivity to linear motion Taking into accountthat the angular seismic sensors could be largely used in oiland gas seismic exploration their compactness low cost andlow power consumption are to be the essential requirementsNowadays among a variety of technologies the molecular-electronic transfer (MET) technology is likely the onlyone to offer a reasonably priced commercial product of therequired performance [4] The sensors based on this tech-nology are also known as electrochemical angular motionsensors Although the MET sensors appeared to be useful for

many applications some of them require significantly betterperformance than that one currently achieved

In this paper we concentrate our efforts on the analysisof the MET angular sensors self-noise Improvement of thenoise characteristics for MET angular sensors is not possiblewithout understanding of the physical mechanisms respon-sible for the self-noise generation We have experimentallyinvestigated the MET angular sensor self-noise for the range1ndash150Hz which covers the frequencies most significant forseismic exploration Additional experiments and analysis ofthe possible noise sources allowed defining the processesresponsible for the sensor self-noise at different frequenciesThe noise model has been developed and compared withthe experimental data Finally the methods for the self-noiseimprovement are suggested

2 Materials and Methods

21 Instruments The critical part of the angular motionsensors is a transducer The mechanical configuration of theangular motion transducer based on the MET technology ispresented in Figure 1 The transducer consists of a toroidalchannel filled with a highly concentrated iodide-iodinewater-based electrolyte An expansion volume allows com-pensating temperature expansions of the liquidThe sensitive

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 512645 5 pageshttpdxdoiorg1011552015512645

2 Journal of Sensors

Ω

q

Expansion volume

Toroidal housing

Electrolyte

Sensitive cell

Figure 1 The MET angular sensor mechanical configuration

Figure 2 View of the angular seismic sensor used in the experi-ments

cell placed across the channel converts liquid motion insidethe channel into the electrical response For the commercialsensors the sensitive cell consists of four mesh electrodessandwiched together with three porous dielectric ceramicspacers [5] Alternative configurations for sensitive cells havebeen reported recently [6ndash9] External electrodes (anodes)are connected to positive potential relative to the internalones (cathodes) The operating principles are based on thesensitivity of the active ions distribution and currents passingthrough the electrodes to the electrolyte motion Commonlythe differential cathodic current is used as an output signal ofthe MET transducer The electrodes of the cell are connectedto the signal conditioning electronic board which convertsthe differential output current from the cell into voltage andshapes the response in specified frequency operational range

In our experiments we used the METR-11 (1ndash150Hzfrequency operational range) sensor manufactured by R-sensors LLC (httpwwwr-sensorsru) The instrumentused in the tests comprises the ceramic transducer with theelectrodes inside filled with an electrolyte and electronicboard The parts are held together by an external case (seephoto on Figure 2) The manufacturer specified that scalefactor is 119870 = 50Vradsec

The transducer toroid has external diameter of 50mmand the squared cross-section of the toroidal channel is 6 times6mm in size The electrodes are made from platinum meshwith cells of 170 times 170 120583m and wire diameter of 45 120583mThe dielectric spacers are of sim120120583m thick with 80 roundthrough-holes 300120583m in diameter each

The block diagram of the electronic signal conditioningboard is shown in Figure 3 The first stage (marked as ldquostage1rdquo in Figure 3) is designated for transducer output currenttransformation to voltage and for scale factor temperaturecompensation The second stage (ldquostage 2rdquo) is responsiblefor high frequency correction and for additional frequency-dependent temperature compensationThe third stage (ldquostage3rdquo) contains low pass and high pass second-order Butter-worth filters having the cut-off frequencies 1Hz and 150Hzcorrespondingly

For further analysis we need to know the instrumenttransfer function which could be presented by a product ofthe MET transducer transfer function 119882trans with transferfunctions of three stages of the electronic circuitry119882

1st 1198822ndand 1198823rd

119882inst = 119882trans1198821st1198822nd1198823rd (1)

The MET transducer transfer function 119882trans convertsrotation rate 120596 into the differential cathodic current 119868diff

119868diff = 119882trans120596 (2)

According to the data given in [10] 119882trans behavesdifferently depending on frequency range It grows up sim119891from 0 to approximately sim01Hz and then it does not dependon frequency up to sim10Hz and goes down to sim1119891 at higherones

The electronics transfer functions could be calculatedanalytically or modeled using electronic designerrsquos standardsoftwareThe first stage converts differential cathodic current119868diff into the first-stage output voltage

1198801= 1198821st119868diff = 119877fb119868diff (3)

Here 119877fb is an equivalent resistance in the feedback ofthe first-stage operational amplifier In practice as it could beseen on Figure 3 119877fb is made of several temperature depen-dent and permanent resistors connected in sequence andin parallel thus providing compensation of the transducersensitivity temperature variations

Transfer functions of the second and third stages areshaped to achieve flat response |119882inst| asymp 119870 = 50Vradsecof the instrument in the operating frequency range with lowand high cut-off frequencies at 1 and 150Hz correspondinglyThe calculated frequency behavior of the product |119882

2nd1198823rd|is shown in Figure 4

22 Experiments and Data Analysis In the first set of ourexperiments we measured the instrument self-noise For thatpurpose we placed two METR-11 sensors in the basement onthe solid concrete foundation with sensitivity axis directedvertically upwardThe recording wasmade by 24-bit digitizerLTR-24 (httpwwwlcardru) over the quietest nighttime

Journal of Sensors 3

Stage 1

Input Output

Stage 2 Stage 3

DA11

AD706R

CZ1

10120583F

RTZ1A

22k

22k

22k

22k

RZ3A

RZ4A

RTZ1

RTZ2

11 k

11 k

12 k

12 k

13 k

13 k

RZ1

RZ4

RZ2

RZ3

RTZ2A

+minus

+minus

21

6

57

1514

161

3

+minus

+minus

23

RZ5

10k

10k10k

TBD

TBD TBD

TBD

TBD

RZ7 RTZ3

120 k 330k RZ12 CZ5CZ2A RZ8 CZ3

180 k

CZ4 RZ1333M 22 120583F

CZ2 RZ9100M 300k

RZ6 DA22 RZ10 RZ11 DA21 RZ17

CZ7

47 120583FRZ16 CZ6

16

k

16k

10 120583F

CZ8

022120583

F

RZ18

510

k

CZ10

0047120583

FRZ

20

24

M

CZ9 RZ19

47120583

F

47 120583F

DA24RZ14

16kAD704RAD704RAD704R

Figure 3 Block diagram of the signal conditioning board

No

units

01 1 10 100003 100000001

001

1

100

(Hz)

Figure 4 The dimensionless electronic amplifier amplituderesponse versus frequency

periodThe different sampling rates were tried and the resultswere compared with the aim of determining an optimalsampling rate when there is no noise transfer from highfrequencies to the frequency range of interests as a result ofthe aliasing

For each sensor the data processing includes the win-dowing of the recorded signal each window 128 seconds inlength calculation of the signal spectrum for each windowand averaging them over all of the windows The outputspectrum has been converted to equivalent angular rate unitsusing the known instrument scale factor K The resultingcurves for one of the tested sensors are presented in Figure 5By comparison of the curves obtained at different samplingrates we can observe that in the 5ndash100Hz frequency rangethe averaged spectrumat sampling rate 400 sps is significantlyhigher than the one found at 4000 sps This effect should beattributed to the aliasing In other experiments we used onlythe data obtained at 4000 sps

The correlation function was calculated for the signalsrecorded by two METR-11 sensors The correlation is high(up to 09) at frequencies corresponding to several peaks at

01 1 10 100002 1000

1e minus 008

1e minus 007

6e minus 009

1e minus 006

(Hz)

(rad

sH

z)

Figure 5 Spectra of the METR-11 sensor output signal The datawere recorded at quiet nighttime Different colors correspond todifferent sampling rates Red 400 sps blue 4000 sps

the spectrum observed in the range 40ndash200Hz These peaksshould be associated with the real seismic signal of artificialnature and that reason cannot be considered as a part ofthe sensors self-noise Beyond these peaks the correlation isless than 02 and we associate the recorded signals with theinstrument self-noise The solid smooth line in Figure 5 isan approximation of the self-noise curve when only parts ofthe signal corresponding to the frequency ranges with lowcorrelation are used for analysis

The resulting self-noise frequency behavior as presentedby solid smooth line has the following features

(1) It goes down from 2 sdot 10minus7 ((radsec)radicHz) to 6 sdot10minus8((radsec)radicHz) in the frequency range 1ndash10Hz

Here the frequency dependence is sim 1radic119891(2) After sim40Hzminimum at sim 3 sdot 10minus8 ((radsec)radicHz)

the self-noise increases approximately twice up to 6 sdot10minus8((radsec)radicHz) at 200Hz

In the next set of the experiments we measured the elec-tronics self-noise The transducer was replaced by a constant


01 1 10 100 10000021e minus 009

1e minus 008

1e minus 007

1e minus 006

(Hz)

(rad

sH

z)

Figure 6 Self-noise of the signal conditioning electronics withdifferent input resistors Red line 119877in = 10Ohm blue line 119877in =100Ohm

resistor modelling its electrical impedance We used 10Ohmand 100Ohm resistors For convenience of the comparisonwith the results presented in Figure 5 the electronic noisehas been converted from output voltage to the equivalentangular rate The resulting noise curves are presented inFigure 6 At frequencies close to 1Hz the self-noise of theelectronics practically does not depend on the resistor valueand is sim6 times lower than the sensor self-noise presented bysolid line in Figure 5 At higher frequencies using 10 timessmaller resistor means significantly higher (almost 10 times)electronics self-noise At high frequencies the electronics self-noise could be either higher or lower than the measuredsensor self-noise depending on the transducer impedanceSo at low frequencies the transducer is the major sourceof the self-noise while at higher frequencies the situationdepends on the input impedance value and could be oppositewhen electronic noise achieves and even exceeds the self-noise produced in the transducer

23 Theoretical Model Several processes responsible for theMET motion sensors self-noise have been described in theliterature [4 11ndash13] Based on the experimental data presentedabove we propose a hypothesis that for the frequency range ofinterest major contributors into the angular sensor self-noiseare the convective self-noise investigated in [12] and the self-noise of the signal conditioning electronics So the total noisecould be presented by the following equation

⟨1198802

119891⟩total= ⟨1198802

119891⟩conv+ ⟨1198802

119891⟩electronics

(4)

As observed in the experiments presented at [11] the PSDof the convective noise in the transducer output current atthe frequencies above 1Hz has approximatelysim 1119891 behaviorTaking into account according to [10] that in this range thetransducer transfer function119882trans is frequency independentwe obtain the following formula

⟨1198802

119891⟩conv=119860

119891 (5)

01 1 10 100003 1000(Hz)

1e minus 009

1e minus 008

1e minus 007

1e minus 006

(rad

sH

z)

Figure 7 Modelling of the electronic board self-noise (blue curveexperiment red curve theoretical approximation)

Only little is known about the parameter 119860 dependenceon the geometry of the signal converting MET cell and hereit is considered as a fitting parameter of a model

For the electronic self-noise we suppose that most of thenoise is generated in the first stage and is the result of avoltage noise of the first stage operational amplifier Afterthis simplification the electronic self-noise in the instrumentoperational frequency range could be given by the following

⟨1198802


= ⟨1198802

119891⟩amp(1 +119877fb119885in)

2 10038161003816100381610038161198822nd1198823 rd10038161003816100381610038162

1198702 (6)

Here ⟨1198802119891⟩amp is voltage noise power spectral density for

the first-stage operational amplifier 119885in is first-stage inputimpedance Values 119860 and 119885in in (5) and (6) are not knowna priori and are considered in the following analysis as fittingparameters

Using (1) and taking into account |1198821st| = 119877fb formula

(6) could be also presented as the following one

⟨1198802

119891⟩electromics

= ⟨1198802

119891⟩amp(1 +119877fb119885in)

21

1003816100381610038161003816119882trans119877fb10038161003816100381610038162 (7)

3 Results and Discussions

Let us substitute the following values 119885in = 119877in =40Ohm 119877fb = 1 kOhm 119870 = 50 (V(radsec)) ⟨1198802

119891⟩amp asymp

20 nVradicHz [14] in (6) The spectrum of the electronic self-noise is presented in Figure 7 as a solid black line Theexperimental behavior of the electronic noise is in goodagreement with the theoretical calculations in the wholerange of interest Some discrepancy is observed at lowerfrequency which is probably the result of simplificationsdone when deriving formula (6) Nevertheless as followsfrom the experimental data this difference is not influentialsince the low frequency electronic noise is only a minorcontributor into the total noise of the instrument

Finally let us put 119860 = 55 sdot 107 (radsec)2 in (5)and substitute ⟨1198802

119891⟩conv⟨119880

2

119891⟩electromics from (5) and (6) into

formula (4) The resultant spectrum is presented in Figure 8as a solid black line


1 10 10004 400(Hz)

1e minus 008

1e minus 007

1e minus 006

5e minus 009

3e minus 006

(rad

sH

z)

Figure 8Modelling of the angular sensor self-noise (red electronicself-noise blue curve sensors self-noise)

As discussed above the peaks on the experimental curveresulted from the real seismic signals and should not beconsidered as an instrument self-noise Taking this intoaccount we can conclude that the theoretical (black line) andthe experimental curves (blue line) are in good agreement

4 Conclusions

The model of the MET angular motion sensor self-noisebased on the assumption that two physical mechanismsare responsible for the instrument self-noise agrees withexperimental data These two sources are the hydrodynamicconvection (first term in (4)) and amplifiers self-noise (sec-ond term in (4)) The noise produced by the convection isdominant at low frequencies and then goes downsim1119891 whilethe electronic noise prevails at high frequencies

The self-noise at low frequencies could be reduced bymodification of the transducer According to earlier analysis[12] this kind of noise could be decreased by using of thesensitiveMET cell geometry characterized by lower Rayleighnumber At high frequencies as follows from formula (7)the improvement could be achieved by using less noisyoperational amplifiers at the first stage The transducerimprovements should be directed toward higher sensitivity|119882trans| and higher output impedance |119885in|

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The results presented in this paper have been obtainedunder the projects supported by Russian Foundation of BasicResearches (Grant no 14-07-00232) and Russian Ministry ofEducation and Science under Project ID RFMEFI57514X0017and state assignment no 315792014K Authors sincerelythankDr Dmitriy Zaitsev formany fruitful discussions of thetopics related to the publication

References

[1] L Chin-Jen and L George ldquoCalibration and applications ofa rotational sensorrdquo httpwwwiriseduhqsits 13 docsmonLinpptx

[2] M Bernauer A Fichtner and H Igel ldquoMeasurements oftranslation rotation and strain new approaches to seismicprocessing and inversionrdquo Journal of Seismology vol 16 no 4pp 669ndash681 2012

[3] N Kapustian G Antonovskaya V Agafonov K Neumoin andM Safonov ldquoSeismic monitoring of linear and rotational oscil-lations of the multistory buildings in Moscowrdquo GeotechnicalGeological and Earthquake Engineering vol 24 pp 353ndash3632013

[4] H Huang V Agafonov and H Yu ldquoMolecular electric trans-ducers as motion sensors a reviewrdquo Sensors vol 13 no 4 pp4581ndash4597 2013

[5] F Bernauer J Wassermann and H Igel ldquoRotational sensorsmdasha comparison of different sensor typesrdquo Journal of Seismologyvol 16 no 4 pp 595ndash602 2012

[6] V G Krishtop V M Agafonov and A S Bugaev ldquoTechnolog-ical principles of motion parameter transducers based on massand charge transport in electrochemicalmicrosystemsrdquoRussianJournal of Electrochemistry vol 48 no 7 pp 746ndash755 2012

[7] G Li D Chen W He and J Wang ldquoMicro-machined elec-trochemical seismic sensors with interdigital electrodesrdquo KeyEngineering Materials vol 503 pp 61ndash66 2012

[8] W He D Chen G Li and J Wang ldquoLow frequency electro-chemical accelerometer with low noise based on MEMSrdquo KeyEngineering Materials vol 503 pp 75ndash80 2012

[9] H Huang B Carande R Tang et al ldquoA micro seismometerbased onmolecular electronic transducer technology for plane-tary explorationrdquoApplied Physics Letters vol 102 no 19 ArticleID 193512 2013

[10] V A Kozlov and M V Safonov ldquoDynamic characteristic ofan electrochemical cell with gauze electrodes in convectivediffusion conditionsrdquo Russian Journal of Electrochemistry vol40 no 4 pp 460ndash462 2004

[11] D L Zaitsev P V Dudkin and V M Agafonov ldquoFluctuatingvortex flows and their contribution to the noise of molecularelectronic convertersrdquo Izvestiya Vysshikh Uchebnykh ZavedeniiRadiofizika no 5 pp 61ndash68 2006 (Russian)

[12] V M Agafonov and D L Zaitsev ldquoConvective noise in molec-ular electronic transducers of diffusion typerdquo Technical Physicsvol 55 no 1 pp 130ndash136 2010

[13] V A Kozlov and M V Safonov ldquoSelf-noise of molecularelectronic transducersrdquo Technical Physics vol 48 no 12 pp1579ndash1582 2003

[14] httpwwwanalogcomstaticimported-filesdata sheetsAD704pdf

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Ω

q

Expansion volume

Toroidal housing

Electrolyte

Sensitive cell

Figure 1 The MET angular sensor mechanical configuration

Figure 2 View of the angular seismic sensor used in the experi-ments

cell placed across the channel converts liquid motion insidethe channel into the electrical response For the commercialsensors the sensitive cell consists of four mesh electrodessandwiched together with three porous dielectric ceramicspacers [5] Alternative configurations for sensitive cells havebeen reported recently [6ndash9] External electrodes (anodes)are connected to positive potential relative to the internalones (cathodes) The operating principles are based on thesensitivity of the active ions distribution and currents passingthrough the electrodes to the electrolyte motion Commonlythe differential cathodic current is used as an output signal ofthe MET transducer The electrodes of the cell are connectedto the signal conditioning electronic board which convertsthe differential output current from the cell into voltage andshapes the response in specified frequency operational range

In our experiments we used the METR-11 (1ndash150Hzfrequency operational range) sensor manufactured by R-sensors LLC (httpwwwr-sensorsru) The instrumentused in the tests comprises the ceramic transducer with theelectrodes inside filled with an electrolyte and electronicboard The parts are held together by an external case (seephoto on Figure 2) The manufacturer specified that scalefactor is 119870 = 50Vradsec

The transducer toroid has external diameter of 50mmand the squared cross-section of the toroidal channel is 6 times6mm in size The electrodes are made from platinum meshwith cells of 170 times 170 120583m and wire diameter of 45 120583mThe dielectric spacers are of sim120120583m thick with 80 roundthrough-holes 300120583m in diameter each

The block diagram of the electronic signal conditioningboard is shown in Figure 3 The first stage (marked as ldquostage1rdquo in Figure 3) is designated for transducer output currenttransformation to voltage and for scale factor temperaturecompensation The second stage (ldquostage 2rdquo) is responsiblefor high frequency correction and for additional frequency-dependent temperature compensationThe third stage (ldquostage3rdquo) contains low pass and high pass second-order Butter-worth filters having the cut-off frequencies 1Hz and 150Hzcorrespondingly

For further analysis we need to know the instrumenttransfer function which could be presented by a product ofthe MET transducer transfer function 119882trans with transferfunctions of three stages of the electronic circuitry119882

1st 1198822ndand 1198823rd

119882inst = 119882trans1198821st1198822nd1198823rd (1)

The MET transducer transfer function 119882trans convertsrotation rate 120596 into the differential cathodic current 119868diff

119868diff = 119882trans120596 (2)

According to the data given in [10] 119882trans behavesdifferently depending on frequency range It grows up sim119891from 0 to approximately sim01Hz and then it does not dependon frequency up to sim10Hz and goes down to sim1119891 at higherones

The electronics transfer functions could be calculatedanalytically or modeled using electronic designerrsquos standardsoftwareThe first stage converts differential cathodic current119868diff into the first-stage output voltage

1198801= 1198821st119868diff = 119877fb119868diff (3)

Here 119877fb is an equivalent resistance in the feedback ofthe first-stage operational amplifier In practice as it could beseen on Figure 3 119877fb is made of several temperature depen-dent and permanent resistors connected in sequence andin parallel thus providing compensation of the transducersensitivity temperature variations

Transfer functions of the second and third stages areshaped to achieve flat response |119882inst| asymp 119870 = 50Vradsecof the instrument in the operating frequency range with lowand high cut-off frequencies at 1 and 150Hz correspondinglyThe calculated frequency behavior of the product |119882

2nd1198823rd|is shown in Figure 4

22 Experiments and Data Analysis In the first set of ourexperiments we measured the instrument self-noise For thatpurpose we placed two METR-11 sensors in the basement onthe solid concrete foundation with sensitivity axis directedvertically upwardThe recording wasmade by 24-bit digitizerLTR-24 (httpwwwlcardru) over the quietest nighttime


Stage 1

Input Output

Stage 2 Stage 3

DA11

AD706R

CZ1

10120583F

RTZ1A

22k

22k

22k

22k

RZ3A

RZ4A

RTZ1

RTZ2

11 k

11 k

12 k

12 k

13 k

13 k

RZ1

RZ4

RZ2

RZ3

RTZ2A

+minus

+minus

21

6

57

1514

161

3

+minus

+minus

23

RZ5

10k

10k10k

TBD

TBD TBD

TBD

TBD

RZ7 RTZ3


180 k

CZ4 RZ1333M 22 120583F

CZ2 RZ9100M 300k


CZ7

47 120583FRZ16 CZ6

16

k

16k

10 120583F

CZ8

022120583

F

RZ18

510

k

CZ10

0047120583

FRZ

20

24

M

CZ9 RZ19

47120583

F

47 120583F

DA24RZ14



No

units

01 1 10 100003 100000001

001

1

100

(Hz)





01 1 10 100002 1000

1e minus 008

1e minus 007

6e minus 009

1e minus 006

(Hz)

(rad

sH

z)









01 1 10 100 10000021e minus 009

1e minus 008

1e minus 007

1e minus 006

(Hz)

(rad

sH

z)




⟨1198802

119891⟩total= ⟨1198802

119891⟩conv+ ⟨1198802


(4)


⟨1198802

119891⟩conv=119860

119891 (5)

01 1 10 100003 1000(Hz)

1e minus 009

1e minus 008

1e minus 007

1e minus 006

(rad

sH

z)




⟨1198802


= ⟨1198802

119891⟩amp(1 +119877fb119885in)

2 10038161003816100381610038161198822nd1198823 rd10038161003816100381610038162

1198702 (6)





⟨1198802


= ⟨1198802

119891⟩amp(1 +119877fb119885in)

21

1003816100381610038161003816119882trans119877fb10038161003816100381610038162 (7)



119891⟩amp asymp



119891⟩conv⟨119880

2




1 10 10004 400(Hz)

1e minus 008

1e minus 007

1e minus 006

5e minus 009

3e minus 006

(rad

sH

z)



4 Conclusions





Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Stage 1

Input Output

Stage 2 Stage 3

DA11

AD706R

CZ1

10120583F

RTZ1A

22k

22k

22k

22k

RZ3A

RZ4A

RTZ1

RTZ2

11 k

11 k

12 k

12 k

13 k

13 k

RZ1

RZ4

RZ2

RZ3

RTZ2A

+minus

+minus

21

6

57

1514

161

3

+minus

+minus

23

RZ5

10k

10k10k

TBD

TBD TBD

TBD

TBD

RZ7 RTZ3


180 k

CZ4 RZ1333M 22 120583F

CZ2 RZ9100M 300k


CZ7

47 120583FRZ16 CZ6

16

k

16k

10 120583F

CZ8

022120583

F

RZ18

510

k

CZ10

0047120583

FRZ

20

24

M

CZ9 RZ19

47120583

F

47 120583F

DA24RZ14



No

units

01 1 10 100003 100000001

001

1

100

(Hz)





01 1 10 100002 1000

1e minus 008

1e minus 007

6e minus 009

1e minus 006

(Hz)

(rad

sH

z)









01 1 10 100 10000021e minus 009

1e minus 008

1e minus 007

1e minus 006

(Hz)

(rad

sH

z)




⟨1198802

119891⟩total= ⟨1198802

119891⟩conv+ ⟨1198802


(4)


⟨1198802

119891⟩conv=119860

119891 (5)

01 1 10 100003 1000(Hz)

1e minus 009

1e minus 008

1e minus 007

1e minus 006

(rad

sH

z)




⟨1198802


= ⟨1198802

119891⟩amp(1 +119877fb119885in)

2 10038161003816100381610038161198822nd1198823 rd10038161003816100381610038162

1198702 (6)





⟨1198802


= ⟨1198802

119891⟩amp(1 +119877fb119885in)

21

1003816100381610038161003816119882trans119877fb10038161003816100381610038162 (7)



119891⟩amp asymp



119891⟩conv⟨119880

2




1 10 10004 400(Hz)

1e minus 008

1e minus 007

1e minus 006

5e minus 009

3e minus 006

(rad

sH

z)



4 Conclusions





Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










01 1 10 100 10000021e minus 009

1e minus 008

1e minus 007

1e minus 006

(Hz)

(rad

sH

z)




⟨1198802

119891⟩total= ⟨1198802

119891⟩conv+ ⟨1198802


(4)


⟨1198802

119891⟩conv=119860

119891 (5)

01 1 10 100003 1000(Hz)

1e minus 009

1e minus 008

1e minus 007

1e minus 006

(rad

sH

z)




⟨1198802


= ⟨1198802

119891⟩amp(1 +119877fb119885in)

2 10038161003816100381610038161198822nd1198823 rd10038161003816100381610038162

1198702 (6)





⟨1198802


= ⟨1198802

119891⟩amp(1 +119877fb119885in)

21

1003816100381610038161003816119882trans119877fb10038161003816100381610038162 (7)



119891⟩amp asymp



119891⟩conv⟨119880

2




1 10 10004 400(Hz)

1e minus 008

1e minus 007

1e minus 006

5e minus 009

3e minus 006

(rad

sH

z)



4 Conclusions





Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 10 10004 400(Hz)

1e minus 008

1e minus 007

1e minus 006

5e minus 009

3e minus 006

(rad

sH

z)



4 Conclusions





Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Self-Noise of the MET Angular Motion Seismic Sensors

Documents

Transcript of Self-Noise of the MET Angular Motion Seismic Sensors