`Case 6‘”"’”'°°799'JRG ”°"””‘e“‘ 2“ Illlllllllllllllllllllllllllllllfillllllllflllllflllfillllfillla17
`
`US007l3676lB2
`
`(12) United States Patent
`Henry et al.
`
`(10) Patent No.:
`
`(45) Date of Patent:
`
`US 7,136,761 B2
`Nov. 14, 2006
`
`11/1982 Sanchez .................... .. 700/31
`'
`11/1983
`73/861.35
`
`12/1983 Zanker et al.
`......... .. 73/861.02
`12/1983 Smith .................. .. 73/861.356
`1/1985 Smith et al.
`. 73/861.355
`8/1987 Cheung et al.
`73/29.01
`3/1988 Mikasa et al.
`.. 73/23.31
`7/1988 Mehrgardt et al.
`386/34
`9/1988 Aslesen et al.
`.......... .. 73/61.44
`
`
`
`4,358,822 A
`RE31,450 E
`4,419,898 A
`4,422,338 A
`4,491,025 A
`4,688,418 A
`4,727,746 A
`4,757,390 A
`4,773,257 A
`
`(Continued)
`FOREIGN PATENT DOCUMENTS
`
`(54) DIGITAL FLOWMETER
`
`(75)
`
`Inventors: Manus P. Henry, Oxford (GB); David
`W. Clarke, Oxford (GB); James H.
`Vignos, Needharn Heights, MA (US)
`
`(73) Assignee:
`
`Invensys Systems, Inc., Foxboro, MA
`(US)
`
`( * ) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. l54(b) by 0 days.
`
`(21)
`
`Appl. No.: 11/130,233
`
`EP
`
`0 698 783 A1
`
`2/1996
`
`(22)
`
`Filed:
`
`May 17, 2005
`
`(65)
`
`Prior Publication Data
`
`US 2005/0209794 A1
`
`Sep. 22, 2005
`
`(63)
`
`(60)
`
`(51)
`
`(52)
`(58)
`
`(56)
`
`Related U.S. Application Data
`
`Continuation of application No. 10/637,620, filed on
`Aug. 11, 2003, now Pat. No. 6,917,887, which is a
`continuation of application No. 09/931,057, filed on
`Aug. 17, 2001, now Pat. No. 6,754,594, which is a
`continuation of application No. 09/111,739, filed on
`Jul. 8, 1998, now Pat. No. 6,311,136.
`
`Provisional application No. 60/066,554, filed on Nov.
`26, 1997.
`
`Int. Cl.
`G01R 1/00
`G01R 23/00
`
`(2006.01)
`(2006.01)
`(2006.01)
`G01R 1/84
`U.S. Cl.
`............. .. 702/45; 73/861.355; 73/861.356
`Field of Classification Search ................... .. None
`
`See application file for complete search history.
`References Cited
`
`U.S. PATENT DOCUMENTS
`
`3,956,682 A
`RE29,383 E
`4,187,721 A *
`
`5/1976 Van Dyck ..... ..
`
`9/1977 Gallatin et al.
`.
`2/1980 Smith .................. .. 73/861.356
`
`(Continued)
`OTHER PUBLICATIONS
`
`A.F. Skea, “Effects of Gas Leaks in Oil Flow on Single-Phase
`Flowmeters”, Flow Measurement and Instrumentation, vol. 10, pp.
`146-150 (1999).
`
`(Continued)
`
`Primary Examiner—Marc S. Hoif
`Assistant Examiner—Manuel L Barbee
`
`(74) Attorney, Agent, or Firm—Fish & Richardson P.C.
`
`(57)
`
`ABSTRACT
`
`A controller for a flowmeter includes an input module
`operable to receive a sensor signal from a sensor connected
`to a vibratable flowtube. The sensor signal is related to a
`fluid flow through the flowtube. The controller also includes
`a signal processing system operable to receive the sensor
`signal, determine sensor signal characteristics, and output
`drive signal characteristics for a drive signal applied to the
`flowtube. An output module is operable to output the drive
`signal to the flowtube and a control system is operable to
`modify the drive signal and thereby maintain oscillation of
`the flowtube during a transition of the flowtube from a
`substantially empty state to a substantially full state.
`
`12 Claims, 71 Drawing Sheets
`
`Massflow
`Measurement
`
`100
`
`
`
`Digital
`Controller
`
`
`
`110
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 2 of 103 PageID #: 618
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 2 of 103 Page|D #: 618
`
`US 7,136,761 B2
`Page 2
`
`U.S. PATENT DOCUMENTS
`
`............ .. 73/61.44
`5/2003 Dutton et al.
`6,564,619 B1
`.. 73/61.44
`3/2002 Dutton et al.
`2002/0033043 A1
`
`................ .. 702/45
`3/2002 Henry et al.
`2002/0038186 A1
`9/2002 Maginnis .................. .. 702/100
`2002/0133307 A1
`FOREIGN PATENT DOCUMENTS
`0696726 A
`2/1996
`0 702 212 A2
`3/1996
`0827096
`3/1998
`W0 93/21505
`10/1993
`W0 00/10059
`2/2000
`W0 02/08703
`1/2002
`
`EP
`EP
`EP
`W0
`W0
`W0
`
`................... .. 73/861.356
`11/1988 Pratt
`1/1989 Flecken
`.. 331/65
`4/1989 Hargarten et al.
`.. 73/861.356
`4/1989 Dahlin ........ ..
`.. 73/861.357
`8/1989 Kolpak
`73/61.44
`8/1989 Corwon et al.
`.. 73/861.355
`11/1989 Zolock ........ ..
`.. 73/861.356
`1/1990 Mattar et al.
`..
`.. 73/861.357
`1/1990 Bergamini et al.
`73/861.355
`3/1990 Hargarten et al.
`.......... .. 73/198
`3/1990 Thompson
`.. 73/861.356
`OTHER PUBLICATIONS
`6/1990 Hussain .... ..
`. 73/861.355
`73/861.356
`6/1990 Romano
` David Spitzer; “Mass Flowmeters”; Industries Flow Measurement,
`73/32 A
`3/1991 Romano
`Chapter 12; pp. 197-210; 1990.
`7/1991 Titlow et al
`.. 73/861.356
`E. Luntta et al., “Neural Network Approach to Ultrasonic Flow
`..... ..
`73/861.04
`7/1991 Liu et al
`Measurements”, Flow Measurement and Instrumentation, vol. 10,
`9/1991 Thompson ..
`.. 73/861.356
`pp. 35-43, 1999.
`.... ..
`10/1991 Christ et al.
`.. 73/861.356
`J. Hemp et al.; “0n the Theory and Performance of Coriolis Mass
`10/1991 Fitzgerald et al.
`.... .. 73/54.27
`Flowmeters”; Proceedings ofthe International Conference on Mass
`10/1991 Mattar ......... ..
`.. 73/861.355
`Flow Measurement Direct and Indirect; IBC Technical Services; 40
`6/1993 Pummer
`73/629
`pages, Feb. 1989.
`7/1993 Bruck
`73/1.34
`J. Reimann, “Developments in Tow-Phase Mass Flow Rate Instru-
`11/1993 Kolpak ..... ..
`. 73/861.355
`mentation”, pp. 339-402.
`....... ..
`12/1993 Mattar et al.
`73/861.355
`J.T. Grumski et al., “Performance of a Coriolis-type Mass Flow
`3/1994 Arunachalam et al.
`..... .. 702/50
`Meter in the Measurement of Two-phase (air-liquid) Mixtures”,
`4/1994 Cage et al.
`.. 73/861.355
`ASME Fluid Engineering Division Publication FED, vol. 17, pp.
`6/1994 Kalotay ....... ..
`.. 73/861.357
`75-84, 1984.
`9/1994 Matter et al.
`..
`.. 73/861.355
`Joseph DeCarlo; “True Mass-Flow Measurement”; Fundamentals
`9/1994 Kalotay et al.
`..... ..
`73/861.357
`ofFlow Measurement, Unit 11-2; pp. 208-220; 1984.
`3/1995 Kawaguchi et al.
`73/861.355
`VI. Henry et al., “The Implications of Digital Communications on
`7/1995 Colman .......... ..
`.. 73/861.356
`Sensor Validation”, Report No. QUEL 1912/92, University of
`11/1995 Kalotay .... ..
`.. 73/861.356
`Oxford, Department of Engineering Science, Apr. 1992.
`3/1996 Cage et al.
`.. 73/861.356
`VI.P. Henry et al., “A New Approach to Sensor Validation”, Improv-
`3/1996 Patten et al.
`.. 73/861.355
`ing Analyser Performacne, IMC, Mar. 17, 1992.
`7/1996 Kolpak ..... ..
`. 73/861.04
`VI.P. Henry et al., “A Self-Validating Digital Coriolis Mass-flow
`9/1996 Derby et al.
`.... .. 702/45
`Vleter” (1); overview, 1999.
`10/1996 Henry et al.
`....... .. 702/45
`VI.P. Henry et al., “A standard Interface for Self-Validating Sen-
`11/1996 Yokoi et al.
`......... .. 73/861.356
`sors”, Report No. QUEL 1884/91, University of Oxford, Depart-
`1/1997 Carpenter et al.
`.. 73/861.356
`ment of Engineering Science, Sep. 1991.
`7/1997 Keel
`........... ..
`.. 73/861.356
`VI.P. Henry et al., “Signal processing, Data Handling and Commu-
`8/1997 Dutton ..... ..
`. 73/152.18
`nications: The Case for Measurement Validation”, Mar. 1992.
`11/1997 Buttler et al
`702/137
`VI.P. Henry et al., “The Self-Validating Sensor: Rationale Defini-
`3/1998
`706/45
`tions and Examples”, Control Engineering Practice,
`1
`(4), pp.
`3/1998
`. 73/861.56
`585-610, 1993.
`6/1998
`702/104
`VI.P. Henry, “Intelligent Behaviour For Self-Validating Sensors”,
`9/1998
`73/861.356
`Advances in Measurement, pp. 1-7 date unknown.
`3/1999 Kimasauskas et al.
`...... .. 700/29
`VI.P. Henry, “Self-Validation Improves Coriolis Meter”, Control
`7/1999 Mattar et al.
`............. .. 340/606
`Engineering, 42 (6), pp. 81-86 (1995).
`10/1999 Rivkin ................ .. 73/861.356
`VI.P. Henry, “Sensor Validation and Fieldbus”, IEE Computing and
`6/2000 Stadler ................ .. 73/861.356
`Control Engineering Journal, 6 (6), pp. 263-269.
`7/2000 Cunningham et al.
`. 73/861.356
`R.P. Liu et al., “A Neural Network to Correct Mass Flow Errors
`2/2001 Pado et al.
`............... .. 700/104
`Caused by Two Phase Flow in a Digital Coriolis Mass Flow Meter”.
`10/2001 Smith .................. .. 73/861.357
`Engineering Science Department, Oxford University.
`10/2001 Blazey et al.
`..
`.... .. 600/26
`
`Kutin, Joie, et al., “Phase-Locking Control of the Coriolis Meter’s
`10/2001 Henry et al.
`................ .. 702/45
`Resonance Frequency Based on Virtual Instrumentation,” Sensors
`11/2001 Dutton et al.
`............ .. 73/61.44
`and Actuators A 104 (2003), pp. 86-93.
`11/2001 Smith et al.
`.. 73/861.356
`
`Merriam-Webster’s Collegiate Dictionary, Tenth Edition, 1998, p.
`12/2001 Dutton ................ .. 73/861.356
`747.
`4/2002 Sharp ....................... .. 73/1.16
`Wood, et al., “A Phase-Locked Loop for Driving Vibrating Tube
`. . . . . . .
`1/2003 Henrot
`. . . .. 702/54
`
`Densimeters,” Rev. Sci. Instrum., vol. 60, No. 3, Mar. 1989, pp.
`......... .. 73/861.356
`1/2003 Henry et al.
`493-494.
`1/2003 Henry et al.
`................ .. 702/45
`4/2003 Zuckerwar et al.
`....... .. 600/528
`
`* cited by examiner
`
`
`
`
`
`
`
`
`
`4,782,711
`4,801,897
`4,817,448
`4,823,614
`4,852,395
`4,852,410
`4,879,911
`4,891,991
`4,895,030
`4,911,006
`4,911,020
`4,934,195
`4,934,196
`4,996,871
`5,027,662
`5,029,482
`5,050,439
`5,052,231
`5,054,313
`5,054,326
`5,218,869
`5,228,327
`5,259,250
`5,271,281
`5,295,084
`5,301,557
`5,321,991
`5,343,764
`5,347,874
`5,400,653
`5,429,002
`5,469,748
`5,497,665
`5,497,666
`5,535,632
`5,555,190
`5,570,300
`5,578,764
`5,594,180
`5,648,616
`5,654,502
`5,687,100
`5,732,193
`5,734,112
`5,774,378
`5,804,741
`5,877,954
`5,926,096
`5,969,264
`6,073,495
`6,092,429
`6,185,470
`6,301,973
`6,309,342
`6,311,136
`6,318,156
`6,318,186
`6,327,914
`6,378,354
`6,505,131
`6,505,519
`6,507,791
`6,551,251
`
`A
`A
`A
`A
`A
`A *
`A
`A
`A
`A
`A
`A
`A
`A
`A
`A
`A
`A
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`A
`A
`A
`A
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`A
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`A
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`A
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`A
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`A
`A
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`A
`A
`B1
`B1
`B1
`B1
`B1
`B1
`B1
`B1
`B1
`B1
`B1
`B1
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 3 of 103 PageID #: 619
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 3 of 103 PagelD #: 619
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 1 of 71
`
`US 7,136,761 B2
`
`Massfiow
`
`Measurement
`
`100
`
`105
`
`Digital
`Controller
`
`Flow Tube
`
`120
`
`F|G.1
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 4 of 103 PageID #: 620
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 4 of 103 Page|D #: 620
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 2 of 71
`
`US 7,136,761 B2
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 5 of 103 PageID #: 621
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 5 of 103 Page|D #: 621
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 3 of 71
`
`US 7,136,761 B2
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 6 of 103 PageID #: 622
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 6 Of 103 Page|D #: 622
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 4 of 71
`
`US 7,136,761 B2
`
`COMMON MODE 1 11 1
`
`CL
`
`111 1
`
`L00.
`
`(3
`
`ans”
`ac:
`D§<
`
`"‘““‘““‘f*“‘"""“‘”‘
`
`©°—
`LO
`
`‘I’
`
`F1(]
`
`1
`
`M
`L3
`__
`L.|_
`
`0.
`
`, «»a7-¢~$veg
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`-
`eg
`6
`5
`E2
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`P
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 7 of 103 PageID #: 623
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 7 of 103 Page|D #: 623
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 5 of 71
`
`US 7,136,761 B2
`
`Bmmoooi
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 8 of 103 PageID #: 624
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 8 of 103 Page|D #: 624
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 6 of 71
`
`US 7,136,761 B2
`
`500
`
`\
`
`L0
`
`Lo
`
`LO
`
`3
`
`L0
`
`120 Measurements
`
`
`
`DigitalController
`
`FIG.5
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 9 of 103 PageID #: 625
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 9 of 103 Page|D #: 625
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 7 of 71
`
`US 7,136,761 B2
`
`600
`
`/V
`
` 610
`
`
`605
`
`615
`
`620
`
`625
`
`630
`
`Determine
`Frequency
`
`Offset
`
`Determine
`
`Amplitude
`
`Determine
`
`Phase
`
`Determine/Eliminate
`
`
`
`
`
`
`Generate Drive
`Signal
`
`635
`
`
`
`Generate
`
`Measurements
`
`
`
`FIG. 6
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 10 of 103 PageID #: 626
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 10 of 103 Page|D #: 626
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 8 of 71
`
`US 7,136,761 B2
`
`start_samp|e_S1
`
`S1-ih
`
`Voltage
`
`
`+1 I-
`
`
`
`start_offset_S1
`
`
`
`
`
`start_offset_S2
`r4
`
`sta rt_sa m p|e_S2
`
`Vouage
`
`F|G.7B
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 11 of 103 PageID #: 627
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 11 of 103 Page|D #: 627
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 9 of 71
`
`US 7,136,761 B2
`
`0.12
`
`0.1
`
`Sensor Voltage
`(W)
`
`0.0.
`
`0.08 Square of
`
`0.04
`
`0.02
`
`00
`
`0.005
`
`0.01
`
`0.015
`
`0.02
`
`0.025
`
`0.03
`
`Time(s1
`
`FIG. 8A
`
`3 X 10-‘
`
`2.5
`
`2
`
`,5
`
`1
`
`0.5
`
`0
`
`Square of
`Sensor Voltage
`(V'V)
`
`_°<'1§o121
`
`0.0121
`
`0.0122
`
`0.0122
`
`0.0123
`
`0.0123
`
`Time(s)
`
`F|G.8B
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 12 of 103 PageID #: 628
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 12 of 103 Page|D #: 628
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 10 of 71
`
`US 7,136,761 B2
`
`905
`
`initialize Variables
`
`910
`
`_
`_
`Estimate end_point
`
`915
`
`Determine # of Points
`for Curve Fitting
`
`900
`
`/l/
`
`iteration_count = O
`
`
`
`
`Smooth zik-1]. z[k], z[k+1]
`
`940
`
`945
`
`950
`
`955
`
`iteration_count<3
`
`975
`
`Calculate Frequency
`
`92
`
`O
`
`92
`
`5
`
`980
`
`935
`
`iteration_count = iteration_count + 1
`
`Select step length
`
`ep_int = int end_point + 0,5)
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 13 of 103 PageID #: 629
`Case 6:12—cv—00799—JRG Document 25-2 Filed 01/31/13 Page 13 of 103 Page|D #: 629
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 11 of 71
`
`US 7,136,761 B2
`
`1005
`
`1000
`
`/M
`
`1010
`
`
`Determine
`T2m1.f1m2
`
`
`1015
`
`Determine Start and
`
`End of d1m2. d2m1
`
`1020
`
`
`
`
`
`
`Determine Phase,
`Amplitude for di and
`d2m1. and Phase
`Difference
`
`
`
`
`1025
`
`1030
`
`Repeat for
`
`d2: d1lT|2
`
`Generate Averages
`of Amplitude &
`Phase Differences
`
`F|G.10
`
`
`
`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 14 of 103 PageID #: 630O36
`a
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 17 of 103 PageID #: 633
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 17 of 103 PagelD #: 633
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 15 of 71
`
`US 7,136,761 B2
`
`1405
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 18 of 103 PageID #: 634
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 18 of 103 PagelD #: 634
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 16 of 71
`
`US 7,136,761 B2
`
`Mass Flo
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`1500
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 20 of 103 PageID #: 636
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 20 of 103 Page|D #: 636
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 18 of 71
`
`US 7,136,761 B2
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 21 of 103 PageID #: 637
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 21 of 103 Page|D #: 637
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 19 of 71
`
`US 7,136,761 B2
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 22 of 103 PageID #: 638
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 22 of 103 Page|D #: 638
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 20 of 71
`
`US 7,136,761 B2
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 23 of 103 PageID #: 639
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 23 of 103 Page|D #: 639
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 21 of 71
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`US 7,136,761 B2
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`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 24 of 103 Page|D #: 640
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`U.S. Patent
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`Nov. 14,2006
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`Sheet 22 of 71
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`US 7,136,761 B2
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`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 25 of 103 PagelD #: 641
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 23 of 71
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`US 7,136,761 B2
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 26 of 103 PageID #: 642
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 26 of 103 Page|D #: 642
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 27 of 103 PageID #: 643
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 27 of 103 Page|D #: 643
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`U.S. Patent
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`Nov. 14,2006
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`Sheet 25 of 71
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`US 7,136,761 B2
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`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 28 of 103 Page|D #: 644
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 26 of 71
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`US 7,136,761 B2
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 29 of 103 PageID #: 645
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 29 of 103 Page|D #: 645
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 27 of 71
`
`US 7,136,761 B2
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 30 of 103 PageID #: 646
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`Case 6:12-cv-00799-JRG Document 25-2 Filed 01/31/13 Page 32 of 103 PageID #: 648
`Case 6:12—cv—OO799—JRG Document 25-2 Filed 01/31/13 Page 32 of 103 Page|D #: 648
`
`U.S. Patent
`
`Nov. 14,2006
`
`Sheet 30 of 71
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`US 7,136,761 B2
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`Nov. 14,2006
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`Nov. 14,2006
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`Sheet 49 of 71
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`Nov. 14,2006
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