engineering circuit analysis
Post on 01-Mar-2016
84 Views
Preview:
DESCRIPTION
TRANSCRIPT
-
Sinusoidal Steady State Analysis1 Characteristics of Sinusoidal 2 Phasors3 Phasor Relationships for R, L and C4 Impedance 5 Examples for Sinusoidal Circuits Analysis
References: Hayt-Ch7; Gao-Ch3; Engineering Circuit Analysis
-
Sinusoidal Steady State AnalysisAny steady state voltage or current in a linear circuit with a sinusoidal source is a sinusoidAll steady state voltages and currents have the same frequency as the sourceIn order to find a steady state voltage or current, all we need to know is its magnitude and its phase relative to the source (we already know its frequency)We do not have to find this differential equation from the circuit, nor do we have to solve itInstead, we use the concepts of phasors and complex impedancesPhasors and complex impedances convert problems involving differential equations into circuit analysis problems Focus on steady state; Focus on sinusoids.
-
1 Characteristics of Sinusoidal Key Words: Period: T , Frequency: f , Radian frequency Phase angle Amplitude: Vm Im Sinusoidal Steady State Analysis
-
1 Characteristics of Sinusoidal Both the polarity and magnitude of voltage are changing. Sinusoidal Steady State Analysis
-
1 Characteristics of Sinusoidal Radian frequency(Angular frequency): = 2f = 2/T (rad/s Period: T Time necessary to go through one cycle. (s)Frequency: f Cycles per second. (Hz)f = 1/TAmplitude: Vm Im i = Imsint v =Vmsint Sinusoidal Steady State Analysis
-
1 Characteristics of Sinusoidal Effective Roof Mean Square (RMS) Value of a Periodic Waveform is equal to the value of the direct current which is flowing through an R-ohm resistor. It delivers the same average power to the resistor as the periodic current does.Sinusoidal Steady State Analysis
-
1 Characteristics of Sinusoidal Phase (angle)Sinusoidal Steady State Analysis
Chart3
70.00000928763.5000053622
6.9950260742-0.26382821043.7260082488
6.9801113652-0.52729077643.9467160243
6.9552770687-0.7900039984.1618150361
6.9205584773-1.05159452794.3709996025
6.8760049302-1.31169061394.5739724465
6.8216797435-1.5699226284.7704451192
6.75766012-1.82592359114.960138409
6.6840370392-2.07932969455.1427827386
6.6009151285-2.32978081755.3181185482
6.5084125143-2.57692103855.4858966644
6.406660654-2.82039914115.6458786538
6.2958041495-3.05986911345.7978371628
6.1760005413-3.29499063945.9415562398
6.0474200848-3.52542958286.0768316424
5.9102455087-3.75085846196.2034711279
5.7646717545-3.97095691476.3212947262
5.6109057005-4.18541215466.4301349956
5.4491658667-4.39391941456.5298372607
5.2796821053-4.59618238046.6202598327
5.1026952732-4.79191361196.7012742099
4.9184568903-4.98083495116.7727652612
4.7272287817-5.16267791796.834631389
4.5292827059-5.33718409126.886784674
4.3248999683-5.50410547656.9291510001
4.1143710216-5.66320485836.9616701595
3.8979950531-5.81425613696.9842959387
3.6760795593-5.95704465016.9969961835
3.4489399093-6.09136747816.9997528454
3.216898896-6.21703373186.9925620069
2.9802862779-6.33386482416.975433887
2.7394383105-6.44169472396.9483928268
2.4946972679-6.54037019176.9114772551
2.246410957-6.62975099776.8647396332
1.9949322228-6.70971012096.8082463811
1.7406184471-6.78013392976.7420777825
1.4838310409-6.84092234326.6663278711
1.2249349302-6.89198897386.5811042967
0.964298038-6.93326124946.4865281724
0.7022907609-6.96468051736.3827339024
0.4392854432-6.98620212676.2698689908
0.1756558475-6.9977954936.1480938326
-0.0882233766-6.99944414046.0175814851
-0.3519772246-6.99114572615.878517422
-0.6152308701-6.97291204315.7310992705
-0.8776101976-6.94476900365.5755365297
-1.1387423343-6.90675660255.412050273
-1.3982561796-6.85892885995.2408728344
-1.6557829327-6.80135374495.0622474779
-1.9109566168-6.73411307874.8764280518
-2.1634145991-6.65730241844.6836786281
-2.412798106-6.57103092154.4842731273
-2.6587527332-6.47542119014.2784949287
-2.9009289493-6.37060909734.0666364683
-3.1389825924-6.25674359393.8489988226
-3.3725753594-6.13398649663.6258912814
-3.6013752864-6.00251225823.3976309074
-3.8250572209-5.86250771963.1645420866
-4.0433032838-5.71417184412.9269560664
-4.2558033207-5.55771543532.6852104855
-4.4622553433-5.39336083662.4396488938
-4.6623659582-5.2213416162.1906202642
-4.8558507837-5.04190223361.9384784967
-5.0424348545-4.85529769471.6835819154
-5.2218530119-4.66179318711.4262927594
-5.3938502807-4.46166370411.1669766678
-5.5581822321-4.25519365420.9060021603
-5.7146153303-4.04267645640.6437401136
-5.8629272647-3.82441412350.3805632339
-6.0029072662-3.60071683270.1168455274
-6.1343564062-3.3719024853-0.1470382307
-6.2570878792-3.1382962541-0.4107130296
-6.3709272692-2.9002301222-0.6738041553
-6.4757127963-2.6580424104-0.9359377234
-6.5712955476-2.4120772969-1.19674121
-6.6575396885-2.1626843281-1.4558439818
-6.7343226554-1.9102179218-1.7128778222
-6.8015353305-1.6550368633-1.9674774547
-6.8590821963-1.3975037961-2.2192810625
-6.9068814718-1.137984706-2.4679308018
-6.9448652284-0.8768484012-2.7130733112
-6.9729794865-0.6144659881-2.9543602133
-6.9911842924-0.351210344-3.1914486101
-6.9994537747-0.0874555874-3.4240015701
-6.99777618170.1764234543-3.6516886073
-6.98615389720.4400517768-3.8741861506
-6.96460343810.7030547322-4.0911780041
-6.93315543010.9650585613-4.3023557959
-6.89185456471.2256909247-4.5074194166
-6.84075953551.4845814323-4.706077446
-6.77994295461.7413621689-4.8980475666
-6.70949124991.9956682181-5.0830569658
-6.62950454172.2471381799-5.2608427225
-6.5400965012.4954146849-5.4311521817
-6.44139418752.7401449021-5.5937433128
-6.33353786912.9809810399-5.7483850541
-6.21668082283.217580841-5.8948576408
-6.09098911663.4496080683-6.0329529176
-5.95664137393.6767329828-6.1624746342
-5.8138285193.8986328123-6.2832387246
-5.66275350644.1149922103-6.3950735683
-5.50363103214.3255037037-6.4978202344
-5.33668722854.5298681301-6.5913327074
-5.1621593434.7277950627-6.6754780946
-4.9802954014.9190032233-6.7501368152
-4.79135385335.1032208818-6.8152027702
-4.59560320895.2801862425-6.8705834928
-4.39332165315.4496478162-6.9162002803
-4.18479665275.6113647772-6.9519883057
-3.97032454715.7651073062-6.97789671
-3.75021012735.9106569162-6.9938886739
-3.52476620266.0478067636-6.9999414712
-3.29431315626.1763619418-6.9960464999
-3.05917849016.2961397582-6.9822092954
-2.81969635916.406969994-6.9584495219
-2.57620709656.5086951458-6.924800945
-2.32905673026.60117065-6.8813113835
-2.07859649086.6842650875-6.8280426412
-1.8251823136.757860371-6.7650704196
-1.56917432916.8218519127-6.6924842098
-1.31093635756.8761487729-6.6103871657
-1.05083538586.920673789-6.5188959571
-0.78924104926.9553636856-6.4181406043
-0.5265251056.9801691642-6.3082642927
-0.26306090466.9950549732-6.1894231701
0.00077713736.9999999579-6.061786124
0.26461407486.994997091-5.9255345424
0.52807496366.9800534822-5.7808620552
0.79078539366.9551903681-5.6279742597
1.05237202136.9204430822-5.467088428
1.31246310036.8758610048-5.2984331985
1.57068900966.8215074923-5.1222482507
1.82668277876.7574597876-4.938783965
2.08008060936.6838089104-4.7483010663
2.33052239236.6006595276-4.5510702542
2.57765221946.5081298045-4.3473718174
2.82111888916.406351237-4.1374952364
3.06057640566.295468465-3.9217387712
3.29568447066.1756390664-3.7004090381
3.52610896716.0470333333-3.4738205735
3.75152243365.90983403-3.2422953872
3.97160453045.7642361336-3.0061625047
4.18604249395.6104465562-2.7657574995
4.39453158175.4486838517-2.5214220164
4.59677550545.2791779046-2.2735032858
4.79248685195.1021696032-2.0223536305
4.98138749144.9179104982-1.7683299646
5.16320897334.7266624439-1.5117932866
5.33769290694.5286972272-1.2531081664
5.50459132964.3242961808-0.9926422271
5.66366705824.1137497833-0.7307656224
5.81469402683.8973572469-0.4678505109
5.95745760783.6754260916-0.2042705268
6.09175491663.44827170870.0595997505
6.21739510053.21621691220.3233853294
6.33419960962.97959148010.5867113383
6.44200245032.73873168590.849203559
6.54065042172.49397982091.1104889582
6.63000333312.2456837071.3701962174
6.70993420311.99419620341.6279562611
6.78032944021.73987470441.8834027809
6.84108900421.48308063172.1361727562
6.89212654831.2241789212.3859069701
6.93336954210.96353750312.6322505199
6.96475937420.70152678112.8748533214
6.98625143580.43851910433.1133706066
6.99781518420.17488823843.3474634134
6.9994341857-0.08899116493.5767990673
6.9911061396-0.35274410093.8010516546
6.9728428811-0.61599574474.019902485
6.9446703645-0.87837198354.2330405449
6.9066286264-1.13949994894.4401629392
6.8587717286-1.39900854624.6409753217
6.8011676817-1.65652898224.8351923136
6.7338983481-1.91169528895.0225379089
6.6570593256-2.1641448445.2027458668
6.5707598118-2.4135188865.3755600897
6.4751224489-2.6594630245.5407349878
6.3702831491-2.90162774155.6980358273
6.256390902-3.13966889295.8472390646
6.1336075621-3.37324819295.9881326637
6.0021076197-3.60203369676.1205163978
5.862077952-3.82570027236.2442021334
5.7137175583-4.04393006256.359014098
5.5572372768-4.25641293596.4647891299
5.392859485-4.46284692886.5613769099
5.2208177837-4.66293867316.648640175
5.0413566651-4.85640381436.7264549135
4.8547311654-5.04296741476.7947105411
4.6612065019-5.22236434496.8533100583
4.4610576969-5.394339666.9021701881
4.2545691862-5.55864896216.9412214943
4.042034415-5.71505874766.9704084802
3.8237554211-5.86334673946.9896896676
3.6000424055-6.0033022026.9990376556
3.3712132916-6.13472624186.9984391594
3.1375932735-6.25743208936.9878950297
2.8995143535-6.37124536436.967420251
2.6573148709-6.47600432466.9370439204
2.4113390206-6.57156009476.8968092063
2.1619363641-6.65777687846.8467732872
1.909461333-6.73453215116.7870072703
1.654272725-6.80171683426.7175960902
1.3967331943-6.85923545026.6386383888
1.1372087357-6.9070062586.5502463745
0.8760681651-6.94496136966.4525456631
0.6136825951-6.9730468466.3456750993
0.3504249074-6.99122277456.2297865591
0.0866692233-6.99946332486.1050447342
-0.1772096283-6.99775678625.9716268979
-0.4408366434-6.98610558375.8297226533
-0.7038371761-6.96452627515.6795336635
-0.9658374705-6.93304952745.5212733653
-1.2264651923-6.89172007285.3551666659
-1.4853499579-6.84059664545.1814496231
-1.7421238604-6.77975189795.00036911
-1.996421993-6.7092722984.812182464
-2.2478829671-6.6292580064.6171571212
-2.4961494259-6.53982273174.4155702363
-2.7408685527-6.44109357364.2077082889
-2.9816925718-6.33321083793.9938666761
-3.218279243-6.2163278393.7743492928
-3.4502923478-6.09061068193.5494681
-3.6774021674-5.9562380263.3195426811
-3.8992859511-5.81340083113.0848997882
-4.115628375-5.66230208642.8458728773
-4.3261219903-5.50315652152.6028016348
-4.5304676598-5.33619030162.3560314946
-4.7283749836-5.1616407062.1059131469
-4.9195627113-4.9797557911.8528020404
-5.1037591417-4.79079403711.5970578768
-5.2807025095-4.5950239821.3390440996
-5.4501413565-4.39272383881.0791273778
-5.6118348895-4.18418110050.8176770848
-5.7655533224-3.96969213180.5550647731
-5.9110782024-3.74956174750.2916636468
-6.0482027212-3.52410277990.027848031
-6.176732008-3.2936356334-0.2360071602
-6.2964834071-3.0584878299-0.4995269565
-6.4072867373-2.8189935431-0.7623368643
-6.5089845333-2.5754931235-1.0240633986
-6.6014322705-2.3283326148-1.2843346143
-6.6844985691-2.0778632622-1.5427806341
-6.758065382-1.824441013-1.799034175
-6.8220281618-1.5684260112-2.0527310695
-6.8762960095-1.3101820852-2.3035107833
-6.9207918039-1.0500762311-2.5510169281
-6.9554523112-0.7884780909-2.7948977674
-6.9802282744-0.5257594274-3.0348067169
-6.995084484-0.2622935957-3.2704028369
-6.99999982740.001544987-3.5013513165
-6.99496731950.2653813742-3.7273239499
-6.97999411180.5288406221-3.9479996024
-6.95510148330.7915483231-4.1630646672
-6.92032480941.0531311377-4.3722135106
-6.87571351191.3132173248-4.5751489066
-6.8213309891.5714372703-4.7715824593
-6.75725452471.8274240122-4.9612350128
-6.68357517972.0808137623-5.1438370477
-6.60039766112.3312464229-5.3191290644
-6.50784017442.5783660986-5.4868619514
-6.4060342552.8218216024-5.6467973401
-6.29512458153.0612669544-5.7987079427
-6.175268773.2963618736-5.9423778758
-6.04663715033.5267722615-6.0776029669
-5.90941252353.7521706769-6.2041910447
-5.76378990253.9722368012-6.3219622122
-5.60997623484.1866578938-6.4307491022
-5.44819010834.3951292361-6.5303971153
-5.27866144084.597354565-6.6207646396
-5.10163115314.7930464937-6.7017232518
-4.91735082694.9819269202-6.7731578998
-4.72608234685.1637274224-6.8349670664
-4.52809752875.3381896396-6.8870629132
-4.3236777335.5050656399-6.9293714056
-4.11311346535.6641182721-6.9618324182
-3.89670396295.8151215031-6.9843998198
-3.674756775.9578607389-6.9970415396
-3.44758730076.0921331297-6.9997396119
-3.21551839036.2177478581-6.9924902027
-2.97887983716.3345264103-6.9753036141
-2.73800793326.4423028298-6.9482042703
-2.49324498696.5409239531-6.911230683
-2.24493883616.6302496276-6.8644353959
-1.99344235416.7101529107-6.8078849109
-1.7391129486.7805202501-6.7416595932
-1.48231205086.8412516453-6.665853557
-1.22340460786.8922607895-6.5805745318
-0.9627585586.9334751925-6.4859437095
-0.70074431116.9648362837-6.3820955721
-0.43773422136.9862994952-6.2691777004
-0.1741020586.997834325-6.1473505644
0.08977752566.9994243809-6.0167872954
0.35352952446.991067403-5.8776734395
0.61677911476.9727752678-5.7302066945
0.87915218696.9445739706-5.5745966286
1.14027587686.9065035888-5.4110643827
1.3997790966.8586182251-5.2398423559
1.65729305876.8009859305-5.0611738755
1.91245180646.7336886073-4.8753128514
2.16489272746.6568218934-4.6825234145
2.41425707246.5704950256-4.4830795421
2.66019046446.474830685-4.2772646682
2.90234340216.3699648221-4.0653712808
3.14037175666.2560464643-3.8477005062
3.37393726096.1332375032-3.624561681
3.60270798976.0017124654-3.3962719127
3.82635883225.861658264-3.1631556287
4.04457195325.713273933-2.9255441158
4.25703724545.5567703446-2.6837750487
4.46345276975.3923699095-2.4381920108
4.66352518455.2203062606-2.1891440053
4.85697016275.0408239214-1.9369849599
5.04351279534.8541779581-1.6820732231
5.22288798264.6606336173-1.4247710557
5.39484081064.4604659491-1.1654441152
5.55912691344.2539594161-0.9044609369
5.71551282054.0414074892-0.6421924095
5.86377628853.8231122305-0.3790112485
6.00370661693.5993838641-0.1152914665
6.13510494783.37054033540.1485921587
6.2577845483.13690685870.4122646164
6.37157107512.89881545580.675351196
6.47630282442.65660448340.9374780193
6.57183095952.41061815281.1982725722
6.65801972322.16120604051.4573642341
6.73474663071.90872259141.714384804
6.80190264391.65352661531.9689690246
6.85939232591.39598077682.2207551006
6.90713397681.13645107972.4693852135
6.94505974990.87530634732.7145060294
6.97311574810.61291769812.9557692021
6.99126210040.34965801833.1928318671
6.99947301870.08590143193.4253571295
6.9977368342-0.17797723093.6530145427
6.9860560142-0.44160296643.8754805778
6.9644471586-0.70460113034.0924390834
6.9329409763-0.96659797034.3035817352
6.8915822413-1.2272211574.5086084737
6.8404297295-1.48610031314.707227931
6.7795561347-1.74286753984.8991578447
6.7090479659-1.99715793975.0841254591
6.6290054235-2.24861013525.2618679125
6.5395422579-2.49686678215.4321326115
6.4407856072-2.74157507755.5946775891
6.3328758164-2.98238726125.7492718492
6.2159662385-3.21896110975.8956956944
6.0902230164-3.45096042286.0337410387
5.9558248463-3.67805550136.1632117029
5.8129627245-3.89992361546.2839236934
5.6618396755-4.11624946356.3957054638
5.5026704633-4.32672562046.4983981585
5.3356812869-4.53105297376.5918558388
5.1611094583-4.72894114946.6759456899
4.9792030651-4.92010892446.75054821
4.7902206186-5.1042846266.8155573797
4.5944306857-5.28120651816.8708808131
4.3921115079-5.45062317326.9164398889
4.1835506052-5.61229382956.9521698621
3.9690443681-5.76598873366.9780199561
3.748897636-5.9114894666.9939534347
3.5234232643-6.04858925276.9999476545
3.2929416794-6.17709325816.9959940971
3.0577804237-6.29681886256.9820983808
2.8182736901-6.40759592116.9582802532
2.5747618466-6.50926700636.9245735628
2.3275909532-6.60168763116.8810262108
2.0771122699-6.68472645466.8277000834
1.8236817574-6.75826546856.7646709634
1.5676595712-6.82220016486.692028423
1.30940955-6.87643968476.6098756959
1.0492986985-6.92090694716.5183295313
0.7876966659-6.95553875876.4175200273
0.5249752205-6.98028590346.3075904465
0.2615077215-6.99511321266.1886970123
-0.0023314119-6.99999961486.0610086867
-0.266167232-6.99493816595.9247069302
-0.5296247961-6.97993605885.7799854444
-0.7923296989-6.95501461335.627049896
-1.0539086049-6.92020924585.4661176251
-1.3139897784-6.8755694195.2974173359
-1.5722036127-6.82115857155.1211887722
-1.8281831543-6.75705402784.9376823762
-2.0815646252-6.68334688824.7471589327
-2.3319879395-6.60014189944.5498891988
-2.5790972152-6.5075573064.3461535188
-2.82254128-6.40572468194.1362414258
-3.0619741702-6.29478874373.9204512306
-3.2970556225-6.17490714473.6990895971
-3.5274515577-6.04625025153.4724711072
-3.752834555-5.90900090093.2409178134
-3.9728843179-5.76335414123.0047587811
-4.1872881287-5.60951695392.7643296209
-4.3957412936-5.44770796062.5199720121
-4.5979475753-5.27815711152.2720332163
-4.7936196141-5.10110535892.020865585
-4.9824793362-4.91680431491.7668260578
-5.1642583489-4.72551589381.5102756558
-5.3386983222-4.52751193971.2515789683
-5.5055513556-4.32307384020.9911036348
-5.6645803307-4.11249212690.7292198225
-5.815559248-3.89606606180.4662997001
-5.9582735479-3.67410321280.2027169091
-6.0925204162-3.4469190162-0.0611539673
-6.2181090718-3.2148363282-0.3249379365
-6.3348610378-2.9781849667-0.5882601293
-6.4426103954-2.737301242-0.850746333
-6.5412040199-2.4925274792-1.1120235225
-6.6305017976-2.2442115315-1.3717203914
-6.7103768255-1.9927062862-1.6294678787
-6.7807155915-1.7383691629-1.8848996938
-6.8414181356-1.4815616054-2.1376528372
-6.8923981921-1.2226485687-2.3873681158
-6.9335833123-0.9619979996-2.6336906538
-6.9649149669-0.6999803142-2.876270397
-6.98634863-0.4369678717-3.11476261
-6.9978538416-0.1733344447-3.3488283663
-6.99941425150.0905453117-3.5781350301
-6.99102764220.3542963921-3.8023567287
-6.9727059320.6175439743-4.0211748157
-6.94447515820.8799139514-4.2342783241
-6.90637544041.1410334636-4.4413644078
-6.85846092271.4005314285-4.6421387722
-6.80079969761.6580390679-4.8363160927
-6.73347370871.9131904319-5.0236204196
-6.65657863452.1656229196-5.2037855706
-6.5702237522.4149777937-5.3765555093
-6.47453178222.6609006905-5.5416847083
-6.3696387152.9030421236-5.6989384992
-6.25569361623.1410579807-5.848093405
-6.13285841573.3746100122-5.9889374586
-6.00130767713.6033663123-6.1212705034
-5.86122835023.8270017904-6.244904478
-5.71281950474.0451986334-6.3596636836
-5.55629204754.257646757-6.4653850333
-5.39186842344.4640442464-6.5619182842
-5.21978229824.6640977859-6.6491262509
-5.04027822724.8575230749-6.7268850001
-4.85361130775.0440452327-6.7950840273
-4.66004681595.2233991884-6.8536264134
-4.45985983065.3953300584-6.9024289625
-4.25333484195.5595935079-6.9414223201
-4.04076534695.7159560986-6.9705510721
-3.82245343275.8641956203-6.989773823
-3.59870934716.0041014065-6.9990632548
-3.36985105766.135474634-6.9984061661
-3.13620379986.2581286056-6.9878034908
-2.89809961486.3718890151-6.9672702965
-2.65587687766.476594195-6.9368357635
-2.40987981636.5720953465-6.8965431428
-2.16045802256.6582567509-6.8464496952
-1.90796595516.7349559624-6.7866266096
-1.65276243586.802083982-6.7171589018
-1.39521014016.8595454127-6.638145294
-1.13567508096.9072585947-6.5496980741
-0.87452608946.9451557219-6.4519429363
-0.61213428986.9731829378-6.3450188026
-0.34887257296.9913004123-6.2290776251
-0.08511506576.9994823983-6.1042841705
0.17876340046.9977172682-5.9708157854
0.44238782196.9860075305-5.8288621446
0.70538355666.964369826-5.6786249815
0.96737685546.9328349047-5.5203178013
1.22799539396.8914475815-5.354165578
1.48686880166.8402666728-5.1804044338
1.74362918796.7793649129-4.9992813047
1.99791166496.7088288506-4.8110535887
2.24935486636.6287587263-4.6159887801
2.49760146086.5392683293-4.4143640898
2.74229865986.4404848364-4.206466051
2.98309871876.3325486309-3.9925901122
3.21965943136.2156131033-3.7730402171
3.45164461626.0898444333-3.5481283728
3.67872459425.9554213534-3.3181742063
3.90057665685.8125348951-3.0835045106
4.11688552555.6613881176-2.8444527798
4.3273437995.5021958187-2.6013587355
4.53165239045.3351842301-2.354567844
4.72952095245.1605906956-2.104430825
4.92066828974.9786633338-1.8513031539
5.10482275864.7896606857-1.5955445557
5.28172265334.593851347-1.3375184945
5.45111657754.3915135866-1.0775916568
5.61276380194.1829349511-0.8161334303
5.76643460593.9684118561-0.5535153789
5.91191060483.748249165-0.2901107148
6.04898505943.5227597558-0.026293768
6.17746317033.29226407630.2375605453
6.29716235443.05708968910.5010772563
6.40791250462.81757080540.7638818755
6.50955623152.57404781081.0256009256
6.6019490872.32686678111.285862472
6.68495976952.07637899061.5442966514
6.75847031091.8229404131.8005361974
6.82237624371.56691121512.0542169623
6.87658674981.30865524592.304978435
6.92102478941.04853951822.552464253
6.95562721070.78693368842.7963227086
6.98034483950.524209533.0362072495
6.9951425490.26074040623.2717769704
Sheet1
070.00000928763.5000053622-10.00010.00069314720.000000024
0.00016.9950260742-0.26382821043.72600824881.0865653633
0.00026.9801113652-0.52729077643.94671602430.9962532192
0.00036.9552770687-0.7900039984.16181503611.0001621707
0.00046.9205584773-1.05159452794.37099960250.9999929808
0.00056.8760049302-1.31169061394.57397244651.0000003038
0.00066.8216797435-1.5699226284.77044511920.9999999869
0.00076.75766012-1.82592359114.9601384091.0000000006
0.00086.6840370392-2.07932969455.14278273861
0.00096.6009151285-2.32978081755.31811854821
0.0016.5084125143-2.57692103855.48589666441
0.00116.406660654-2.82039914115.64587865381
0.00126.2958041495-3.05986911345.79783716281
0.00136.1760005413-3.29499063945.94155623981
0.00146.0474200848-3.52542958286.07683164241
0.00155.9102455087-3.75085846196.20347112791
0.00165.7646717545-3.97095691476.32129472621
0.00175.6109057005-4.18541215466.43013499561
0.00185.4491658667-4.39391941456.52983726071
0.00195.2796821053-4.59618238046.62025983271
0.0025.1026952732-4.79191361196.70127420991
0.00214.9184568903-4.98083495116.77276526121
0.00224.7272287817-5.16267791796.8346313891
0.00234.5292827059-5.33718409126.8867846741
0.00244.3248999683-5.50410547656.92915100011
0.00254.1143710216-5.66320485836.96167015951
0.00263.8979950531-5.81425613696.98429593871
0.00273.6760795593-5.95704465016.99699618351
0.00283.4489399093-6.09136747816.99975284541
0.00293.216898896-6.21703373186.99256200691
0.0032.9802862779-6.33386482416.9754338871
0.00312.7394383105-6.44169472396.94839282681
0.00322.4946972679-6.54037019176.91147725511
0.00332.246410957-6.62975099776.86473963321
0.00341.9949322228-6.70971012096.80824638111
0.00351.7406184471-6.78013392976.74207778251
0.00361.4838310409-6.84092234326.66632787111
0.00371.2249349302-6.89198897386.58110429671
0.00380.964298038-6.93326124946.48652817241
0.00390.7022907609-6.96468051736.38273390241
0.0040.4392854432-6.98620212676.26986899081
0.00410.1756558475-6.9977954936.14809383261
0.0042-0.0882233766-6.99944414046.01758148511
0.0043-0.3519772246-6.99114572615.8785174221
0.0044-0.6152308701-6.97291204315.73109927051
0.0045-0.8776101976-6.94476900365.57553652971
0.0046-1.1387423343-6.90675660255.4120502731
0.0047-1.3982561796-6.85892885995.24087283441
0.0048-1.6557829327-6.80135374495.06224747791
0.0049-1.9109566168-6.73411307874.87642805181
0.005-2.1634145991-6.65730241844.68367862811
0.0051-2.412798106-6.57103092154.48427312731
0.0052-2.6587527332-6.47542119014.27849492871
0.0053-2.9009289493-6.37060909734.06663646831
0.0054-3.1389825924-6.25674359393.84899882261
0.0055-3.3725753594-6.13398649663.62589128141
0.0056-3.6013752864-6.00251225823.39763090741
0.0057-3.8250572209-5.86250771963.16454208661
0.0058-4.0433032838-5.71417184412.92695606641
0.0059-4.2558033207-5.55771543532.68521048551
0.006-4.4622553433-5.39336083662.43964889381
0.0061-4.6623659582-5.2213416162.19062026421
0.0062-4.8558507837-5.04190223361.93847849671
0.0063-5.0424348545-4.85529769471.68358191541
0.0064-5.2218530119-4.66179318711.42629275941
0.0065-5.3938502807-4.46166370411.16697666781
0.0066-5.5581822321-4.25519365420.90600216031
0.0067-5.7146153303-4.04267645640.64374011361
0.0068-5.8629272647-3.82441412350.38056323391
0.0069-6.0029072662-3.60071683270.11684552741
0.007-6.1343564062-3.3719024853-0.14703823071
0.0071-6.2570878792-3.1382962541-0.41071302961
0.0072-6.3709272692-2.9002301222-0.67380415531
0.0073-6.4757127963-2.6580424104-0.93593772341
0.0074-6.5712955476-2.4120772969-1.196741211
0.0075-6.6575396885-2.1626843281-1.45584398181
0.0076-6.7343226554-1.9102179218-1.71287782221
0.0077-6.8015353305-1.6550368633-1.96747745471
0.0078-6.8590821963-1.3975037961-2.21928106251
0.0079-6.9068814718-1.137984706-2.46793080181
0.008-6.9448652284-0.8768484012-2.71307331121
0.0081-6.9729794865-0.6144659881-2.95436021331
0.0082-6.9911842924-0.351210344-3.19144861011
0.0083-6.9994537747-0.0874555874-3.42400157011
0.0084-6.99777618170.1764234543-3.65168860731
0.0085-6.98615389720.4400517768-3.87418615061
0.0086-6.96460343810.7030547322-4.09117800411
0.0087-6.93315543010.9650585613-4.30235579591
0.0088-6.89185456471.2256909247-4.50741941661
0.0089-6.84075953551.4845814323-4.7060774461
0.009-6.77994295461.7413621689-4.89804756661
0.0091-6.70949124991.9956682181-5.08305696581
0.0092-6.62950454172.2471381799-5.26084272251
0.0093-6.5400965012.4954146849-5.43115218171
0.0094-6.44139418752.7401449021-5.59374331281
0.0095-6.33353786912.9809810399-5.74838505411
0.0096-6.21668082283.217580841-5.89485764081
0.0097-6.09098911663.4496080683-6.03295291761
0.0098-5.95664137393.6767329828-6.16247463421
0.0099-5.8138285193.8986328123-6.28323872461
0.01-5.66275350644.1149922103-6.39507356831
0.0101-5.50363103214.3255037037-6.49782023441
0.0102-5.33668722854.5298681301-6.59133270741
0.0103-5.1621593434.7277950627-6.67547809461
0.0104-4.9802954014.9190032233-6.75013681521
0.0105-4.79135385335.1032208818-6.81520277021
0.0106-4.59560320895.2801862425-6.87058349281
0.0107-4.39332165315.4496478162-6.91620028031
0.0108-4.18479665275.6113647772-6.95198830571
0.0109-3.97032454715.7651073062-6.977896711
0.011-3.75021012735.9106569162-6.99388867391
0.0111-3.52476620266.0478067636-6.99994147121
0.0112-3.29431315626.1763619418-6.99604649991
0.0113-3.05917849016.2961397582-6.98220929541
0.0114-2.81969635916.406969994-6.95844952191
0.0115-2.57620709656.5086951458-6.9248009451
0.0116-2.32905673026.60117065-6.88131138351
0.0117-2.07859649086.6842650875-6.82804264121
0.0118-1.8251823136.757860371-6.76507041961
0.0119-1.56917432916.8218519127-6.69248420981
0.012-1.31093635756.8761487729-6.61038716571
0.0121-1.05083538586.920673789-6.51889595711
0.0122-0.78924104926.9553636856-6.41814060431
0.0123-0.5265251056.9801691642-6.30826429271
0.0124-0.26306090466.9950549732-6.18942317011
0.01250.00077713736.9999999579-6.0617861241
0.01260.26461407486.994997091-5.92553454241
0.01270.52807496366.9800534822-5.78086205521
0.01280.79078539366.9551903681-5.62797425971
0.01291.05237202136.9204430822-5.4670884281
0.0131.31246310036.8758610048-5.29843319851
0.01311.57068900966.8215074923-5.12224825071
0.01321.82668277876.7574597876-4.9387839651
0.01332.08008060936.6838089104-4.74830106631
0.01342.33052239236.6006595276-4.55107025421
0.01352.57765221946.5081298045-4.34737181741
0.01362.82111888916.406351237-4.13749523641
0.01373.06057640566.295468465-3.92173877121
0.01383.29568447066.1756390664-3.70040903811
0.01393.52610896716.0470333333-3.47382057351
0.0143.75152243365.90983403-3.24229538721
0.01413.97160453045.7642361336-3.00616250471
0.01424.18604249395.6104465562-2.76575749951
0.01434.39453158175.4486838517-2.52142201641
0.01444.59677550545.2791779046-2.27350328581
0.01454.79248685195.1021696032-2.02235363051
0.01464.98138749144.9179104982-1.76832996461
0.01475.16320897334.7266624439-1.51179328661
0.01485.33769290694.5286972272-1.25310816641
0.01495.50459132964.3242961808-0.99264222711
0.0155.66366705824.1137497833-0.73076562241
0.01515.81469402683.8973572469-0.46785051091
0.01525.95745760783.6754260916-0.20427052681
0.01536.09175491663.44827170870.05959975051
0.01546.21739510053.21621691220.32338532941
0.01556.33419960962.97959148010.58671133831
0.01566.44200245032.73873168590.8492035591
0.01576.54065042172.49397982091.11048895821
0.01586.63000333312.2456837071.37019621741
0.01596.70993420311.99419620341.62795626111
0.0166.78032944021.73987470441.88340278091
0.01616.84108900421.48308063172.13617275621
0.01626.89212654831.2241789212.38590697011
0.01636.93336954210.96353750312.63225051991
0.01646.96475937420.70152678112.87485332141
0.01656.98625143580.43851910433.11337060661
0.01666.99781518420.17488823843.34746341341
0.01676.9994341857-0.08899116493.57679906731
0.01686.9911061396-0.35274410093.80105165461
0.01696.9728428811-0.61599574474.0199024851
0.0176.9446703645-0.87837198354.23304054491
0.01716.9066286264-1.13949994894.44016293921
0.01726.8587717286-1.39900854624.64097532171
0.01736.8011676817-1.65652898224.83519231361
0.01746.7338983481-1.91169528895.02253790891
0.01756.6570593256-2.1641448445.20274586681
0.01766.5707598118-2.4135188865.37556008971
0.01776.4751224489-2.6594630245.54073498781
0.01786.3702831491-2.90162774155.69803582731
0.01796.256390902-3.13966889295.84723906461
0.0186.1336075621-3.37324819295.98813266371
0.01816.0021076197-3.60203369676.12051639781
0.01825.862077952-3.82570027236.24420213341
0.01835.7137175583-4.04393006256.3590140981
0.01845.5572372768-4.25641293596.46478912991
0.01855.392859485-4.46284692886.56137690991
0.01865.2208177837-4.66293867316.6486401751
0.01875.0413566651-4.85640381436.72645491351
0.01884.8547311654-5.04296741476.79471054111
0.01894.6612065019-5.22236434496.85331005831
0.0194.4610576969-5.394339666.90217018811
0.01914.2545691862-5.55864896216.94122149431
0.01924.042034415-5.71505874766.97040848021
0.01933.8237554211-5.86334673946.98968966761
0.01943.6000424055-6.0033022026.99903765561
0.01953.3712132916-6.13472624186.99843915941
0.01963.1375932735-6.25743208936.98789502971
0.01972.8995143535-6.37124536436.9674202511
0.01982.6573148709-6.47600432466.93704392041
0.01992.4113390206-6.57156009476.89680920631
0.022.1619363641-6.65777687846.84677328721
0.02011.909461333-6.73453215116.78700727031
0.02021.654272725-6.80171683426.71759609021
0.02031.3967331943-6.85923545026.63863838881
0.02041.1372087357-6.9070062586.55024637451
0.02050.8760681651-6.94496136966.45254566311
0.02060.6136825951-6.9730468466.34567509931
0.02070.3504249074-6.99122277456.22978655911
0.02080.0866692233-6.99946332486.10504473421
0.0209-0.1772096283-6.99775678625.97162689791
0.021-0.4408366434-6.98610558375.82972265331
0.0211-0.7038371761-6.96452627515.67953366351
0.0212-0.9658374705-6.93304952745.52127336531
0.0213-1.2264651923-6.89172007285.35516666591
0.0214-1.4853499579-6.84059664545.18144962311
0.0215-1.7421238604-6.77975189795.000369111
0.0216-1.996421993-6.7092722984.8121824641
0.0217-2.2478829671-6.6292580064.61715712121
0.0218-2.4961494259-6.53982273174.41557023631
0.0219-2.7408685527-6.44109357364.20770828891
0.022-2.9816925718-6.33321083793.99386667611
0.0221-3.218279243-6.2163278393.77434929281
0.0222-3.4502923478-6.09061068193.54946811
0.0223-3.6774021674-5.9562380263.31954268111
0.0224-3.8992859511-5.81340083113.08489978821
0.0225-4.115628375-5.66230208642.84587287731
0.0226-4.3261219903-5.50315652152.60280163481
0.0227-4.5304676598-5.33619030162.35603149461
0.0228-4.7283749836-5.1616407062.10591314691
0.0229-4.9195627113-4.9797557911.85280204041
0.023-5.1037591417-4.79079403711.59705787681
0.0231-5.2807025095-4.5950239821.33904409961
0.0232-5.4501413565-4.39272383881.07912737781
0.0233-5.6118348895-4.18418110050.81767708481
0.0234-5.7655533224-3.96969213180.55506477311
0.0235-5.9110782024-3.74956174750.29166364681
0.0236-6.0482027212-3.52410277990.0278480311
0.0237-6.176732008-3.2936356334-0.23600716021
0.0238-6.2964834071-3.0584878299-0.49952695651
0.0239-6.4072867373-2.8189935431-0.76233686431
0.024-6.5089845333-2.5754931235-1.02406339861
0.0241-6.6014322705-2.3283326148-1.28433461431
0.0242-6.6844985691-2.0778632622-1.54278063411
0.0243-6.758065382-1.824441013-1.7990341751
0.0244-6.8220281618-1.5684260112-2.05273106951
0.0245-6.8762960095-1.3101820852-2.30351078331
0.0246-6.9207918039-1.0500762311-2.55101692811
0.0247-6.9554523112-0.7884780909-2.79489776741
0.0248-6.9802282744-0.5257594274-3.03480671691
0.0249-6.995084484-0.2622935957-3.27040283691
0.025-6.99999982740.001544987-3.50135131651
0.0251-6.99496731950.2653813742-3.72732394991
0.0252-6.97999411180.5288406221-3.94799960241
0.0253-6.95510148330.7915483231-4.16306466721
0.0254-6.92032480941.0531311377-4.37221351061
0.0255-6.87571351191.3132173248-4.57514890661
0.0256-6.8213309891.5714372703-4.77158245931
0.0257-6.75725452471.8274240122-4.96123501281
0.0258-6.68357517972.0808137623-5.14383704771
0.0259-6.60039766112.3312464229-5.31912906441
0.026-6.50784017442.5783660986-5.48686195141
0.0261-6.4060342552.8218216024-5.64679734011
0.0262-6.29512458153.0612669544-5.79870794271
0.0263-6.175268773.2963618736-5.94237787581
0.0264-6.04663715033.5267722615-6.07760296691
0.0265-5.90941252353.7521706769-6.20419104471
0.0266-5.76378990253.9722368012-6.32196221221
0.0267-5.60997623484.1866578938-6.43074910221
0.0268-5.44819010834.3951292361-6.53039711531
0.0269-5.27866144084.597354565-6.62076463961
0.027-5.10163115314.7930464937-6.70172325181
0.0271-4.91735082694.9819269202-6.77315789981
0.0272-4.72608234685.1637274224-6.83496706641
0.0273-4.52809752875.3381896396-6.88706291321
0.0274-4.3236777335.5050656399-6.92937140561
0.0275-4.11311346535.6641182721-6.96183241821
0.0276-3.89670396295.8151215031-6.98439981981
0.0277-3.674756775.9578607389-6.99704153961
0.0278-3.44758730076.0921331297-6.99973961191
0.0279-3.21551839036.2177478581-6.99249020271
0.028-2.97887983716.3345264103-6.97530361411
0.0281-2.73800793326.4423028298-6.94820427031
0.0282-2.49324498696.5409239531-6.9112306831
0.0283-2.24493883616.6302496276-6.86443539591
0.0284-1.99344235416.7101529107-6.80788491091
0.0285-1.7391129486.7805202501-6.74165959321
0.0286-1.48231205086.8412516453-6.6658535571
0.0287-1.22340460786.8922607895-6.58057453181
0.0288-0.9627585586.9334751925-6.48594370951
0.0289-0.70074431116.9648362837-6.38209557211
0.029-0.43773422136.9862994952-6.26917770041
0.0291-0.1741020586.997834325-6.14735056441
0.02920.08977752566.9994243809-6.01678729541
0.02930.35352952446.991067403-5.87767343951
0.02940.61677911476.9727752678-5.73020669451
0.02950.87915218696.9445739706-5.57459662861
0.02961.14027587686.9065035888-5.41106438271
0.02971.3997790966.8586182251-5.23984235591
0.02981.65729305876.8009859305-5.06117387551
0.02991.91245180646.7336886073-4.87531285141
0.032.16489272746.6568218934-4.68252341451
0.03012.41425707246.5704950256-4.48307954211
0.03022.66019046446.474830685-4.27726466821
0.03032.90234340216.3699648221-4.06537128081
0.03043.14037175666.2560464643-3.84770050621
0.03053.37393726096.1332375032-3.6245616811
0.03063.60270798976.0017124654-3.39627191271
0.03073.82635883225.861658264-3.16315562871
0.03084.04457195325.713273933-2.92554411581
0.03094.25703724545.5567703446-2.68377504871
0.0314.46345276975.3923699095-2.43819201081
0.03114.66352518455.2203062606-2.18914400531
0.03124.85697016275.0408239214-1.93698495991
0.03135.04351279534.8541779581-1.68207322311
0.03145.22288798264.6606336173-1.42477105571
0.03155.39484081064.4604659491-1.16544411521
0.03165.55912691344.2539594161-0.90446093691
0.03175.71551282054.0414074892-0.64219240951
0.03185.86377628853.8231122305-0.37901124851
0.03196.00370661693.5993838641-0.11529146651
0.0326.13510494783.37054033540.14859215871
0.03216.2577845483.13690685870.41226461641
0.03226.37157107512.89881545580.6753511961
0.03236.47630282442.65660448340.93747801931
0.03246.57183095952.41061815281.19827257221
0.03256.65801972322.16120604051.45736423411
0.03266.73474663071.90872259141.7143848041
0.03276.80190264391.65352661531.96896902461
0.03286.85939232591.39598077682.22075510061
0.03296.90713397681.13645107972.46938521351
0.0336.94505974990.87530634732.71450602941
0.03316.97311574810.61291769812.95576920211
0.03326.99126210040.34965801833.19283186711
0.03336.99947301870.08590143193.42535712951
0.03346.9977368342-0.17797723093.65301454271
0.03356.9860560142-0.44160296643.87548057781
0.03366.9644471586-0.70460113034.09243908341
0.03376.9329409763-0.96659797034.30358173521
0.03386.8915822413-1.2272211574.50860847371
0.03396.8404297295-1.48610031314.7072279311
0.0346.7795561347-1.74286753984.89915784471
0.03416.7090479659-1.99715793975.08412545911
0.03426.6290054235-2.24861013525.26186791251
0.03436.5395422579-2.49686678215.43213261151
0.03446.4407856072-2.74157507755.59467758911
0.03456.3328758164-2.98238726125.74927184921
0.03466.2159662385-3.21896110975.89569569441
0.03476.0902230164-3.45096042286.03374103871
0.03485.9558248463-3.67805550136.16321170291
0.03495.8129627245-3.89992361546.28392369341
0.0355.6618396755-4.11624946356.39570546381
0.03515.5026704633-4.32672562046.49839815851
0.03525.3356812869-4.53105297376.59185583881
0.03535.1611094583-4.72894114946.67594568991
0.03544.9792030651-4.92010892446.750548211
0.03554.7902206186-5.1042846266.81555737971
0.03564.5944306857-5.28120651816.87088081311
0.03574.3921115079-5.45062317326.91643988891
0.03584.1835506052-5.61229382956.95216986211
0.03593.9690443681-5.76598873366.97801995611
0.0363.748897636-5.9114894666.99395343471
0.03613.5234232643-6.04858925276.99994765451
0.03623.2929416794-6.17709325816.99599409711
0.03633.0577804237-6.29681886256.98209838081
0.03642.8182736901-6.40759592116.95828025321
0.03652.5747618466-6.50926700636.92457356281
0.03662.3275909532-6.60168763116.88102621081
0.03672.0771122699-6.68472645466.82770008341
0.03681.8236817574-6.75826546856.76467096341
0.03691.5676595712-6.82220016486.6920284231
0.0371.30940955-6.87643968476.60987569591
0.03711.0492986985-6.92090694716.51832953131
0.03720.7876966659-6.95553875876.41752002731
0.03730.5249752205-6.98028590346.30759044651
0.03740.2615077215-6.99511321266.18869701231
0.0375-0.0023314119-6.99999961486.06100868671
0.0376-0.266167232-6.99493816595.92470693021
0.0377-0.5296247961-6.97993605885.77998544441
0.0378-0.7923296989-6.95501461335.6270498961
0.0379-1.0539086049-6.92020924585.46611762511
0.038-1.3139897784-6.8755694195.29741733591
0.0381-1.5722036127-6.82115857155.12118877221
0.0382-1.8281831543-6.75705402784.93768237621
0.0383-2.0815646252-6.68334688824.74715893271
0.0384-2.3319879395-6.60014189944.54988919881
0.0385-2.5790972152-6.5075573064.34615351881
0.0386-2.82254128-6.40572468194.13624142581
0.0387-3.0619741702-6.29478874373.92045123061
0.0388-3.2970556225-6.17490714473.69908959711
0.0389-3.5274515577-6.04625025153.47247110721
0.039-3.752834555-5.90900090093.24091781341
0.0391-3.9728843179-5.76335414123.00475878111
0.0392-4.1872881287-5.60951695392.76432962091
0.0393-4.3957412936-5.44770796062.51997201211
0.0394-4.5979475753-5.27815711152.27203321631
0.0395-4.7936196141-5.10110535892.0208655851
0.0396-4.9824793362-4.91680431491.76682605781
0.0397-5.1642583489-4.72551589381.51027565581
0.0398-5.3386983222-4.52751193971.25157896831
0.0399-5.5055513556-4.32307384020.99110363481
0.04-5.6645803307-4.11249212690.72921982251
0.0401-5.815559248-3.89606606180.46629970011
0.0402-5.9582735479-3.67410321280.20271690911
0.0403-6.0925204162-3.4469190162-0.06115396731
0.0404-6.2181090718-3.2148363282-0.32493793651
0.0405-6.3348610378-2.9781849667-0.58826012931
0.0406-6.4426103954-2.737301242-0.8507463331
0.0407-6.5412040199-2.4925274792-1.11202352251
0.0408-6.6305017976-2.2442115315-1.37172039141
0.0409-6.7103768255-1.9927062862-1.62946787871
0.041-6.7807155915-1.7383691629-1.88489969381
0.0411-6.8414181356-1.4815616054-2.13765283721
0.0412-6.8923981921-1.2226485687-2.38736811581
0.0413-6.9335833123-0.9619979996-2.63369065381
0.0414-6.9649149669-0.6999803142-2.8762703971
0.0415-6.98634863-0.4369678717-3.114762611
0.0416-6.9978538416-0.1733344447-3.34882836631
0.0417-6.99941425150.0905453117-3.57813503011
0.0418-6.99102764220.3542963921-3.80235672871
0.0419-6.9727059320.6175439743-4.02117481571
0.042-6.94447515820.8799139514-4.23427832411
0.0421-6.90637544041.1410334636-4.44136440781
0.0422-6.85846092271.4005314285-4.64213877221
0.0423-6.80079969761.6580390679-4.83631609271
0.0424-6.73347370871.9131904319-5.02362041961
0.0425-6.65657863452.1656229196-5.20378557061
0.0426-6.5702237522.4149777937-5.37655550931
0.0427-6.47453178222.6609006905-5.54168470831
0.0428-6.3696387152.9030421236-5.69893849921
0.0429-6.25569361623.1410579807-5.8480934051
0.043-6.13285841573.3746100122-5.98893745861
0.0431-6.00130767713.6033663123-6.12127050341
0.0432-5.86122835023.8270017904-6.2449044781
0.0433-5.71281950474.0451986334-6.35966368361
0.0434-5.55629204754.257646757-6.46538503331
0.0435-5.39186842344.4640442464-6.56191828421
0.0436-5.21978229824.6640977859-6.64912625091
0.0437-5.04027822724.8575230749-6.72688500011
0.0438-4.85361130775.0440452327-6.79508402731
0.0439-4.66004681595.2233991884-6.85362641341
0.044-4.45985983065.3953300584-6.90242896251
0.0441-4.25333484195.5595935079-6.94142232011
0.0442-4.04076534695.7159560986-6.97055107211
0.0443-3.82245343275.8641956203-6.9897738231
0.0444-3.59870934716.0041014065-6.99906325481
0.0445-3.36985105766.135474634-6.99840616611
0.0446-3.13620379986.2581286056-6.98780349081
0.0447-2.89809961486.3718890151-6.96727029651
0.0448-2.65587687766.476594195-6.93683576351
0.0449-2.40987981636.5720953465-6.89654314281
0.045-2.16045802256.6582567509-6.84644969521
0.0451-1.90796595516.7349559624-6.78662660961
0.0452-1.65276243586.802083982-6.71715890181
0.0453-1.39521014016.8595454127-6.6381452941
0.0454-1.13567508096.9072585947-6.54969807411
0.0455-0.87452608946.9451557219-6.45194293631
0.0456-0.61213428986.9731829378-6.34501880261
0.0457-0.34887257296.9913004123-6.22907762511
0.0458-0.08511506576.9994823983-6.10428417051
0.04590.17876340046.9977172682-5.97081578541
0.0460.44238782196.9860075305-5.82886214461
0.04610.70538355666.964369826-5.67862498151
0.04620.96737685546.9328349047-5.52031780131
0.04631.22799539396.8914475815-5.3541655781
0.04641.48686880166.8402666728-5.18040443381
0.04651.74362918796.7793649129-4.99928130471
0.04661.99791166496.7088288506-4.81105358871
0.04672.24935486636.6287587263-4.61598878011
0.04682.49760146086.5392683293-4.41436408981
0.04692.74229865986.4404848364-4.2064660511
0.0472.98309871876.3325486309-3.99259011221
0.04713.21965943136.2156131033-3.77304021711
0.04723.45164461626.0898444333-3.54812837281
0.04733.67872459425.9554213534-3.31817420631
0.04743.90057665685.8125348951-3.08350451061
0.04754.11688552555.6613881176-2.84445277981
0.04764.3273437995.5021958187-2.60135873551
0.04774.53165239045.3351842301-2.3545678441
0.04784.72952095245.1605906956-2.1044308251
0.04794.92066828974.9786633338-1.85130315391
0.0485.10482275864.7896606857-1.59554455571
0.04815.28172265334.593851347-1.33751849451
0.04825.45111657754.3915135866-1.07759165681
0.04835.61276380194.1829349511-0.81613343031
0.04845.76643460593.9684118561-0.55351537891
0.04855.91191060483.748249165-0.29011071481
0.04866.04898505943.5227597558-0.0262937681
0.04876.17746317033.29226407630.23756054531
0.04886.29716235443.05708968910.50107725631
0.04896.40791250462.81757080540.76388187551
0.0496.50955623152.57404781081.02560092561
0.04916.6019490872.32686678111.2858624721
0.04926.68495976952.07637899061.54429665141
0.04936.75847031091.8229404131.80053619741
0.04946.82237624371.56691121512.05421696231
0.04956.87658674981.30865524592.3049784351
0.04966.92102478941.04853951822.5524642531
0.04976.95562721070.78693368842.79632270861
0.04986.98034483950.524209533.03620724951
0.04996.9951425490.26074040623.27177697041
Sheet1
t
vc(t)
Sheet2
Sheet2
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t
vc(t)
Sheet3
Sheet3
70.00000928763.5000053622
6.9950260742-0.26382821043.7260082488
6.9801113652-0.52729077643.9467160243
6.9552770687-0.7900039984.1618150361
6.9205584773-1.05159452794.3709996025
6.8760049302-1.31169061394.5739724465
6.8216797435-1.5699226284.7704451192
6.75766012-1.82592359114.960138409
6.6840370392-2.07932969455.1427827386
6.6009151285-2.32978081755.3181185482
6.5084125143-2.57692103855.4858966644
6.406660654-2.82039914115.6458786538
6.2958041495-3.05986911345.7978371628
6.1760005413-3.29499063945.9415562398
6.0474200848-3.52542958286.0768316424
5.9102455087-3.75085846196.2034711279
5.7646717545-3.97095691476.3212947262
5.6109057005-4.18541215466.4301349956
5.4491658667-4.39391941456.5298372607
5.2796821053-4.59618238046.6202598327
5.1026952732-4.79191361196.7012742099
4.9184568903-4.98083495116.7727652612
4.7272287817-5.16267791796.834631389
4.5292827059-5.33718409126.886784674
4.3248999683-5.50410547656.9291510001
4.1143710216-5.66320485836.9616701595
3.8979950531-5.81425613696.9842959387
3.6760795593-5.95704465016.9969961835
3.4489399093-6.09136747816.9997528454
3.216898896-6.21703373186.9925620069
2.9802862779-6.33386482416.975433887
2.7394383105-6.44169472396.9483928268
2.4946972679-6.54037019176.9114772551
2.246410957-6.62975099776.8647396332
1.9949322228-6.70971012096.8082463811
1.7406184471-6.78013392976.7420777825
1.4838310409-6.84092234326.6663278711
1.2249349302-6.89198897386.5811042967
0.964298038-6.93326124946.4865281724
0.7022907609-6.96468051736.3827339024
0.4392854432-6.98620212676.2698689908
0.1756558475-6.9977954936.1480938326
-0.0882233766-6.99944414046.0175814851
-0.3519772246-6.99114572615.878517422
-0.6152308701-6.97291204315.7310992705
-0.8776101976-6.94476900365.5755365297
-1.1387423343-6.90675660255.412050273
-1.3982561796-6.85892885995.2408728344
-1.6557829327-6.80135374495.0622474779
-1.9109566168-6.73411307874.8764280518
-2.1634145991-6.65730241844.6836786281
-2.412798106-6.57103092154.4842731273
-2.6587527332-6.47542119014.2784949287
-2.9009289493-6.37060909734.0666364683
-3.1389825924-6.25674359393.8489988226
-3.3725753594-6.13398649663.6258912814
-3.6013752864-6.00251225823.3976309074
-3.8250572209-5.86250771963.1645420866
-4.0433032838-5.71417184412.9269560664
-4.2558033207-5.55771543532.6852104855
-4.4622553433-5.39336083662.4396488938
-4.6623659582-5.2213416162.1906202642
-4.8558507837-5.04190223361.9384784967
-5.0424348545-4.85529769471.6835819154
-5.2218530119-4.66179318711.4262927594
-5.3938502807-4.46166370411.1669766678
-5.5581822321-4.25519365420.9060021603
-5.7146153303-4.04267645640.6437401136
-5.8629272647-3.82441412350.3805632339
-6.0029072662-3.60071683270.1168455274
-6.1343564062-3.3719024853-0.1470382307
-6.2570878792-3.1382962541-0.4107130296
-6.3709272692-2.9002301222-0.6738041553
-6.4757127963-2.6580424104-0.9359377234
-6.5712955476-2.4120772969-1.19674121
-6.6575396885-2.1626843281-1.4558439818
-6.7343226554-1.9102179218-1.7128778222
-6.8015353305-1.6550368633-1.9674774547
-6.8590821963-1.3975037961-2.2192810625
-6.9068814718-1.137984706-2.4679308018
-6.9448652284-0.8768484012-2.7130733112
-6.9729794865-0.6144659881-2.9543602133
-6.9911842924-0.351210344-3.1914486101
-6.9994537747-0.0874555874-3.4240015701
-6.99777618170.1764234543-3.6516886073
-6.98615389720.4400517768-3.8741861506
-6.96460343810.7030547322-4.0911780041
-6.93315543010.9650585613-4.3023557959
-6.89185456471.2256909247-4.5074194166
-6.84075953551.4845814323-4.706077446
-6.77994295461.7413621689-4.8980475666
-6.70949124991.9956682181-5.0830569658
-6.62950454172.2471381799-5.2608427225
-6.5400965012.4954146849-5.4311521817
-6.44139418752.7401449021-5.5937433128
-6.33353786912.9809810399-5.7483850541
-6.21668082283.217580841-5.8948576408
-6.09098911663.4496080683-6.0329529176
-5.95664137393.6767329828-6.1624746342
-5.8138285193.8986328123-6.2832387246
-5.66275350644.1149922103-6.3950735683
-5.50363103214.3255037037-6.4978202344
-5.33668722854.5298681301-6.5913327074
-5.1621593434.7277950627-6.6754780946
-4.9802954014.9190032233-6.7501368152
-4.79135385335.1032208818-6.8152027702
-4.59560320895.2801862425-6.8705834928
-4.39332165315.4496478162-6.9162002803
-4.18479665275.6113647772-6.9519883057
-3.97032454715.7651073062-6.97789671
-3.75021012735.9106569162-6.9938886739
-3.52476620266.0478067636-6.9999414712
-3.29431315626.1763619418-6.9960464999
-3.05917849016.2961397582-6.9822092954
-2.81969635916.406969994-6.9584495219
-2.57620709656.5086951458-6.924800945
-2.32905673026.60117065-6.8813113835
-2.07859649086.6842650875-6.8280426412
-1.8251823136.757860371-6.7650704196
-1.56917432916.8218519127-6.6924842098
-1.31093635756.8761487729-6.6103871657
-1.05083538586.920673789-6.5188959571
-0.78924104926.9553636856-6.4181406043
-0.5265251056.9801691642-6.3082642927
-0.26306090466.9950549732-6.1894231701
0.00077713736.9999999579-6.061786124
0.26461407486.994997091-5.9255345424
0.52807496366.9800534822-5.7808620552
0.79078539366.9551903681-5.6279742597
1.05237202136.9204430822-5.467088428
1.31246310036.8758610048-5.2984331985
1.57068900966.8215074923-5.1222482507
1.82668277876.7574597876-4.938783965
2.08008060936.6838089104-4.7483010663
2.33052239236.6006595276-4.5510702542
2.57765221946.5081298045-4.3473718174
2.82111888916.406351237-4.1374952364
3.06057640566.295468465-3.9217387712
3.29568447066.1756390664-3.7004090381
3.52610896716.0470333333-3.4738205735
3.75152243365.90983403-3.2422953872
3.97160453045.7642361336-3.0061625047
4.18604249395.6104465562-2.7657574995
4.39453158175.4486838517-2.5214220164
4.59677550545.2791779046-2.2735032858
4.79248685195.1021696032-2.0223536305
4.98138749144.9179104982-1.7683299646
5.16320897334.7266624439-1.5117932866
5.33769290694.5286972272-1.2531081664
5.50459132964.3242961808-0.9926422271
5.66366705824.1137497833-0.7307656224
5.81469402683.8973572469-0.4678505109
5.95745760783.6754260916-0.2042705268
6.09175491663.44827170870.0595997505
6.21739510053.21621691220.3233853294
6.33419960962.97959148010.5867113383
6.44200245032.73873168590.849203559
6.54065042172.49397982091.1104889582
6.63000333312.2456837071.3701962174
6.70993420311.99419620341.6279562611
6.78032944021.73987470441.8834027809
6.84108900421.48308063172.1361727562
6.89212654831.2241789212.3859069701
6.93336954210.96353750312.6322505199
6.96475937420.70152678112.8748533214
6.98625143580.43851910433.1133706066
6.99781518420.17488823843.3474634134
6.9994341857-0.08899116493.5767990673
6.9911061396-0.35274410093.8010516546
6.9728428811-0.61599574474.019902485
6.9446703645-0.87837198354.2330405449
6.9066286264-1.13949994894.4401629392
6.8587717286-1.39900854624.6409753217
6.8011676817-1.65652898224.8351923136
6.7338983481-1.91169528895.0225379089
6.6570593256-2.1641448445.2027458668
6.5707598118-2.4135188865.3755600897
6.4751224489-2.6594630245.5407349878
6.3702831491-2.90162774155.6980358273
6.256390902-3.13966889295.8472390646
6.1336075621-3.37324819295.9881326637
6.0021076197-3.60203369676.1205163978
5.862077952-3.82570027236.2442021334
5.7137175583-4.04393006256.359014098
5.5572372768-4.25641293596.4647891299
5.392859485-4.46284692886.5613769099
5.2208177837-4.66293867316.648640175
5.0413566651-4.85640381436.7264549135
4.8547311654-5.04296741476.7947105411
4.6612065019-5.22236434496.8533100583
4.4610576969-5.394339666.9021701881
4.2545691862-5.55864896216.9412214943
4.042034415-5.71505874766.9704084802
3.8237554211-5.86334673946.9896896676
3.6000424055-6.0033022026.9990376556
3.3712132916-6.13472624186.9984391594
3.1375932735-6.25743208936.9878950297
2.8995143535-6.37124536436.967420251
2.6573148709-6.47600432466.9370439204
2.4113390206-6.57156009476.8968092063
2.1619363641-6.65777687846.8467732872
1.909461333-6.73453215116.7870072703
1.654272725-6.80171683426.7175960902
1.3967331943-6.85923545026.6386383888
1.1372087357-6.9070062586.5502463745
0.8760681651-6.94496136966.4525456631
0.6136825951-6.9730468466.3456750993
0.3504249074-6.99122277456.2297865591
0.0866692233-6.99946332486.1050447342
-0.1772096283-6.99775678625.9716268979
-0.4408366434-6.98610558375.8297226533
-0.7038371761-6.96452627515.6795336635
-0.9658374705-6.93304952745.5212733653
-1.2264651923-6.89172007285.3551666659
-1.4853499579-6.84059664545.1814496231
-1.7421238604-6.77975189795.00036911
-1.996421993-6.7092722984.812182464
-2.2478829671-6.6292580064.6171571212
-2.4961494259-6.53982273174.4155702363
-2.7408685527-6.44109357364.2077082889
-2.9816925718-6.33321083793.9938666761
-3.218279243-6.2163278393.7743492928
-3.4502923478-6.09061068193.5494681
-3.6774021674-5.9562380263.3195426811
-3.8992859511-5.81340083113.0848997882
-4.115628375-5.66230208642.8458728773
-4.3261219903-5.50315652152.6028016348
-4.5304676598-5.33619030162.3560314946
-4.7283749836-5.1616407062.1059131469
-4.9195627113-4.9797557911.8528020404
-5.1037591417-4.79079403711.5970578768
-5.2807025095-4.5950239821.3390440996
-5.4501413565-4.39272383881.0791273778
-5.6118348895-4.18418110050.8176770848
-5.7655533224-3.96969213180.5550647731
-5.9110782024-3.74956174750.2916636468
-6.0482027212-3.52410277990.027848031
-6.176732008-3.2936356334-0.2360071602
-6.2964834071-3.0584878299-0.4995269565
-6.4072867373-2.8189935431-0.7623368643
-6.5089845333-2.5754931235-1.0240633986
-6.6014322705-2.3283326148-1.2843346143
-6.6844985691-2.0778632622-1.5427806341
-6.758065382-1.824441013-1.799034175
-6.8220281618-1.5684260112-2.0527310695
-6.8762960095-1.3101820852-2.3035107833
-6.9207918039-1.0500762311-2.5510169281
-6.9554523112-0.7884780909-2.7948977674
-6.9802282744-0.5257594274-3.0348067169
-6.995084484-0.2622935957-3.2704028369
-6.99999982740.001544987-3.5013513165
-6.99496731950.2653813742-3.7273239499
-6.97999411180.5288406221-3.9479996024
-6.95510148330.7915483231-4.1630646672
-6.92032480941.0531311377-4.3722135106
-6.87571351191.3132173248-4.5751489066
-6.8213309891.5714372703-4.7715824593
-6.75725452471.8274240122-4.9612350128
-6.68357517972.0808137623-5.1438370477
-6.60039766112.3312464229-5.3191290644
-6.50784017442.5783660986-5.4868619514
-6.4060342552.8218216024-5.6467973401
-6.29512458153.0612669544-5.7987079427
-6.175268773.2963618736-5.9423778758
-6.04663715033.5267722615-6.0776029669
-5.90941252353.7521706769-6.2041910447
-5.76378990253.9722368012-6.3219622122
-5.60997623484.1866578938-6.4307491022
-5.44819010834.3951292361-6.5303971153
-5.27866144084.597354565-6.6207646396
-5.10163115314.7930464937-6.7017232518
-4.91735082694.9819269202-6.7731578998
-4.72608234685.1637274224-6.8349670664
-4.52809752875.3381896396-6.8870629132
-4.3236777335.5050656399-6.9293714056
-4.11311346535.6641182721-6.9618324182
-3.89670396295.8151215031-6.9843998198
-3.674756775.9578607389-6.9970415396
-3.44758730076.0921331297-6.9997396119
-3.21551839036.2177478581-6.9924902027
-2.97887983716.3345264103-6.9753036141
-2.73800793326.4423028298-6.9482042703
-2.49324498696.5409239531-6.911230683
-2.24493883616.6302496276-6.8644353959
-1.99344235416.7101529107-6.8078849109
-1.7391129486.7805202501-6.7416595932
-1.48231205086.8412516453-6.665853557
-1.22340460786.8922607895-6.5805745318
-0.9627585586.9334751925-6.4859437095
-0.70074431116.9648362837-6.3820955721
-0.43773422136.9862994952-6.2691777004
-0.1741020586.997834325-6.1473505644
0.08977752566.9994243809-6.0167872954
0.35352952446.991067403-5.8776734395
0.61677911476.9727752678-5.7302066945
0.87915218696.9445739706-5.5745966286
1.14027587686.9065035888-5.4110643827
1.3997790966.8586182251-5.2398423559
1.65729305876.8009859305-5.0611738755
1.91245180646.7336886073-4.8753128514
2.16489272746.6568218934-4.6825234145
2.41425707246.5704950256-4.4830795421
2.66019046446.474830685-4.2772646682
2.90234340216.3699648221-4.0653712808
3.14037175666.2560464643-3.8477005062
3.37393726096.1332375032-3.624561681
3.60270798976.0017124654-3.3962719127
3.82635883225.861658264-3.1631556287
4.04457195325.713273933-2.9255441158
4.25703724545.5567703446-2.6837750487
4.46345276975.3923699095-2.4381920108
4.66352518455.2203062606-2.1891440053
4.85697016275.0408239214-1.9369849599
5.04351279534.8541779581-1.6820732231
5.22288798264.6606336173-1.4247710557
5.39484081064.4604659491-1.1654441152
5.55912691344.2539594161-0.9044609369
5.71551282054.0414074892-0.6421924095
5.86377628853.8231122305-0.3790112485
6.00370661693.5993838641-0.1152914665
6.13510494783.37054033540.1485921587
6.2577845483.13690685870.4122646164
6.37157107512.89881545580.675351196
6.47630282442.65660448340.9374780193
6.57183095952.41061815281.1982725722
6.65801972322.16120604051.4573642341
6.73474663071.90872259141.714384804
6.80190264391.65352661531.9689690246
6.85939232591.39598077682.2207551006
6.90713397681.13645107972.4693852135
6.94505974990.87530634732.7145060294
6.97311574810.61291769812.9557692021
6.99126210040.34965801833.1928318671
6.99947301870.08590143193.4253571295
6.9977368342-0.17797723093.6530145427
6.9860560142-0.44160296643.8754805778
6.9644471586-0.70460113034.0924390834
6.9329409763-0.96659797034.3035817352
6.8915822413-1.2272211574.5086084737
6.8404297295-1.48610031314.707227931
6.7795561347-1.74286753984.8991578447
6.7090479659-1.99715793975.0841254591
6.6290054235-2.24861013525.2618679125
6.5395422579-2.49686678215.4321326115
6.4407856072-2.74157507755.5946775891
6.3328758164-2.98238726125.7492718492
6.2159662385-3.21896110975.8956956944
6.0902230164-3.45096042286.0337410387
5.9558248463-3.67805550136.1632117029
5.8129627245-3.89992361546.2839236934
5.6618396755-4.11624946356.3957054638
5.5026704633-4.32672562046.4983981585
5.3356812869-4.53105297376.5918558388
5.1611094583-4.72894114946.6759456899
4.9792030651-4.92010892446.75054821
4.7902206186-5.1042846266.8155573797
4.5944306857-5.28120651816.8708808131
4.3921115079-5.45062317326.9164398889
4.1835506052-5.61229382956.9521698621
3.9690443681-5.76598873366.9780199561
3.748897636-5.9114894666.9939534347
3.5234232643-6.04858925276.9999476545
3.2929416794-6.17709325816.9959940971
3.0577804237-6.29681886256.9820983808
2.8182736901-6.40759592116.9582802532
2.5747618466-6.50926700636.9245735628
2.3275909532-6.60168763116.8810262108
2.0771122699-6.68472645466.8277000834
1.8236817574-6.75826546856.7646709634
1.5676595712-6.82220016486.692028423
1.30940955-6.87643968476.6098756959
1.0492986985-6.92090694716.5183295313
0.7876966659-6.95553875876.4175200273
0.5249752205-6.98028590346.3075904465
0.2615077215-6.99511321266.1886970123
-0.0023314119-6.99999961486.0610086867
-0.266167232-6.99493816595.9247069302
-0.5296247961-6.97993605885.7799854444
-0.7923296989-6.95501461335.627049896
-1.0539086049-6.92020924585.4661176251
-1.3139897784-6.8755694195.2974173359
-1.5722036127-6.82115857155.1211887722
-1.8281831543-6.75705402784.9376823762
-2.0815646252-6.68334688824.7471589327
-2.3319879395-6.60014189944.5498891988
-2.5790972152-6.5075573064.3461535188
-2.82254128-6.40572468194.1362414258
-3.0619741702-6.29478874373.9204512306
-3.2970556225-6.17490714473.6990895971
-3.5274515577-6.04625025153.4724711072
-3.752834555-5.90900090093.2409178134
-3.9728843179-5.76335414123.0047587811
-4.1872881287-5.60951695392.7643296209
-4.3957412936-5.44770796062.5199720121
-4.5979475753-5.27815711152.2720332163
-4.7936196141-5.10110535892.020865585
-4.9824793362-4.91680431491.7668260578
-5.1642583489-4.72551589381.5102756558
-5.3386983222-4.52751193971.2515789683
-5.5055513556-4.32307384020.9911036348
-5.6645803307-4.11249212690.7292198225
-5.815559248-3.89606606180.4662997001
-5.9582735479-3.67410321280.2027169091
-6.0925204162-3.4469190162-0.0611539673
-6.2181090718-3.2148363282-0.3249379365
-6.3348610378-2.9781849667-0.5882601293
-6.4426103954-2.737301242-0.850746333
-6.5412040199-2.4925274792-1.1120235225
-6.6305017976-2.2442115315-1.3717203914
-6.7103768255-1.9927062862-1.6294678787
-6.7807155915-1.7383691629-1.8848996938
-6.8414181356-1.4815616054-2.1376528372
-6.8923981921-1.2226485687-2.3873681158
-6.9335833123-0.9619979996-2.6336906538
-6.9649149669-0.6999803142-2.876270397
-6.98634863-0.4369678717-3.11476261
-6.9978538416-0.1733344447-3.3488283663
-6.99941425150.0905453117-3.5781350301
-6.99102764220.3542963921-3.8023567287
-6.9727059320.6175439743-4.0211748157
-6.94447515820.8799139514-4.2342783241
-6.90637544041.1410334636-4.4413644078
-6.85846092271.4005314285-4.6421387722
-6.80079969761.6580390679-4.8363160927
-6.73347370871.9131904319-5.0236204196
-6.65657863452.1656229196-5.2037855706
-6.5702237522.4149777937-5.3765555093
-6.47453178222.6609006905-5.5416847083
-6.3696387152.9030421236-5.6989384992
-6.25569361623.1410579807-5.848093405
-6.13285841573.3746100122-5.9889374586
-6.00130767713.6033663123-6.1212705034
-5.86122835023.8270017904-6.244904478
-5.71281950474.0451986334-6.3596636836
-5.55629204754.257646757-6.4653850333
-5.39186842344.4640442464-6.5619182842
-5.21978229824.6640977859-6.6491262509
-5.04027822724.8575230749-6.7268850001
-4.85361130775.0440452327-6.7950840273
-4.66004681595.2233991884-6.8536264134
-4.45985983065.3953300584-6.9024289625
-4.25333484195.5595935079-6.9414223201
-4.04076534695.7159560986-6.9705510721
-3.82245343275.8641956203-6.989773823
-3.59870934716.0041014065-6.9990632548
-3.36985105766.135474634-6.9984061661
-3.13620379986.2581286056-6.9878034908
-2.89809961486.3718890151-6.9672702965
-2.65587687766.476594195-6.9368357635
-2.40987981636.5720953465-6.8965431428
-2.16045802256.6582567509-6.8464496952
-1.90796595516.7349559624-6.7866266096
-1.65276243586.802083982-6.7171589018
-1.39521014016.8595454127-6.638145294
-1.13567508096.9072585947-6.5496980741
-0.87452608946.9451557219-6.4519429363
-0.61213428986.9731829378-6.3450188026
-0.34887257296.9913004123-6.2290776251
-0.08511506576.9994823983-6.1042841705
0.17876340046.9977172682-5.9708157854
0.44238782196.9860075305-5.8288621446
0.70538355666.964369826-5.6786249815
0.96737685546.9328349047-5.5203178013
1.22799539396.8914475815-5.354165578
1.48686880166.8402666728-5.1804044338
1.74362918796.7793649129-4.9992813047
1.99791166496.7088288506-4.8110535887
2.24935486636.6287587263-4.6159887801
2.49760146086.5392683293-4.4143640898
2.74229865986.4404848364-4.206466051
2.98309871876.3325486309-3.9925901122
3.21965943136.2156131033-3.7730402171
3.45164461626.0898444333-3.5481283728
3.67872459425.9554213534-3.3181742063
3.90057665685.8125348951-3.0835045106
4.11688552555.6613881176-2.8444527798
4.3273437995.5021958187-2.6013587355
4.53165239045.3351842301-2.354567844
4.72952095245.1605906956-2.104430825
4.92066828974.9786633338-1.8513031539
5.10482275864.7896606857-1.5955445557
5.28172265334.593851347-1.3375184945
5.45111657754.3915135866-1.0775916568
5.61276380194.1829349511-0.8161334303
5.76643460593.9684118561-0.5535153789
5.91191060483.748249165-0.2901107148
6.04898505943.5227597558-0.026293768
6.17746317033.29226407630.2375605453
6.29716235443.05708968910.5010772563
6.40791250462.81757080540.7638818755
6.50955623152.57404781081.0256009256
6.6019490872.32686678111.285862472
6.68495976952.07637899061.5442966514
6.75847031091.8229404131.8005361974
6.82237624371.56691121512.0542169623
6.87658674981.30865524592.304978435
6.92102478941.04853951822.552464253
6.95562721070.78693368842.7963227086
6.98034483950.524209533.0362072495
6.9951425490.26074040623.2717769704
-
1 Characteristics of Sinusoidal Phase difference Sinusoidal Steady State Analysis
-
1 Characteristics of Sinusoidal Review The sinusoidal waves whose phases are compared must: Be written as sine waves or cosine waves. With positive amplitudes. Have the same frequency.Sinusoidal Steady State Analysis
-
2 PhasorsKey Words: Complex Numbers Rotating Vector PhasorsA sinusoidal voltage/current at a given frequency , is characterized by only two parameters :amplitude an phaseSinusoidal Steady State Analysis
-
2 PhasorsE.g. voltage responseSinusoidal Steady State Analysis
-
2 PhasorsRotating VectorIm Sinusoidal Steady State Analysisi(t1)Imag
-
2 PhasorsRotating VectorSinusoidal Steady State Analysis
-
2 PhasorsComplex Numbers Sinusoidal Steady State Analysis
-
2 PhasorsPhasors A phasor is a complex number that represents the magnitude and phase of a sinusoid:Phasor DiagramsA phasor diagram is just a graph of several phasors on the complex plane (using real and imaginary axes).A phasor diagram helps to visualize the relationships between currents and voltages. Sinusoidal Steady State Analysis
-
2 PhasorsComplex Exponentials A real-valued sinusoid is the real part of a complex exponential. Complex exponentials make solving for AC steady state an algebraic problem. Sinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and CKey Words: I-V Relationship for R, L and C, Power conversionSinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and C v~i relationship for a resistorWave and Phasor diagrams ResistorSupposeSinusoidal Steady State Analysis
(
EMBED Equation.3
EMBED Equation.3
(
(
(
(
(I1
(
-
+
(U1
(
(I1
(
E
(
IS
US
_
+
+
5(
5(
5(
5(
R
R1
R1
(
(
(
(
I1
I1
I1
I1
I1
I1
i
v
_
(
_1202715897.unknown
_1202715928.unknown
-
3 Phasor Relationships for R, L and CWith a resistor , v(t) and i(t) are in phase . Sinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and CResistorSinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and C v~i relationshipInductor Sinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and C v~i relationshipInductorSinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and C v ~ i relationshipInductor The derivative in the relationship between v(t) and i(t) becomes a multiplication by j in the relationship between and . The time-domain differential equation has become the algebraic equation in the frequency-domain. Phasors allow us to express current-voltage relationships for inductors and capacitors in a way such as we express the current-voltage relationship for a resistor.
Sinusoidal Steady State Analysis
-
3. Phasor Relationships for R, L and C v ~ i relationshipInductorWave and Phasor diagrams Sinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and CInductorP4.5L = 10mHv = 100sintFind iL when f = 50Hz and 50kHz. Sinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and C v ~ i relationshipCapacitor Sinusoidal Steady State Analysis
(
EMBED Equation.3
EMBED Equation.3
(
(
(
(
(I1
(
-
+
(U1
(
(I1
(
E
(
IS
US
_
+
+
5(
5(
5(
5(
C
R1
R1
(
(
(
(
I1
I1
I1
I1
I1
I1
i
v
_
(
_1202715897.unknown
_1202715928.unknown
-
v(t) = Vm ejtRepresent v(t) and i(t) as phasors: The derivative in the relationship between v(t) and i(t) becomes a multiplication by j in the relationship between and . The time-domain differential equation has become the algebraic equation in the frequency-domain. Phasors allow us to express current-voltage relationships for inductors and capacitors much like we express the current-voltage relationship for a resistor. 3 Phasor Relationships for R, L and C v ~ i relationshipCapacitor Sinusoidal Steady State Analysis
(
EMBED Equation.3
EMBED Equation.3
(
(
(
(
(I1
(
-
+
(U1
(
(I1
(
E
(
IS
US
_
+
+
5(
5(
5(
5(
C
R1
R1
(
(
(
(
I1
I1
I1
I1
I1
I1
i
v
_
(
_1202715897.unknown
_1202715928.unknown
-
3 Phasor Relationships for R, L and C v ~ i relationshipCapacitorWave and Phasor diagrams Sinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and CCapacitorP4.7Suppose C=20FAC source v=100sintFind XC and I for f = 50Hz, 50kHz Sinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and CReview (v-I relationship)Sinusoidal Steady State Analysis
-
3 Phasor Relationships for R, L and CSummary Frequency characteristics of an Ideal Inductor and Capacitor: A capacitor is an open circuit to DC currents; A Inducter is a short circuit to DC currents.Sinusoidal Steady State Analysis
-
4 ImpedanceKey Words: complex currents and voltages. Impedance Phasor DiagramsSinusoidal Steady State Analysis
-
AC steady-state analysis using phasors allows us to express the relationship between current and voltage using a formula that looks likes Ohms law:4 ImpedanceComplex voltage Complex current Complex ImpedanceSinusoidal Steady State Analysis
-
4 ImpedanceComplex ImpedanceComplex impedance describes the relationship between the voltage across an element (expressed as a phasor) and the current through the element (expressed as a phasor)Impedance is a complex number and is not a phasor (why?).Impedance depends on frequencySinusoidal Steady State Analysis
-
4 ImpedanceComplex ImpedanceSinusoidal Steady State Analysis
-
4 ImpedanceComplex ImpedancePhasors and complex impedance allow us to use Ohms law with complex numbers to compute current from voltage and voltage from currentHow do we find VC?First compute impedances for resistor and capacitor:ZR = 20kW = 20kW 0 ZC = 1/j (377 *1mF) = 2.65kW -90 Sinusoidal Steady State Analysis
-
4 ImpedanceComplex ImpedanceNow use the voltage divider to find VC: Sinusoidal Steady State Analysis
*
*P4.2, vivi/3vivi /3 vi
*P4.2, vivi/3vivi /3 vi
*P4.2, vivi/3vivi /3 vi j90*P4.2, vivi/3vivi /3 vi
*P4.2, vivi/3vivi /3 vi
top related