大学物理实验报告英文版非线性与混沌.docx
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大学物理实验报告英文版非线性与混沌.docx
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大学物理实验报告英文版非线性与混沌
PhysicalLabReport:
Nonlineardevicesandchaos
Writer:
[Purpose]
1.Togetfamiliarwiththenonlineardevicesandthephenomenoninchaos.
2.Tolearntousethedevicesaboutnonlinearandchaos.
3.TogetfamiliarwithOriginanduseittodealwithdata.
[Principle]
1.Diodeisanasymmetricelectriccomponentwithlowresistancetoelectricalcurrentinonedirection,andhighintheother.Thesymbolofthediodeisshownbelow.Thedirectionwherethetriangleispointingtoisthedirectionoftheconduction.
Ingeneral,theV-Acharacterofadiodeisshowninthefigurebelow.
Introductiontodiodes:
a.Detectordiode:
itregulatesthepassingofelectricalcurrents-pulseswillberestrictedfrompassinginthereversedirection,andwillpassonlyintheforwarddirection.
b.Rectifierdiode:
anelectricaldevicethat converts ACcurrenttoDCcurrent(flowingonlyindirection).Thefigurebelowillustratestheprincipleofoperationofarectifier.
Normallyadetectordiodeisapoint-contactPNjunction,whichlimitedworkingcurrent,highbandwidth,andaverylowreversevoltage.Rectifierisasurface-contactPNjointwithlargelimitingcurrent,lowoperationfrequency,andhighreversevoltage.
c.Zenerdiode:
itworksinthereverseddirectionclosetothebreakdownregime.Itconductswhenthevoltagereachesthediode'sreversebreakdownvoltage.Fromthatpointon,therelativelylowimpedanceofthediodekeepsthevoltageacrossthediodeatthatvalue.Itcanbeusedasavoltageregulatorasshowninthediagrambelow.
d.Light-emittingdiode (LED):
itisa semiconductor lightsourceworkingintheforwarddirection(seepicturebelow).Whenalight-emittingdiodeisswitchedon, electrons areabletorecombinewithholeswithinthedevice,releasingenergyintheformof photons.Thecolorofthelight(correspondingtotheenergyofthephoton)isdeterminedbytheenergybandgapofthesemiconductor.Theturn-onvoltageU0isbetween1.6to3V,whichcanbeestimatedbyeU0=hc/lwhereliswavelengthofthediode.Forvoltagebeyondthat,thecurrentincreasesrapidlyandtheLEDconductsandemitsvisuallights.Whenthevoltageislessthanthat,theLEDworkslikeaninsulator.
2.Consideracircuitasshowninthefigurebelow.TheinductorLandC1/2leadtoanoscillatingcircuit.Onecanwritedownthefollowingdifferentialequations:
NotethatifRandR0arelineardevices,thesolutionforUC1andUC2willbearegularsinusoidaloscillator,andR0controlsthephasebetweenthetwo.NowifRisnonlinear,e.g.withaV-Irelationlikewhat’sshowninthefigurebelow,thenthissetofequationscannotbesolvedanalytically.
Onecansolveditnumericallywithacomputerprogram,bywhichonecanobservedchaoticbehaviorsonthesolutionsforappropriateparameters.
WhenR0isadjustsothatthesystemisoscillating(positivefeedbackwinsoverthenegativefeedback),thetwo-stageopampandthe6resistorsunitwilleffectivelyactasanonlinearresistorifviewedfromCandD.
[Procedure&Analysis]
1Detectordiode
a)ForwardV-Acurve:
constructcircuitryusingthebreadboardasinthefigurebelow.Useacurrentlimitingresistortoprotectthediode.LimitI<20mAandU<1.2V.Usethemultimeterasacurrentmeter,andusethevoltagesupplyreadingtogetthevoltage.Take20datapoints.MaketheV-Acurve.
b)ReverseV-Acurve:
constructcircuitryusingthebreadboardasinthefigurebelow.Useacurrentlimitingresistortoprotectthediode.LimitI<20mAandU<20V.Usethemultimeterasacurrentmeter,andusethevoltagesupplyreadingtogetthevoltage.Take10datapoints.MaketheV-Acurve.
c)Notethatthesuppliedvoltagewillbedividedbetweentheresistorandthediode.Canyoumakeacorrectiontothe300OhmresistorwhenmakingtheV-Acurve?
wegetthefollowingdata:
U/V
0.30
0.60
0.90
1.20
1.50
1.80
2.10
2.40
2.70
3.00
I/mA
0.292
1.122
2.015
2.925
3.868
4.792
5.744
6.674
7.628
8.564
U/V
3.30
3.60
3.90
4.20
4.50
4.80
5.10
5.40
5.70
6.00
I/mA
9.495
10.430
11.391
12.330
13.271
14.231
15.172
16.111
17.076
18.015
Afterwesubtractthevoltageofprotectiveresistance,weget:
U/V
0.2124
0.2634
0.2955
0.3225
0.3396
0.3624
0.3768
0.3978
0.4116
0.4308
I/mA
0.292
1.122
2.015
2.925
3.868
4.792
5.744
6.674
7.628
8.564
U/V
0.4515
0.471
0.4827
0.501
0.5187
0.5307
0.5484
0.5667
0.5772
0.5955
I/mA
9.495
10.430
11.391
12.330
13.271
14.231
15.172
16.111
17.076
18.015
UseOrigintogetthegraph:
Reverse:
Aftertheexperiment,wegetthefollowingdata:
U/V
I/μA
U/A
I/μA
2.00
0.10
12.00
0.16
4.00
0.11
14.00
0.17
6.00
0.13
16.00
0.18
8.00
0.14
18.00
0.20
10.00
0.15
20.00
0.21
Afterwesubtractthevoltageofpro
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