实验报告Word格式.docx

实验报告Word格式.docx

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transmissionparametersonly）,themethodofthemeasurementandcalculationwillbeshortlyandexpresslyillustratedinthepartofTheoreticalBackgrounds,withintheknowledgeofmeasuringindividualparameters,weareaimingtoinvestigatetherelationshipsbetweentheseandthoseoftwo-portnetworksincascadeandparallel;

part2istofindoutthetwo-portnetworktransientresponsecontainingcapacitiveandinductivereactances.

✧TheoreticalBackgrounds

MeasurementofY-Parameters（Admittanceparameters）

Theequationsfortheparametersare:

I1=y11V1+y12V2

I2=y21V1+y22V2

i.e.[I]=[Y][V]

wherearetheY-parametersofthetwo-portnetwork.

Experimentally,theseparameterscanbedeterminedbyshortcircuitingoneportatatime.Thisiswhytheseparametersarealsotermedtheshort-circuitadmittanceparameters.

Thefollowingshowshowtocalculatetheparameters:

Whenoutputportisshorted（asshowninFigure2）:

V2=0

Figure2

y11=I1/V1andy21=I2/V1

Wheninputportisshorted:

V1=0

Figure3

y12=I1/V2andy22=I2/V2

MeasurementofTransmission（ABCD-）Parameters

V1=AV2-BI2

I1=CV2-DI2

or

where[t]isthetransmissionparametersofthetwo-portnetwork.

Experimentally,thet-parameterscanbeobtainedbyshortcircuitingandopencircuitingtheoutputoneatatime.

Outputportisopen-circuited:

I2=0

Figure4

A=V1/V2andC=I1/V2

Outputportisshort-circuited:

V2=0

Figure5

B=-V1/I2andD=-I1/I2

CascadeInterconnectionof2Two-portNetworks

Considerthe2two-portnetworksAandB（asshowninFIigure1）connectedincascade,asshowninFigure6.TheoveralltransmissionparametersofthecombinednetworkNcanbeobtainedasthefollowing（foreachsinglenetwork,themeasurementofparameterscanbeobtainedasprevious）:

Figure6

[t]N=[t]A[t]B

sothat,thefollowingcanbeobtained:

ParallelInterconnectionof2Two-PortNetworks

Considerthe2two-portnetworksAandB（asshowninFIigure1）connectedincascade,asshowninFigure7.Theoveralladmittance（Y-）parametersofthecombinednetworkNcanbeobtainedasthefollowing:

Figure7

Itisobviousthat

I1=I1A+I1B

I2=I2A+I2B

V1=V1A=V1B

V2=V2A=V2B;

and

==+

=+

=

ItcanbeseenthattheoverallY-parameterscanbeobtainedbysummingthecorrespondingY-parametersofindividualnetworksAandB,whentheA,Bnetworksarenotalteredbytheparallelconnection.

TransientResponsesofTwo-portNetwork

Accordingtothedampingratio,（Theratiooftheactualresistanceindampedharmonicmotiontothatnecessarytoproducecriticaldamping.Alsoknownasrelativedampingratio）,wedividethetransientresponsesintothreetypes,whichareoverdampedresponse（>

1）,underdampedresponse（<

1）andcriticallydampedresponse（=1）.Itdetermineshowmuchthesystemoscillatesastheresponsedecaystowardsteadystate. 

Andforastepthatsteadystatewilldependontheinputstepsize.

Thecharacteristicequationdescribesthepolesofthetransferfunctionofthenetwork.Itdeterminesthetypeoftransientresponse.

Overdamped:

If>

1,thepolesarerealanddistinct,thesolutionissimplyadecayingexponentialwithnooscillationandthetransientresponsewillbeoverdamped.Thisresponseisslowandhasnoovershootsandundershoots.

Underdamped:

Thepolesarecomplex,andthetransientresponsewillbeunderdampedif<

1,thenthesolutionisadecayingexponentialcombinedwithanoscillatoryportion.Overshootsandundershootswillbeproduced.

Criticallydamped:

when=1,thepolesarerealandequal,andthetransientresponsewillbecriticallydamped.Noovershootsorundershootswillbeproducedandtheresponsewillbefasterthanoverdampedresponse.Thisturnsouttobeadesirableoutcomeinmanycaseswhereengineeringdesignofadampedoscillatorisrequired

Inthisexperiment,wearemainlyusingthesecondtype,whichistheunderdampedresponse.

Andthecharacteristicequationisgivenby:

S2+2ωnS+ωn2

where

ωn=undampednaturalfrequency=1/√（LC）

ωn√（1-2）=dampednaturalfrequency

=dampingratio=

DetailedmethodofcalculationisshowninAppendixBattachedwiththelaboratorymanual.

✧Objectives

Ø

Tomeasuretheadmittance-parametersandtransmissionparametersoftwo-portnetwork

Toinvestigatetherelationshipsbetweenindividualnetworkparametersandtwo-portnetworksincascadeandparallelconnections

Tostudythetransientresponseofatwo-portnetworkcontainingcapacitiveandinductivereactances.

✧Equipment

DigitalStorageOscilloscope

FunctionGenerator（50Ω）

DigitalMultimeter

Inductorwith2inductancesteps

Capacitors:

22μF,100μF

Resistors:

33,100

（2）,220,330,560,680,3.9k,4.7k

（2）,5.6k,6.8kΩ

Bread-board

✧Procedures

MeasurementofAdmittance-ParametersandTransmissionParameters

ConnecttheresistivenetworkAasshowninFigure8.

Withthenetworkconnected,applya1kHz,10voltspeaktopeaksinusoidalvoltage:

a）Port1withport2open-circuited

b）Port1withport2short-circuited

c）Port2withport1short-circuited

Measurethevoltageandcurrentattheinputandoutputterminalsineachcase.

TabulatetheresultsinTable1.

Figure8TheResistiveNetworkA

ConnecttheresistivenetworkBasshowninFigure9.

Measuretheresultsforthetestinthesecondstep,andtabulatethecalculatedvaluesinTable1.

Figure9TheresistiveNetworkB

ConnectnetworksAandBincascadeasshowninFigure10.

Repeatthesecondstepforthecascadednetwork.

Figure10NetworksinCascade

ReconnectnetworksAandBinparallelasshowninFigure11.

Repeatthesecondstepfortheparallel-connectednetwork.

Figure11NetworksinParallel

Table1（Allvaluesinrms）

Results

I1（mA）

V1（V）

V2（V）

I2（mA）

NetworkA

（measured）

2.29

3.54

2.50

5.53

4.43

4.42

5.89

NetworkB

0.69

3.23

3.89

3.39

3.47

Cascaded

2.59

2.04

3.34

1.32

Parallel

13.75

12.23

12.14

14.05

Questions

ThevoltagesV1andV2shouldnotbeconnectedtochannel1and2ofthescopesimultaneously.Why?

Fromthecircuit,itcanbeobservedthatV1andV2havedifferentground.Iftheyareconnectedtochannel1andchannel2oftheoscilloscopesimultaneously,boththedifferentgroundwillbeshort-circuited,thereforecausethenetworkundertesttobeshort-circuitedattheground.Meanwhileithaschangedthecircuit’sconfiguration.Thus,therewillbeabigerrorbetweenthereadingsobtainedandtherealvalues.

Whatshouldyoudotothereadingsofpeaktopeakvoltageinordertomakethemcompatiblewiththecurrentsmeasuredbythedigitalmeter?

Thecurrentmeasuredbythedigitalmeterisinroot-mean-squarevalues（rms）.Soitisobligatorytoconvertpeaktopeakvoltagevaluesintormsvalues.Thefollowingshowstherelationshipbetweenpeaktopeakvaluesanditsrespectivermsvalues:

peaktopeakvoltagevalues=2x2xrmsvalues

Therefore,thepeaktopeakvoltagevaluesshouldbedividedby2x2tomakethemcompatiblewiththecurrentsmeasuredbythedigitalmeter.

Verifythetheoreticalrelat