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Telecommunication Networks Distributed P arameter Networks

Telecommunication Networks Distributed P arameter Networks. Distributed Parameter Networks 1. d. EM waves t heory , but if d<< , we can examine t he topic with quasi-stationary method. Lecher wire. koaxial cable. The electromagnetic wave passes on the wire.

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Telecommunication Networks Distributed P arameter Networks

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  1. TelecommunicationNetworks DistributedParameterNetworks

  2. DistributedParameterNetworks 1. d EM wavestheory, butifd<<, wecanexaminethetopicwithquasi-stationarymethod. Lecherwire koaxialcable The electromagneticwavepassesonthewire. The electric and magneticpowerdistributehomogeneouslyalongthewire, butthecurrentchangesintime. Consumer Generator

  3. DistributedParameterNetworks 2. Inductionlawfor ABCD loop: Loopequationfordx : The flux is proportionaltothecurrent: =Ldxi

  4. DistributedParameterNetworks 3. Ondxsectioncharchesaccumulate, oraccumulatedchargesdisappear. Thisincreasesthedifferencebetween input and output current. Ondxthechange of chargesintime: Continuityequation : where u(x,t)Gdx is theleakagecurrent is thedisplacementcurrenteltolási betweenthetwowires Rearranging:

  5. DistributedParameterNetworks 4. The equvalentcircuit of dxonpowertransmission line: Twoequationsonpure sine signal:

  6. DistributedParameterNetworks 5. Telegram equations The 2. equationdifferentiatedby x and weput du/dxfrom 1. equationinto 2. equationweget:

  7. DistributedParameterNetworks 6. Wetrytoget a formula likethis: substituting back : – propagationcoefficient Considering a pozitive , weget: Attenuationfactor Phasefactor

  8. DistributedParameterNetworks 7. If a is considered Thismeans a wavepassingtowardnegativexdirectiononratev The length of periodis: Formula forwavelength and phasefactor Wavepassingonpositive x is:

  9. DistributedParameterNetworks 8. The timedependence of thevoltagemeasuredin a givenpositiononthewire is puresinusoidal. Atdxdistancetheamplitudedecreases and thephasechanges. Substitutingvoltagewaveinto equation, weget:

  10. DistributedParameterNetworks 9. Fromthepreviouspicturewesupposethatthecurrent formula is: Thus: Waveimpedance

  11. DistributedParameterNetworks 10. Substitutingthenegativedirectionwaveweget: The generalsolution of thevoltagewave is: The generalsolution of thecurrentwave is: or:

  12. DistributedParameterNetworks 11. Idealwire: thus Phasefactor rate és Thomson formula: where [L]=Henry and [C]=Farad Ifwedecreasethevalue of L and C towards 0, v doesnotreach c (speed of light). Onidlewirethewavespassby c rate.

  13. DistributedParameterNetworks 12. Twowires Capacity Induction Waveresistance Ifweincreasecapacitieswithgeometricalsizestheinductivitydecreases and vice versa. Thusit is impossibletomake a constructionwhichcanoperateonhigherratethan c.

  14. DistributedParameterNetworks 13. Foridlewire: Inidlecasetherate and waveimpedancedonotdependonfrequency. Ifratewoulddependonfrequency, distortionwouldoccureforexampleonpulsesignal, becausethespectra is: 0, 30, 50, … etc. and wewouldgetdifferentphasedelaysondifferentfrequencies. Onthecableswithbigattenuationthebigdelaytimecausesbigproblems: 

  15. DistributedParameterNetworks 14. Weexaminethetransmission line with Z atthe end: Let’ssay: U0+ =A and U0- =B and x=-l. Wedonotconsiderthetimedependencecase, thus: Ir Ih Ur Uh

  16. DistributedParameterNetworks 15. Let’scountthevalue of A and B with UZ and IZ: If =0, itmeansU=UZand I =IZ Adding and substracting:

  17. DistributedParameterNetworks 16. Voltagereflectionfactor: Reflectionfactorat Z Currentreflectionfactor is:

  18. DistributedParameterNetworks 17. A and B arecomplexnumbers: thus: The direct and reflectedwavesoncomplexplain:

  19. DistributedParameterNetworks 18. Wherethetwovectorsareinphase voltage-maximum Wherethephasedifference is 180ovoltage-minimum IfZZ0 alongthe line standing wavesareselfcreated IfZ=Z0, therearenot standing waves

  20. DistributedParameterNetworks 19. Voltage standing wave: or: Fromthefigure: • Distancebetweentwo minimum or maximum values is /2 • Distancebetween maximum and minimum values is /4

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