Heaviside condition
The importance of the Heaviside condition is that it showed the possibility of dispersionless transmission of telegraph signals.[1]: 131 In some cases, the performance of a transmission line can be improved by adding inductive loading to the cable.A transmission line is distortionless if it is dispersionless and the attenuation coefficient is independent of frequency.To prevent intersymbol interference it was necessary to reduce the transmission speed of the transatlantic telegraph cable to the equivalent of 1⁄15 baud.An analogous Heaviside condition for dispersionless propagation in left-handed transmission line metamaterials cannot be derived, since no combination of reactive and resistive elements would yield a constant group velocity.The relationship between the primary and secondary line constants is given by If the Heaviside condition holds, then the square root function can be carried out explicitly as: where Hence Velocity is independent of frequency if the productA real line will have a G that is very low and will usually not come anywhere close to meeting the Heaviside condition.The normal situation is that To make a line meet the Heaviside condition one of the four primary constants needs to be adjusted and the question is which one.This not only makes the cable much bulkier, but also adds significantly to the amount of copper (or other metal) being used and hence the cost and weight.Decreasing the capacitance is difficult because it requires using a different dielectric with a lower permittivity.Gutta-percha insulation used in the early trans-Atlantic cables has a dielectric constant of about 3, hence C could be decreased by a maximum factor or no more than 3.Instead, regularly spaced digital repeaters are now placed in long lines to maintain the desired shape and duration of pulses for long-distance transmission.[1]: 132 Achieving the Heaviside condition is more difficult when some or all of the line parameters depend on frequency.There are three red curves indicating typical low, medium, and high-quality dielectrics.Pulp insulation (used for telephone lines in the early 20th century), gutta-percha, and modern foamed plastics are examples of low, medium, and high-quality dielectrics.The curve is depicted as flat on the figure, but loss tangent shows some frequency dependence.The value of G/(ωC) at all frequencies is determined entirely by properties of the dielectric and is independent of the transmission line cross-section.
transmission lineOliver Heavisideloadingdistributed-element modelprimary line constantscapacitancefaradsinductancehenriesresistanceconductancesiemenstransmission functionphase velocitydispersionattenuation coefficienttransatlantic telegraph cableLord Kelvintelegraphintersymbol interferencemetamaterialssecondary line constantsattenuation constantnepersphase constantradianscharacteristic impedanceimpedance matchelementsrational functionsGutta-perchamagnetic permeabilityloading coilscut-off frequencyrepeatersloss tangentMaxwell's equationsTelegrapher's equationsCaloz, C.Itoh, T.IEEE Transactions on Antennas and PropagationTelecommunicationsHistoryBroadcastingCable protection systemCable TVData compressionDigital mediaInternet videoonline video platformsocial mediastreamingEdholm's lawInformation AgeInformation revolutionInternetMobile phoneSmartphoneOptical telecommunicationOptical telegraphyPhotophonePrepaid mobile phoneRadiotelephoneSatellite communicationsSemaphorePhryctoriaSemiconductordeviceMOSFETtransistorSmoke signalsTelecommunications historyTelautographTelegraphyTeleprinterTelephoneThe Telephone CasesTelevisiondigitalVideotelephonyWhistled languageWireless revolutionNasir AhmedEdwin Howard ArmstrongMohamed M. AtallaJohn Logie BairdPaul BaranJohn BardeenAlexander Graham BellEmile BerlinerTim Berners-LeeFrancis BlakeJagadish Chandra BoseCharles BourseulWalter Houser BrattainVint CerfClaude ChappeYogen DalalDaniel Davis Jr.Donald DaviesAmos DolbearThomas EdisonLee de ForestPhilo FarnsworthReginald FessendenElisha GrayRobert HookeErna Schneider HooverHarold HopkinsGardiner Greene HubbardInternet pioneersBob KahnDawon KahngCharles K. KaoNarinder Singh KapanyHedy LamarrRoberto Landell de MouraInnocenzo ManzettiGuglielmo MarconiRobert MetcalfeAntonio MeucciSamuel MorseJun-ichi NishizawaCharles Grafton PageRadia PerlmanAlexander Stepanovich Popov