primary line primary line parameters describe characteristics transmission lines pairs copper wires terms physical electrical properties line primary line relevant lines contrasted secondary line derived generally applicable secondary line instance compare characteristics copper line primary meaning conductor resistance convention given symbols respectively terms unit length circuit representation elements requires distributed element model consequently circuit secondary characteristic propagation constant derived way number special cases particularly simple solutions important practical applications low loss cable requires included analysis useful short lengths cable low frequency applications twisted pair telephone lines dominated high frequency applications cable dominated lines loaded prevent distortion need elements analysis simple elegant solution primary line circumstances small ignored analysis simplified symbols units follows elements series line properties conductor elements line properties material represents current cables small word loop emphasise resistance taken account instance line consists identical wires resistance loop resistance double values small common manufacturers quote kilometre metre english speaking world mile word constant misleading variation frequency particular heavily influenced skin effect furthermore virtually effect audio frequency cause noticeable losses high frequency materials cables high loss avoiding losses caused reason cables designed use air foam makes virtually air actual meaning constant context constant distance line assumed condition true vast majority transmission lines use today typical values common cables manufacturers commonly value data sheets values estimated figures characteristic formula circuit representation line simply represented elements circuit described distributed elements instance pieces pieces resistance pieces broken argued broken apart properly represent circuit division number circuit increased shown figure true representation circuit elements small element distributed line elements distance formula given formula formula formula formula convenient purposes analysis roll elements general series elements formula formula analysis network figure yield secondary line propagation constant formula real imaginary parts constant formula phase change constant formula respectively characteristic formula general real formula imaginary formula parts making total secondary derived primary term constant misleading secondary usually vary strongly frequency frequency dependence primary ignored circuit formula formula introduce dependence formula possible choose specific values primary result formula formula constant condition case formula directly proportional formula primary meaning secondary vary distance line independent frequency characteristic characteristic transmission line formula defined looking infinitely long line line return reflection incident wave reach end reflected considering finite initial length line remainder line replaced formula equivalent circuit remainder line infinitely long considering section equivalent circuit line network consisting element formula formula remainder replaced formula results network shown figure analysed formula usual network analysis formula arranges formula taking limits sides formula line assumed formula propagation constant ratio line input voltage voltage distance formula line section equivalent circuit given standard voltage calculation remainder line right characteristic calculation replaced formula formula section voltage drop factor formula sections voltage ratio formula distance formula line number sections formula formula limit formula formula second order term formula disappear limit write loss accuracy formula comparing mathematical identity formula yields formula definition propagation constant formula formula special cases ideal transmission line loss implies elements zero results purely real characteristic ideal line realised practice useful circumstances especially true instance short pieces line circuit components short line little loss ignored treated ideal line secondary circumstances formula formula formula formula twisted pair typically twisted pair cable audio frequencies low data rates line dominated loss usually frequencies close zero case low frequency formula means ignored circumstances secondary formula formula formula formula cable type increases frequency causing distortion obviously variation formula frequency causes distortion type called avoid requirement formula directly proportional formula actually proportional formula results formula varies frequency partly features cause reflections line termination undesirable effect nominal quoted type cable case nominal valid spot frequency usually quoted cable cable operated high frequency radio frequency high data rates meet conditions formula formula eventually case frequency increased cable conditions ignored purpose calculating cable loss secondary formula formula formula formula loaded line loaded lines lines designed deliberately increased adding iron magnetic metal cable adding purpose ensure line meets condition distortion caused frequency dependent ensures formula constant secondary related primary formula formula formula formula velocity velocity propagation given formula formula formula formula cases taken formula velocity propagation given formula lower higher velocity air cable low loss cable velocity propagation close speed light
Primary line constants