reflections signals conducting lines signal travelling electrical transmission line partly wholly reflected opposite direction travelling signal encounters characteristic line far end line terminated characteristic happen instance lengths transmission lines joined article signal reflections electrically conducting lines lines loosely referred copper lines telecommunications generally copper metals notably aluminium power lines article limited describing reflections conducting lines essentially phenomenon optical reflections lines microwave reflections reflections cause undesirable effects including modifying frequency responses causing power power lines reflection phenomenon use devices special cases open circuit short circuit lines particular relevance reflections cause standing waves set line conversely standing waves indication reflections present relationship measures reflection standing wave ratio specific cases approaches understanding reflections relationship reflections conservation laws particularly simple example step voltage formula formula height step formula unit step function time formula applied end line consider happens line terminated ways step propagated line according equation velocity formula incident voltage formula point formula line given formula incident current formula found dividing characteristic formula formula open circuit line incident wave travelling line affected way open circuit end line effect step actually reaches point signal end line affected local characteristics line line length formula step arrive open circuit time formula point current line zero definition open circuit charge continues arrive end line incident current current leaving line conservation electric charge requires equal opposite current end line essentially current law operation equal opposite current reflected current formula formula reflected voltage formula drive reflected current line reflected voltage exist reason conservation energy source supplying energy line rate formula energy dissipated line termination available direction line reflected current equal magnitude incident current formula add step reflected twice incident voltage appears output line reflection proceeds line reflected voltage continues add incident voltage reflected current continues incident current interval formula reflected step arrives generator end condition double voltage zero current length line generator matched line formula step absorbed generator internal reflections counter intuitive doubling voltage circuit considered line short ignored purposes analysis equivalent circuit generator matched load formula delivering voltage formula represented figure generator represented ideal voltage generator twice voltage deliver internal formula generator left open circuit voltage formula appears generator output figure situation short transmission line inserted generator open circuit longer line characteristic formula noticeable end end delay inserted generator initially matched line formula output interval reflected return end line information line actually terminated voltage formula short circuit line reflection short line described similar terms open line open circuit case current zero end line short circuit case voltage zero volts short circuit energy reflected line reflected voltage equal opposite incident voltage voltage law formula formula reflection travels line cancel currents add reflection double negative negative current travelling reverse direction dual situation open circuit case arbitrary general case line terminated arbitrary usual describe signal wave travelling line frequency domain consequently represented frequency complex function line terminated characteristic reflection definition terminating characteristic effect infinitely long line result reflection magnitude reflection smaller magnitude incident wave terminating wholly partly energy incident wave absorbed resistance voltage formula terminating formula calculated replacing output line equivalent generator figure given formula reflection formula exact required formula formula reflection formula defined formula expression formula formula general formula complex function expression shows magnitude limited formula formula physical interpretation reflection greater incident wave passive elements involved negative resistance example condition hold special cases described formula formula purely formula purely real general case formula complex interpreted shift phase reflected wave relative incident wave termination special case occurs formula purely real formula formula purely imaginary formula case formula formula formula showing incident wave reflected absorbed termination expected pure change phase formula reflection given formula line length line results incident wave reflected transmitted onward second section line shown figure reflection case given formula similar manner transmission formula defined describe portion wave formula transmitted forward direction formula kind caused sections line identical characteristic element formula example shown figure element formula formula similar expressions developed series element electrical network matter networks reflections complex scenarios found network cables result complicated long lasting cable simple pulse entering cable system power found typical private home result disturbance pulse reflected multiple circuit ends ring waves known persist far longer original pulse bears little obvious resemblance original disturbance containing high frequency components tens range standing waves transmission line carrying waves phase reflected wave continually changing distance respect incident wave proceeds line continuous change certain points line reflection phase incident wave waves add points waves anti phase consequently points minimum known incident wave totally reflected line complete cancellation zero signal present despite ongoing transmission waves directions points waves phase anti represent peak anti alternate line combined wave varies continuously combined incident plus reflected wave appears standing line called standing wave incident wave characterised terms line propagation constant formula source voltage formula distance source formula formula convenient work terms distance load formula incident voltage arrived formula formula positive formula measured reverse direction line voltage increasing closer source likewise reflected voltage given formula total voltage line given formula convenient express terms functions formula similarly total current line formula voltage current locations anti occur formula easy solution general case case lines lines short considered formula replaced formula formula phase change constant voltage equation reduces functions formula partial differential magnitude yields condition formula expressing formula terms formula allows formula solved terms formula formula formula purely real termination short circuit open circuit formula formula purely cases anti given formula formula formula formula point formula point anti alternate purely remain pattern shifted line constant related phase formula voltage standing wave ratio ratio formula anti called voltage standing wave ratio related reflection formula line line expression valid adjacent termination approaches unity distance termination positions parameters directly measured instrument called line instrument makes use reflection phenomenon different measurements microwave frequencies use position test component terminating line useful method measuring directly measuring currents difficult frequencies conventional means expressing match radio antenna important power reflected high power damage output input input looking transmission line terminated characteristic far end formula function length line value found dividing expression total voltage expression total current given formula formula length line dividing formula reduces formula considering short pieces transmission line formula replaced formula expression reduces functions formula applications structures particular importance use reflected waves modify short length line terminated short circuit open circuit produces purely imaginary input formula suitable choice length place circuit structure quarter wave suggests line exactly formula length formula produce terminating formula structures widely distributed element filters matching networks
Reflections of signals on conducting lines