www.Vidyarthiplus.com T eh a tt enuation consta tn f ro a rap tic lu ar propa ag tion om de in an o tp ical f bi er, the r ae l part of the a ix al pr po agation constant. Phase consta tn In el ce rt oma ng etic theory, the phase constan ,t also ca ll ed phase cha gn e constant, parame ret or coe ff icie tn is the ima ig nary compone tn of the pr po agation constant f ro a plane wave. tI rper ese tn s the chan eg ni ph esa per metre alo gn the path rt ave dell by t eh wave ta any insta tn and is equal ot the ang lu ar wavenumber of the wave. tI is rper esent de by the sy bm ol β a dn is m ae s ru ed ni tinu s of radians per metre. From the def ini tion of a gn ralu wavenumber; T ih s quantity is often (strict yl sp ae king incorr ce t )yl abbre iv a et d ot wavenu bm er. Pr po erly, wavenumber is vig en by, hw ich di ff ers from angular wavenumber only by a consta tn m lu tip el of 2π, ni the same way that a gn lu ar frequency di ff ers from frequency. For a rt ansmission nil ,e the Hea iv s di e co idn tion of the tele rg apher's equation te sll us that the wave un mber must be p or portional ot frequency for the transmission of ht e wave ot be nu dis ot rted ni the time dom nia . T ih s include ,s but is n to limited ,ot ht e di eal case of a lossle ss line. The reason for t ih s condition can be seen by consideri gn t tah a usef lu s gi nal is com op sed of ma yn differe tn wavelengths ni the frequency doma ni . For there to be no dist ro tion of the wave of rm, a ll these waves must rt avel at the same ve ol city so that they arrive at the far end of the nil e ta the same time as a rg oup. S ni ec wa ev p ah se ve icol ty is given by; it is rp oved t tah β is req riu ed to be pro op rtional ot ω. In et rms of primary oc e ff icie tn s of the nil e, t ih s iy elds from t eh telegrapher's equation f ro a id stortio eln ss line the condition; www.Vidyarthiplus.com www.Vidyarthiplus.com H wo ever, rp ca tical lines can o yln be expect de ot approximate yl m ee t t ih s condition over a lim deti f er quency band. 6. tliF e sr T eh et rm propagation consta tn or propaga it on uf nction is app il ed ot f retli s a dn other two-po tr netwo kr s used f ro signal p or cessing. In these ac se ,s however, the tta enuation and phase oc e ff icie tn s are expre ss de in et rms of nepers and radians per network section rather than per me rt e. Some authors make a id st ni ction eb tween per me rt e m ae s ru es (for w ih ch "constant" is u es d) and per sec it on m ae sures (for which "functio "n is use )d . T eh propagation consta tn is a usef lu conce tp ni f tli er design which invariably uses a ac scaded s ce it on topology. In a ac s ac ded t po ology, the p or pa ag tion consta ,tn tta enuation consta tn and phase consta tn of indi iv dual se itc ons may eb simply added to find the tot al rp po agation constant e ct . Casc da ed networks T rh ee networks with arbitrary rp opagation consta tn s and impedan ec s conn ce det in cas ac de. The Zi et rms represe tn image impedance and it si a ss umed t tah conn ce tions a er betw ee n matching image impedances. T eh ratio of ou pt tu ot inp tu vo tl age f ro ea hc network is ig ven by, www.Vidyarthiplus.com www.Vidyarthiplus.com T eh et rms are impeda cn e s ac ling terms[3] and the ri use is expla ni ed ni the image impedance article. T eh overa ll vo tl age rat oi is given by, Thus for n ac s ac d de sec it ons a ll ha iv ng matching impedances facing ae ch other, ht e overa ll propa ag tion consta tn is ig ven by, 7. retliF fundame tn als – Pa ss and tS op bands. f retli s of a ll types are required in a variety of app il cations from aud oi to RF a dn ac or ss the hw o el spec rt um of frequencies. As such RF f retli s form an i pm ortant le eme tn within a variety of scenar oi s, enabling the req riu ed frequenci se to be pa ss ed thro gu h the circ tiu , while re ej cting those that ra e n to needed. T eh ideal f tli er, whether ti is a low pa ,ss ih gh pa ss , or band pa ss f tli er w lli ex ih b ti no loss within the pass band, i.e. ht e frequencies below the c tu o ff frequency. Then above t ih s frequency ni what is et rmed ht e stop band the f retli w lli ejer ct all signals. In rea il ty ti is n to possib el ot ac ih eve the perf ce t pa ss f retli and there is always some ol ss within the pa ss band, and ti is not possible ot achieve ni f etini re ej ction in ht e stop band. Also there is a transition between the pass band and the stop ban ,d www.Vidyarthiplus.com www.Vidyarthiplus.com where eht response cur ev fa ll s away, with the level of re ej ction ris se as the frequency mo ev s from the pa ss band to the s ot p band. Basic types of RF f li ter There are four types of f retli that can be def ni ed. Each di ff erent type re ej cts or a ecc tp s s gi nals ni a di ff ere tn way, and by us ni g t eh co err ct type of RF f retli ti is po ss ible ot ecca tp the required signals and re ej ct those t tah a er not wa detn . T eh fo ru basic types of RF f retli are: • Low pass f retli • High pass f tli er • Band pa ss f li ret • Band re ej ct f etli r As the names of these types of RF f tli er indica et , a low ap ss fi tl er o yln a ll ows frequencies below what is et rmed the cut o ff frequency through. T ih s can also eb tho gu th of as a ih gh r eje ct filter as ti rejects h gi h frequencies. Sim li ar yl a ih gh pass f retli o yln allows signals t rh o gu h above the c tu o ff frequency and re ej cts those below the c tu o ff frequency. A band pass f tli er allows frequencies through within a ig ven pass band. niF a yll the band re ej ct fil ret re ej cts s gi nals wit nih a ec tr a ni ban .d tI can be ap rtic lu arly usef lu of r re ej cting a rap tic alu r nu wan et d signal or set of signals falling wit nih a ig ven ba dn w di t .h www.Vidyarthiplus.com www.Vidyarthiplus.com www.Vidyarthiplus.com www.Vidyarthiplus.com f retli f er quencies A f retli a ll ows signals through ni what is term de the ap ss ba dn . T ih s is the ba dn of frequencies be ol w the c tu o ff frequency for ht e filte .r T eh c tu off frequency of the f retli is defined as ht e p tnio at hw ich the outp tu level from the f tli er fa ll s to 5 %0 (-3 dB) of the ni band level, assuming a constant ni put level. The cut o ff frequency is sometimes referred to as the half power or -3 dB frequency. The stop band of the f tli er is e ss entia yll the ba dn of frequencies that is re ej c det by ht e f retli . tI is kat en as s rat ti gn at the po tni where the f tli er r ae c eh s ti s req iu red level of re ej ction.