Figura B.2: Possibili connessioni di due elementi. (a) parallelo: somma delle matrici Y; (b) serie: somma delle matrici Z; (c) cascata: prodotto delle matrici ABCD
Alle volte, per degli elementi connessi a cascata si preferisce calcolare i pa- rametri di scattering S avendo a disposizione quelli di scattering per i singoli elementi della rete. Non `e difficile provare che, nel caso in cui l’impedenza di carico in uscita ad E0 sia stata la stessa di quella di carico in ingresso ad E00durante la determinazione dei parametri S, la matrice di scattering dei due elementi in cascata ´e: S11 S12 S21 S22 = S0 11+ kS120 S210 S1100 kS120 S1200 kS0 21S2100 S2200 + kS1200S2100S220 dove k = 1 1 − S220 S1100
B.5
Parametri ABCD di linee particolari
In fig B.3 sono riportati i parametri ABCD per alcune linee di trasmissione. Il semplice elemento di trasmissione del segnale (fig B.3(e)) viene descrit- to in termini dell’impedenza caratteristica della linea Zc e della costante di
propagazione γ. Se consideriamo una linea di trasmissione la cui resistenza, induttanza, capacit`a verso massa e conduttanza verso massa possono essere considerate uniformemente distribuite lungo tutta la linea (ed indicate ripettri- vamente R, L, C, G per unit`a di lunghezza), dall’equazione dei telegrafisti si ha che Zc= s R + jωL G + jωC γ =p(R + jωL)(G + jωC) = α + jβ
La costante di propagazione γ `e un numero complesso. La parte reale α indica di quanto si attenua il segnale per ogni metro, ed `e chiamata costante di attenuazione; la sua unit`a di misura `e il Neper/metro ma viene spesso convertita in dB/metro tramite la seguente
α(dB/m) = (20 log10e)α ' 8.686α
La parte immaginaria β indica di quanto ruota la fase del segnale per ogni metro, si misura in radianti/metro ed `e chiamata costante di rotazione.
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