F.4 Calcul des conditions initiales A et B
G.1.3 Fonction de transfert du filtre d’ordre 2
1 + iω ω0 k. (G.3)
Le module de cette fonction de transfert d’ordre k est donné par :
|Hk(ω)| = 1 s 1 + ω ω0 2 k. (G.4)
La pulsation de coupure ωk d’un tel filtre est telle que :
|Hk(ωk)| = |Hk(ωk)|max √
2 (G.5)
Dans notre cas, on a |Hk(ωk)|max= 1 et donc : 1 s 1 + ωk ω0 2 k = √1 2 (G.6) Soit : 1 + ωk ω0 2!k = 2 (G.7) et donc : ωk = ω0 q 21/k− 1 (G.8)
G.1.3 Fonction de transfert du filtre d’ordre 2
Pour démoduler le signal de la photodidiode, nous utilisons un filtre passe-bas d’ordre 2 de fréquence de coupure f2. La fonction de transfert de ce filtre est alors donnée par :
H2(ω) = 1
1 + iω ω0
avec :
ω0= q√2πf2 2 − 1
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