Activité 2 Premier ordre
Equation dif 1er ordre tau * ds/dt +s = K*e tau= constante de temps en s K= 0s/0e= K*A /A Condensateur: Ur = R*i i= C* ds/dt K=1 tau=RC e'(t)=K*e(t) Bobine: e= uL + s uL = L* di/dt i= s/R di/dt= 1/R * ds/dt e= uL + s = L* di/dt + s = L/R * ds/dt +s K=1 et tau=L/R --------------------------------- Entree Eq diff Sortie e=A tau* ds/dt +s =K*A =cte Sortie (reponse indicielle) s=K*A(1-e**-t/tau) ---------------------------------- temps:t Tr=5% Tr=1% 0 1*tau 3*tau 5*tau 10*tau 0 0,63*KA 0,95KA 0,99Ka 1*KA ----------- s=K*A(1-e**-t/tau) -> S= KA/p(1+tau*p) --------------------------------- T_ = S_ /E_ = K/ 1+j*(w/wc) =K/ 1+j*(f/fc) T=10**G/20 1decade = *10 -20,-40,-60,-80 Emax=E*rac2 w(rad.s)=2pi*f wc(rad.s)= 1/tau(s) =2pifc fc(hz)= wc(rad.s)/2pi = 1/2pi*tau Go=20logK Gwc= Go-3dB Gfc= Go-3dB