Question

(i) Find the transfer function G(s) = Vo(s)/Vi(s) of this system using electrical impedances. Express the transfer function as a ratio of two s polynomials. (ii) Plot the output voltage v, as a function of time by means of the transfer function determined at (i) for an input voltage vi= 120e0.18 Volt, R2 = 110 9, R2 = 900, R3 = 100 0, L = 3H and C= 80-106 F. Use MATLAB's step command to plot volt). Also use Simulink to plot volt). Assume zero initial conditions. Mell R. L R2

Answer 1

Solni Ri uw L R₂ Vi V. R a In Laplace domain; www Rj LS R V. (S) Vis) R3 وا۔ CS Vo(s) Vis) (R311 /s) + R2 (R3 11 Ćs )+ Rey + Ritus J _Cs + R₂ R3 Rtv (Rs/cs) Rzt es CS + Rit R₂ + Ls

it R R3 Racsti R3 +RitR₂ tis R₂ CS tl = LS R3 + R₂ R₃ Cs + R₂ Rz + RiR3CS +R R3CS+CR1+R2) +R$ LCS24 given, Rielloni L=3H R2= 90n, C = 80x1OF Rz=100 Now, Vo(s) Il 100 +9000X80X10 + 5 + 90 100+ 110+90)+([10+90)x100x80x1g6 St3s +100X 34fbx Vi 10-652 Vo(s) Vio Z 0.728 + 190 0.0245?+ 4.65+ 300 30S+ 4916.67 Vo(s) = Vis) s?+191.67 5 + 12500

(1) Now, given Vi= 120 e o.lt 120 Vo(s) Visz (S+0.1) 120 (305+79) 6.67) 5+191.675+12500 Soo)(S+0.1) Volt) is shown in the graph 1st graph shows step response of transfer function Second graph shows response to given input.

0.633334 0.633334 0.633334 0.633334 у 0.633334 0.633334 t 0.2 0.4 0.6 0.8 1.0 1.2

70 60 50 40 t 0.5 1.0 1.5 2.0 2.5