WOLFRAM

Wolfram Language & System Documentation Center

AC-DC Full-Wave Rectifier

Model an AC to DC full-wave rectifier with four diodes and a capacitor for smoothing the output.

    
Plot the input voltage vi and the voltage vr rectified by the diodes:
Wolfram Language code: vi[t_] = Sin[t]; vr[t_] = Abs[vi[t]]//PiecewiseExpand[#, t∈Reals]&; Plot[{vi[t], vr[t]}, {t, 0, 16}]
When vr increases, ; it charges the capacitor and supplies current to the load. When vr starts to decrease (), the capacitor discharges through the load and the output voltage follows :
Wolfram Language code: system = {vo'[t] == charging[t]vr'[t] - (1 - charging[t])vo[t] / (r c), vo[0] == 0}; control = {charging[0] == 1, WhenEvent[vr'[t] < 0, charging[t] -> 0], WhenEvent[And[vo[t] < vr[t], charging[t] == 0, vr'[t] > 0], charging[t] -> 1]};
Simulate the system:
Wolfram Language code: pars = {r -> 0.1, c -> 1000}; sol = NDSolve[{system, control} /. pars, vo, {t, 0, 16}, DiscreteVariables -> charging∈{0, 1}];
Plot the output voltage smoothened by the capacitor:
Wolfram Language code: Plot[{vo[t] /. sol, vr[t]}, {t, 0, 16}]