Half wave rectifier Ripple Voltage

SteDolan

1. The problem statement, all variables and given/known data

A capacitor of capacitance C is connected in paralell with a resistor of R ohms impedance. Calculate the size of the peak to peak voltage of the ripple produced relative to the peak output voltage V_p.

2. Relevant equations

Q=CV
dQ/dt = I
V=IR
V_c=V_pe^-t/RC (am i allowed to use this in an AC circuit?)
or V_c=-jI/R[tex]\omega[/tex]C

V = V_pcos([tex]\omega[/tex]t)

3. The attempt at a solution

Voltage drop across the resistor is just:

V = V_pcos([tex]\omega[/tex]t)

Voltage drop across the capacitor can be aproximated to:

V_c=V_p(1-e^-t/RC)

The alteration to the equation in 2 is to ensure the capacitor voltage is 0 at t=0.

At t=0

V_R - V_c = V_p

at t=T/2 or at 1/f

V_R - V_c = V_pe^-1/fRC

The ripple voltage will be the differance between these two:

V_Ripple= V_p(1-e^-/fRC)