The Junction Rectifier — Question 7

Question 7

A reservoir capacitor limits full-wave ripple through charge balance

A full-wave bridge is driven at 50.0 Hz and charges a capacitor to 15.0 V near each peak. A constant-current load draws 20.0 mA. Assume short recharge intervals and nearly linear discharge between peaks.

1. Find the minimum capacitance for peak-to-peak ripple at most .500 V.

2. For $C=470\,\mu\mathrm F$, estimate ripple and mean output voltage.

Question 7 - Solution

A reservoir capacitor limits full-wave ripple through charge balance

(a) Method and calculation

$$\Delta t\simeq1/(2f),\quad\Delta Q=I_L\Delta t=C\Delta V.$$$$\boxed{C_{\min}=I_L/(2f\Delta V_{\max})=400\,\mu\mathrm F}.$$

(b) Interpretation and further calculation

$$\boxed{\Delta V=.0200/[100(470\times10^{-6})]=.4255\,\mathrm V}.$$$$\boxed{V_{\mathrm{dc}}\simeq15.0-\Delta V/2=14.787\,\mathrm V}.$$

Physical check

The approximation is consistent with ripple much smaller than output voltage. Actual diode charging pulses depend on source resistance and conduction duration.