# Formula question about the Bridge and full wave rectifier,where are these number from?

i learn something formula of Bridge and full wave rectifier from my book

1. DC voltage $$\V_{DC}=V_m-\frac{V_{r_{(pp)}}}{2}\$$,$$\V_m\$$ is the amplitude of sine wave voltage, $$\V_{r_{(pp)}}\$$ is the peak to peak voltage of ripple wave

2. The RMS voltage value of ripple $$\V_{r_{(rms)}}=\frac{V_{r_{(pp)}}}{2\sqrt{3}}\$$

3. If $$\f=60Hz,V_{r_{(rms)}}=\frac{2.4V_{DC}}{R_L C}\$$

4. Ripple factor $$\ =\frac{2.4}{R_L C} \times 100 \% \$$

i have some questions about the formula above

Q1

In the 2. formula,how is the $$\2\sqrt{3}\$$ calculated?i mean,based on what reason,so we can say $$\V_{r_{(rms)}}=\frac{V_{r_{(pp)}}}{2\sqrt{3}}\$$,not $$\V_{r_{(rms)}}=\frac{V_{r_{(pp)}}}{any \ number}\$$?

Q2

In the 3. and 4. formula,how is the $$\2.4\$$ calculated? i mean,based on what reason,so we can say $$\V_{r_{(rms)}}=\frac{2.4V_{DC}}{R_L C}, \$$and Ripple factor $$\=\frac{2.4}{R_L C} \times 100 \% \$$ not $$\V_{r_{(rms)}}=\frac{any \ number \times V_{DC}}{R_L C} \$$ or Ripple factor $$\=\frac{any \ number}{R_L C} \times 100 \% \$$ ?

• Jun 8, 2020 at 11:03

1. The ripple can be approximated by a sawtooth. The ratio of peak to RMS of a sawtooth (proof involves a bit of calculus and is left as an exercise) of a sawtooth is Vr(pp)/(2$$\\sqrt{3})\$$. Keep in mind that the ripple goes plus Vr/2 and minus Vr/2 so you need only integrate one half of the triangle.