Rectifier design calculation

I am working on a rectifier design. For that I am analyzing the formula for capacitor selection. I came across a video reference.

• Io: average output current
• Vo: Average output voltage
• Vc: capacitor voltage
• Im: peak current
• α:duration of peak current
• π: half cycle duration
• Vr: ripple voltage
• Vm1,Vm2:capacitor peak voltage

I understood that for capacitor selection the formula is:

c=(π-α)/π * Io/2fVr

I don't understood how Vm2=Vm1 * Cosα.

• Simply follow the cosine curve in that picture, left from the peak Vm1, for angle alpha. It's right there in the picture. – user_1818839 Sep 24 '20 at 11:13
• thanks for help @Brian Drummond – power machines Sep 24 '20 at 11:16
• You can also have a look at a paper I published on the bulk capacitor selection for ac-dc converters. – Verbal Kint Sep 24 '20 at 11:26
• @ VerbalKint i will refer this paper for calculations thanks – power machines Sep 24 '20 at 11:58

Simple trigonometry:

$$\V_{m1}\$$ is the voltage at $$\t = \pi/2\$$. and $$\V_{m2}\$$ is the voltage at $$\t = \pi/2 - \alpha\$$.

$$\\sin (\pi/2-\alpha) = \cos\alpha\$$

• thanks for help @RohatKılıç – power machines Sep 24 '20 at 11:15
• You can accept my answer so that the question does not remain open. – Rohat Kılıç Sep 24 '20 at 11:17

If alpha is 90 degrees, then the stored voltage has decayed down to zero volts.

This is consistent with VM2 = VM1 * cos(90).

• thanks for help@analogsystemsrf – power machines Sep 24 '20 at 11:16