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#1
04-15-2012, 11:25 PM
 suzuki Senior Member Join Date: Aug 2011 Posts: 119
full bridge rectifier equations

Hi, I am having some trouble deriving or finding some help on this.

I want to get an equation which describes the output of a full bridge rectifier.

I have found the following information thus far,

$V_o = V_{peak} - 0.5V_{ripple}$

$V_{ripple} = \frac{V_{peak}}{fCR}$

When you calculate this value, you will get a singular output dc value. However, I want to have an equation which gives more details, one that includes the ripple voltage. In my mind, this equation should be in a sinusoidal form, but I can't seem to think of have to arrive at that.

Does anybody know how i can do this analysis? or maybe have some references available for this?

tia
#2
04-16-2012, 12:12 AM
 MrChips Super Moderator Join Date: Oct 2009 Posts: 9,287 Blog Entries: 24

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#3
04-16-2012, 12:25 AM
 #12 Senior Member Join Date: Nov 2010 Location: 15 miles west of Tampa, Florida Posts: 9,058 Blog Entries: 9

radical 2 C Er F = I
.707 Capacitance [Ripple voltage (p-p)] Frequency = current.

I don't know how to make that into a sinusoidal form.
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#4
04-16-2012, 12:46 AM
 MrChips Super Moderator Join Date: Oct 2009 Posts: 9,287 Blog Entries: 24

After rectification it is no longer sinusoidal.
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#5
04-16-2012, 01:17 AM
 suzuki Senior Member Join Date: Aug 2011 Posts: 119

Quote:
 Originally Posted by MrChips After rectification it is no longer sinusoidal.
i agree with this, but in reality, i don't think a pure dc output can be achieved. the output voltage should still exhibit some ripple, which (i believe) can be described by some sinusoidal equation. But this is the part where I cannot seem to find any information.

thanks again for all replies
#6
04-16-2012, 01:29 AM
 mlog Senior Member Join Date: Feb 2012 Location: USA Posts: 276

If you want a "sinusoidal" equation that describes diode conduction, then you will have to write an equation for each segment of time or alternatively as a segment of the angle (θ=ωt). For example, you might have one equation for the segment 0 < θ < ∏ and a second equation for the segment ∏ < θ < 2∏.
#7
04-16-2012, 02:17 AM
 suzuki Senior Member Join Date: Aug 2011 Posts: 119

Quote:
 Originally Posted by mlog If you want a "sinusoidal" equation that describes diode conduction, then you will have to write an equation for each segment of time or alternatively as a segment of the angle (θ=ωt). For example, you might have one equation for the segment 0 < θ < ∏ and a second equation for the segment ∏ < θ < 2∏.
i had thought about it in this way before as well. seems to be that the diode bridge itself can just be written as the abosolute value of the input ac voltage. But the tricky part is how to deal with the equations that involve the capacitor charging and discharging. Not quite sure how to approach this.
#8
04-16-2012, 02:37 AM
 MrChips Super Moderator Join Date: Oct 2009 Posts: 9,287 Blog Entries: 24

It is possible to work this out exactly but it is simpler if you make some approximations.
You need to include a load resistor as well as the filter capacitor.
Without a load the capacitor will reach full charge at the peak voltage (assuming the diode voltage drop is zero at zero current).
When the load is included you need to determine the phase angles when the diode is conducting and not conducting. From this you can determine the shape of the ripple voltage.

More importantly, you need to calculate the shape of the current pulse through the diodes.
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#9
04-16-2012, 03:07 PM
 wayneh Senior Member Join Date: Sep 2010 Location: Roscoe, IL Posts: 7,602

Modeling the output, under load, of a full wave bridge + filter cap is not simple but can be accomplished by breaking the wave into segments (conduction, RC decay). Then you need iterative calculations to determine where the segments intersect to produce the continuous output.

I'm not sure I ever posted the spreadsheet I mentioned in that thread. I will if you're interested.
#10
04-16-2012, 05:24 PM
 #12 Senior Member Join Date: Nov 2010 Location: 15 miles west of Tampa, Florida Posts: 9,058 Blog Entries: 9

For my own education, if you develop this equation, what purpose does it serve?

I've designed hundreds of these rectifier/capacitor/load circuits without the benefit of this equation and have very little idea what you are doing. Please educate me as to what the goal is.
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 Tags bridge, equations, rectifier

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