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Comments on Duty cycle of buck-boost converter

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Duty cycle of buck-boost converter

+5
−1

I have the following problem: -

Image alt text

Using Wikipedia I find that during CCM we have the relation: -

$$\frac{V_{out}}{V_{in}} = -\frac{D}{1-D} $$

Solving for $D$ and inserting values gives me

$$D=\frac{20\text{V}}{20\text{V}-24\text{V}} = -5 $$

But this doesn't seem to make sense. First of all, the duty cycle is negative... Second the duty cycle is more than 100%!

Why do I get this erroneous result?

EDIT

Turns out I used the wrong formula. Using the formulas given by my instructor for the course: -

Image alt text

yields $d=0.454545 $

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What I'm calculating is $$D=\frac{20\text{V}}{-24\text{V}-20\text{V}} = -0.45... $$ (1 comment)
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+4
−0

If you're referring to this Wikipedia page then the topology has a negative output. In that case, the problem as you have it stated in the OP, is misleading: it should be Vo=-20. With that, extracting D will give:

$$D=\dfrac{V_{out}}{V_{out}-V_{in}}=\dfrac{-20}{-20-24}=0.4545$$

Sure enough, a quick check shows the confirmation:

D=0.4545 => Vo=-20

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1 comment thread

Thank you very much for your clear answer. Also, thank you very much for that LT-Spice simulation. I ... (2 comments)
Thank you very much for your clear answer. Also, thank you very much for that LT-Spice simulation. I ...
Carl‭ wrote about 2 years ago

Thank you very much for your clear answer. Also, thank you very much for that LT-Spice simulation. I encourage you to keep including these kind of simulations in your answers, because they inspire and teach the rest of us how to use LT-Spice!

a concerned citizen‭ wrote about 2 years ago

Carl‭ Just so you know, the formulas that you gave imply a positive voltage output, but for the classical topology (non-isolated) the first formula you gave was the correct one. The second one is valid for flyback topologies (or for the awkward case of the classical one with negative input, or shifted ground). Since, as Olin said, you didn't show any schematic, some presumptions had to be made.