Buck-Boost Converter Problem

[Captain1024]

Homework Statement

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Homework Equations

Switching Frequency $f_s=\frac{1}{T_s}$
$K=\frac{2L}{RT_s}$, $K_{CR}=(D')^2$
$R=\frac{V_o^2}{P_L}$
In CCM: $D'=(1-D)$, $D'=\frac{-DV_{IN}}{V_O}$
In DCM: $D_2=\sqrt{K}$, $\frac{V_O}{V_{IN}}=\frac{-D_1D_2R}{2Lf_s}$

The Attempt at a Solution

See attached .pdf for my work. Everything makes sense until I get a value greater than 1 for $D_2$. (Where $D_2$ is the second region of a full period. In DCM regions 1 and 2, either diode or transistor are conducting. In region 3 neither diode or transistor is conducting and diode current is 0.)

 

[KataKoniK]

Hello,

Thank you for sharing your work with us. Your solution looks very thorough and well thought out. However, I did notice a few potential errors that may be causing your issue with getting a value greater than 1 for D2 in the DCM case.

Firstly, in your equation for D2, you have written D1D2R instead of D1D2L. This may be causing your issue with getting a value greater than 1, as it would result in a larger value for D2.

Secondly, in your equation for D2 in the DCM case, you have not included the switching frequency fs in the denominator. This may also be causing your issue with getting a value greater than 1, as it would result in a smaller value for D2.

I would recommend double checking these equations and making any necessary corrections. I hope this helps and good luck with your calculations!