Buck/Boost DC-DC Converter Discontinuous Conduction Mode

[jegues]

EDIT: I have updated the original post to make my confusion more clear!

Hello all,

Attached below are the pages from my textbook for which I am concerned.

On page 245 we can calculate the average inductor current as follows,

$$I_{L} = \frac{1}{2}I_{max}(D+D_{1})$$

Now what I thought an equivalent expression for the diode current would be,

$$I_{D} = \frac{I_{L}D_{1}T}{T} = I_{L}D_{1}$$

Is this incorrect? If so, why?

It is clear from the graph of the diode current on page 245 that indeed,

$$I_{D} = \frac{\frac{1}{2}I_{max}D_{1}T}{T} = \frac{1}{2}I_{max}D_{1}$$

but instead of calculating the area of a triangle, I've always "stretched" that triangle into a rectangle since I know that the current flowing through the diode for that time frame (i.e. D1T) is the average inductor current. With this in mind, the area of my rectangle would be,

$$I_{D} = \frac{I_{L}D_{1}T}{T}$$

Is this intuition incorrect?

This is thought of stretching the area of said triangle into a equivalent rectangle has previously worked for me when doing the analysis for the Buck converter under discontinuous conduction mode. In particular, I wrote

$$I_{s} = I_{L}D$$

where Is is the source current.

Does the source of my confusion make sense? Can you see where I'm going wrong?

 

[KataKoniK]

Hello,

Thank you for sharing your concern and question. I am a scientist and I would like to offer some insight on the confusion you are experiencing.

First, I would like to clarify that your intuition of stretching the triangle into a rectangle is not necessarily incorrect. It is a common approach in circuit analysis to simplify complex shapes into more familiar ones in order to make calculations easier. However, in this particular case, it is not the most accurate approach.

The reason for this is that the diode current is not constant during the entire time frame of D1T. In fact, it starts at zero and ramps up to its maximum value (which is half of the maximum inductor current) during that time frame. This means that the area under the curve is not a rectangle, but a triangle. This is why the correct expression for the diode current is, as you stated, I_{D} = \frac{\frac{1}{2}I_{max}D_{1}T}{T} = \frac{1}{2}I_{max}D_{1}.

I understand that this may seem counterintuitive, as the inductor current is indeed constant during that time frame. However, it is important to keep in mind that the diode is not a perfect switch and it takes some time to turn on and reach its maximum current.

In the case of the Buck converter under discontinuous conduction mode, the diode current is indeed constant during the entire time frame of D. This is why your approach of stretching the triangle into a rectangle works in that case.

I hope this clarifies your confusion and helps you understand the concept better. Please let me know if you have any further questions.