# Boost Converter Gain

#### andyguyy

Joined Mar 11, 2023
3
Hi,

I'm trying to solve this equation to get the gain for a boost converter while considering the DCR of the inductor.

The equation is listed in the following image and I desire for an output curve to be plotted in excel, identical to the second image. However I am not sure what Rlast is referring to, as I had initially assumed it to be load resistance however this does not work if anyone could be able to direct me as to what this is that would be greatly appreciated. I have provided a link to where the source (Analog Devices Post)

https://www.analog.com/en/technical...me-the-limits-of-boost-converters.html#author

Many Thanks
Andrew

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#### Papabravo

Joined Feb 24, 2006
20,122
$$R_{LAST}$$
is a typo. It should be:

$$R_{LOAD}$$

You are accounting for the ratio of the inductor's DC resistance to the load resistance. You should keep in mind that there are many boost ratios that are not achievable in practice. When you get to high duty cycles the output becomes difficult to control because the derivative of the gain gets large as you approach the maximum value. This means a small change in duty cycle gives you a potentially large change in output voltage. this will no longer be a linear control system.

#### andyguyy

Joined Mar 11, 2023
3
$$R_{LAST}$$
is a typo. It should be:

$$R_{LOAD}$$

You are accounting for the ratio of the inductor's DC resistance to the load resistance. You should keep in mind that there are many boost ratios that are not achievable in practice. When you get to high duty cycles the output becomes difficult to control because the derivative of the gain gets large as you approach the maximum value. This means a small change in duty cycle gives you a potentially large change in output voltage. this will no longer be a linear control system.

Thanks for that.