# Is a boost converter actually non linear control?

#### mike _Jacobs

Joined Jun 9, 2021
223
So have been studying the effects of certain losses brought into the model of certain converters.

In the case of a boost converter we typical say that the transfer function of the converter is....

Vout = Vin * 1/(1-D)

I dont think i realized i realized that was non linear until i saw this plot in a book today. The book is trying to show the relationship between inductors DC resistive losses and the load impedance and how that ratio effects the gain essentially.
It seems fairly obvious to me that from a control standpoint, the controller must control a non linear system....
Is that correct?

Also, with that being said, does that mean that a converter with less lossy components is inherently more stable?

#### Ian0

Joined Aug 7, 2020
10,277
Let's make it a synchronous converter, so we have two MOSFETs instead of a MOSFET and a diode.

If you look at it from left to right, then it's a buck converter, M2 behaves as a diode, and Vright/Vleft = d
If you look at it from right to left, then it's a boost converter, M1 behaves as a diode, and Vright/Vleft = d
You only get the 1-d term because you are considering the ON time of a different semiconductor.
If you think of the ON time for the top transistor on both occasions, then the equations are identical.
So, is it non-linear?
The resistance of the inductor is important. If the resistance of the inductor is 10% of the load resistor, then you are potentially reducing the efficiency by 10%. You would avoid inductors that lossy.

You would also avoid a simple non-isolated converter for large step-up or step-down values (say, more than 4) and use a different type of converter, probably with a transformer instead of an inductor, because the pulse currents will be getting rather large.

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