If the input voltage of the solar panel as Vin in the picture below. if Vin is in the range of 10 V to 37V.The average voltage value in the node in yellow during switch 1 is on and switch 2 is off is the Duty CycleVinTsw. And during q1 is off and q2 is on, the yellow node voltage average value is -Vo(1-duty cycle)Tsw

so for the q1 to work as a switch (in saturation region), Vgs1 > Vgt1 and Vds1 > Vgs1 - Vt1

now for q2 to work as a switch ,it is the same. but note that during (1-duty cycle)Tsw, VDS2 is ID*Ron2, which is normally very low average voltage value, that might be below Vgs2 - Vt2, which can not work in saturation region?

is my approach correct ? and what relationship is VDS with the mosfets to work as a switch ?

The reason I am asking is, the duty cycle will change in specific range and I want these two mosfets to work as switches for duty cycle ranges.

Note that Vin is changing when the duty cycle changes because the buck converter works as a variable resistance seen from the solar panel.

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