# Question about the MOSFET saturation condition

I'm solving a problem in my textbook and I got stuck, and I have the solution manual of the textbook, so I went to see through the solution and I found a thing that I suspect to be wrong, due to my understanding, but It obviously could be wrong, so I wanted to get help, as I'm self-studying electronics.

At first, the book says that it will use this model for the MOSFET:

To my knowledge, and due to calculations that is previously in the book using the (switch-current source) model the boundaries of the saturation region are: $$V_T\le v_{in} \le V_T + \frac{-1 + \sqrt{1 + 2V_sRK}}{RK}$$

now comes what I don't understand. I will quote the solution manual.

this condition on the saturation region is what I don't get. It's essentially the same as the upper bound of the condition that I provided above, but it has the boundaries on $$\ V_{s} \$$ How are both of them related as I can't see what I'm having wrong?

Also, I think that the details I provided are sufficient for my question, I can provide the whole question and answer from the textbook if needed.

• May I know the name of the book you are self-studying please? Commented Jan 28, 2020 at 21:45
• @Drake Yes sure, It's Foundations of analog and digital electronics by Anant Agarwal and Jeffrey Lang Commented Feb 10, 2020 at 7:56

First of all, if $$\V_{in}\le V_T\$$ then $$\V_{MID}=V_S\$$, so the second FET ...
That is, in this condition, the "$$\V_{in}\$$" for the second FET is $$\V_S\$$.