MOSFET Region/Biasing Confusion

[CoolDude420]

Homework Statement

I just encountered some MOSFET problems that made me rethink what biasing and the regions really mean.
Okay, so here is what I know:

Consider the following circuit

The regions of the MOSFET are Cut-Off, Linear and Saturation. Considering Saturation, the conditions for the mosfet to be in saturation are,

$$Vgs>Vt$$ and $$Vgd<Vt$$

Now. In textbooks, we say that we can keep in the MOSFET in saturation by applying a bias gate voltage Vg. I undersntad that we can set Vgs = Vg >Vt and we obey the first condition. But for the second condition,

$$ Vgd < Vt $$
where $$Vgd = Vg - Vd = Vg - RdId$$

Now, Vgd is dependant on Id. Here's the confusion. We have been told that depending on what region the MOSFET is in a different Id equation applies. So how come Id is required to find what region it is in but if we know the region we have a particular Id equation?

Homework Equations

The Attempt at a Solution

 

[analogdesign]

Biasing problems are sometimes "chicken-and-egg". The best way to proceed is to assume a region of operation based on your best guess, calculate the relevant voltages, and then see if they are consistent with your initial assumption. With a resistively loaded MOSFET, whether it is in saturation depends on if the IR drop across the resistor is small enough so that Vds > (VGS-Vt). For some values of R it is, for others it isn't. If R is too big, the device goes into triode. This kind of issue comes up all the time in practical circuits.

 

[CoolDude420]

Biasing problems are sometimes "chicken-and-egg". The best way to proceed is to assume a region of operation based on your best guess, calculate the relevant voltages, and then see if they are consistent with your initial assumption. With a resistively loaded MOSFET, whether it is in saturation depends on if the IR drop across the resistor is small enough so that Vds > (VGS-Vt). For some values of R it is, for others it isn't. If R is too big, the device goes into triode. This kind of issue comes up all the time in practical circuits.

Oh alright. So it's sort of like when we analyse diodes, we assume if its off or on and go with that and then unless our assumption is proven otherwise, we keep it?

 

[analogdesign]

Yep, that's right!