There are different structures for implementing MOS pseudoresistance.
How to describe - in term of mathematical expressions - the equivalent resistance realized by the circuits given in the attached file and their associated noise?
This is not a resistor. I am sorry. Take the top figure, call the left voltage V1, the right voltage V2, the middle voltage Vm. Then, for Vm > V1, we have I = K*(Vgs - VT)**2, or I = K*(Vm-V1-VT)**2. For the
right transistor, with Vm >V2, we have I = K*(Vm-V2-VT)**2.
Now, this is a contradiction. I mean, Vm lies between V1 and V2, and cannot be higher than both. As a result, as long as VT > 0, in first approximation, there is no current in these circuits.