Lecture Notes:- http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/lecture-notes/

To make the MOSFET operate in the saturation region, the signal first needs to be boosted by applying a DC value, a DC voltage source, V_I , then after that apply a signal of interest, V_A which operates within the saturation region.

The output is an inversion of the input and there is a fair bit of distortion as the saturation region is not a straight line. There is amplification for sure but the signal is distorted so the amplifier is non linear.

How do we get a linear amplifier? This can be done with the small signal trick, where we focus on a small piece of the non-linear curve. So after boosting with a DC voltage, the input voltage needs to be shrunk to a small signal that gives a linear response.

Let's look at the small signal method

(1)graphically, (2) mathematically, and (3) from a circuit viewpoint - in the next sequence.

(1) Graphically, recall the small Signal Model Notation where v_I (total variable)= V_I (dc bias) + v_i (small signal) and v_O=V_O + v_o. From this method we will notice that a linear output can be obatined.

(2) Mathematically, first we need to substitute v_I=V_I+ v_i into

v_O=V_S -( k/2(v_I - V_T)^2)*R_L. The Bias Point Equation is V_O=V_S - (k/2(V_I - V_T)^2)*R_L and this is marked with an asterisk, to be used later. Then,v_O=V_O+ v_o is substituted as well. From this point we should realize that v_o is an amplification of v_i , giving an equation v_o= A*V_i where A is the amplification.

Removing the terms of V_O ( the bias point equation), and neglecting higher order terms of v_i, we will get v_o=- (k*R_L(V_I - V_T))*v_i.

v_o=- g_m*R_L*v_i where g_m=k*(V_I - V_T) so v_o=- A*V_i . A is a constant w.r.t. v_i

so the circuit behaves linearly for small signals.

Another way is to differentiate v_O=V_S -( k/2(v_I - V_T)^2)*R_L w.r.t. v_I taking v_I=V_I . This will be the slope at V_I. This value will need to be multiplied by v_i and it will be equal to v_o as v_o/v_i is equal to the slope. (see lecture 7 for a similar case)

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