CMOS Transistor Small signal model

What is the small-signal model?

The CMOS transistor is normally used as an amplifier when it is working in the saturation region (it has a low dependence with $V_{DS}$ and a high sensitivity to $V_{GS}$). To characterize the transistor for that purpose, it is used a model that considers that small signals are injected in the terminals of the transistor. That model linearizes the $I_D-V_{GS}$ and $I_D-V_{DS}$ curves around a point of operation, called the bias or operating point.

The bias or operating point

Consider the following circuit:

A gate voltage $v_{GS}$ is applied to the transistor. A current will be generated that will match the current that flows through the resistance. This will in turn generate a voltage drop across the resistance and set the drain-source voltage of the transistor. This will lead to a stable condition for the transistor, for which we call bias or operating point.

The slider represents $R$. As you decrease $R$ (go left), the current sunk by the transistor has a small voltage drop at the resistance and the operating point goes to higher $v_{DS}$. If you increase $R$ (go right), the voltage drop is higher and $v_{DS}$ decreases. If the resistance was too large, it would put the transistor in triode region for this $v_{GS}$.