220-A3.2

Activity: MOS Small Signal Characteristics

• Instructions: This activity is structured as a tutorial with an activity at the end. Should you have any questions, clarifications, or issues, please contact your instructor as soon as possible.
• At the end of this activity, the student should be able to:

1. Obtain the small signal parameters of NMOS and PMOS transistors.

Two-Port Small Signal Analysis

Most of the time, we are interested in the small signal behavior of our amplifiers, i.e. what happens to the amplifier voltages and currents as we introduce small disturbances (information carrying signals) at the input. To gain intuition and to facilitate circuit analysis using nonlinear devices, we linearize our circuits to obtain the two-port model shown in Fig. 1. For MOSFETs at low frequencies, the two-port model is composed of the transconductance, and the output resistance.

Transconductance

Transconductance is defined as:

$g_{m}={\frac {\partial I_{D}}{\partial V_{GS}}}$

(1)

Graphically, this is the slope of the transfer characteristic curves. Thus, by numerically differentiating the $I_{D}$ vs. $V_{GS}$ curve using this Python script, we can obtain the transconductance plot shown in Fig. 2.

Output Resistance

Similarly, we can take the derivative of the output characteristics to get the output resistance, which is defined as:

$r_{o}=\left({\frac {\partial I_{D}}{\partial V_{DS}}}\right)^{-1}$

(2)

The output resistance as a function of $V_{DS}$ is shown in Fig. 3.