Model-Based Analog Circuit Design

Being able to analyze and design analog circuits using "hand analysis" allows us to build intuition, and this intuition enables us to create designs that are optimal and innovative. However:

• Our simple models such as the square-law model or velocity-saturation model, cannot accurately describe the behavior of key parameters such as output resistance, $r_{o}$, or completely misses operating regions such as the moderate inversion region.
• Using more accurate and complex models, such as BSIM, is ideal for verification, but not really suited for "hand analysis" since
  • We have to work with hundreds of parameters per transistor, or
  • Make many assumptions to reduce these parameters, but then only ending up in the same situation as using the simple models.

One solution around this problem is to use the simulator, in conjunction with the BSIM models, as a "calculator".

Small-Signal Model

In circuit design, we are normally interested in the following parameters:

• Gain
• Bandwidth
• Power
• Voltage Swing
• Noise

It turns out we can most of these small-signal parameters by using our BSIM models as lookup tables, since our small signal equations remain the same:

$i_{ds}={\frac {\partial I_{D}}{\partial V_{GS}}}\cdot v_{gs}+{\frac {\partial I_{D}}{\partial V_{BS}}}\cdot v_{bs}+{\frac {\partial I_{D}}{\partial V_{DS}}}\cdot v_{ds}=g_{m}v_{gs}+g_{mb}v_{bs}+g_{ds}v_{ds}$

(1)

Where $g_{m}$ is the device transconductance, $g_{mb}$ is the device body (effect) transconductance, or backgate transconductance, and $g_{ds}={\tfrac {1}{r_{o}}}$ is the output conductance.