Summary

• The inverter threshold is set by the beta ratio and transistor thresholds.
• Noise margins determine robustness to electrical noise.
• Pass transistors have voltage degradation issues; use transmission gates for full-swing signaling.
• Skewed inverters can optimize for speed or noise immunity in specific directions.

Static CMOS Inverter DC Characteristics

DC transfer function $V_{out}$$ vs $V_{in}$ is derived for a CMOS inverter, key regions of operation:

Key Regions of Operation

• Inverter threshold $V_{inv}$ ****is where $V_{in} = V_{out}$
• For symmetric inverters ($\beta_n = \beta p$), $V{inv} = V_{DD}/2$

Beta Ratio Effects

Beta ratio $r = \frac{\beta _p}{\beta _n}$ affects the inverters switching point

• High skew (r > 1): stronger pMOS → higher $V_{inv}$
• Low skew (r < 1): weaker pMOS → lower $V_{inv}$
  • Where $r = \frac{W_p V_{sat-p}}{W_n V_{sat-n}}$

Long Channel Model

$$ V_{inv} = \frac{V_{DD} + V_{tp} + V_{tn}}{1 + \sqrt{\frac{1}{r}}} $$

Velocity Saturated Model