Inverter Transfer Characteristics

Q. How do you define the Noise Margin of an inverter ??
Noise Margin from the Transfer Characteristics
NMH = VOH-VIH = VDD - VM
NML = VIH-VOH = VM - GND

This is because when the input crosses VM the output switches to the other state. This indicates that we cannot tolerate any noise more than VM on the input lines.

To have NMH=NML we should have VM= VDD/2.

Q. How do we set the slope of the inverter TC ??
The slope is nothing but the gain in the saturation region and thus it depends on the 'gm' of the
NMOS and the 'ro' of the PMOS.
gm = sqrt(2.Id.K'.W/L) , so increasing the W/L of the NMOS will increase the slope.
ro = K/lambda.Id , so reducing Id will increase the total gain, we can do this by reducing VDD.

Q. Why would someone want to increase the slope of the transition region ??
The current for both NMOS and PMOS is maximum in the saturation region.
Both the NMOS and the PMOS are turned on in the transition region. This means that a lot of static power is being burnt if the transistors spend more time in this region.

Of course the savings in static power will be traded off with area and maybe speed too.