# gm/ID Design Methodology

Traditionally operating a MOS transistor in strong inversion region is the analog designers choice in their design space[1, 2]. Transconductance of a MOS transistor is . We have three degrees of freedom.

EKV Model is a physical model, was proposed by Enz, Krummenacher, and Vittoz from EPFL.

The channel current in weak inversion region is given by

(1)

where,
and
n is subthreshold slope factor (~ 1.5 in 180nm CMOS tech).

Trans-conductance in weak inversion region is

(2)

(3)

gm/id methodology is used to size transistors, particularly in short channel devices or deep sub-micron technologies.
The following data is generated over a reasonable range of and channel lengths
Generate data for the following over a reasonable range of gm/ID and channel lengths

• Transit frequency (fT)
• Intrinsic gain (gm/gds)
• Current density (ID/W)

These parameters are (to first order) independent of transistor width, which enables “normalized design”.

In a MOS transistor as increases, generation efficiency decreases. is maximum in weak inversion, and almost constant over a large range in this region.