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 g_m = f(I_D, W, L). 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)   \begin{equation*} I_D = I_{D0} {W \over L} e^{(V_{gs}-V_T) \over \eta U_T} \end{equation*}

where,
U_T = {kT \over q} and
n is subthreshold slope factor (~ 1.5 in 180nm CMOS tech).

Trans-conductance in weak inversion region is

(2)   \begin{equation*} g_m = {\partial I_D \over \partial V_{gs}} = {I_D \over \eta U_T} \end{equation*}

(3)   \begin{equation*} {g_m \over I_D} ={\partial I_D / \partial V_{gs} \over I_D} = {\partial(\log I_D) \over \partial V_{gs}} \end{equation*}

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 g_m/Id 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 I_D increases, g_m generation efficiency decreases. g_m/I_D is maximum in weak inversion, and almost constant over a large range in this region.

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