gm of transistor vs gm of OTA operating in subthreshold

[sci-fi_guy]

Hello, from what I understand from literature, in the subthreshold region of operation, the g_m of a transistor can be found with the following equation:

g_m = I_D/(n*U_T) where n is the substrate factor.

What I couldn't understand is if the same equation could be used to find the bias current - g_m relationship of an operational transconductance amplifier?

If not, is there an equation I can use to find the g_m - bias current relationship for a subthreshold OTA?

 

[ljp2706]

If you size your input pair large enough, or place your common mode voltage such that you can ensure that your transistors are operating in subthreshold that equation should work for setting the gm of your input. If you're in saturation you'll have to use the typical gm equation for saturation then.

 

[erikl]

... in the subthreshold region of operation, the gm of a transistor can be found with the following equation:
g_m = I_D/(n*U_T) where n is the substrate factor.

What I couldn't understand is if the same equation could be used to find the bias current - g_m relationship of an operational transconductance amplifier?

Sure, simply by division by ID: g_m/I_D = 1/(n*U_T)

Inversion of this equation gives your bias current - g_m relationship: I_D/g_m = n*U_T

Only valid in weak inversion (IC ≦ 0.1) !