Input linear range of mosfet

Discussion in 'Homework Help' started by njdubbs, Apr 29, 2013.

1. njdubbs Thread Starter New Member

Apr 29, 2013
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Hello I am trying to prove the input linear range of a sat. mosfet is vgs <= 0.2(VGS-VTN). HELP. Assuming the MOSFET is in active mode, id=(kn/2)*(vGS-Vtn)^2 --> id=Id+gm*vgs, gm=2*Id/(VGS-VTN) --> vgs=(id-Id)/gm --> vgs=(id-Id)/(2*Id/(VGS-VTN)) then i am stuck....how do you know how much you can vary the drain current? This is a small signal model btw.

2. WBahn Moderator

Mar 31, 2012
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You have to define what is meant by "linear". You have a relationship between two parameters, say a voltage and a current, that is off the form:

i(v) = f(v)

The small signal resistance is

r(v) = dv/df(v) = r + dr(v)]

This is "linear" to within ε as long as |dr(v)/r| < ε. The range of v for which this is true is the "linear range".

Not surprisingly, if you want it to be linear within 0.01% then the linear range is generally going to be considerably smaller than if you only need it to be linear within 10%.